Insight into the Mechanism of [NiFe] Hydrogenase by means
of Magnetic Resonance Experiments and DFT Calculations
vorgelegt von
Diplom-Chemiker, Master of Science
Matthias Stein
aus Berlin
Vom Fachbereich 5 – Chemie –
der Technischen Universit¨
at Berlin
zur Erlangung des akademischen Grades
Doktor der Naturwissenschaften
– Dr. rer. nat. –
genehmigte Dissertation
Promotionsausschuß:
Vorsitzender: Prof. Dr. Schoen
Berichter: Prof. Dr. Lubitz
Berichter: Prof. Dr. Koch
Tag der m¨
undlichen Pr¨
ufung: 02. Februar 2001
Berlin 2001
D 83
Abstract
Stein, Matthias
Insight into the Mechanism of [NiFe] Hydrogenase by means of Magnetic Resonance Experiments
and DFT Calculations
Hydrogenasen katalysieren die reversible heterolytische Dissoziation von molekularem Wasserstoff. Die
Untersuchung dieses Elementarprozesses ¨ubergangsmetallhaltiger Enzymkatalyse ist der zentrale Aspekt
dieser Arbeit. [NiFe]-Hydrogenasen besitzen ein heterobimetallisches aktives Zentrum, an dem die Um-
setzung des Wasserstoffs erfolgt. EPR und verwandte experimentelle magnetische Resonanzmethoden
lassen sich auf die paramagnetischen Redoxzust¨ande des Nickelzentrums anwenden und liefern Aus-
sagen ¨uber die elektronische Struktur und Ligandenumgebung der Metalle. Diese werden erg¨anzt durch
theoretische Berechnung im Rahmen der Dichtefunktionaltheorie (DFT).
Im Rahmen dieser Doktorarbeit wurde die Berechnung von Observablen der magnetischen Resonanz
(
- und
-Tensoren) mit der relativistischen DFT und dem ZORA (zero-order regular approximation)
Hamiltonoperator an zwei Nickelmodellkomplexen etabliert und evaluiert. Beide Verbindungen wiesen
strukturelle und elektronische ¨
Ahnlichkeiten mit dem aktiven Zentrum der [NiFe]-Hydrogenase auf. Der
Einfluß relativistischer Effekte auf die geometrische und elektronische Struktur wurde kritisch diskutiert.
Der Einfluß verschiedener m¨oglicher verbr¨uckender Liganden
im aktiven Zentrum auf die ge-
ometrische Struktur und die Verteilung der ungepaarten Spindichte wurde mit DFT Rechnungen unter-
sucht. Sauerstoffverbr¨uckte Strukturen erscheinen plausibel f¨ur die oxidierten Ni-A und Ni-B Zust¨ande,
w¨ahrend im reduzierten Ni-C Zustand die Position wahrscheinlich durch ein Hydridanion besetzt wird.
In Proteineinkristallen der [NiFe]-Hydrogenase aus Desulfovibrio vulgaris Stamm Miyazaki F wurde
die Protonenumgebung des Ni-Zentrums mit gepulster ENDOR Spektroskopie in den Zust¨anden Ni-A
und Ni-B charaketrisiert. Drei Hyperfeintensoren konnten
-CH
Protonen von Cysteinaminos¨auren in
der Umgebung des Nickels zugeordnet werden. Die Meßergebnisse wurden unterst¨utzt von DFT berech-
neten Hyperfeintensoren. Ni-A und Ni-B unterscheiden sich im Protonierungsgrad des Br¨uckenliganden.
Ein
-Oxo-Ligand im Ni-A Zustand und eine
-Hydroxo-Br¨ucke im Ni-B Zustand f¨uhrten zu einer
leicht unterschiedlichen Spindichteverteilung. Diese wirkte sich auch auf die Hyperfeinwechselwirkung
der
-CH
Protonen der terminalen Cysteine aus. Eine Protonenkopplung des terminalen Cysteines 81
konnte im Ni-B, aber nicht im Ni-A Zustand gemessen werden.
Relativistische DFT Rechnungen lieferten atomare Vorstellungen von den paramagnetischen
Zust¨anden Ni-A, Ni-B, Ni-C, Ni-L und Ni-CO. Die berechneten
-Tensoren sind in guter
¨
Ubereinstimmung mit experimentellen Ergebnissen, soweit vorhanden. Ni-A und Ni-B sind
-
Oxo- und
-Hydroxo verbr¨uckt. Ni-L geht aus dem Ni-C Zustand durch Photodissoziation des
verbr¨uckenden Liganden hervor. Die berechneten Hyperfeintensoren f¨ur alle Kerne sind ebenfalls in
guter ¨
Ubereinstimmung mit experimentellen Werten. Kohlenmonoxid als Inhibitor des Enzyms bindet
im Ni-L Zustand in axialer Position an das Ni Atom und kann so diese Koordinationsstelle blockieren.
Der Ni-C Zustand der regulatorischen Hydrogenase (RH) aus Ralstonia eutropha wurde in gefrorener
L¨osung mit Hilfe der orientierungsselektierten ENDOR Spektroskopie untersucht. Mit Hilfe der theo-
retisch berechnete
-Tensororientierung und der Gr¨oße und Orientierung der Protonenhyperfeintensoren
konnten f¨unf Hyperfeintensoren zu Protonen in der molekularen Struktur zugeordnet werden. Die Struk-
tur des aktiven Zentrums im Ni-C Zustand ist der der Standardhydrogenasen sehr ¨ahnlich.
Auf der Grundlage der gewonnenen experimentellen und theoretischen Ergebnisse wird ein Reak-
tionsmechanismus f¨ur die [NiFe]-Hydrogenase vorgeschlagen. Dieser deutet auf eine Beteiligung der
Proteinumgebung hin. Das terminale Cystein 530 k¨onnte die heterolytische Spaltung des Wasserstoffs als
Base unterst¨utzten. W¨ahrend das Hydrid in der Br¨ucke verbleibt, kann das Proton vom Br¨uckenliganden
aufgenommen werden und das aktive Zentrum als H
O
oder ¨uber einen Protonentransferkanal ver-
lassen.
Teile der vorliegenden Arbeit wurden bereits ver¨
offentlicht
Wissenschaftliche Publikationen
1. M. Brecht, M. Stein, O. Trofanchuk, F. Lendzian, R. Bittl Y. Higuchi, W. Lubitz
Catalytic Center of the [NiFe] Hydrogenase: A Pulse ENDOR and ESEEM Study
In: Magnetic Resonance and Related Phenomena Vol.II Technische Universit¨atBerlin, pp. 818-819, (1998).
2. M. Stein and W. Lubitz
Electronic Structure of the Active Center [NiFe] Hydrogenase
In: Magnetic Resonance and Related Phenomena Vol. II, Technische Universit¨at Berlin, pp. 820-821,
(1998).
3. O. Trofanchuk, M. Stein, Ch. Gessner, F. Lendzian, Y. Higuchi, W. Lubitz
Single Crystal EPR Studies of the Oxidized Active Site of [NiFe] Hydrogenase from Desulfovibrio vulgaris
Miyazaki F
J. Biol. Inorg. Chem.,5, 36-44 (2000).
4. W. Lubitz, M. Stein, M. Brecht, O. Trofanchuk, S. Foerster, Y. Higuchi, E. van Lenthe, F. Lendzian
Single Crystal EPR and DFT Studies of the Paramagnetic States of [NiFe] Hydrogenase from Desulfovibrio
vulgaris
Biophys. J.,78 A, 1660 (2000).
5. M. Stein, E. van Lenthe, E. J. Baerends, W. Lubitz
G- and A-Tensor Calculations in the Zero-Order Approximation for Relativistic Effects of Ni-Complexes
Ni(mnt)
and Ni(CO)
H as Model Complexes for the Active Center of [NiFe]-Hydrogenase
J. Phys. Chem. A,105, 416-425 (2001).
6. M. Stein, E. van Lenthe, E. J. Baerends, W. Lubitz
Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase. Implications for
the Enzymatic Mechanism.
J. Am. Chem. Soc., in press (2001).
7. M. Stein, W. Lubitz
DFT Calculations of the Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase
PCCP, submitted (2001).
8. M. Stein, O. Trofanchuk, M. Brecht, F. Lendzian, R. Bittl, Y. Higuchi, W. Lubitz
Pulsed-ENDOR Crystallography of Oxidized Single Crystals of [NiFe] Hydrogenase from Desulfovibrio
vulgaris Miyazaki F
J. Am. Chem. Soc. manuscript in preparation.
Konferenzbeitr¨
age
1. W. Lubitz, Ch. Gessner, F. Lendzian, O. Trofanchuk, Ch. Reichle, M. Stein, Y. Higuchi
Single Crystal EPR and ENDOR of the Active Site of the [NiFe]-Hydrogenase From Desulfovibrio vulgaris
Hydrogenases 97, Albertville, France, 12-17 July 1997.
2. M. Stein, W. Lubitz
H
-Evolving Complexes: A DFT Study of Nickelbisthiolenes as Model Complexes for NiFe-Hydrogenases
DFT97, Vienna, Austria, 2-6 September 1997.
3. O. Trofanchuk, M. Stein, M. Brecht, W. Hofbauer, F. Lendzian Y. Higuchi, W. Lubitz
Catalytic Center of [NiFe]-Hydrogenases: X- and W-Band EPR Studies
RSC 31st EPR Annual International Meeting, Manchester, UK, 29 March-2 April 1998.
4. M. Brecht, M. Stein, O. Trofanchuk, F. Lendzian, R. Bittl, Y. Higuchi, W. Lubitz
Catalytic Center of the [NiFe] Hydrogenase: ENDOR and ESEEM Studies RSC 31st EPR Annual Interna-
tional Meeting, Manchester, UK, 29 March-2 April 1998.
5. M. Stein, O. Trofanchuk, M. Brecht, F. Lendzian, Y. Higuchi, W. Lubitz
Determination of Protons in the Environment of D. vulgaris Miyazaki F Single Crystals. Pulsed-ENDOR
Spectroscopy and DFT Calculations.
COST818 Workshop, Umea, Sweden, 11-14 June 1998.
6. M. Stein, O. Trofanchuk, M. Brecht, F. Lendzian, Y. Higuchi, W. Lubitz
Determination of Proton Hyperfine Tensors in Single Crystals of
D. vulgaris Miyazaki F [NiFe] Hydrogenase. Pulsed-ENDOR Spectroscopy
and DFT Calculations.
“Quantum Chemical Calculations of NMR and EPR Parameters”,
Smolenice Castle, Slovakia, 14-18 September 1998.
7. M. Stein, O. Trofanchuk, M. Brecht, F. Lendzian, Y. Higuchi, W. Lubitz
Determination of Proton Hyperfine Tensors in Single Crystals of D. vulgaris Miyazaki F [NiFe] Hydroge-
nase. Pulsed-ENDOR Spectroscopy and DFT Calculations.
Jahrestagung der Deutschen Gesellschaft fuer Biophysik, Frankfurt/Main Germany, 21-23 September 1998.
8. W. Lubitz, M. Stein, M. Brecht, O. Trofanchuk, F. Lendzian, R. Bittl, Y. Higuchi
EPR, ENDOR and ESEEM Studies of Hydrogenase Single Crystals from Desulfovibrio vulgaris
COST818 Workshop, Sintra, Portugal, 9-13 December 1998.
9. W. Lubitz, M. Stein, S. Foerster, M. Brecht, O. Trofanchuk, F. Lendzian, Y. Higuchi
Structure and Function of [NiFe] Hydrogenase - Advanced EPR and Theoretical Investigations
5th European Biological Inorganic Chemistry Conference, Toulouse, France, 17-20 July 2000.
10. M. Stein, W. Lubitz
A Quantum Chemical Description of the Paramagnetic States of [NiFe] Hydrogenases - Towards an Under-
standing of the Reaction Mechanism (Invited Lecture)
6th International Conference on the Molecular Biology of Hydrogenases, Potsdam, Germany, 5-10 August
2000.
11. M. Brecht, M. Stein, T. Buhrke, S. Foerster, B. Friedrich, W. Lubitz
Characterization of the Active Site of the Hydrogen Sensor from Ralstonia eutropha by ENDOR and ES-
EEM Spectroscopy
6th International Conference on the Molecular Biology of Hydrogenases, Potsdam, Germany, 5-10 August
2000.
12. S. Foerster, O. Trofanchuk, M. Stein, Y. Higuchi , W. Lubitz
On the Active Site of [NiFe]-Hydrogenase from Desulfovibrio vulgaris Miyazaki F: EPR Spectroscopic
Investigation of Single Crystals and of the 61Ni Labeled Protein
6th International Conference on the Molecular Biology of Hydrogenases, Potsdam, Germany, 5-10 August
2000.
13. S. Foerster, M. Brecht, M. Stein, O. Trofanchuk, Y. Higuchi, W. Lubitz
EPR and ENDOR Spectroscopic Investigations of Single Crystals of the [NiFe]-Hydrogenase from Desul-
fovibrio vulgaris Miyazaki F
DFG-Rundengespr¨ach “Anwendungen der Magnetischen Resonanz in der Bio- und Materialwissenschaft”
17-22 September 2000, Hirschegg, Austria.
Weitere Publikationen
1. W. Byers Brown, I. H. Hillier, A. J. Masters, I. J. Palmer D. H. V. DosSantos, M. Stein, M. A. Vincent
Modelling the Photonucleation of Water Vapour by UV in the Presence of Oxygen and the Absence of
Pollutants
Faraday Diss. 100 253-267, (1995).
2. M. Stein, J. Sauer
Formic Acid Tetramers: Structure Isomers in the Gas Phase
Chem. Phys. Lett. 267, 111-115, (1997).
3. Ch. Gessner, M. Stein, S. P. J. Albracht, W. Lubitz
Orientation-Selected ENDOR of the Active Center in C. vinosum [NiFe]-Hydrogenase in the Oxi-
dized,‘Ready‘ State
J. Biol. Inorg. Chem.,4, 379-389 (1999).
4. W. Koch, M. Stein
Handbook of Computational Chemistry by D. B. Cook (book review)
Angew. Chem.,111, 1059-1060, (1999);
Angew. Chem. Int. Ed. 38, 1680-1681, (1999).
5. R. Isaacson, F. Lendzian, M. Stein, W. Lubitz, C. Boullais
Identification of ENDOR Lines in Q
and Q
in RCs of Rb. sphaeroides by Selective Isotopic Labeling
Biophys. J. ,78 A , 2001 (2000).
6. M. Stein
DFT - A Promising Tool for Studying Transition Metal Enzymes
In: Hydrogenases - What can we learn from Nature, M. Frey, R. Cammack, Eds.; Academic Press, to appear
2001.
Weitere Konferenzbeitr¨
age
1. M. Stein, D.H.V. DosSantos, W. Byers Brown, A. J. Masters
Modelling the Water-Hydrogens Peroxide System
“How to Derive Interatomic Potentials Needed for Computer Simulations”
Oxford, UK, July 1994.
2. M. Stein, D.H.V. DosSantos, W. Byers Brown, A. J. Masters
Modelling the Water-Hydrogens Peroxide System
Annual Meeting of the RSC Statistical Mechanics and Thermodynamics Group,
Manchester, UK, August 1994.
3. M. Stein, J. Sauer
Formic Acid Gas Phase Structures
CCP1 Study Weekend “Quantum Theory of Large Molecules”
Daresbury, UK, September 1996.
Contents
1 Introduction 1
2 Hydrogenases 5
2.1 Classification of [NiFe] Hydrogenases . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Molecular Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3 The Redox States of [NiFe] Hydrogenases . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.4 Specific Properties of the Paramagnetic States . . . . . . . . . . . . . . . . . . . . . . . 17
2.5 Motivation and Perspective of this Work . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Theory and Fundamentals 23
3.1 EPR Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 The Spin-Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.3 The
-Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.4 The Hyperfine Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.5 DFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.6 DFT and Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.7 Relativistic Quantum Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.7.1 The ZORA-Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.8 Calculations of Magnetic Resonance Parameters . . . . . . . . . . . . . . . . . . . . . . 35
3.8.1 Hyperfine Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.8.2 ZORA Calculations of Hyperfine Tensors . . . . . . . . . . . . . . . . . . . . . 36
3.8.3 g-Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.8.4 ZORA Calculations of g-Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . 37
4 Nickel Model Complexes 39
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
iii
iv CONTENTS
4.2 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3.1 Ni(mnt)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3.1.1 Geometrical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.3.1.2 Electronic Structure and g-Tensor Calculations . . . . . . . . . . . . . 44
4.3.1.3 Spin Density Distribution and Hyperfine Interactions . . . . . . . . . 47
4.3.2 Ni(CO)
H . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
4.3.2.1 g-Tensor and Hyperfine Interaction . . . . . . . . . . . . . . . . . . . 55
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
5 The Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase 61
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5.2 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.3.1 Structural Parameters for The Oxidized States . . . . . . . . . . . . . . . . . . . 63
5.3.2 Electronic Structure of the Oxidized States . . . . . . . . . . . . . . . . . . . . 66
5.3.3 Structural Parameters for the Reduced Enzyme (Ni-C) . . . . . . . . . . . . . . 69
5.3.4 Electronic Structure of the Reduced Enzyme (Ni-C) . . . . . . . . . . . . . . . 72
5.3.5 Influence of the Small Ligands at the Iron on the Electronic Structure . . . . . . 74
5.4 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6 ENDOR Crystallography of the Oxidized States 79
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.2.1 Protein Purification and Crystal Mounting . . . . . . . . . . . . . . . . . . . . . 82
6.2.2 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.2.3 EPR and ENDOR Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.2.4 EPR Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2.5 ENDOR Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.3.1 cw-EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.3.2 Pulsed-EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.3.3 Pulsed-ENDOR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.3.4 Analysis of ENDOR Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
CONTENTS v
6.3.4.1 Assignment of
and
. . . . . . . . . . . . . . . . . . . . . . . 97
6.3.4.2 Assignment of
. . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.3.5 DFT Calculations of the Electronic Ground State . . . . . . . . . . . . . . . . . 101
6.3.6 DFT Calculated Hyperfine Tensors . . . . . . . . . . . . . . . . . . . . . . . . 105
6.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
6.5 Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7 Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase 113
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7.2 Computational Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
7.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.3.1 Ni-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.3.1.1 g-Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
7.3.1.2 Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 118
7.3.2 Ni-A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.3.2.1 g-Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
7.3.2.2 Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 124
7.3.3 Ni-C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.3.3.1 g-Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
7.3.3.2 Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . 130
7.3.4 Ni-L . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.3.4.1 g-Tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.3.4.2 Hyperfine Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 133
7.3.5 Ni-CO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
7.4 Discussion of Hyperfine Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.4.1
Ni Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
7.4.2
Fe Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.4.3
S Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
7.4.4
O Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
7.4.5
H Hyperfine Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.5
N Hyperfine and Quadrupole Interaction . . . . . . . . . . . . . . . . . . . . . . . . . 144
7.6 The Influence of the Protein Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
vi CONTENTS
8 Orientation-Selected ENDOR of the Ni-C State 151
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
8.2 Materials and Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.2.1 Sample Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.2.2 EPR and ENDOR Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
8.2.3 Orientation-Selected ENDOR . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
8.2.4 Simulation of ENDOR Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.3.1 Characterization by EPR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
8.3.2 Analysis of Orientation-Selected Pulsed-ENDOR Spectra . . . . . . . . . . . . 157
8.3.3 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
8.3.3.1 ENDOR Signals from
-CH
Protons . . . . . . . . . . . . . . . . . 160
8.3.3.2 ENDOR Signals from the Bridging Hydride Ion . . . . . . . . . . . . 163
8.4 Discussion and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
9 Proposal of a Reaction Mechanism 171
10 Zusammenfassung und Ausblick 185
Bibliography 191
Chapter 1
Introduction
Hydrogenases belong to the oldest bacteria and archae on Earth. Although the production and consump-
tion of H
by microorganisms had been known since end of the 19
[1] and the beginning of the 20
!
century [2,3], it was not until 1931 that the name ‘hydrogenase’ was proposed [4]. Hydrogenases are
involved in the respiration of elemental sulphur and/or polysulphide. The ability to reduce sulphur us-
ing H
or organic substrates as electron donors is widespread among bacteria and archae. Some of the
hypothermophilic organisms live in water-containing volcanic areas at up to 80
"
C. In vivo nearly all
hydrogenases function in one way only, they catalyze an ‘irreversible’ reaction: either split or produce
molecular hydrogen. Only in presence of an excess of electron donors or acceptors, they may reverse the
preferred reaction
#
%$&
#
('
#
)
(1.1)
The investigation of the heterolytic cleavage of the strongest single bond (436 kJ mol
at 298 K, pK
*
=
35) at room or body temperature is the subject of this dissertation.
The combustion of fossil carbon compounds, which were accumulated for millions of years on earth,
to carbon dioxide is going to disturb the sensitive equilibrium of our atmosphere. The ‘green-house ef-
fect’ and the global warming threaten to change our climate. When hydrogen were used as energy carrier
for automobiles, no exhaust gases would be produced. The investigation of one of the major problems
of today’s world, related to the fossil fuel question, requires a combined interdisciplinary approach from
various fields (for a perspective see i.e. [5]).
The direct combustion of hydrogen requires a controlled explosion of H
and O
(Knallgasreaktion).
In fuel cells, hydrogen and oxygen react but not in a direct combustion which produces a lot of thermal
energy but in a ‘cold’ process mediated by an electrolyte (for a review see [6]). Fuel cells are electro-
chemical cells which convert chemical energy from a reaction between a fuel and an oxidant directly into
1
2 1. Introduction
electrical energy. A schematic diagram of a fuel cell is given in Figure 1.1. Fuel cells are open devices,
2H + 2eH
2+ - 1/2 O + 2e
2-O2 -
electrolyte
airfuel
load
cathodeanode
Figure 1.1: Schematic drawing of a fuel cell
unlike batteries. Fuel and oxidant are continuously supplied to the electrodes (fuel, i.e. H
, to the an-
ode side, air or oxygen to the cathode side). Anode and cathode are separated by a polymer electrolyte
membrane (PEM) which also acts as a proton conductor. The electrochemical reactions at the anode and
cathode are also displayed in Figure 1.1. At the anode, hydrogen is oxidized to protons and electrons and
at the cathode oxygen is reduced to oxide. As the electrons, produced by the electrochemical reaction,
move through the external circuit (see Figure 1.1) a current can be measured and used to drive an electric
motor. Protons are transfered via the PEM to the cathode side. When pure hydrogen is used in fuel cells,
the combustion product of a fuel cell is water - a true zero emission process. The thermal heat liberated
by a fuel cell can be used to heat individual homes, co-generating steam for the reformer in a power
plant or discarded as waste heat. Today, many large automobile manufacturers operate a fleet of fuel cell
driven vehicles (for a review see [7]) 1.
Apart from the electrolysis of water, the biological production of hydrogen is the most promising
route (“bio-hydrogen”). An efficient coupling of solar energy conversion and biological hydrogen pro-
duction is achieved by combining photosystem II (PSII) and hydrogenases. PSII delivers oxygen and
protons from the photolytically driven splitting of water (water oxidation). Hydrogenases can make use
of the protons generated and yield H
(Figure 1.2).
The activity of [Fe]-only hydrogenases is usually larger than that of [NiFe] hydrogenases. [NiFe]
hydrogenases act mostly as ‘hydrogen-uptake’ hydrogenases and consume hydrogen whereas [Fe] hy-
drogenases most frequently produce hydrogen. The efficiency of hydrogenases is demonstrated in an
example: 1 mole of the [Fe] hydrogenase from D. desulfuricans can fill the airship Graf Zeppelin in ten
minutes (assuming a sufficient supply of reductants and protons) [8].
1A comprehensive list of fuel cell applications is given at the web site http://www.fuelcells.org
3
+-,/.0. 1325476
8
9;:
< =?>
@BADC
EGF
HJIBKMLON
PRQTS
νh
Figure 1.2: Photoproduction of biohydrogen
Nature’s choice of Ni for the active site of enzymes is peculiar, given the modern distribution of
soluble metals on Earth. Still, Ni plays a versatile role in enzymatic catalysis [9]. One possibility is that
the choice of Ni reflects a selection that was made under different atmospheric conditions. Before O
became abundant, many transition metals would have been present as sulphides and nickel sulphides are
among the more soluble transition metal sulphides [10]. [NiFe] hydrogenases are resistant to oxygen
whereas [Fe]-only hydrogenases are destroyed in the presence of oxygen. This may indicate an adaption
of the hydrogenases to an increase of oxygen in the atmosphere. Nature’s choice of Ni as a redox active
switch may be due to the following reasons [11]:
U
Ni is a good catalyst for H
heterolytic cleavage
U
A nickel hydride may serve as an electron storage device and guarantee reversibility
U
Compared to Fe, Ni is resistant to oxidation (but at lower battery efficiency).
In order to contribute to the understanding of the heterolytic splitting of molecular hydrogen by [NiFe]
hydrogenases, Electron Paramagnetic Resonance (EPR) and Electron Nuclear Double Resonance (EN-
DOR) spectroscopies and modern theoretical approaches, namely Density Functional Theory (DFT), are
used in this thesis.
The EPR and pulsed-ENDOR spectra in Chapter 6 were recorded together with Dr. Olga Trofan-
chouk. The orientation-selected ENDOR spectra of the Ni-C state were measured together with Dipl.-
Phys. Marc Brecht.
4
Chapter 2
Hydrogenases
Hydrogenases are a family of oxidoreductase enzymes of different constitution that catalyze the re-
versible oxidation of molecular hydrogen H
(enzyme classification EC 1.18.99.1). Hydrogenases have
been classified according to the contents of their active sites as [NiFe] [12], [NiFeSe] [12], [Fe]-only [13]
and transition metal-free [14] hydrogenases. Nickel-containing hydrogenases have been isolated from
eubacteria (i.e. Desulfovibrio,Azobacter,Rhodobacter,Ralstonia) and archaebacteria (i.e. Methanobac-
terium and Methanothermus) [15]. The mesophilic sulphate-reducing bacteria Desulfovibrio live at an
optimum of body-temperature (37
"
C) and pH 7.2 [16]. Desulfovibrio use H
as a source of energy by
coupling its oxidation (electron flow) to the reduction of sulphate to sulphide [17]
V7W
'YXRZ
[
X
'
V7W
Z
(2.1)
or H
S (see Figure 2.1).
SO42- SO32- S3O62- S2-
H2H2
ATP
\
AMP
3 ADP
]
3 ATP
]
S2O32- H2
H2
2 H+
hydrogenase cytochrome c
^
3ferredoxin
X
_
S2O32-
thiosulphate
`
reductase
SO32- + H2S
Figure 2.1: H
metabolism in Desulfovibrio, X denotes unknown electron carrier(s) [17].
5
6 2. Hydrogenases
Hydrogenases from the anaerobic bacteria of Desulfovibrio use cytochrome c
as the physiological
electron carrier but may also employ artificial electron acceptors such as methyl viologen and benzyl
viologen (see Figure 2.2.). The heterolytic cleavage of molecular hydrogen into protons and electrons
H2
Hydrogenase
2H+
2e-
Cytochrome c3
Figure 2.2: The heterolytic cleavage of H
by Hydrogenases from Desulfovibrio
(or one proton and one hydride anion) has been shown by hydrogen-deuterium exchange reactions and
the para/ortho conversion of H
[17].
2.1 Classification of [NiFe] Hydrogenases
The molecular biology of hydrogenases has been reviewed in [15,18, 19]. Genetically, [NiFe] hydro-
genases can be classified into five groups according to [15]. Group I is the [NiFeSe] hydrogenase from
Desulfovibrio (Desulfomicrobium) baculatum, group II hydrogenases comprise D. gigas,D. vulgaris
Miyazaki F and D. fructosovorans. Group III hydrogenases are slightly more divergent and display less
homology (i.e. Rhodobacter capsulatus,Azobacter vinelandii). All enzymes in group I-III represent
two-subunit enzymes, consisting of a small
(28-35 kDa) and a large
a
(56-68 kDa) subunit. Groups I
and II are encoded by simple two-gene operons, group III by more complex operons. The “large” subunit
binds the active site nickel, whereas the “small” subunit has an electron transfer function. This structural
difference between group II and III [NiFe] hydrogenases is manifested in their mode of action: group II
hydrogenases donate their electrons to a soluble, non-membrane-bound, periplasmic cytochrome while
electrons from group III hydrogenases are delivered directly to a membrane-bound electron transport
chain.
Enzymes in groups IV (i.e. Ralstonia eutropha,Methanobacterium autotrophicum) and V (E. coli
hydrogenase-3) have a more complex subunit composition and fading homology with the group I-III
hydrogenases.
It can be concluded that the [NiFe] hydrogenases from D. gigas,D. vulgaris Miyazaki F and D.
fructosovorans genetically exhibit a high homology (65-70%) and represent a subclass of [NiFe] hydro-
2.1 Classification of [NiFe] Hydrogenases 7
genases. The identity of the amino acid sequence in the large subunit of D. vulgaris with that from D.
gigas is 69% (FASTA alignment), with that from D. fructosovorans 66% and with the [NiFeSe] hydro-
genase from D. baculatum still 42%. These [NiFe] hydrogenases are sometimes referred to as ‘standard
hydrogenases‘. Figure 2.3 shows the classification of hydrogenases according to a protein sequence
comparison of the large (
a
) subunit.
"Standard" [NiFe] Hydrogenases
D. baculatum
D. fructosovorans
D. vulgaris Miyazaki F
D. gigas
E. coli 2
H. pylori
W. succinogenes
R. eutropha SH
H. pylori 2
Figure 2.3: Dendogram of the [NiFe] hydrogenases based on a protein sequence homology of the large (
b
)
subunit with the FASTA algorithm. The comparison was only done for hydrogenases for which the complete
protein sequence is available.
The [NiFe] hydrogenases from Allochromatium vinosum (formerly Chromatium vinosum) and Thio-
capsa roseopersicina may also be associated with group II hydrogenases due to their spectroscopic char-
acteristics. These two bacteria belong to the group of purple-sulphate bacteria and still possess the ability
to perform photosynthesis and grow phototrophically - an ability the usual class II hydrogenases have
lost during evolution. Until now, there is no primary structure available for A. vinosum. The [NiFe] hy-
drogenase from Th. roseopersicina BBS has recently been sequenced for a 8000 base pair fragment [20].
The homology of the gene for the large subunit with that from D. vulgaris was 58% and justifies their
assignment to a class II hydrogenase. The protein similarity between A. vinosum and Th. roseopersicina
8 2. Hydrogenases
may also be fortuitous. The two organisms seem to have developed independently to perform dissimilar
metabolic functions [21].
Nevertheless, all [NiFe] hydrogenases which have been sequenced so far, possess two highly con-
served consensus Cys–X–X–Cys in the
a
subunit, one towards the N-terminus and one further down
towards the C-terminus. In [NiFeSe] hydrogenases the first cysteine of the latter motif is replaced by a
selenocysteine. Those cysteine amino acids can be shown to coordinate the heterobinuclear metal active
site (see below). The conservation of amino acids is less pronounced in the
subunit which is responsi-
ble for the electron transfer. A varying number of Fe-S clusters of different composition may participate
in the electron transfer chain.
Comparing [NiFe] and [Fe] hydrogenases, there is no significant homology between the polypeptides
encoding the active sites of these enzymes. The two families must therefor have evolved independently.
The [NiFe] hydrogenases with their high homology must have developed from a common ancestor. It
appears plausible to assume that a cytoplasmic, nickel-containing hydrogenase existed before the evolu-
tionary path towards a periplasmic enzyme left the nickel-binding site relatively conserved and invented
a more variable electron-transferring subunit.
2.2 Molecular Structure
The arrangement of the conserved residues and the composition of the active sites became clear from
X-ray crystallographic studies and from spectroscopic work. Since 1995, crystal structures at atomic
resolution of several nickel-containing enzymes have been determined and contributed to the under-
standing of biological nickel in catalysis (see Table 2.1). The progress in nickel bioinorganic structural
chemistry has been described in some reviews [9,22–25]. Recently, two X-ray structures of [Fe]-only
Table 2.1: Overview of Ni-containing protein X-ray structures
Protein Resolution [ ˚
A] Metal binding References
Urease 2.1 Binuclear nickel [26]
[NiFe] hydrogenase 1.8, 2.5 Binuclear nickel and iron [27,28]
Methyl-CoM reductase 1.45 Ni-porphinoid [29]
hydrogenases from Clostridium pasteurianum [30] and Desulfovibrio desulfuricans [31] were indepen-
dently published. Until now, there is no X-ray structure of the metal-free hydrogenase.
2.2 Molecular Structure 9
A milestone in [NiFe] hydrogenase research was the first X-ray structure of the D. gigas enzyme at
2.85 ˚
A resolution [32]. The crystal form was triclinic with two molecules in the unit cell. While the
small subunit, containing 1 [3Fe-4S] and 2 [4Fe-4S] clusters, displayed similarities to the flavodoxin
redox protein, the large subunit presented a new topological class of enzyme with an unusual Ni coordi-
nation sphere. Figure 2.4 shows the cofactor arrangement in the [NiFe] hydrogenase from Desulfovibrio
vulgaris Miyazaki F [28]. The large subunit bears the active site, the small subunit contains three iron–
sulphur clusters which are arranged in a chain and participate in electron transfer to and from the active
site. The active centre contains a nickel and a second metal ion, the discovery of the latter came as a sur-
Ni-Fe active site
large subunit
[3Fe-4S]
[4Fe-4S]
[4Fe-4S]
small subunit
Figure2.4: Cofactorarrangement in DesulfovibriovulgarisMiyazaki F [28]. The largesubunit (left) harbours
the Ni-Fe active site, the small subunit (right) incorporates the proximal [4Fe-4S] cluster, the [3Fe-4S] cluster
and the distal [4Fe-4S] cluster which may be involved in electron transfer.
prise. It was only tentatively assigned to a Fe atom [32]. Cysteines 68 and 533 serve as bridging ligands
between the metals whereas Cys65 and Cys530 (in D. gigas enumeration of amino acids) are terminally
bound to the nickel atom (see Figure 2.5). Higher temperature factors of the Ni and its surrounding
sulphur atoms were determined which could originate from disorder, X-ray damage to the crystal, only
partial Ni occupancy of the active sites in the crystal or the presence of several Ni redox states. The latter
was investigated by EPR spectroscopy and revealed that the X-ray structure corresponds primarily to
that of the Ni-A form (see below) [32]. This was also supported by activation of the crystallized enzyme
which required hours to recover full hydrogen uptake activity. The three non-protein ligands of the sec-
ond metal were modelled as water molecules since a positive assignment of the electron density peaks
10 2. Hydrogenases
was not possible. The heterobinuclear center then led the authors to a speculation of the CO inhibitor
and H
substrate binding in the bridging position between the nickel and iron atoms. Speculations about
possible electron and proton transfer pathways were also made. An electron transfer from the active site
via two Fe-S cluster to the distal [4Fe-4S] cluster and then to cytochrome c
was proposed. A highly
conserved His/Glu motif would represent a separate possible way of proton transfer. Table 2.2 gives
details of the active site structural parameters from the refined X-ray analysis. The Ni
cdcdc
Fe distance
was given as 2.69 ˚
A, the Ni-S distances were 2.23 ˚
A (Cys68), 2.04 ˚
A (Cys65), 2.42 ˚
A (Cys530), and
2.60 ˚
A for Cys533. A non-protein ligand bridging the nickel and iron atoms (labelled ‘X’ in Table 2) is
not included in this model. This position was vacant in the initial structure.
In a later publication by the same authors, a new, pseudo-hexagonal crystal form was investigated
[27]. This time the second metal atom was unambiguously identified to be iron by collecting data at
wavelengths close to either side of the Fe absorption edge. The resolution was increased to 2.54 ˚
A. The
bridging cysteines (Cys68 and 533) refined to distances of 2.6 ˚
A, that of the terminal cysteines were
shorter (2.2 ˚
A for Cys65 and 2.3 ˚
A for Cys530) (see Table 2.2). A strong peak in the electron density
map indicated the presence of an additional ligand in a bridging position between the Ni and Fe centres.
This peak was tentatively assigned to an oxygen species, leaving the nickel atom in a highly distorted
square pyramidal coordination sphere with a vacant axial sixth ligand site. The iron atom has six ligands
in a distorted octahedral environment (see Figure 2.5).
Ni
Fe Fe
XX
SO
C
O
CN
C
O
Cys546
N
C
O
C
Cys533 Cys549
Cys530
Cys68 Cys84
Ni
Cys81
Cys65
Figure 2.5: Details of the active centres of the [NiFe] hydrogenases from D. gigas [27] (left) and D. vulgaris
Miyazaki F [28] (right). The bridging ligand Xis supposed to be an oxygen or sulphur species in D. gigas
and D. vulgaris, respectively.
2.2 Molecular Structure 11
Candidates for the bridging ligand are mono-oxygenated species derived from the reduction of O
.
Inclusion of a diatomic molecule would be sterically hindered according to the authors [27]. Higher
temperature factors were only observed for the Ni ion, the S atom of Cys530 and the bridging species
which were assigned to static disorder due to structural differences between the various active sites
present in the crystal. The findings for the D. gigas [NiFe] hydrogenase together with a speculation
about the mechanism have been reviewed in [11,33–35].
Table 2.2: Selected structural parameters of the active centre of ‘as-isolated’ [NiFe] hydrogenases from
different X-ray structures. Bond lengths in ˚
A, bond angles (
e
) in
f
.
D. gigas D. gigas D. vulgaris Miyazaki F D. fructosovorans
˚
A,
"
/res., ref. 2.85 ˚
A [32] 2.54 ˚
A [27] 1.8 ˚
A [28] 2.7 ˚
A [36]
Ni
cdcdc
Fe 2.69 2.90 2.52 3.23
Ni–SCys533 2.60 2.62 2.36 2.45
Ni–SCys68 2.23 2.58 2.15 1.62
Ni–SCys530 2.42 2.27 2.33 2.12
Ni–SCys65 2.04 2.16 2.22 2.16
Ni
cdcdc
X not given 1.74 2.19 not given
Fe–SCys533 2.26 2.20 2.36 2.31
Fe–SCys68 2.62 2.23 2.15 2.22
Fe
cdcdc
X not given 2.14 2.28 not given
g
Ni-X-Fe not given 96.5 68.4 not given
g
Ni-SCys533-Fe 66.7 73.6 64.1 85.6
g
Ni-SCys68-Fe 66.8 73.9 66.2 113.9
The [NiFe] hydrogenase from D. vulgaris Miyazaki F is highly related to that of D. gigas (see above).
After first single crystals became available [37] the active site and the Fe-S clusters were localized at
a resolution of 4 ˚
A [38]. The membrane-bound hydrogenase is solubilized by trypsin digestion thus
facilitating the crystallization. The hydrogenase from D. vulgaris crystallizes in the space group P2
2
h
.
The folding pattern of the protein and structural features of the metal centres are very similar to those of
D. gigas. The two structures can be superimposed with a root mean square deviation of 0.82 ˚
A for all
main chain atoms [28]. The coordination of the Ni-Fe active centre is very similar to that of D. gigas. Ni
12 2. Hydrogenases
is coordinated by four sulphur atoms of cysteines(amino acid residues 80, 84, 546 and 549). The Fe atom
(as identified by anomalous dispersion difference maps) is coordinated by two bridging cysteines (Cys84
and Cys549) and exhibits three distinctive electron density peaks as terminal ligands. A comparison of
the active centres of the [NiFe] hydrogenases from D. gigas and D. vulgaris Miyazaki F is done in Table
2.2 and depicted in Figure 2.5. At closer inspection, however, differences in the structural parameters of
the active site become apparent (see Table 2.2). The Ni
cdcdc
Fe distance is 2.55 ˚
A, the diatomic ligands
to the Fe were refined to one S=O, and two CO or CN molecules (higher electron density peak for one
non-protein ligand and pyrolysis MS experiments with an usual mass peak at 48 (S=O) [28]) and the
bridging ligand is assigned to a sulphur atom based on a higher electron density although an oxygen
species remained a possible second candidate. Unexpectedly, a magnesium ion was also discovered near
the C terminus of the large subunit which might be involved in proton transfer reactions.
The [NiFe] hydrogenase from D. fructosovorans has been also crystallized and its structure was elu-
cidated by X-ray crystallography. Until now, it has only been published in the context of a [3Fe-4S]
[
[4Fe-4S] cluster conversion by site-directed mutagenesis of a glycin into a cysteine residue after hetero-
loguous expression in D. gigas [36]. The coordinates of the [NiFe] hydrogenase from D. fructosovorans,
however, have been deposited at the Brookhaven Protein Data Bank (PDB) as a ‘layer 1’ file. This in-
dicates that the structural parameters are still not definite and must be used with caution. They are also
included in Table 2.2 .
Thus for all hydrogenases of the group II, X-ray structures have become available. The hydrogenases
from D. gigas and D. vulgaris Miyazaki F are spectroscopically very similar [39]. It thus remains to be
investigated whether an agreement about the composition of the active centre can be reached.
2.3 The Redox States of [NiFe] Hydrogenases
Hydrogenases are oxidoreductases which means that they oxidize a substrate, transport the electrons and
reduce a reductant.
In particular, they oxidize H
to 2 H
and 2 electrons, pass the electrons to their physiological electron
acceptor cytochrome c
and finally utilize them to reduce sulphur to sulphide.
During the course of the redox cycle, [NiFe] hydrogenases pass through a number of different redox
states. Electron paramagnetic resonance spectroscopy (EPR) and related techniques (see below) are the
method of choice to characterize the paramagnetic states involved in the redox cycle. Figure 2.6 gives
a schematic picture of the complex redox states of the [NiFe] hydrogenase. There are potentially four
paramagnetic centres in the [NiFe] hydrogenase: namely the heterobimetallic NiFe cluster in the large
2.3 The Redox States of [NiFe] Hydrogenases 13
Ni-R
Ni-Si
Ni-C
Ni-A/B
4Fe-4S
Ni-Fe
-E/mV
3Fe-4S 4Fe-4S
∗
∗
∗
∗∗
∗ ∗
ikjml
ikn
ikn
ikl
ikn
iklpo
o
q
q
q
o
Figure 2.6: Redox-States of the [NiFe] Hydrogenase. Asterists denote paramagnetic (S = 1/2) states, squares
symbolize the cubane [4Fe-4S] clusters, a triangle stands for the [3Fe-4S] cluster. The active centre is given by
the rectangle with rounded corners. Open symbols stand for oxidized, filled symbols for completely reduced
states. The redox potential of the protein in solution is lowered when going from the oxidized Ni-A/B states
to the completely reduced Ni-R form. On the right hand side, the numbers of protons and electrons are given
which are involved in each redox step. These were determined by redox titrations in the presence of dyes
(see [40] and references therein). The number of protons are derived from the pH-dependence of the midpoint
potentials.
subunit, the proximal [4Fe-4S] cluster in the small subunit, one [3Fe-4S] cluster, and the distal [4Fe-4S]
cluster.
In the ‘as-isolated’ form the active site of the enzyme is in its oxidized, enzymatic inactive, paramag-
netic states Ni-A or Ni-B. Ni-A displays EPR spectra with
-tensor principal values g
rts ums v
= 2.32, 2.24,
2.01 and Ni-B with g
rts uws v
= 2.33, 2.16, 2.02. In addition, at low temperatures (
x
60 K) a rather isotropic
EPR signal at g = 2.01 is visible which is assigned to the oxidized [3Fe-4S]
cluster in the small subunit.
EPR experiments with
Ni enriched protein samples [41,42] and the observed
Ni hyperfine splitting
therein unambiguously showed that the EPR signals originate from the Ni atom in the active centre. The
correlation between the EPR signals and enzymatic activity was first established by Fernandez et al. [43].
They showed that Ni-A and Ni-B differ in their rates of activation. Whereas Ni-B is activated by incu-
bation under an H
atmosphere within minutes (therefore sometimes referred to as ‘ready’ or Ni
y
) Ni-A
requires incubation for hours (sometimes called ‘unready’ Ni
z
). During activation, the Ni-A and Ni-B
EPR signals disappear and a diamagnetic, EPR-silent state Ni-SI is reached.
EPR analysis of the first protein crystals from D. gigas revealed a constitution of 85% Ni-A and
14 2. Hydrogenases
15% Ni-B [32], the amount of EPR-silent fraction was not determined. Later Dole et al. examined a
polycrystalline powder sample of the D. gigas hydrogenase and obtained an EPR spectrum essentially
identical to that of a frozen solution of Ni-A [44]. A constitution of 10% Ni-B, 40 % Ni-A and 50%
Ni-SI was determined.
Upon reduction from the oxidized states to the EPR-silent form Ni-SI, the [3Fe-4S] cluster is reduced
to its S = 2 [3Fe-4S]
{
form. Upon further reduction, a new rhombic EPR signal of the active site “Ni-C”
with principal values g
rts ums v
= 2.20, 2.14, 2.02 appears. This state is believed to be two electrons more
reduced than Ni-A/B and belong to a catalytic intermediate in the redox cycle. The relation between
catalytic activity and the appearance of the Ni-C EPR signal was given by Moura et al. [45]. Here,
EPR spectroscopy provides a direct spectroscopic assay of enzyme activity. The Ni-C state displays
unusual features. The Ni-C state is light-sensitive and converts into a fourth paramagnetic state Ni-L
with
-tensor principal values g
rts ums v
= 2.28, 2.11, 2.05. The reaction is carried out at low temperatures
between 4 and 77 K. Upon further ‘warming’ the sample to 120 K in the dark, the Ni-L signal disappears
and the Ni-C signal is recovered. In addition, in the Ni-C state, both the proximal and the distal [4Fe-
4S] clusters become paramagnetic (S = 1/2) in their reduced [4Fe-4S]
forms. Magnetic interaction
between the proximal [4Fe-4S]
cluster and the NiFe active site induces the appearance of a complex
EPR spectrum (called “split Ni-C”) at low temperatures and a significant enhancement of the relaxation
rates of the Ni centre. The magnetic interaction between the two centres was analyzed by Guigliarelli et
al. [46,47]. Based on numerical simulations, they determined the parameters of exchange and dipolar
interactions between the two closely spaced paramagnets and also obtained the relative orientations of the
-tensors with respect to each other. Furthermore, the
-values of the proximal [4Fe-4S] cluster, which
are observed by the spin-coupling with the distal [4Fe-4S] cluster, were given. The study was later
extended to the interaction of the Ni-L state and the proximal [4Fe-4S] (in the “split Ni-L” signal) and
led the authors to the conclusion that the
-tensor orientations in Ni-C and Ni-L were very similar [48].
Finally, the fully reduced diamagnetic ‘resting’ state Ni-R is obtained for which hardly any spectro-
scopic data apart from Fourier-transformed infrared spectroscopy (FTIR) are available.
Whereas EPR suffers from the drawback of being applicable only to the paramagnetic states of the
enzyme, FTIR covers the complete range of redox states. After the initial discovery of unusual high
frequency bands in [NiFe] hydrogenases and their speculative assignment to non-protein CO and CN
ligands at the Fe atoms in the active centre [27, 49, 50], they were unambiguously assigned to 2 CN
and 1 CO ligand in A. vinosum upon cultivation with
N and
C enriched media and observing the
respective isotope shifts of the IR bands [51]. The band around 1930-1940 cm
corresponds to the
stretching frequency of the C=O bond. The two bands above 2040 cm
belong to the symmetric and
2.3 The Redox States of [NiFe] Hydrogenases 15
antisymmetric stretching frequencies of the C
|
N triple bonds (see Figure 2.7).
1800 1900
}
2000
}
2100
}
Frequency [cm
~
−1]
0
IR Signal Intensity
ν
CO
ν
CN
Figure 2.7: BLYP/DZVP calculated high frequency IR vibrational frequencies of a small cluster model of
the Ni-B state. The positions of the vibrations approximately correspond to those observed experimentally
(see text). B3LYP/6-311+G IR frequencies were also obtained for larger Ni-A, Ni-B, Ni-C and Ni-L model
clusters. The respective frequencies were 1988, 1995, 1612 cm
R
(Ni-A), 2016, 2002, 1697 cm
5
(Ni-B),
2014, 2009, 1687 cm
R
(Ni-C), 1969, 1963, 1586 cm
5
(Ni-L). The magnitude of the deviations are a typical
systematic error inherent in DFT methods in the calculation of IR frequencies (in particular for CO stretching
vibrations [52]) and also originate from the drastic influence of spin-contamination on the calculated IR
vibrations [53] (
!
values are 0.94 for Ni-A, 0.80 for Ni-B, 0.79 for Ni-C, 1.18 for Ni-L).
The characterization of all redox states of [NiFe] hydrogenases by means of their IR spectra, the
in situ following of their bands upon oxidation/reduction has matured to near perfection [50, 54, 55].
Table 2.3 collects FTIR data for the two most intensively investigated [NiFe] hydrogenases D. gigas and
A. vinosum. In general, the shift in IR bands is rather small between the different redox states of the
enzymes. FTIR spectroscopy probes the strength of the C=O and C
|
N bonds. The force constant of the
bond depends on the balance between
ligand-metal bonding and
-back bonding. Metal-ligand
-back
donation into anti-bonding
orbitals of the C
|
N triple bond weakens the C-N bond. A decrease of
3-5 cm
in the CN IR bands upon reduction from Ni-B to Ni-C thus indicates a slight increase in the
metal-ligand
-back donation caused by an increase of charge density at the Fe atom. The changes are
all in the range of 30-35 cm
and smaller than that expected for a one electron change of the electron
16 2. Hydrogenases
Table 2.3: Characterization of the redox states of [NiFe] hydrogenases by their IR bands
Redox state High frequency IR bands [cm
]
D. gigas [27] A. vinosum [55]
5 R 5
Ni-A 1947 2083 2093 1945 2083 2093
Ni-B 1946 2079 2090 1944 2079 2090
Ni-C 1952 2073 2086 1950 2074 2087
Ni-L 1898 2043 2058
Ni-R 1940 2060 2073 1936 2059 2073
Ni-SU 1950 2089 2099 1950 2089 2099
Ni-SI
1914 2055 2069 1910 2051 2067
Ni-SI
1934 2075 2086 1932 2074 2086
density on an iron atom (102 cm
[56]). The largest shifts are observed for the reduction Ni-B to Ni-
SI (a concerted shift downwards by approx. 30 cm
) and the Ni-C to Ni-L conversion (30 cm
for
the CN bands and 50 cm
for the CO band). These two processes must be accompanied by a larger
change of electron density at the Fe metal site, i.e. an increase in electron density due to liberation or
photodissociation of a ligand.
During the catalytic cycle, paramagnetic and diamagnetic states alternate. The appearance or disap-
pearance of the corresponding EPR signal serves as an assay of the redox state of the Ni centre. Redox
titrations of [NiFe] hydrogenases gave a midpoint potential for the Ni-A/B
[
Ni-SI (Ni(III)/Ni(II)) con-
version between -410 and -110 mV [12,57] (see Figure 2.6). The midpoint potential of Ni(III) was found
to be pH-dependent by -60 mV per pH unit. The first reduction step can thus be written as
M
'
W
'
[
W
)
(2.2)
The Ni-SI
[
Ni-C conversion exhibited a pH-dependence twice as large as that of the initial step which
indicates that two protons might enter the active centre [40]. The Ni-C
[
Ni-R reduction, again, is a
step associated with a single protonation ( [58], see Figure 2.6).
2.4 Specific Properties of the Paramagnetic States 17
2.4 Specific Properties of the Paramagnetic States
Table 2.4 gives an overview about the measured hyperfine splittings in EPR and ENDOR spectra with nu-
clei which possess a nuclear spin I
1/2. Very often, the reported hyperfine splittings are only deduced
from linewidth broadening effects in EPR spectra and are thus only crude estimates, often simulations
were not performed. The given hyperfine interactions are also those measured along the
-tensor prin-
cipal values. In the case where hyperfine tensor and
-tensor are not collinear, the true hyperfine tensor
principal values might differ. After the first discovery of an EPR signal from [NiFe] hydrogenases [41],
Table 2.4: Collection of hyperfine data in MHz for [NiFe] hydrogenases
Nucleus State Organism
*
Hyperfine Coupling Ref. Remarks
A
r
A
u
A
v
Ni Ni-A M. t. 21 42 76 [59] simulated
Ni-A D. g. 6-17 6-17 76 [45] A
r
, A
u
estd.
Ni-C – – 76 A
r
,A
u
not resolved
Ni-C R. a. 17 14 - [60] A
v
not resolved
Ni-L 56 28 14
Fe Ni-A D. g.
1 [61]
Fe-ENDOR
Ni-B D. d. none
Ni-C D. g. none
S Ni-B W. s. 27 39 – [62]
O Ni-A A. v. 14 11 13 [63]
Ni-B 0 11 20
CO Ni-CO A. v. 81 85 90 [63] g=2.12, 2.07, 2.02
Abbreviations: M.t. M. thermoautotrophicum, D. g. D. gigas, R. a. R. eutropha (SH), D. d. D.
desulfuricans, W. s. W. succinogenes, A. v. A. vinosum
actual proof of it being a Ni signal was obtained from
Ni enrichment and subsequent detection of line
broadening and hyperfine splitting [59,64]. Moura et al. produced evidence that all three paramagnetic
states Ni-A, Ni-B and Ni-C showed
Ni hyperfine broadening or splitting [45]. In the literature, how-
ever, only one complete
Ni hyperfine tensor is found which was obtained from simulations of the EPR
spectra [59]. All other delivered only estimates from the line broadening effects. For an overview of
Ni hyperfine splittings in [NiFe] hydrogenases see [65].
18 2. Hydrogenases
The detection of a second metal ion (the Fe) in the active centre of then termed “[NiFe]”-
hydrogenases in the X-ray structure analysis was a surprise to the magnetic resonance community. So
far, a second metal situated close to the nickel had not been detected. There was no effect of
Fe en-
richment on the EPR spectrum of Ni-A from D. gigas [66]. The absence of
Fe line broadening alone is
not sufficient to demonstrate that the Ni-Fe binuclear centre is not a spin-coupled system. In case of an
exchange-coupled system one would expect a deviation from Curie’s law at low temperatures. The very
existence of a spin-coupled centre is ruled out by analysis of the temperature dependence of the Ni-A,
Ni-B, Ni-C and Ni-L EPR signal intensities [44]. No deviation from Curie’s law was detected between
10K and 240K. Further support comes from recent
Fe-ENDOR experiments (see Table 2.5) in which
no hyperfine interaction could be detected for Ni-B and Ni-C and only a very small one (approx. 1 MHz)
for Ni-A [61]. The total spin multiplicities of the metals in the active centre necessarily must therefor be
assumed to be S = 1/2 for the Ni and S = 0 for the Fe atom. The low spin Fe(II) 3d
state is plausible
because of the CN and CO non-protein ligands (see above) which impose a strong ligand field on the
iron atom.
The spectroscopic detection of spin density at a sulphur ligand to the Ni atom comes from
S en-
riched protein from the [NiFe] hydrogenase from Wollinella succinogenes [62]. Hyperfine splitting due
to interaction between the I = 3/2 nuclear spin from
S and the electron spin of the Ni centre in Ni-B
was detected (see Table 2.4). Simulations of the measured line broadening of the g
r
-component and hy-
perfine splitting of the g
u
-component assuming an enrichment of 70% and hyperfine interaction with one
S nucleus gave good agreement with the experimental spectrum. For Ni-C line broadening was also
observed. A difference spectrum of the Ni-L minus Ni-C spectrum also revealed a
S hyperfine splitting
of the g
v
-component in Ni-L. The experiments are indicative of the fact that hyperfine interaction to one
sulphur nucleus is present in Ni-B, Ni-C and Ni-L states. It cannot be said, however, whether this is the
same sulphur atom in all these states.
In order to investigate the hypothesis of an oxygenic species present in the oxidized states of the
[NiFe] hydrogenase, the effect of
O
upon the EPR spectra in the oxidized states Ni-A/B was studied
by van der Zwaan et al. [63]. They measured a nearly isotropic line broadening of all
-components in
EPR spectra of Ni-A (see Table 2.4) but also some detectable hyperfine broadening in the Ni-B state. It
was concluded that either O
or a reduction adduct binds in the vicinity of the oxidized states. According
to the authors, the difference between Ni-A and Ni-B species, therefore, cannot be explained by assuming
that only in one state (the unready Ni-A) O
or one of its species is bound to the active site.
When Ni-C is treated with CO, its EPR signal transforms into a Ni-C
signal with g
rts ums v
= 2.12,
2.04, 2.02 [63]. The bound CO is photolabile and the Ni-C signal is recovered upon illumination. The
2.4 Specific Properties of the Paramagnetic States 19
effect of
CO (I = 1/2) on the EPR spectra of the CO-inhibited Ni-C
was investigated [63] (see Table
2.4). From the nearly isotropic hyperfine splitting from
C of
CO about 85 MHz along the
principal
values, an axial bonding situation for the CO is discussed. Very recently, it was investigated whether it
would be the Ni-C or the Ni-L state that actually binds the carbon monoxide molecule [58].
The investigation of
H hyperfine interactions in the different paramagnetic states of the [NiFe]
hydrogenase is of particular relevance. Since the enzyme is involved in hydrogen metabolism, either
substrate H
, or the products H
, H
or H
are expected to be bound in the vicinity of the Ni atom in
the active centre and thus should be detectable by EPR or ENDOR spectroscopies.
When the enzyme in the Ni-C form is solvent-exchanged with D
O/D
, a slight but significant re-
duction of line width of the g
r
- and g
u
components was noticed (maximum effect on g
u
of 14 MHz (0.5
mT)) [67]. This indicates a solvent-exchangeable proton in the ligand surrounding of the Ni atom in the
Ni-C state. The Ni-C to Ni-L conversion is six-fold slower when the enzyme is prepared in D
O/D
solvent [67] which indicates that a hydrogen species (respectively a deuterium species) is lost upon illu-
mination. Likewise the re-appearance of the Ni-C signal at high temperatures is also five-fold slower in
D
O/D
[68].
The ultimate detection of
H or
H nuclear hyperfine interaction in the vicinity of the Ni active site
is complicated by the large EPR linewidth but can be resolved by double resonance experiments such as
ENDOR and electron spin echo envelope modulation (ESEEM). Chapman et al. used two-pulse ESEEM
spectroscopy to address the question of solvent accessibility of the Ni-A and Ni-C states by comparing
spectra in H
O and D
O [68]. The Ni signal in Ni-A showed no modification upon solvent exchange.
This indicates that there is no proton bound to the active centre which can be substituted by a deuteron.
The [3Fe-4S]
signal, however, showed the presence of a solvent exchangeable proton. The Ni-C signal
exhibited a significant modulation in D
O due to a deuterium nucleus in the vicinity of the Ni. Table 2.5
collects
H- and
H-ENDOR data. Fan et al. investigated the active site of the [NiFe] hydrogenase from
D. gigas in three paramagnetic states Ni-A, Ni-B, Ni-C by means of ENDOR spectroscopy [69]. Ni-A
spectra were identical in H
O and D
O in agreement with the finding by Chapman (see above). Large
hyperfine couplings of 12.8 MHz at g
u
were assigned to
-CH
protons. The
H-ENDOR spectrum
of the Ni-C form displays an additional large hyperfine coupling of 16.8 MHz at g
u
which is lost upon
solvent exchange with D
O. The corresponding
H-ENDOR signal was also detected. The second signal
which also showed a D
O effect (4.4 MHz) was later shown to originate from the Ni-B form. The
-CH
proton couplings increase from 12.8 MHz in Ni-A to 15 MHz in Ni-B.
Whitehead et al. later repeated ENDOR experiments on a different organism, the [NiFe] hydrogenase
from Th. roseopersicina [70]. Here, the Ni-C to Ni-L conversion was also investigated. In Ni-C, two
20 2. Hydrogenases
Table 2.5: Overview of
H-ENDOR Data of [NiFe] Hydrogenases
State Organism
*
Hyperfine Coupling Remark/Assignment Ref.
Ni-A D. g. 12.8 MHz at g
u
cysteinyl
-CH
[69]
in D
O identical
Ni-B 15 MHz at g
u
cysteinyl
-CH
4.4 MHz at g
r
loss in intensity in D
O/OH
or H
O
Ni-C 16.8 MHz at g
r
solvent exchangeable A
= [15, 22, 25]
line narrowing in D
O (3, 7, 8 MHz)
H-ENDOR 2.4 MHz/in plane H
Ni-C T. r. A(
H
) 16-20 MHz in D
O A(
H
)
3.1 MHz [70]
solvent exchangeable proton
A(
H
)
12 MHz isotropic, not exchangeable
A(
H
)
x
5 MHz
Ni-L A(
H
) lost photololabile species
A(
H
)
10 MHz neither photolabile nor exchangeable
Abbreviations D.g. D. gigas, T. r. Th. roseopersicina
large
H hyperfine couplings were detected. The isotropic, non-exchangeable coupling of 12 MHz was
assigned to
-CH
protons of a cysteine residue. The larger coupling of 16-20 MHz is D
O exchangeable
and lost upon photoillumination in the Ni-L state. Unresolved signals smaller than 5 MHz in the Ni-C
state could not be assigned. The largest
H couplings in the Ni-L state are 8-10 MHz and thus smaller
than in the Ni-A, Ni-B and Ni-C forms.
2.5 Motivation and Perspective of this Work
Albeit there was a large amount of very detailed spectroscopic data in the literature, their interpretation
in the context of structural changes between the redox states was not possible before the work in this
thesis was started. This was due to several complications.
The elucidation of the X-ray structure of a [NiFe] hydrogenase in 1995 revealed atomic details of
the active Ni site in the enzyme for the first time. The detection of a heterobimetallic cluster with an
additional Fe atom was unexpected. The unusual coordination sphere of the Ni raised more questions
than it answered. Is Ni the catalytic site? Is there a bridging ligand in all states, what is its nature and
2.5 Motivation and Perspective of this Work 21
role, do the cysteine ligands participate in the cleavage of the H–H bond, what is the role of the Fe atom,
how do the different paramagnetic states differ from each other? How do the H
¡
and proton channels
look like? What is the influence of the protein environment?
Only in 1999, an X-ray structure of the reduced enzyme were published. Some of the information
can be gained from EPR investigations of protein single crystals. The large and well-ordered protein
single crystals of the [NiFe] hydrogenase from D. vulgaris Miyazaki F opened a new field. One can
deduce the spatial arrangement of i.e.
¢
-tensors with respect to the ligand environment, orientations
of hyperfine interaction tensors of, for example
£
H nuclei, and possibly detect the binding situation of
molecular hydrogen or its dissociation products in the active centre.
The correlation between magnetic resonance parameters and structural modifications is still difficult.
Changes in EPR or ENDOR spectra can only indirectly be interpreted in terms of changes in the X-
ray structure. It is not possible to perform a high-resolution collection of X-ray diffraction data of a
crystal mounted in an EPR quartz tube. However, the determination of the unit cell parameters and the
orientation of the crystal axes is feasible. Likewise, after massive X-ray diffraction data collection in
a synchrotron beam, the protein single crystal suffers from X-ray damage and from the generation of
additional radicals.
Here, a theoretical approach which yields hyperfine parameters and
¢
-tensors for a given geometry
may provide useful information. Is it possible to find a methodology that allows the prediction of mag-
netic resonance parameters for a system as complex as the active site of a metalloprotein with sufficient
accuracy and affordable computing resources?
This combination of protein single crystal EPR and ENDOR and theoretical calculations in the frame
of approximate Density Functional Theory (DFT) is the central aspect of this work.
When this work was started, there was no theoretical study of [NiFe] hydrogenases, neither on the
electronic structure nor on the reaction mechanism published. This metalloenzyme recently gained atten-
tion and a number of publications based on first principles calculations appeared in the last years [71–76].
None of them, however, dealt with a theoretical description of the paramagnetic states of the enzyme for
which many experimental data exist.
Until recently, there was also no rigorous approach to reliably deal with the magnetic resonance pa-
rameters of transition metal complexes, not to say that the treatment of systems as complex as the active
centre of a metalloenzyme was out of reach with conventional post-Hartree Fock methods. Thus, a new
relativistic DFT approach has been critically evaluated and was used here for the characterization of the
paramagnetic intermediates of [NiFe] hydrogenase. Based upon the results obtained for the intermedi-
ates, a plausible enzymatic mechanism can be suggested which considers experimental findings.
22
Chapter 3
Theory and Fundamentals
3.1 EPR Spectroscopy
The basics and more sophisticated details of EPR spectroscopy are given in many text books [77,78].
In the following only a very concise treatment of the aspects which are necessary for the understanding
of this thesis is given. Electron Paramagnetic Resonance (EPR) spectroscopy detects the interaction of
an unpaired electron spin with a magnetic field and with its environment. Paramagnetism of the sample
thus is a prerequisite.
3.2 The Spin-Hamiltonian
The interaction of an electron spin with an external magnetic field
¤¦¥
is described by the electron-
Zeeman term
§
¨©«ª
¢T¬¤¦¥¯®
°
(3.1)
where
¢
is the electron
¢
-factor,
¬
is the Bohr magneton and
®
°
the electron spin operator (see Figure
3.1).
The electron, however, does not sense the external magnetic field
¤¦¥
but an effective field, weakened
or enforced by shielding or deshielding.
¤²±M³
ª
¤¦¥%´µ¤J¶¸·º¹»w¶
ªG¼¾½À¿ÂÁÃ
¤¦¥
ªG¼
¢5Äw¢tÅ
Ã
¤¦¥
(3.2)
Thus any deviation from
¢tÅ
is a measure of the chemical environment of the unpaired electron. In tran-
sition metal complexes it is not only the electron’s angular momentum that contributes to the deviation
from
¢Å
. Some complexes (i.e.
Æ
-metal complexes) possess a resulting orbital angular momentum which
23
24 3. Theory and Fundamentals
E = h νE
ME = +1/2 g B
E = -1/2 g B
β
∆
se
+ 1/2
- 1/2
B = 0 B
α
β
αβ
β
e
e e
Figure 3.1: Electron-Zeeman Splitting in a Magnetic Field. In the presence of a homogeneous, time-
independent magnetic field
ÇÈ
the two degenerate energetic states split into a spin-up (
É
M
Ê
= +1/2) and
a spin-down (
Ë
M
Ê
= -1/2) energy level. The energetic difference between the two states is
ÌÍYÎÐÏÒÑËÓѾÔ
and
must be matched by the microwave radiation
ÌÍYÎ;ÕTÖ
.
may cause a significant deviation from the free electron value due to spin-orbit coupling (
×
°
coupling).
§
ØÚÙ
ªÜÛ/Ý
ÞàßÐá
Ý
â
(3.3)
Electronic ground states may also acquire orbital magnetic momentum due to spin-orbit coupling from
higher states with
×äã
ªæå
into the ground state wavefunction and display
¢
-values different from
¢tÅ
.
Due to the anisotropic surrounding, the local field also becomes orientation-dependent. This depen-
dency can be taken into account in the spin-Hamiltonian by replacing the scalar
¢
-factor by a matrix
ç
.
§
¨è© ª
¬¤ ¥
ç
®
°
(3.4)
This matrix
ç
is usually referred to as ‘
¢
-tensor’. 1The
¢
-tensor can be diagonalized to yield its principal
values
¢tédé
,
¢ºêëê
, and
¢tìì
in its principal axes system (
í
,
î
,
ï
). The “
¢
-tensor principal axes system” is
related to the orbital axes system and thus to the molecular bonding situation of the complex.
The nuclear Zeeman-term describes the energy of a paramagnetic nucleus (
ðñã
ªæå
) in the presence of
a magnetic field in analogy to the electron-Zeeman term
§
򩫪
¬óô¤«¥º¢ó ®
ð
(3.5)
It is of the order of
¢Ú¬ôÄw¢ó-¬õó÷ö
1000 smaller than the electron-Zeeman term but often as large as the
hyperfine interaction.
1Note that mathematically only the
ø¯ù
matrix is a tensor.
3.3 The
¢
-Tensor 25
The hyperfine term arises from the interaction of the electron spin
®
°
with the nuclear spin
®
ð
.
ð
can
be a ligand nucleus (i.e.
£
H,
£ú
N) or the metal nucleus itself.
§
ûü
ª
®
°þý
®
ð
(3.6)
The hyperfine tensor
ý
describes the magnitude and orientation of the coupling in the molecule or
complex.
The nuclear-quadrupole term originates from an additional interaction of the electric field gradient at
the position of the nucleus with its nuclear spin (
ð ÿ
½
) exhibiting an electric quadrupole moment.
§
ª
®ð
®ð
(3.7)
The total spin Hamiltonian is of the form
§
ª
§
¨è©
´
§
ûü
´
§
ò©
´
§
ª
¬¤¦¥
ç
®
°
´ ®
°þý
®ð ´;¬õó-¤¦¥º¢ó¦®ð ´ ®ð
µ®ð
(3.8)
3.3 The
-Tensor
Depending on the orbital angular momentum of the electronic ground state and the nature of the co-
ordinating ligands, transition metal complexes may exhibit EPR spectra with
¢
-values different from
¢Å
. For transition metal complexes, the
¢
-tensor is mostly rhombic, e.g.
¢éã
ª
¢êã
ª
¢ì
. That means
that the interaction of the magnetic field is anisotropic and different along the
í
-,
î
-, and
ï
-directions
of the molecule. This is the most general case. Special cases e.g. axial (
¢é
ª
¢êã
ª
¢ì
) or isotropic
(
¢é
ª
¢ê
ª
¢ì
)
¢
-tensors arise from accidentally or orbital-symmetrically degenerate spin density distri-
butions and spin-orbit couplings. The theory of EPR spectroscopy of transition metal ions is described
in various text books [79–81]. The EPR-spectra of [NiFe] hydrogenases usually display such a rhombic
EPR spectrum (see Figure 3.2). The
¢
-anisotropy, nevertheless, is still modest with a
¼
¢é
¿
¢ì
Ã
å
compared to e.g. low-spin ferric (Fe(III)) haem with
¼
¢ºé
¿
¢tì
Ã
ö
3. For Ni, there is no simple model
which can predict the
¢
-values of a Ni complex. The variations in nature and number of coordinating
ligands, ligand strengths and coordination geometries make it impossible to suggest an instructive way
to predict
¢
-values.
3.4 The Hyperfine Tensor
When the hyperfine interaction Ais larger than the EPR linewidth, a splitting of the EPR lines by this
hyperfine interaction can be observed. In [NiFe]-hydrogenases, the EPR linewidth is so large (usually of
26 3. Theory and Fundamentals
2800
3000
3200
3400
Magnetic Field [G]
Absorption
Absorption
derivative
g
xg
yg
z
z
y
x
Figure 3.2: Rhombic EPR spectrum: Left: Simulated EPR spectrum with parameters typical for the Ni-B
EPR signal of [NiFe] hydrogenase:
Ï
= 2.32,
Ï
= 2.16 ,
Ï
= 2.01; linewidth 19 G, microwave frequency
9.480 GHz, centre field 3150 G, sweep width 700 G. Top: absorption spectrum, bottom: derivative spectrum.
Right: Geometrical shape associated with a rhombic
Ï
-tensor.
the order of 10-20 G) that only very large hyperfine interactions can be detected, in favourable cases. The
electron-nuclear double resonance (ENDOR) spectroscopy allows the measurement of small hyperfine
interaction by means of a high-resolution double resonance experiment [82]. In ENDOR spectroscopy,
the influence of a second swept radiation frequency, in the radio-frequency (RF) range, on the microwave
absorption of an EPR transition is observed. When the RF field matches one of the NMR transitions
with
Ø
= 0,
= 1 in Figure 3.3 (corresponding to two transitions between hyperfine levels),
the effective relaxation rates of the systems are changed and so is the EPR absorption. This change of
EPR absorption is detected while sweeping the RF field. The higher resolution of ENDOR is obtained
at the expense of experimental sensitivity (the ENDOR effect is only of the order of a few percent).
However, ENDOR is much more sensitive than the respective NMR experiment. Further details of
ENDOR spectroscopy are given in [81,83–85].
The two NMR transitions correspond to two ENDOR transition frequencies
and
which are
detected in an ENDOR experiment. They are obtained as two lines
ª
tó
(3.9)
around the nuclear Larmor frequency
tó
. The splitting of the two ENDOR frequencies corresponds to
the hyperfine coupling.
The hyperfine tensor
ý
is the sum of an isotropic, scalar part (
!"$#&%
) and an anisotropic part (
ý
('*)
"$#+%
)
ý
-,
%
,
ª
!"$#+%
½
/.
´
ý
('0)
"$#&%
(3.10)
3.4 The Hyperfine Tensor 27
νe
νn
νn
hyperfine
coupling
electron
spin |mSmI>
Wn1
Wn2
We1
We2
Wx1
Wx2
transfer rates
NMR
EPR
EPR
NMR
|+->
|++>
|-->
|-+>
A/4
A/4
nuclear spin
Zeeman splitting:
E/h
Figure 3.3: Four level diagram of a S=1/2 and I= 1/2 system. Schematic drawing of the energy levels of a S
= 1/2 and I = 1/2 system in an external magnetic field due to electron Zeeman, nuclear Zeeman and hyperfine
interaction. The allowed EPR and NMR transitions are marked with arrows (left). On the right hand side the
transfer rates are given
.
where
½
1.
is the unity matrix. The isotropic coupling (Fermi contact term) arises from the probability of
finding the unpaired electron (or a fraction of the unpaired spin density) at the position of the nucleus.
!"$#+%
ª
2
¢Å¬õÅ¢
43
/¬
53768
¼ åÚÃ
6
¡
(3.11)
Only
9
-orbitals have a non-vanishing probability density at the nucleus;
:
-,
Æ
-, or
;
-orbitals all have
nodes at the nucleus. The detection of an isotropic hyperfine interaction in
Æ
-metal complexes can
either originate from a direct occupation of
9
-orbitals, from a polarization of
9
-orbitals by higher angular
momentum orbitals (i.e.
:
- or
Æ
-orbitals) or from an admixture of excited states into the ground state
wavefunction by spin-orbit coupling.
The anisotropic, or dipolar, contribution
ý
'0)
"<#+%
is caused by the interaction of the magnetic dipoles of
nucleus and unpaired electron. Its energy is given by the classical equation for the interaction of two
dipoles.
§
=?>@
ª
¬¢Ú¬ó¢tó
A
B
2
¼
®
°
á
DC
à ¼
®ð
á
C
Ã
EF
¿
®
°
á
®ð
EHGJI
(3.12)
28 3. Theory and Fundamentals
where
C
is the vector connecting the two dipoles and
E
its modulus. In matrix form
§
=?>@
ª
®
°
á
ý
=?>@
á
®
ð
(3.13)
with
¼
ý
=?>@
Ã
"LK
ª
¬¢Ú¬ ó¢ó
A M
2
E
"
E
K
¿
N
"LK
E
¡
EF O P
(3.14)
with the angular brackets indicating the integration over the electron wavefunction in order to remove
the explicit spatial dependence of the angle between the magnetic field and the
C
-vector.
The analysis of isotropic hyperfine couplings for organic
Q
-radicals is done by the McConnell equa-
tions and more sophisticated treatments of the same form [86]. It relates the measured isotropic
£
H
hyperfine coupling to the p
ì
spin density at the nucleus of the neighbouring sp
¡
hybridized carbon atom
by an empirical relation. For transition metal ions or complexes, a quantitative interpretation is not pos-
sible in the same way because more electrons are involved with a tendency to more variations in their
bonding situations and no simple hybridization scheme is applicable. If a detailed and reliable interpre-
tation of the electronic structure of transition metals is required, one should attempt a thorough analysis
of the total hyperfine and
¢
-tensors and their relative orientations.
Furthermore, there is an additional, second-order contribution to the hyperfine interaction in transi-
tion metal complexes [79,87]. So far, the magnetic hyperfine interaction was assumed to originate from
the interaction of nuclear magnetic moment and electron spin angular momentum. In systems, where the
¢
-values differ appreciably from
¢tÅ
there is a resulting orbitalangular momentum which can interact with
the one from the electron spin (‘spin-orbit coupling’) and contribute to the hyperfine tensor [79,87]. This
plays a role for central metal hyperfine coupling but also for ligand hyperfine interactions in transition
metal complexes. It is described by
ý
RS
ª
UT
K
T
VXW VZY
¢
V
¢
Y
Å
[ \
VY+]
¡
^
¼
E
K
W V
Ã
E
G
K
W V
E
G
K
W V Y _`
¼
C
K
W V
á
DC
K
W V Y
à ¼
â
K
á
ba
V
tÃô¿ ¼
â
K
á
bC
K
W V Y
à ¼
a
V
á
bC
K
W V
ºÃ
&c
(3.15)
where
d
runs over the number of electrons,
P
Y
run over all nuclei.
The use of EPR and ENDOR techniques to study metalloproteins is extensively reviewed in [88].
3.5 DFT
Density Functional Theory (DFT) as a tool of electronic structure calculations has received recognition
by the award of the 1998 Nobel Prize in Chemistry
“to Walter Kohn for his development of the density-functional theory and to John Pople for
his development of computational methods in quantum chemistry.”
3.5 DFT 29
The underlying principles of DFT are given in a series of monographs [89, 90]. Electronic structure
calculations try to numerically solve the time-independent, electronic Schr¨odinger equation in the Born-
Oppenheimer approximation
§
Å
+e
Å
+f 8
Å
ge
¸Å
gf
ª
Jh
Å
ge
¸Å
gf 8
Å
ge
¸Å
gf
(3.16)
with the electronic Hamiltonian
§
Å
+e
Å
+f
ª ¿
½
3
T
"$i
£
kj
¡
"
¿
3
T
"<i
£
ml
T
n
i
£
\
n
E
"
n
´
3
T
"$i
£
3
T
KDop"
½
E
"LK
ª
®
q
Åô´ ®
r
3
kÅ?´ ®
r
ÅÅ
(3.17)
The nuclear-nuclear repulsion enters only parametrically
h
)bs
f
ª
l
T
n
i
£
tl
T
u
o
n
\
n
\
u
E
n
u
(3.18)
and the total energy of the system then is
h
,
%
,
ª
Jh
Å
+e
Å
+f
´
h
)bs
f
(3.19)
In DFT, unlike in Hartree-Fock theory, the electron density is the central quantity. The one-particle
electron density is the probability of finding any of
v
electrons in a finite volume element
w
¼
?x
E
£
ÃDª
vzy
ádádá
y{68
¼
x
í
£
P
x
íõ¡
P
||
x
í
}3
Ã
6
¡
Æ
~9
£
Æ
x
í ¡
||
MÆ
x
í
}3
(3.20)
Two conditions must be fulfilled by the electron density: It must vanish at infinity (
E
) and integrate
to the total number
v
of electrons in the system
w
¼
E
à ª å
P
y
w
¼
?x
E
£
Ã
Æ
x
E
£
ª
v
(3.21)
Two electrons do not move independently from each other. Rather, the probability of finding two elec-
trons with spins
Á
£
and
Á
¡
simultaneously within two volume elements
Æ
x
E
£
and
Æ
x
E
¡
is diminished by the
exchange-correlation hole
A
¼
x
í
£
|
x
í¡
Ã
. The exchange-correlation hole has two contributions: the Fermi
hole and the Coulomb hole. The first originates from the hole due to the Pauli principle and applies to
two electrons with the same spin only. The latter results from the classic 1/r
£
¡
electrostatic repulsion of
two particles with the same charge.
The approach taken by DFT is not new. The first attempt to use the electron density rather than the
wavefunction comes from the work by Thomas and Fermi in 1927. Further improvement was made by
30 3. Theory and Fundamentals
Slater in 1951 (the so-called ‘
’ approximation). The theoretical justification of the use of DFT were
later given by Hohenberg and Kohn in 1964.
The first Hohenberg-Kohn theorem proves that the complete ground state energy (and all other properties
thereof) is a functional of the ground state electron density
w
^
v
P
\
n
P0
n
§
8
^
h
^
(3.22)
albeit the functional itself is unknown. In the second Hohenberg-Kohn theorem they have shown that the
variational principle applies to the Hohenberg-Kohn functional
h
^
h
`&
w
c
(3.23)
and the best solution to the exact value (if the functional was known) is obtained by minimizing the
energy of the trial density
w
.
Kohn and Sham in 1965 facilitated the practical use of DFT. They chose the kinetic energy of a
non-interacting (
q
)
"
) system as reference and all deviations thereof were put into the non-classical con-
tributions to electron-electron repulsion (the exchange-correlation energy
h
)
`
w
¼
|x
E
Ã
&c
Bª
q
)
"
`
w
¼
?x
E
Ã
&c
´
t
`
w
¼
?x
E
Ã
&c
´
h
`
w
¼
|x
E
Ã
&c
(3.24)
with
h
`
w
¼
|x
E
Ã
&c}
¼
q
`
w
c
õ¿
q
)
"
`
w
c
Ã
´
¼
h
ÅèÅ
`
w
c
õ¿
`
w
c
ÃDª
q
"
`
w
c
´
h
)
fe
`
w
c
(3.25)
q
"
is the part of the true kinetic energy that is not covered by the non-interacting reference system
q
)
"
.
Finally, the energy of the true, interacting system is written as
h
`
w
¼
|x
E
Ã
&c
ª
q
)
"
`
w
¼
?x
E
Ã
&c
´
t
`
w
¼
|x
E
Ã
&c
´
h
`
w
¼
?x
E
Ã
&c
´
h
3
kÅ
`
w
c
ª ¿
½
3
T
"
"06
j
¡
6
"&
´
½
3
T
"
3
T
K
yy6
"
¼
|x
E
"
Ã
6
¡
Æ
x
E
£
Æ
x
E
¡
´
h
`
w
¼
?x
E
Ã
&c
õ¿
3
T
"
y
l
T
n
6
"
¼
|x
E
"
Ã
6
¡
Æ
x
E
£
(3.26)
The effective potential in which an electron moves is
r
Å
D
¼
?x
E
ÃDª
y
w
¼
?x
E
¡
Ã
E
£
¡
Æ
x
E
¡ ´
rp
¼
?x
E
£
Ãô¿
r
3
£
(3.27)
in which only
rp
is not known. The obtained Kohn-Sham orbitals are those of a non-interacting system
with the same electron density as the interacting one.
3.5 DFT 31
There are a number of possibilities for approximating the exact an exchange-correlation functional.
The simplest is the local density approximation (LDA)
h¡£¢
n
`
w
c
Bª
T
w
¼
?x
E
Ã
¤
¼
w
¼
?x
E
Ã
Æ
x
E
(3.28)
which contains the exchange functional per particle from Slater
¤
ª ¿
2
¦¥
2
w
¼
|x
E
Ã
Q
(3.29)
and the correlation functional
¤
derived from numerical quantum Monte Carlo simulations of the ho-
mogeneous electron gas by Ceperly and Alder 1980. Surprisingly, already the LDA gives structural
parameters comparable to or sometimes better than Hartree-Fock. The performance of LDA for energet-
ics, however, is poor. DFT has received interest in the 1980’s when improved functionals appeared and
made a step from the solid-state physicists’ community to those interested in calculations of chemical
accuracy. These functionals make use of the generalized gradient approximation (GGA). The function-
als do not only depend on the electron density
w
¼
?x
E
Ã
but also on the gradient of the density
j
w
¼
|x
E
Ã
in order
to consider a non-homogeneous density distribution.
h¨§©§
n
`
w
P
wª
c
Bª
T
;
¼
w
P
wª
P
j
w
P
j
wª
Ã
Æ
x
E
(3.30)
There is an increasing number of separate exchange and correlation functionals. To mention only a few
of the most popular ones Becke’s exchange functional B88 [91], Lee-Yang-Parr’s correlation functional
(LYP) [92], Perdew’s 1986 correlation functional [93]. More details can be found in the original refer-
ences. Further work to improve current functionals is to also include the Laplacian of the electron density
j
¡
w
¼
|x
E
Ã
, use high-level electron densities for fitting new functionals (HCTH [94]) or use a hybrid density
functional (see below).
In Hartree-Fock, the exchange energy of a Slater determinant can be computed exactly. The idea is
to use this exchange energy in DFT calculations
h
ª
Jh
Åé
'
f
,
´
h¨«
Ø
(3.31)
This does not work well, because
h
Åé
'
f
,
is not a good match with
h
«
Ø
. Therefore a weighted mixture
of
h
Åé
'
f
,
and
h
«
Ø
is required (adiabatic connection). The most successful approach along that line is
Becke’s empirical three parameter combination of Hartree-Fock exchange and PW91 correlation func-
tional [95] which was later replaced [96] by the LYP correlation functional to yield the hybrid density
functional B3LYP
h
u
G
¡¬®
ªG¼¾½À¿
!
Ã
gh ¡
Ø
¢
´
¯!
h°
i
^
´
²±
h
u©³´³
´
²µ
h¡¬¶
´
¼¾½À¿
µ
Ã
gh ¡
Ø
¢
(3.32)
32 3. Theory and Fundamentals
Here,
Û ª å
refers to the exact Hartree-Fock exchange. There are, recently, attempts to reduce the
numbers of empirical parameters.
The success of DFT in the last 10-15 years originates from two facts. One, the implicit consider-
ation of electron correlation in the exchange-correlation functionals. Two, the moderate computational
costs for DFT. Hartree-Fock formally scales with the size of the treated system
v
of the order of the
fourth power (
·
¼
v
ñú
Ã
) and DFT
·
¼
v
G
Ã
. When electron correlation is considered in post-Hartree-Fock
approaches the computation time increases to
·
¼
v
F
Ã
for second-order Møller-Plesset perturbation the-
ory, and
·
¼
v¹¸
Ã
for quadratic configuration interaction (QCI) with single and double excitations and
perturbatively added triples (CISD(T)) and coupled-cluster (CCSD(T)). This formal scaling behaviour
reduces quickly for larger systems. The last two methods are the most accurate ones but their demands
make them hardly feasible for systems larger a few atoms.
One must bear in mind, however, that the results from DFT calculations have to be evaluated crit-
ically. There is no systematic route of improvement as opposed to wavefunction based methods. The
accuracy of B3LYP is about 2-3 kcal/mol for atomization energies of the G2 training set of data, the
pure GGA functionals like BLYP, BP86 are in error by about 5 kcal/mol. But, B3LYP gives up on the
favourable scaling compared to HF calculations because HF exchange is explicitly included and two
electron four-centre integrals must be evaluated.
3.6 DFT and Transition Metals
The field of transition metal complexes is a matter of the success story of DFT (for a review, see for
example[97–99]). This fact originates from the difficulties associated with the nature of these complexes.
A large number of energetically close lying states, often open-shell species and a large variability of
bonding situations. The bonding situation is an interplay of donor and acceptor contributions from both
the central metal and its ligands. The necessity of using electron correlation becomes obvious [100]. For
a comparison of DFT and conventional quantum chemical methods see a review by Siegbahn [101] and
references therein. For transition-metal complexes the BP86 functional proved to be most accurate of
the pure functionals [102] and the B3LYP hybrid functional gives results of the same accuracy. Bond
distances are often reproduced within 0.02 ˚
A and bond angles within 0.4
º
(for a collection of critical
comparisons see [90]).
The feasibility of DFT to treat large bioinorganic system has recently been reviewed by Siegbahn
and Blomberg [103].
3.7 Relativistic Quantum Chemistry 33
3.7 Relativistic Quantum Chemistry
Relativistic effects manifest themselves in heavy atoms. The magnitude of the kinetic energy of the
core electrons leads to a contraction and stabilization of atomic
9
- and
:
-orbitals. Increased shielding of
the nuclear charge on the other hand causes an expansion and destabilization of
Æ
- and
;
-type orbitals.
Relativistic bond length contraction, on the other hand, is mainly due to a reduction of the electronic
kinetic energy (for a review see [104]).
Traditional relativistic quantum chemistry makes use of the four-component Dirac-Fock wavefunc-
tion. In its full implementation, very high system requirements with respect to memory, disk space and
computing time have to be met [105, 106]. In relativistic density functional theory (RDFT) (see for
example [107]) a “fully-relativistic” four-component Dirac-Kohn-Sham model is the reference. More
approximate, two-component schemes project out the positronic states and give the “fully-relativistic”
electronic states at a lower computational effort. The decomposition can go even further and introduce
spin-free (“scalar relativistic”) and spin-dependent (“spin-orbit”) contributions. One-component meth-
ods treat mass-velocity and Darwin corrections but neglect spin-orbit coupling completely. One of the
oldest approximate treatments of this kind is the quasi-relativistic (QR) scheme by Ziegler et al. which
uses the Pauli operator self-consistently [108]. There is theoretical scepticism because the Pauli operator
is not bounded from below and one may end up with non-physical low energies due to the variational
treatment. The Douglas-Kroll-Hess (DK) approach transforms into a one- or two-component form [109].
Relativistic effective core potentials (RECP) (for a review see e.g. [110,111]) are an efficient way to treat
scalar-relativistic effects. They represent an analytic fit of the core-close electron distribution to results
from atomic four-component calculations.
3.7.1 The ZORA-Hamiltonian
The approach taken in this thesis to consider relativistic effects is the “zeroth-order regular approxi-
mation” (ZORA) which is a perturbational expansion of the Dirac equation [112,113]. It was already
presented by Chang, P´elissier and Durand as the CPD equation [114]. It follows the propositions by Har-
riman which he called ‘modified partitioning of the Dirac equation’ [87]. In the two-component ZORA
calculations, spin-orbit coupling is treated self-consistently such that p
£
+»
¡
and p
G
»
¡
have different radial
extensions from the beginning. Here, stationary states are classified by the total momentum
ª
×p´
°
.
The two-component spinors transform in a special way under symmetry operations which require the
introduction of double group symmetry in close relation and analogy to point group symmetry.
34 3. Theory and Fundamentals
The total energy of a particle is
¼
ª
¾½ ¿
¡
^
µ
ú
´
¹:
¡
µ
¡
´
r
(3.33)
In chemical applications,
6
h
6
¼
¿
^
µ
¡
¿
r
Ã
which leads to
h
ª
¾½ ¿
¡
^
µ
ú
´
À:
¡
µ
¡
¿
m¿
^
µ
¡
´
r
(3.34)
The non-relativistic result
h
3ÂÁ
ª
r
´
:
¡
¿
^
(3.35)
and the first-order Pauli energies are obtained
h
'0s
e"
ª
h
3ÃÁ
¿ ¼
h
3ÃÁ
¿
r
¿
^
µ
¡
Ã
:
¡
¿
^
(3.36)
ª
r
´
:
¡
¿
^
¿
:
ú
[
¿
G
^
µ
¡
which correspond to an expansion in
¼
h
3¿
r
Ã
Ä
¼
¿
^
µ
¡
Ã
. The Pauli-type Hamiltonian has problems when
E¹
å
then
h
¿
rÅÄ
¿
¡
^
. The Hamiltonian of the ‘zero-order regular approximation´ (ZORA) for
relativistic effects corresponds to an expansion in
¼
h
¿
r
Ã
Ä
¼
Æ¿
^
µ
¡
¿
r
Ã
which gives
h¨Ç
Ù
Á
n
ª
:
¡
µ
¡
¿
^
µ
¡
¿
r
´
r
(3.37)
The scaled ZORA energy even contains certain higher order terms
h
#f
'
e
Å
+È
ª
h
Ç
Ù
Á
n
½
´
ÉÊ
f
Ê
Ë
¡
ÌÂÍ*f
Ê
5ÎÐÏ
Ê
(3.38)
The transformation from the four-component Dirac-Hamiltonian to a two-component form is defective
for most traditional approaches. A more systematic approach is the Foldy-Wouthuysen transformation
which eliminates the small component. The ZORA Hamiltonian incorporates relativistic effects that
traditionally are only introduced at the level of the Pauli Hamiltonian. The great advantage of the ZORA
Hamiltonian
Ñ
Ç
Ù
Á
n
is that it can be used variationally and that it does not suffer from the singularities
for
EÒ
å
like the Pauli Hamiltonian. One other approach, which is also regular for Coulomb potentials,
is the Douglas-Kroll-Hess Hamiltonian which will not be discussed further here. In situations in quantum
chemistry where spin-orbit coupling is not important, a pure ‘scalar-relativistic´ Hamiltonian may be
advantageous
Ñ
Ç
Ù
Á
n
Ø
Á Ó
Ç
Ù
Á
n
Ø
Á
ª ¼
r
´
x
:
µ
¡
µ
¡
¿
r
x
:
Ã
Ó
Ç
Ù
Á
n
Ø
Á
ª
hÇ
Ù
Á
n
Ø
ÁÓ
Ç
Ù
Á
n
Ø
Á
(3.39)
3.8 Calculations of Magnetic Resonance Parameters 35
The full ZORA Hamiltonian leads to the eigenvalue equation
Ñ
Ç
Ù
Á
n
Ó
Ç
Ù
Á
n
ª ¼
r
´
x
:
µ
¡
µ
¡
¿
r
x
:
¦´
µ
¡
¼
µ
¡
¿
r
Ã
¡
x
ÁÃ
á
¼
x
j
_
x
:
Ã
ª
hÇ
Ù
Á
n
Ó
Ç
Ù
Á
n
(3.40)
which is bounded from below.
3.8 Calculations of Magnetic Resonance Parameters
3.8.1 Hyperfine Tensors
Semi-empirical calculations like UHF-INDO [115] were used to calculate the isotropic hyperfine in-
teraction of very large systems. The s-orbital occupancies from a spin-unrestricted wavefunction were
converted into isotropic hyperfine coupling constants (hfcc) by means of empirical conversion factors.
These empirical correlations were necessary because semi-empirical methods only consider the valence
electrons and the isotropic hfcc is a property of electrons near the nucleus.
Hartree-Fock calculations at the UHF level suffer from the drawback of major spin contamination
and the complete neglect of electron correlation and make it an unsuitable method for calculating hfccs.
The RHF-INDO/SP approach tried to circumvent this deficiency by a perturbatively added spin-polarized
calculation on top of a self-consistent spin-restricted INDO calculation [116].
Post-Hartree Fock (the explicite consideration of electron configuration by e.g. configuration inter-
action CI) approaches for the calculation of the hfccs of small molecules lead to very accurate results at
the price of massively increasing computational requirements (see for example [117–119]).
The use of DFT methods in the calculation of hfccs was established in 1993 independently by two
research groups [120,121]. The results are non-relativistic and of first-order only, neglecting relativis-
tic effects and spin-orbit coupling contributions to the isotropic and anisotropic hyperfine interactions.
Accurate results were obtained for light elements but they still fall behind more expensive post-HF cal-
culations. Since then an increasing number of publications using this approach appeared (for a review
see [122–124]). Fora comparison of CIand DFT calculated hfccs see [125]. Munzarova and Kaupp [126]
and Hayes [127] used this first-order approach to calculate hfccs of transition metal complexes. Mun-
zarova and Kaupp made a fortuitous choice of complexes for which spin-orbit coupling effects are ex-
pected to be small and obtained reasonable results. Hayes came, however, to a very pessimistic conclu-
sion about the use of DFT to calculate the hyperfine interaction of transition metal complexes [127]. This
was due to the complete neglect of higher-order effects.
36 3. Theory and Fundamentals
A perturbative treatment of spin-orbit coupling on top of a non-relativistic calculation was introduced
by Belanzoni et al. [128,129] and later also used by Swann and Westmoreland [130]. The spin-orbit
coupling parameters are either taken from experimental values or from relativistic atomic calculations.
RECPs cannot be used in the context of hyperfine coupling constants. The isotropic hyperfine interaction
is a property of electrons near the nucleus which are not explicitly considered in RECP calculations.
3.8.2 ZORA Calculations of Hyperfine Tensors
In this work, the ZORA Hamiltonian is used to evaluate hyperfine coupling constants for both light and
heavy nuclei [131].
The Hamiltonian of Eq 3.40 can be used to calculate the interaction between an effective electronic
spin and a magnetic nucleus. Spin-orbit coupling is already included variationally in the ZORA Hamilto-
nian which means that only a first order perturbation theory (FOPT) is necessary to evaluate the influence
of spin-orbit coupling on the hyperfine tensors
ý
. If one includes spin-orbit coupling, the spin used in
the effective spin Hamiltonian is in fact a fictitious spin. The hyperfine Hamiltonian can be formulated
as
ѹÔ
ê
É
Å
&Õ0 "
)
Å
ª
¢Å
4µ
` Ö
Á
á
¤
V
´
Ö
ý
V
á
D×
´
×
pá
ý
V
Ö
´
Á
á
¼
j
ÖÅ_
ý
V
Ã
&c
(3.41)
where
ý
V
is the vector field of the magnetic dipole of the nucleus
and the corresponding magnetic field
¤
V
ª
j
_
ý
V
.
Ö
ª
`
½
´
¼
h
¿
r
Ã
Ä
µ
¡
c
£
. The first term is the electron spin hyperfine interaction and
the last term is the spin-orbit hyperfine correction while the remaining terms (second and third) are the
orbital hyperfine interaction. For reasons of simplicity, they can be rewritten as
electron spin hyperfine interaction
¢Å¢
V
[
µ
¡
Á
á
¼
Ö
¼
2
C
V
5¼
aV
á
DC
V
Ã
EF
V
¿
aV
EG
V
´
[
Q
2
N
Ó¼
C
V
Ã
a
V
Ã
P
(3.42)
spin-orbit hyperfine correction
¢Å¢
V
[
Uµ
¡
Á
á
¼
j
ÖØ_
¼
aV
_
C
V
EG
V
ÃÃ
P
(3.43)
and orbital hyperfine interaction with
Þ
V
ª
C
V
_
×
¢ÅM¢
V
[
µ
¡
EG
V
` Ö
a
V
ámÞ
V
´
a
V
ámÞ
V
Ö
c
(3.44)
For spin-orbit coupling, the spin-restricted formalism is used since spin-polarization effects in spin-
orbit coupled equations are difficult to calculate (see for example [132]). For the isotropic hyperfine
3.8 Calculations of Magnetic Resonance Parameters 37
interactions for which spin-polarization is dominant, one has to resort to spin-polarized scalar relativistic
results.
3.8.3 g-Tensors
The electronic
¢
-tensor can be obtained from any wavefunction by an a posteriori perturbation approach.
Spin-orbit coupling is treated as a perturbation to the non-relativistic wavefunction.
Semi-empirical calculations are feasible for organic radicals because the
¢
-tensor is a property of the
valence electrons and core electrons are omitted from these calculations. Spin-orbit coupling is intro-
duced via experimental spin-orbit coupling constants (for a recent application see for example [133]).
The use of Hartree-Fock wavefunctions to evaluate the
¢
-tensors of organic radicals is also possi-
ble [134,135]. Generalized Hartree-Fock theory was also used and gave reasonable results [136].
The benchmarks for small molecules come from MRCI [137,138], CI [139] and MCSCF calcula-
tions [140,141]. These calculations yield very accurate results for smallest deviations from
¢Å
. Their
applicability, however, is limited to systems with only a few atoms.
DFT methods, certainly, cannot compete with those sophisticated approaches. Belanzoni et al. [128]
treated spin-orbit coupling as a perturbation to a non-relativistic Kohn-Sham wavefunction. Later this
approach was also used by Swann and Westmoreland [130]. Schreckenbach and Ziegler used a quasi-
relativistic (QR) approach and calculated the
¢
-tensor from a relativistic Pauli DFT wavefunction by
means of perturbation theory [142–144]. For a review of DFT calculations of
¢
-tensors see [145].
In this thesis, the
¢
-tensor is calculated from a ZORA wavefunction in which spin-orbit coupling is
treated variationally [146] and gauge-including atomic orbitals (GIAOs) are used. Until recently, there
was no publication on
¢
-tensor calculations from a Kohn-Sham wavefunction using RECPs although
such a treatment of relativistic effects, in principle, would be possible. This method was only very
recently presented by Malkina et al. in the treatment of systems containing heavy atoms [147].
3.8.4 ZORA Calculations of g-Tensors
The ZORA-Hamiltonian in the presence of a time-independent magnetic field
x
Ù
and with substitution
x
:
x
Ú
ª
Ûx
:
¿
x
(3.45)
one arrives at
Ñ
Ç
Ù
Á
n
ª
r
´
x
Á
á
x
Ú µ
¡
µ
¡
¿
r
x
Á
á
x
Ú
ª
r
´
x
Ú µ
¡
µ
¡
¿
r
x
Ú
¿
µ
¡
µ
¡
¿
r
x
Á
á
x
Ù
´
µ
¡
¼
µ
¡
¿
r
Ã
¡
x
Á
á
¼
x
j
_
x
Ú
Ã
(3.46)
38 3. Theory and Fundamentals
where
x
is the vector potential (Maxwell equation) such that
x
Ù
ª
x
j
_
x
. The terms that arise from
this Hamiltonian are similar to that in the Pauli approximation, namely the spin-Zeeman kinetic energy
correction (relativistic mass correction to the spin-Zeeman term)
¿
½
4µ
G
:
¡
Á
á
¤
(3.47)
and the one-electron spin-orbit Zeeman gauge correction
½
4µ
G
Á
á
¼
j
r
_
ý
Ã
(3.48)
The Zeeman Hamiltonian
Ñ
Ç
is then (
Þ
ª
C
_
×
)
Ñ
Ç
ª
¢Å
µ
`
Ö
Á
á
¤ ´
Ö
¤
^
ámÞ
´µ¤
^
áwÞ
Ö
´
ÁD¼
j
Ö
_
ý
^
Ã
&c
(3.49)
where
Ö
ª ½
corresponds to the non-relativistic case and
Ö
ª
`
½ ¿
r
Ä
µ
¡
c
£
to the ZORA equation.
From the last term in Eq. 3.49, complex matrix elements arise which must be evaluated. For the energy
in first order in the magnetic field, matrix elements of the derivative of the Zeeman-Hamiltonian with
respect to the external magnetic field have to be calculated (see Abragam and Bleaney [79])
Ü
Ü
Ù
^
Ý
Ñ
Ç
ª
¢tÅ
µ
`
½
Á
Ý
´
Ö
×
Ý
´µ×
Ý
Ö
´
j
á
¼
Ö
¿ ½
C
ÃÁ
Ý
¿
j
Ý
¼
Ö
¿Y½
Á
á
DC
Ã
&c
P
]
ª
í
P
î
P
ï
(3.50)
Gauge-invariance is ensured using ‘gauge-including atomic orbitals´ (GIAOs).
Chapter 4
Nickel Model Complexes
4.1 Introduction
Transition metals are required for many biochemical processes, as catalysis, electron transfer or gene
regulation [10]. Consequently, the investigation of biologically essential transition metals is a field of
intense research. In recent years, six nickel-containing enzymes were discovered (for a review, see
ref. [9, 23–25, 65]). A prominent example are the [NiFe] hydrogenases [12, 34]. Hydrogenases are
enzymes that catalyze the reversible oxidation of molecular hydrogen into protons and electrons. There is
considerable interest in understanding the electronic structure of [NiFe] hydrogenases which is available
from a combined approach of EPR techniques and theoretical (DFT) calculations. However, before
DFT methods can be applied to calculate magnetic resonance parameters of [NiFe] hydrogenase, their
accuracy must be evaluated on simple model complexes, which is the aim of this chapter.
The bio-mimetic chemistry of inorganic nickel compounds has been extensively reviewed by Hal-
crow and Christou [148].
The choice of the model compounds (Fig. 4.1) containing Ni as the central metal atom was made on
the following grounds:
In bis(maleonitriledithiolato)nickelate(III) (Ni(mnt)
¡
) (I) the nickel atom possesses a similar coordina-
tion sphere as in [NiFe] hydrogenases. In the hydrogenases, Ni in the active centre is coordinated in a
distorted tetrahedron sphere by four cysteine amino acid residues [28,32]. In Ni(mnt)
¡
, nickel is also
bound to four sulphur atoms in a square planar coordination sphere. The Ni(III) oxidation state present
in Ni(mnt)
¡
is also discussed for the oxidized forms Ni-A and Ni-B of the [NiFe] hydrogenase. In the
neutral complex Ni(CO)
G
H (II) the nickel is formally in its +1 oxidation state and a hydride ion is axially
bound to the Ni. This bonding situation resembles the one discussed for the catalytic intermediate Ni-C
39
40 4. Nickel Model Complexes
NC
NC S
S
Ni
S
S
CN
CN
x
yz
Ni
OC CO
CO
Hz
y
x
I
II
Figure 4.1: Schematic representation of the investigated Nickel complexes
bis(maleonitriledithiolato)nickelate(III) Ni(mnt)
Þ
ß
(I) and nickeltricarbonylhydride Ni(CO)
à
H (II) with
their local coordinate axes systems.
of the hydrogenase [12].
Ni(mnt)
¡
has been very well characterized and the calculations performed on this complex may
therefore serve as a benchmark for evaluating the methodology . The g-tensor orientation was obtained
from single crystal measurements [149]. From
á
£
Ni enriched single crystals Maki and Edelstein ob-
tained the Ni hyperfine tensor [149]. Furthermore, all
G´G
S hyperfine tensors were determined from an-
gular dependent EPR spectra [150]. Recently, Ni(mnt)
¡
regained interest as model cluster for [NiFe]
hydrogenase and, in addition to the existing data, the ligand
£
G
C hyperfine tensor and
£ú
N hyperfine and
quadrupole tensors and
£
F
N hyperfine tensor were determined by orientation selected pulsed-ENDOR
and ESEEM spectroscopy [151].
X
calculations [152] and recent BLYP calculations [151] only gave atomic spin populations. Very
recently, a publication on the DFT calculation of hyperfine tensor of Ni(mnt)
¡
appeared [127]. Discour-
aging results were obtained from various functionals. The calculated hyperfine tensors were of first-order
only and no route of improvement was suggested. There are a number of quantum chemical investiga-
tions for the Ni complex with hydrogens replacing the CN groups. They range from H¨uckel [153] and
Pariser-Parr-Pople [154] to Hartree-Fock [153,155,156], MP2 [157] and DFT calculations [158]. For
Ni(CO)
G
H there is only one DFT study to our knowledge that aimed to calculate the hyperfine interac-
tion [126].
Very often, the analysis of experimental hyperfine splittings is limited to the discussion of atomic spin
densities. The measured hyperfine couplings are related to theoretical values of singly occupied atomic
4.2 Computational Details 41
orbitals [159] and the orbital occupation is obtained as the ratio of experimental to theoretical values.
A more direct route to the comparison of experimental and calculated magnetic resonance parameters
is given by the first principles calculations of the EPR parameters, e.g. as done in this paper from a
density functional theory (DFT) wave function. Although the merit of DFT methods in the calculation of
hyperfine parameters of organic radicals is unquestionable, its value for the description of paramagnetic
resonance parameters of heavier elements, i.e. transition metal complexes, is still largely unexplored
[127]. Belanzoni et al. demonstrated the importance of un-freezing core electrons in the calculation of
g- and A-tensors [128, 129]. Swann and Westmoreland [130] investigated molybdenum(V) oxyhalide
anions using a spin-polarized wave function without un-freezing the core. Schreckenbach and Ziegler
[142,145] used a Pauli-type relativistic Hamiltonian with the inclusion of spin-orbit coupling based on
second order perturbation theory which was later also applied to study transition metal complexes [143].
Recently, Munzarova and Kaupp critically evaluated the use of various DFT functionals inthe calculation
of hyperfine parameters of a number of transition metal complexes [126]. They used a non-relativistic
calculation of hyperfine parameters based on geometries that were optimized using a relativistic effective
core potential (RECP). However, in this work no g-tensors were calculated.
With the zero-order regular approximation (ZORA) for relativistic effects [112,113] one has a fast and
powerful tool at hand to calculate the hyperfine tensor A, the quadrupole tensor Qand the g-tensor of
systems containing heavy elements [131,146]. Here the ZORA formalism is applied in order to validate
its application for the calculation of magnetic resonance parameters for transition metal complexes, in
particular [NiFe] hydrogenases. The ZORA formalism seems to overcome the shortcomings of the other
approaches used so far. In addition, the influence of scalar-relativistic and variationally spin-orbit coupled
DFT wave functions on the g- and A-tensors for light and heavy elements can be separately studied
so that the influence of second order contributions to the hyperfine coupling can be rationalized. The
computational efficiency of the ZORA method makes it an ideal tool for investigating the active centres
of metalloenzymes.
4.2 Computational Details
The calculations reported here are based on the Amsterdam Density Functional program package [160]
characterized by Slater-type orbital (STO) basis sets, the use of a density fitting procedure to obtain
accurate Coulomb and exchange potentials in each SCF cycle and an accurate and efficient numerical
integration of the effective one-electron Hamiltonian matrix elements [161]. All electrons were included
in the calculations there were no frozen core electrons. The ZORA Hamiltonian [112, 113] was used
42 4. Nickel Model Complexes
for the inclusion of relativistic effects which will be referred to as scalar-relativistic (SR) effects and
spin-orbit (SO) coupling. Both are treated variationally. Geometry optimizations were performed at the
ZORA SR level for which gradients are available [162]. The A-tensors and g-tensor are obtained from
the ZORA Hamiltonian in the presence of a homogeneous time-independent magnetic field which is
then introduced via first-order perturbation theory [131,146]. The g-tensor is obtained from a spin-non-
polarized wave function since spin-polarization effects in spin-orbit coupled equations are difficult to
calculate, see e.g. [132]. The effect of spin-polarization is assumed to be similar to that observed when
going from a SR spin-restricted open shell Kohn-Sham (ROKS) calculation to a SR spin-unrestricted
open shell Kohn-Sham (UKS) calculation. The g-tensor deviates from that of a free electron g
Å
due
to spin-orbit coupling. It is convenient to give the principal values of the g-tensor (g
é
, g
ê
, g
ì
) as the
deviation from g
Å
multiplied by a factor 1000 (in ppt), e.g.
g
"
= (g
"
- g
Å
)
_
1000,
â
= x, y, z.
The Becke exchange functional [91,163] was used in conjunction with the Perdew correlation func-
tional [93,164] (BP86). The BP86 functional has been shown to yield best magnetic resonance parame-
ters of the pure GGA functionals [129]. The basis sets used were relativistic ZORA basis sets from the
ADF1999 distribution. Basis set II refers to a double-
ã
basis set for light atoms and triple-
ã
for first row
transition metals. Basis set IV denotes a triple-
ã
basis set with one added polarization function for light
atoms (C, N, S), basis V has a further polarization function on atoms C, N, S. Basis set V+1s (for Ni
and S only) possesses an added tight 1s function in order to improve the description of the wave function
near the atomic core. The basis set ”Big” denotes a large basis set. This basis set is triple-
ã
in the core
and quadruple-
ã
in the valence with at least three polarization or diffuse functions added.
Calculations for the g-tensor were also performed using a traditional second-order perturbation the-
ory (SPT) approach. The spin-orbit coupling constants were calculated from fully relativistic numerical
(basis-free) atomic calculations:
ä
(Ni) = 855.4 cm
£
and
ä
(S) = 460.4 cm
£
. For comparison Gaus-
sian94 [165] calculations were also performed using the B3LYP hybrid functional with an admixed exact
Hartree-Fock (HF) exchange [95,96]. The hyperfine coupling constants in this case are non-relativistic
and of first-order only following refs. [122–124].
4.3 Results and Discussion
4.3.1 Ni(mnt)
¡
In the Bis(malenonitriledithiolato)-nickelate(III) complex (I, Figure 4.1) the central nickel atom is co-
ordinated in a square-planar arrangement by four sulphur atoms (point group D
¡
Ô
). From the magnetic
resonance studies on single crystals, the orientation of the principal axes of the hyperfine tensor Aand
4.3 Results and Discussion 43
the g-tensor were obtained in a molecule-fixed coordinate system. Maki et al. determined the ori-
entation of the g- and
á
£
Ni A-tensors in magnetically diluted single crystals of the diamagnetic host
(n-Bu
ú
N)
¡
[Ni(mnt)
¡
] [149]. They found that g- and
á
£
Ni A-tensors are collinear (within experimental
error of 2-3
º
) and that the magnetic axes systems in the crystal are coincident with the symmetry axes of
the complex in the crystal. A (3d
êëì
)
£
electronic configuration was inferred with the z-axis perpendicular
to the molecular plane and the y-axis bisecting each ligand (see Figure 4.1 top). This assignment was
later confirmed by EPR experiments of the
G´G
S enriched complex in single crystals [150]. The
G´G
S hy-
perfine tensor has axial symmetry within experimental error and the unique axis was found to lie along
the molecular z-axis. The measured hyperfine tensor is consistent with the g-tensor analysis and a 3d
êì
unpaired electron with significant delocalization into sulphur ligand p
ì
orbitals [150]. Experimental g-
and hyperfine tensors are given in Tables 4.2 and 4.3.
4.3.1.1 Geometrical Parameters
Table 4.1 compares calculated structural parameters with averaged experimental data from the X-ray
structure analysis [166]. With a small basis set (Basis II) the deviation in bond lengths is 0.07 ˚
A for Ni–S
bonds and 0.08 ˚
A for S–C bonds, while bond angles are satisfactorily described. Carbon-carbon single
and double bonds as well as C
N bonds are well described (deviation 0.01 to 0.05 ˚
A). A systematic
improvement in bond lengths is obtained when the basis set is enlarged from double-
ã
to triple-
ã
(basis
set II to IV) and when a further set of polarization functions is added (basis set V). The average deviation
at the ZORA SR BP86/V geometry is 0.02 ˚
A in bond lengths and 0.9
º
in bond angles and therefore
agrees with the X-ray structure analysis to within experimental uncertainty.
The effect of (scalar)-relativistic effects on the structural parameters of Ni(mnt)
¡
is shown by com-
paring scalar-relativistic (SR) ZORA and non-relativistic (NR) geometries. Both calculations used the
same functional and basis set. The Ni–S bond lengths are reduced by 0.01 ˚
A when SR effects are in-
cluded in the ZORA Hamiltonian. The decrease in Ni–S bond lengths causes an increase in the S-Ni-S
bond angle form 91.70
º
to 91.91
º
when SR effects are considered. All other bond lengths and bond
angles remain nearly unaffected upon inclusion of such effects.
For comparison also calculations with the B3LYP hybrid-functional are included. A large Gaussian
type orbital (GTO) valence-triple-
ã
basis set with added polarization functions (VTZP) was used [167].
Hayes [127] very recently reported a UKS B3LYP/6-311+G* geometry optimization of the Ni(mnt)
¡
complex. His findings for the structural parameters are essentially identical to our B3LYP/VTZP results
and are therefore not given here. The B3LYP functional proves to be better in the description of bonding
parameters of light elements, i.e. the C=C double bond, the C-CN single bond and the C
N triple bond
44 4. Nickel Model Complexes
Table 4.1: Comparison of experimental and calculated structural parameters of Ni(mnt)
Þ
ß
.
Bond lengths (r) in ˚
A, bond angles (
å
) in degree.
X-ray ZORA SR ZORA SR ZORA SR NR NR
structure [166] BP86/II BP86/IV BP86/V BP86/V B3LYP/VTZP
r(Ni-S) 2.15 2.216 2.163 2.156 2.165 2.190
r(S-C) 1.72 1.805 1.737 1.733 1.733 1.747
r(C=C) 1.37 1.381 1.390 1.388 1.389 1.372
r(C-C) 1.44 1.415 1.419 1.417 1.418 1.421
r(C
æ
N) 1.13 1.181 1.169 1.167 1.168 1.156
å
(S-Ni-S) 92.5 92.58 92.04 91.91 91.70 91.80
å
(Ni-S-C) 103.0 103.39 104.23 104.45 104.43 103.61
å
(S-C=C) 120.0 120.32 119.74 119.59 119.73 120.49
å
(C=C-C) 121.0 122.59 122.75 122.89 122.84 122.44
å
(C-C
æ
N) 179.0 179.02 178.71 178.77 178.70 178.57
are slightly more accurately reproduced (by
ö
0.01 ˚
A) compared to the ZORA SR/V case. Ni-S and
S-C bond lengths are, however, too long with the B3LYP functional with respect to the data from X-ray
analysis. The hybrid functional also gives slightly better results for bond angles as compared with the
X-ray data but the differences between the pure GGA and the hybrid functional are very small (less than
0.8
º
).
4.3.1.2 Electronic Structure and g-Tensor Calculations
In the calculations the unpaired electron resides in the 5b
Gç
orbital. A Mulliken population analysis of
this singly occupied molecular orbital (SOMO) yields only a 21% contribution of the Ni 3d
êì
orbital,
60% S 3p
ì
orbitals, 12% C=C 2p
ì
orbitals and 6% N 2p
ì
orbitals. The exact numbers will depend on the
basis set used but the overall picture remains unchanged. The SOMO has a node on the C
N carbon atom
which contributes to less than 1%. The highest fully occupied molecular orbital (HOMO-1) is made up of
62% Ni 3d
émì
, 19% S 3p
ì
, 11% C 2p
ì
and 5% N 2p
ì
. The lowest unoccupied molecular orbital (LUMO)
consists of 33% Ni 3d
édê
, 32% S 3p
é
and 22% S 3p
ê
. Upon electrochemical two electron reduction, the
SOMO would be doubly and the LUMO singly occupied to yield the paramagnetic complex Ni(mnt)
GX
¡
[168].
The g-values determined by Maki et al. [149] and by Huyett et al. [151] differ in the g
é
and g
ì
values
4.3 Results and Discussion 45
(See Table 4.2). The deviation along g
é
(0.02) and along g
ì
(0.01) is probably due to crystal packing
effects or interaction with the host lattice in the single crystal experiments [149] or solvent effects in
the case of the frozen solution measurements [151]. The g principal values from the most recent frozen
solution experiments [151] are to be favoured because they provided the basis for the complex analysis
and simulation of ENDOR and ESEEM spectra. Table 4.2 gives a comparison of experimental and
Table 4.2: Comparison of calculated and experimental g-tensor of Ni(mnt)
Þ
ß
.
Ì
g
è
= g
è
- g
Ñ
,
é
= x,y,z.
g-value
g
g
g
Ì
g
è
[ppt]
exp. [149] 2.16 2.04 2.00 158 38 -2
exp. [151] 2.14 2.04 1.99 138 38 -12
ZORA SO BP86/II 2.102 2.032 1.978 100 30 -24
ZORA SO BP86/IV 2.092 2.031 1.976 90 29 -26
ZORA SO BP86/V 2.094 2.031 1.976 92 29 -26
ZORA SO BP86/V+1s 2.094 2.031 1.976 92 29 -26
ZORA SO BP86/Big 2.101 2.033 1.974 99 31 -28
SPT ROKS BP86/II 2.123 2.020 1.988 121 18 -14
SPT UKS BP86/II 2.105 2.020 1.984 103 18 -18
SPT UKS BP86/II (
ê
(S)=0) 2.104 2.020 1.984 102 18 -18
SPT UKS BP86/II (
ê
(Ni)=0) 2.0024 2.0023 2.0023 0.1 0 0
All calculations were performed at the ZORA SR UKS BP86/V optimized geometry.
The orientation of the g-tensor axes is along the symmetry axes of the complex. See Figure 4.1.
calculated g-tensor components for Ni(mnt)
¡
. The calculations using the ZORA approach for relativistic
effects with inclusion of spin-orbit coupling and a small basis set (basis II) yields g-values of 2.102,
2.032, 1.978 for g
é
, g
ê
and g
ì
, respectively. The deviation of the calculation is largest for the g
é
-
component (38 ppt), smallest for g
ê
(8 ppt) and intermediate for g
ì
(12 ppt) as compared with the
experimental values. The extension of the basis set from a double-
ã
to a triple-
ã
basis (basis IV) and
to one with added polarization functions (basis V) does not improve results but slightly increases the
deviation of the calculated g-tensor components from the experimental ones. Patchkovskii and Ziegler
also observed such an independence of the DFT calculated g-tensors from the basis set [143]. Increase
of the core region, obtained by adding a further tight 1s function to basis V, does also not improve the
g-tensor results. This is due to the fact that the g-tensor is a property of the valence electrons [142]. All
calculated g-tensor principal values are systematically smaller than the experimental ones. This is due to
46 4. Nickel Model Complexes
the fact that the paramagnetic contribution to the g-tensor is too small which is also observed in g-tensor
calculations of other transition-metal complexes (M. Kaupp, personal communication).
In order to validate whether the deviations of the calculated g-tensors were due to the ZORA ap-
proach, a traditional second-order perturbation approach was also used (SPT). A restricted open shell
Kohn-Sham calculation in the SPT treatment gives a g-tensor with smaller deviation along g
é
(17 ppt)
and g
ì
(2 ppt) but larger deviation along g
ê
(20 ppt). The consideration of spin-polarization effects in
the perturbation treatment leads to g-values of 2.105, 2.020 and 1.984 and, again, comes very close to
the ZORA BP86/II results. The effect of spin-orbit coupling is incorporated in the second-order pertur-
bation approach and the ZORA formalism. Both give a very similar value for the influence of spin-orbit
coupling [131].
It is known that the deviation of the g-value from that of the free electron g
Å
is determined by spin-
orbit coupling which gives the unpaired electron some small angular momentum and thus alters its effec-
tive magnetic moment. The SPT methodology offers the opportunity to selectively switch the spin-orbit
coupling of different nuclei on or off. The contribution of spin-orbit coupling by the nickel nucleus
alone to the g-tensor can be obtained by setting the spin-orbit coupling constant of the sulphur nucleus
to zero. In the SPT UKS BP86/II(
ä
(Ni)=0) calculation only spin-orbit coupling due to the sulphur nuclei
is considered. As expected, for g
ì
and g
ê
isotropic values of the free electron g-factor are obtained. The
spin-orbit coupling of the sulphur nuclei only contribute to g
é
for which a marginal deviation from g
Å
(2.0024 vs. 2.0023) is obtained. From the comparison of the SPT UKS BP86/II(
ä
(S)=0) calculation to
the SPT UKS BP86/II calculations it is immediately clear that 100% of the g
ì
- and g
ê
-values originate
from spin-orbit coupling of the nickel atom. The only slight reduction is obtained for g
é
(2.105 vs.
2.104).
For Ni(mnt)
¡
, ZORA calculations with a small basis set already give g-tensor magnitude and ori-
entation in satisfying agreement with the experimental values. The agreement cannot be significantly
improved by enlarging the basis set. The absolute deviation between calculation and experiment in-
creases with the deviation from the free electron value while the relative error remains about constant.
Patchkovskii and Ziegler also observed that the deviation between calculated and experimental g-tensors
increased when going from 3d to 4d and 5d transition metal complexes [143]. This gives an indication
of the accuracy of g-tensor calculations one could expect in related work on the active centre of [NiFe]
hydrogenases. For the oxidized Ni(III) Ni-B EPR spectrum with g
é
W
ê
W
ì
= 2.33, 2.16, 2.01 one might
get the largest deviation for g
é
(if the error is strictly proportional to the deviation from g
Å
one would
expect a deviation of up to 0.1) and better agreement for the g
ê
and g
ì
components. Furthermore, for
the comparison of “gas phase” g-tensor calculations and experiments in single crystals an agreement of
4.3 Results and Discussion 47
10-15% would already be considered satisfying [126].
4.3.1.3 Spin Density Distribution and Hyperfine Interactions
Figure 4.2 shows contour plots of the unpaired spin density at 0.003 e/a
G
^
. The spin density is not fully
localized at the central nickel atom, but the four surrounding sulphur atoms carry significant spin density
in p
ë
lobes oriented perpendicular to the horizontal mirror plane. The carbon atoms of the carbon-carbon
double bond also bear unpaired spin density in their
Q
-bonds. In contrast, the carbon atoms of the cyanide
group carry no unpaired spin density while the terminal nitrogen atoms exhibit a small lobe of unpaired
spin in a p-orbital perpendicular to the plane of the molecule.
Figure 4.2: Views of the unpaired spin density distribution of Ni(mnt)
Þ
ß
at 0.003 e/a
à
ì
. The left view is along
the
íî
-plane of the complex with the
ï
-axis coming out of the paper plane. In the right view, the complex is
rotated in the xy-plane by 90
ð
and tilted by approx. 20
ð
out of the plane .
Unrestricted ZORA SR BP86/V calculations yield total atomic spin populations of 0.26 at the nickel
atom, 0.16 at each sulphur atom, 0.02 at each carbon in the double bond, -0.003 at each carbon of the
cyanide group and 0.01 at each N. The Ni-S
ú
core thus bears 90% of the unpaired spin. This value is
slightly larger than the one from BLYP/LANLDZ results by Huyett et al. [151], who found 75%, and is
close to X
ñ
[152] calculations where 82% were found. In the non- and scalar relativistic calculations one
may discuss atomic spin densities as the difference between
ñ
and
¬
electron densities. In relativistic
calculations, where spin-orbit coupling requires spin mixing, the resulting SO-coupled states will no
longer be pure spin states. This will complicate the interpretation in atomic spin densities [132].
The high covalency of Ni–S bonds and the significant delocalization of spin density into ligand
48 4. Nickel Model Complexes
orbitals might have a significant influence on the interpretation of EPR and ENDOR spectra of a
biological Ni–S centre, for instance in the case of [NiFe] hydrogenase for which large isotropic
£
H
hyperfine coupling constants were measured for
¬
-CH
¡
protons of a cysteine amino acid adjacent to a
nickel atom [169].
The single crystal experiments by Maki et al. [149] yielded the
á
£
Ni hyperfine tensor. It was found
to be collinear with the g-tensor principal axes within experimental error. Unfortunately. the signs of the
principal hyperfine tensor components (A
édé
= 45
6 MHz, A
êëê
= 9
3 MHz, A
ìMì
=
6 MHz) are
not known. From the measured hyperfine interaction in liquid solution is a
"$#&%
= +12.6
2.8 MHz. If
one assumes that the A
ìì
component is zero, one only arrives at two possibilities: Choice I, where all
tensor components are positive: A
édé
W
êëê
W
ìì
= (+45, +9, 0) MHz yields a
"$#+%
= +18 MHz and for the purely
anisotropic components A’
édé
W
êMê
W
ìMì
= (+27, -9, -18) MHz. Choice II: A
édé
W
êMê
W
ìì
= (+45, -9, 0) yields a
"$#+%
=
+12 MHz, A’
édé
W
êMê
W
ìMì
= (+33, -21, -12). Estimates where A
ìì
is small but not zero, do not fundamentally
change the discussion of the results 1. A discrimination between the two combinations can be done on
the basis of calculations of the (anisotropic)
á
£
Ni hyperfine interaction (see Table 4.3).
The analysis of naturally abundant
G´G
S satellites yielded an axial
G´G
S hyperfine tensor (A
ìì
= A
ò
= 42.8 MHz, A
édé
= A
êëê
= A
ó
= 13.6 MHz). Two choices of the signs of the hyperfine tensor were
discussed in ref. [150]. I: All signs are positive, the isotropic value is 23.3 MHz and the anisotropic
values A’
édé
W
êëê
W
ìì
(-9.7, -9.7, 19.5) MHz. II: A
ó
= A
édé
= A
êMê
is negative, then the isotropic coupling is
5.2 MHz and the anisotropic hyperfine tensor A’
édé
W
êëê
W
ìì
= (-18.8, -18.8, 37.6) MHz. The atomic spin
population at the sulphur was estimated from the uniaxial hyperfine tensor and using the theoretical
atomic values of Morton and Preston [159] to be between 0.13 (A
ò
and A
ó
same sign) and 0.26 (A
ò
and A
ó
opposite signs) [150]. This agrees with the picture in which a 3p
ì
orbital occupation induces a
polarization of the Ni–S
Á
orbitals. From this, one expects a small isotropic hyperfine interaction. The
larger value of 23.3 MHz, however, appears unrealistic.
Table 4.3 shows a comparison of experimental and calculated hyperfine tensors of Ni(mnt)
¡
. For
the experimental
á
£
Ni and
G´G
S hyperfine interactions a plausible choice of signs of the hyperfine tensor
components was made (see above). In the case of
£
G
C and
£ú
N nuclei the choice of hyperfine tensor
signs from ref. [151] is given (which proved to be in agreement with the calculations). All calculations
1Assuming that A
ô+ô
takes the largest value (6 MHz) one has: I: All tensor components positive yields a
õ/öÆ÷
= +20 MHz and
A’
ø´øXù úúZù ô+ô
= (+25, -11, -14) MHz II: A
ø´øXù úúZù ô&ô
= (+45, +9, -6) MHz yields a
õ/öÆ÷
= +16 MHz and anisotropic A’
ø´øXù úú*ù ô+ô
= (+29,
-7, -22) MHz). III: A
ø´øXù úúZù ô&ô
= (+45, -9, -6) MHz yields a
õ1öÆ÷
= +10 MHz, A’
ø´øXù úúZù ô&ô
= (+35, -19, -16) MHz. IV: A
ø´øXù úúZù ô+ô
=
(+45, -9, +6) yields a
õ/öÆ÷
= +14 MHz and A’
ø´øXù úúZù ô&ô
= (+31, -23, -8) MHz.
4.3 Results and Discussion 49
were done at the unrestricted SR ZORA geometry (see Table 4.1). For means of comparison also spin-
unrestricted B3LYP calculation with a valence-triple-
ã
basis set with polarization functions given by
Sch¨afer et al. [167] were performed.
SR ROKS calculations yield reliable anisotropic hyperfinetensors while the isotropic hyperfine inter-
action is not trustworthy since the effect of spin-polarization is not considered. For
á
£
Ni, the calculated
anisotropic hyperfine tensor deviates by a factor of two for the anisotropic hyperfine tensor components
A’
édé
, A’
êMê
. The agreement for A’
ìì
is much better. Spin-polarized ZORA SR calculations (SR UKS)
yield an isotropic hyperfine interaction of +18.60 MHz for
á
£
Ni which nicely corresponds to an experi-
mental value of +18 MHz (choice I). The effect of spin-polarization on the anisotropic hyperfine tensor
components is less pronounced. A’
édé
and A’
ìì
are increased by approx. 4 MHz in absolute numbers
upon consideration of polarization effects, whereas the effect on A’
êëê
is very small. Still, the agreement
with experimental data is far from satisfying. Non-relativistic UKS B3LYP calculations with a VTZP
basis set give similar numbers but the agreement with experimental data is even worse. This obvious
discrepancy which was also observed by Hayes [127] led the author to the pessimistic conclusion that
density functional calculations on Ni(mnt)
¡
are unable to reliably assign the signs of the
á
£
Ni hyperfine
tensor. The disagreement with experimental data, however, is not due to deficiencies of either the basis
set or the functional but due to a systematic neglect of spin-orbit coupling as shown below.
The spin-orbit coupling manifests itself as a pseudocontact contribution to a
"$#&%
and a second-order
contribution to the anisotropic hyperfine tensor [77,79,80,87,128]. The effect of spin-orbit coupling is
very large for nickel. The inclusion of spin-orbit coupling even inverts the sign of the a
"<#+%
(Table 4.3). It
must be kept in mind that a considerable part of this difference is due to the neglect of spin-polarization
in the spin-orbit coupled equations. A better estimate of the effect of spin-orbit coupling can be made
if the spin-restricted SR results and those including spin-orbit coupling are compared. This gives an
effect of spin-orbit coupling of approximately 15 MHz. When isotropic hyperfine interactions are to be
calculated one still has to resort to spin-polarized (UKS) SR ZORA values until spin-polarized spin-orbit
coupling can be treated in the ZORA Hamiltonian. This work is in progress.
The influence of SO coupling on the anisotropic hyperfine tensor (second order contribution) can,
however, calculated very calculated in the ZORA approach. The absolute signs of the anisotropic hyper-
fine interaction are retained upon inclusion of spin-orbit coupling but their magnitude is decreased by 22
MHz, 16 MHz and 6 MHz for A’
édé
, A’
êMê
and A’
ìì
, respectively when comparing SR ROKS and SR+SO
ROKS calculations. The lower hyperfine values agree to within a few MHz with the experimental ones
of Choice I. If one assumes that the effect of spin-polarization on the spin-orbit coupled anisotropic hy-
perfine tensor is the same as for the scalar-relativistic anisotropic hyperfine tensor then the effect can be
50 4. Nickel Model Complexes
estimated to increase A’
édé
and A’
ìMì
by approx. 4 MHz and leave A’
êMê
unchanged and thus give a perfect
agreement with the Choice I of signs of the hyperfine tensor.
The other choice (Choice II) of the signs of the experimental
á
£
Ni hyperfine tensors can therefore be
ruled out on the basis of our ZORA calculations. Neither isotropic (from the spin-polarized SR ZORA
calculation) nor SO-coupled anisotropic hyperfine tensors support this possibility.
Our findings indicate that the inclusion of spin-orbit coupling is an absolute necessity when trying
to calculate the hyperfine interaction of a transition metal ion. The influence of SO coupling on the
anisotropic
á
£
Ni hyperfine interaction reduces it by a factor of two and brings it to within excellent
agreement with experimental values.
For the
G´G
S hyperfine interaction in Ni(mnt)
¡
, the effect of spin-orbit coupling is less pronounced
than for the
á
£
Ni nucleus but still noticeable. ZORA SR UKS calculations give an isotropic hyperfine
interaction of +3.11 MHz which corresponds to the choice of experimental signs II ( a
>ûÆü
= +5.2 MHz).
Choice I would lead to an unrealistic high value of +23.3 MHz which can also not be reproduced by
the calculations. Furthermore, the calculated hyperfine interaction of (-15.79,-14.38,+30.16) MHz sup-
ports choice II whereas the anisotropic hyperfine tensor components of choice I appear too low. The
effect of spin-polarization becomes obvious when comparing restricted (ROKS) and unrestricted (UKS)
open shell SR ZORA calculations. Spin-polarization leads to an increase of A’
édé
, A’
êëê
and A’
ìì
in ab-
solute magnitude by 2.3, 1.2 and 3.5 MHz, respectively. The agreement with the experimental values
is improved. ZORA calculations with spin-orbit coupling yield an a
"$#+%
value of only 0.19 MHz. The
anisotropic hyperfine tensor does not change much upon inclusion of spin-orbit coupling (changes lie
within 0.5 MHz). If the effect of spin-polarization is taken from the SR calculations, values to within
0.5 MHz of the SR UKS can be estimated. The isotropic hyperfine interaction of
G´G
S is due to spin
polarization and yields a small but detectable isotropic hyperfine interaction.
For the
£
G
C hyperfine interaction in the C=C double bond, ZORA SR UKS calculations yield
isotropic and anisotropic hyperfine interactions to within 0.5 MHz of the experimental ones. The
importance of spin polarization again is illustrated by comparing restricted and unrestricted SR
calculations. Spin polarization reduces the anisotropic hyperfine tensor components by 0.5-1 MHz
and brings them closer to the experimental values. When the effect of spin-polarization is taken
from SR calculations the results with SO coupling represent an improvement of 0.4 MHz. B3LYP
calculations give good results for the
£
G
C isotropic hyperfine interaction but the anisotropic part is
less well reproduced (see also [127]). The experimental
£
G
C hyperfine tensor was assumed to be
collinear with the g-tensor principal axes system. Only in this coordinate system the tensor is of
4.3 Results and Discussion 51
uniaxial symmetry. The deviation of the calculated anisotropic hyperfine tensor from uniaxiality
is indeed small. The orientation, however, is not collinear with the g-tensor principal axes system
but rotated by 6
º
from the x- and y-axes. A’
ìMì
is along the g
ì
-axis. This was also noticed by Hayes [127].
The case of the
£
G
C nucleus of the cyanide group is more difficult. The negative isotropic hyperfine
interaction is well reproduced by unrestricted calculations (-2.47 MHz calculated vs. -2.9 MHz exper-
imental). All theoretical calculations, however, agree that A’
édé
is negative and A’
êMê
positive while the
simulation of the experimental spectra yielded A’
édé
and A’
êMê
both of positive sign. Theory and exper-
iment agree that the component perpendicular to the molecular plane, A’
ìMì
is negative. One must bear
in mind that the experimental values give the hyperfine tensor in the g-tensor’s principal axes system,
e.g. g- and Aare assumed to be collinear. The calculations yield the diagonalized hyperfine tensor in its
own principal axes system A’
édé
, A’
êëê
, A’
ìì
which is not necessarily collinear with the g-tensor. In fact,
A’
édé
and A’
êMê
are rotated by 30
º
from the respective g-tensor principal axes and A’
ìì
is along g
ì
(similar
values were obtained by Hayes [127]).
For the
£ú
N hyperfine interactions of the CN group spin-polarized (UKS) ZORA SR calculations give
excellent results. The deviation from the experimental values is less than 0.5 MHz for both isotropic and
anisotropic contributions. B3LYP calculations give slightly better values for the anisotropic hyperfine
interaction of the
£ú
N nucleus. The numbers given in [127] for the experiment from ref. [151] correspond
to the experimental values for the
£
F
N nucleus and have to be corrected by the ratio of the
£
F
N and
£ú
N
Larmor frequencies (1.403). For a cyanide group one expects a nearly axial quadrupole tensor with its
largest component along the C
N triple bond. The calculated
£ú
N (I = 1) quadrupole tensor agrees well
with the experimental values. The deviation from experimental values might be due to environmental
effects in frozen solution. The calculated quadrupole tensor has its smallest component perpendicular
to the molecular plane (0.85 MHz) and its largest component (-2.09 MHz) along the C
N triple bond.
The third component (1.23 MHz) lies in the molecular plane and is perpendicular to the C
N bond.
This orientation was also found experimentally by Huyett et al. [151]. The thorough analysis of pulsed-
ENDOR and ESEEM data by simulation of the experimental spectra and the assignment of absolute
signs [151] of the hyperfine tensors is confirmed by our calculations.
For means of comparison, a calculation using the popular B3LYP functional and a valence-triple-
ã
basis set with polarization functions (VTZP) of Sch¨afer et al. [167] was also performed. The geometry
of the ZORA SR UKS BP86/V (Table 4.1) calculation was used. The hyperfine interactions were cal-
culated using a non-relativistic, first-order approach (see for example [122–124]). Strictly speaking, the
comparison can only be made with spin-polarized scalar relativistic ZORA calculations where spin-orbit
52 4. Nickel Model Complexes
coupling is not considered. The isotropic
á
£
Ni hyperfine interaction is of positive sign and significantly
larger than the ZORA SR value. This may be due to the different density functionals or basis sets used
in the calculations. Gaussian basis functions do not correctly describe the cusp region near the core in
contrast to the use of Slater basis functions in ADF, which means that one needs more GTOs than STOs
in the basis set to obtain the same accuracy2. The signs of the anisotropic hyperfine tensor components
are reproduced in the B3LYP calculations but the values are larger than the corresponding ZORA values.
This deficiency is due to the neglect of spin-orbit coupling as shown above. For all other nuclei, the
absolute signs of the tensor components agree with the ZORA results. The agreement is of the order of
a few MHz or less but the B3LYP functional does not represent a systematic improvement over the pure
GGA functional. This observation was also made by Munzarova and Kaupp who compared all usual
GGA and hybrid functionals in the calculation of transition metal hyperfine interactions [126].
To summarize, ZORA calculations yield hyperfine parameters for all (light and heavy) atoms in
Ni(mnt)
¡
in good agreement with experimental values. The ambiguity of the signs of the
G´G
S and
á
£
Ni
hyperfine tensors could be resolved on the basis of our ZORA calculations. The calculations support one
specific choice of signs of the hyperfine tensor components. Spin-orbit coupling plays an important role
in the calculation of heavy element anisotropic hyperfine interaction. The isotropic hyperfine interaction
must still be taken from a spin-polarized SR ZORA calculation.
In the oxidized states of the [NiFe] hydrogenase, the EPR signal also originates from the Ni metal
alone as was shown by
á
£
Ni enrichment [64]. The Fe metal in the active centre does not contribute
to the EPR spectrum. The hyperfine interaction of the
á
£
Ni enriched hydrogenase from Desulfovibrio
gigas in the oxidized Ni-B state shows a hyperfine splitting of 6 to 17, 6 to 17, and 76 MHz along the
g-tensor components g
édé
, g
êëê
and g
ìì
, respectively [45]. The hyperfine interaction is thus of the same
order of magnitude as in Ni(mnt)
¡
and the spin population at the Ni nucleus in [NiFe] hydrogenase can
be expected to be similar to that in this model complex Ni(mnt)
¡
.
2NR BP86/VTZP calculations with a GTO basis set yielded a
õ1öÆ÷
(
ýgþ
Ni) = +69.85 MHz. The difference between spin-
polarized SR ZORA and NR BP86 calculations still lies in the different basis sets (STOs vs. GTOs) and/or the consideration of
scalar relativistic effects in the ZORA Hamiltonian.
4.3 Results and Discussion 53
Table 4.3: Experimental and calculated hyperfine and quadrupole parameters of Ni(mnt)
Þ
ß
in MHz.
Nucleus exp. SR ROKS SR UKS SO+SR ROKS UKS B3LYP
exp. ref. BP86/V+1s BP86/V+1s BP86/V+1s VTZP
ÿ
Ni
[149] a
è
OÊ
+18 -0.12 +18.60 -15.03 +30.82
A’
X
+27 +47.15 +51.93 +25.87 +66.92
A’
0
-9 -23.53 -24.03 -7.88 -28.52
A’
-18 -23.85 -27.35 -17.99 -38.40
S
[150] a
è
OÊ
+5.2 +0.12 +3.11 +0.19 +7.20
A’
X
-18.8 -13.49 -15.79 -13.81 -18.46
A’
0
-18.8 -13.15 -14.38 -12.65 -15.32
A’
+37.6 +26.65 +30.16 +26.45 +33.77
C=C
[151] a
è
OÊ
-2.1 +0.003 -1.63 +0.11 -2.32
A’
X
-2.5 -3.49 -2.95 -3.09 -2.09
A’
0
-2.5 -3.15 -2.63 -3.26 -1.49
A’
+5.0 +6.65 +5.59 +6.37 +3.58
CN
[151] a
è
OÊ
-2.9 -0.001 -2.47 +0.01 -1.95
A’
X
+0.33 -0.31 -0.25 -0.51 -0.50
A’
0
+0.13 +0.81 +0.80 +0.83 +0.62
A’
-0.47 -0.50 -0.54 -0.31 -0.12
N
[151] a
è
OÊ
+0.39 +0.001 +0.15 +0.007 +0.15
A’
X
-0.26 -0.72 -0.59 -0.73 -0.40
A’
0
-0.29 -0.60 -0.47 -0.59 -0.22
A’
+0.55 +1.33 +1.05 +1.31 +0.62
Q
Z
+0.85 +0.86 +0.85 +0.86 +0.41
Q
+1.10 +1.23 +1.23 +1.23 +1.80
Q
-1.95 -2.09 -2.09 -2.09 -2.21
a
è
is the isotropic (Fermi contact) hyperfine interaction, A’
= x,y,z are the anisotropic hyperfine tensor compo-
nents. a Only Choice I of the signs of the experimental hyperfine tensor components is given (see text for details).
b Only Choice II of the experimental hyperfine tensor components is given (see text for details).
c The absolute signs of the experimental tensors are fixed assuming a 2p
spin population [151].
The best agreements with experimental values are given in bold font.
54 4. Nickel Model Complexes
4.3.2 Ni(CO)
H
In Ni(CO)
H (II Figure 4.1) the central nickel atom is coordinated by three CO ligands in the equatorial
plane and axially by a hydrogen atom (C
symmetry). Formally, the complex may be described either as
a Ni(I) with a H
bound ((CO)
-Ni(I)-H
) or as a Ni(0) with a hydrogen atom bound ((CO)
-Ni(0)-H)).
In the thorough analysis of the krypton matrix EPR spectrum Morton and Preston concluded that the
structure of the complex is best described as (CO)
-Ni(I)-H
[170]. While the oxidized states of the
hydrogenase are usually referred to as Ni(III), the two electron more reduced form Ni-C might be a Ni(I)
species. Since Ni-C is an intermediate in the catalytic process, either a H
molecule, or a H
or H
are
supposed to be bound to the Ni. Ni(CO)
H therefore represents a good model for the calculation of the
magnetic resonance parameters for such a bonding situation.
For Ni(CO)
H there is no X-ray structure available. The comparison of calculated structural param-
eters is therefore made with DFT calculations by Munzarova and Kaupp [126] who used the B3LYP
functional with a relativistic pseudopotential for Ni. Table 4.4 compares the calculated structural pa-
Table 4.4: Comparison of calculated structural parameters of Ni(CO)
H. Bond lengths (r) in ˚
A, bond angles
(
) in degree.
ZORA SR ROKS ZORA SR UKS NR UKS B3LYP/RECP(Ni)
BP86/V BP86/V BP86/V [126]
r(Ni-H) 1.485 1.495 1.502 1.512
r(Ni-C) 1.807 1.807 1.824 1.851
r(C=O) 1.150 1.149 1.150 1.135
(H-Ni-C) 90.87 90.93 89.90 90.87
(Ni-C=O) 173.19 173.79 172.38 171.29
rameters of Ni(CO)
H in the ZORA approach at the scalar-relativistic (SR) level using a large basis set
(basis V) with those using a relativistic effective core potential (RECP) [126] and non-relativistic all
electron calculations. NR calculations agree well with the B3LYP/RECP(Ni) calculations in the Ni–H
bond length (1.502 vs. 1.512 ˚
A). The Ni–C bond length is shorter by 0.027 ˚
A in the NR calculation and
so is the C=O bond length by 0.015 ˚
A. The difference in bond angles is only
1 degree. The influence
of scalar relativistic effects can be observed by comparing non-relativistic ADF calculations with SR
ZORA calculations. They are manifested in a reduction of the Ni–H bond length by 0.007 ˚
A and of the
Ni–C bond length by 0.017 ˚
A. The effect on the C=O bond length is almost negligible. Due to the shorter
Ni–H and Ni–C bonds the H–Ni-C and Ni–C=O bond angles widen by 0.4 degrees. The importance of
4.3 Results and Discussion 55
spin-polarization for structural parameters is highlighted by comparing restricted open shell Kohn-Sham
and unrestricted Kohn-Sham scalar-relativistic ZORA calculations (Table 4.4). Spin-polarization leads
to an increase in Ni–H bond length by 0.01 ˚
A while all other structural parameters remain nearly un-
changed. In general, SR UKS ZORA calculations agree well with those using the B3LYP functional and
a relativistic core potential. Spin-polarization is important for the description of the Ni–H bond.
4.3.2.1 g-Tensor and Hyperfine Interaction
The EPR spectrum of Ni(CO)
H was measured in a krypton matrix by Morton and Preston [170]. They
found an axial g-tensor with g
= g
= 2.0674 and g
= g
= g
!
= 2.0042. The orientation of the
g-tensor is g
along the
"
-axis and g
in the
#%$
-plane of the complex (see Figure 4.1). Table 4.5 gives
Table 4.5: Comparison of ZORA calculated and experimental g-Tensor of Ni(CO)
&
H.
'
g
= g
- g
(
, i =
)
,
*
.
g-value
g
g
+
g
,
[ppt]
exp. [170] 2.0674 2.0042 65 2
BP86/II 2.0468 2.0003 45 -2
BP86/IV 2.0478 2.0003 46 -2
BP86/V 2.0480 2.0003 46 -2
BP86/V+1s 2.0486 2.0003 46 -2
the results of ZORA calculations of the g-tensor of Ni(CO)
H. All calculated values are smaller than
the corresponding experimental values. For the small double-
-
basis (basis set II) the deviation of the g
component is 4 ppt from the experimental value and for g
it is 20 ppt. A better description of the valence
electrons does not significantly improve the results. The increase is only 1 ppt in g
. The addition of an
extra tight 1s function also only marginally improves the results.
Figure 4.3 shows a contour plot of the unpaired spin density at a value of 0.003 e/a
.
. The contour
plot shows that the spin density distribution is of centroid symmetry. The form of the spin density at
the Ni resembles that of a d
!/
orbital. A Mulliken analysis yields atomic spin populations of
0
(Ni) 0.48,
0
(H) 0.22,
0
(C) 0.06 and
0
(O) 0.04. The contribution of the atomic orbitals to the 13A
1
SOMO are
as follows (arranged by decreasing percentage): 24% 3d
2/
(Ni), 21% 4p
(Ni), 19% 2p
(C), 17% 1s(H),
14% 2p
(O), and 4% 2s(C). This indicates that the 4p
of the Ni contributes significantly.
56 4. Nickel Model Complexes
Figure 4.3: View of the Unpaired Spin Density Distribution of Ni(CO)
&
H at 0.003 e/a
&
3
.
Due to the axial bonding of the hydride ion to the Ni atom, the H atom may acquire a significant
amount of spin density which leads to a very large hyperfine coupling caused by the large magnetic
moment of the nucleus. Consequently, the
1
H hyperfine structure could be resolved in the Kr matrix
EPR spectra [170]. The hyperfine interaction is dominated by a very large isotropic hyperfine interaction
a
,5476
of 293 MHz while the uniaxial anisotropic interaction is only 5.5 MHz.
Table 4.6 compares the
8
1
Ni and
1
H experimental hyperfine interactions with ZORA calculations
at various levels of theory and non-relativistic B3LYP calculations by Munzarova and Kaupp [126].
The comparison is only made with the results using the B3LYP functional because it is the one most
frequently used in DFT investigations of transition metals. The ZORA SR UKS BP86/V optimized
geometry of Table 4.4 was used.
The
8
1
Ni isotropic hyperfine interaction is well reproduced by unrestricted (UKS) SR ZORA calcu-
lations whereas the B3LYP functional overestimates the isotropic coupling constant by a factor of three.
The inclusion of spin-polarization reduces A’
and A’
by 2 and 4 MHz indicating only a moderate effect
of polarization. SO coupling reduces the anisotropic coupling by 5 and 10 MHz for A’
and A’
, respec-
tively, when comparing SR ROKS and SO + SR ROKS calculations. The effect is weaker than in the
case of Ni(mnt)
because the SOMO consists here of p
and d
/
orbitals at the Ni. If the assumption of
similar spin-polarization for SR and SO-coupled calculations holds, the agreement with the experimental
values is perfect. A’
would be brought down to 44 MHz and A’
to 88 MHz by spin-polarization. The
resulting anisotropic tensor is in excellent agreement with the experimental value and superior to the
results by Munzarova and Kaupp [126]. (The BP86 values by Munzarova and Kaupp [126] are in close
agreement with our values. Still, the isotropic coupling constant is overestimated by a factor of two.)
The isotropic hyperfine interaction of the Ni changes from +10.10 to -18.70 MHz upon inclusion of spin-
orbit coupling and neglecting spin-polarization. This large effect of -28.8 MHz agrees very well with the
4.3 Results and Discussion 57
Table 4.6: Comparison of experimental and calculated hyperfine and quadrupole interactions in Ni(CO)
&
H
in MHz.
Nucleus exp. SR ROKS SR UKS SR+SO ROKS B3LYP/DZPD(Ni),
[170] BP86/V+1s BP86/V+1s BP86/V+1s IGLO-III [126]
9:
Ni a
+9.0 -9.94 +10.10 -18.70 +33.3
A’
;
+44.0 +50.88 +48.56 +45.76 +56.9
A’
<
-88.0 -101.75 -97.11 -91.52 -113.8
Q
;
-4.1 -4.4 -4.1 -4.4 /
Q
<
+8.2 +8.8 +8.2 +8.8 /
H a
+292.8 +276.54 +335.58 +275.25 +208.0
A’
;
-5.50 -4.05 -2.68 -4.21 -3.15
A’
<
+11.10 +8.11 +5.36 +8.42 +8.43
&
C a
+20.75 +7.61 +20.74 +5.10
A’
=2=
-5.46 -5.71 -5.59 -5.50
A’
!
-1.34 -2.60 -1.19 -3.20
A’
+6.80 +8.31 +6.79 +8.70
7>
O a
-1.31 -3.72 -1.35 -3.70
A’
=2=
+7.92 +8.60 +8.00 -8.70
A’
!
+6.98 +6.99 +6.83 -5.30
A’
-14.90 -15.59 -14.83 +14.0
Calculations were performed at the ZORA SR UKS BP/V geometry (see Table 4.4).
Best agreements with experimental values are given in bold font.
estimated value of spin-orbit coupling by Munzarova and Kaupp [126] who used an empirical formula
by Abragam and Pryce (see ref. [79]) and obtained -26.8 MHz. This effect is overestimated, since in our
calculated effect also spin-polarization is neglected. A comparison of the SR ROKS results with the SR
UKS results shows that spin-polarization effects already explain for a large part the calculated difference.
Because of the cylindrical spin density distribution (see Figure 4.3) one expects the largest
quadrupole interaction of the
8
1
Ni nucleus (I = 3/2) to be along the Ni–H bond and smaller values
perpendicular to it. This is found experimentally: Q
= 8.2 MHz and Q
= -4.1 MHz. These num-
bers are exactly obtained from a spin-polarized SR calculation while non-polarized calculations slightly
overestimate the parallel value and underestimate the perpendicular value.
The
1
H isotropic hyperfine interaction is overestimated by SR UKS calculations by 43 MHz and also
58 4. Nickel Model Complexes
the anisotropic part is not very well described (deviation 3 and 6 MHz). It is in particular the isotropic
component that is most sensitive to spin polarization. The calculated B3LYP
1
H value by Munzarova
and Kaupp [126] deviates from the experimental value by 85 MHz but into the other direction (208 MHz
calculated vs. 293 MHz measured). A comparison of the spin-restricted (ROKS) SR results and those
including spin-orbit (SR + SO ROKS) coupling shows that the effect of spin-orbit coupling is small for
the
1
H nucleus.
For the
1
C and
1?
O nuclei there are no experimental values available. Here, a comparison is made
with the calculated B3LYP values by Munzarova and Kaupp [126] which are also included in Table 4.6.
For the
1
C nucleus the agreement between SR UKS ZORA and non-relativistic B3LYP calculations is
very good. The difference in the isotropic hyperfine interaction is 2.5 MHz at most. In the case of
1?
O, in
contrast, the SR UKS calculated signs of the anisotropic hyperfine interaction are inverted with respect
to the values by Munzarova and Kaupp (see Table 4.6). The calculation was repeated using the SR
ZORA BP/V geometry, a VTZP basis set by Sch¨afer et al. [167] and the B3LYP hybrid functional in the
Gaussian94 program. The obtained values are, in general, very similar to that of Munzarova and Kaupp
and are therefore not given here. The only noteworthy difference is in the
1?
O hyperfine interaction.
The isotropic part in our calculation is a
,546
= -4.35 MHz and the anisotropic part A’
A@ 2 B@
= (+9.64,
+6.11, -15.75) MHz. Our findings of the absolute signs of the anisotropic hyperfine interaction are in
agreement with our ZORA results and contradict the signs given by Munzarova and Kaupp. This may
be due to a typing error in their manuscript. The effect of spin-orbit coupling is very small for ligands in
the molecular
#C$
-plane. The anisotropic part of the hyperfine tensor of the
1
C and
1?
O nuclei remains
nearly unchanged upon inclusion of SO coupling.
It should be mentioned as an aside that the popular B3LYP functional does not necessarily lead to
an improvement in the calculation of hyperfine parameters compared to pure GGA functionals as was
already stated by Munzarova and Kaupp [126] and by Hayes [127].
The Ni-C state of the [NiFe] hydrogenase is two electrons more reduced than the oxidized states,
and might formally correspond to a Ni(I) species. The observation of the Ni-C EPR spectrum correlates
with the catalytic activity of the enzyme [45] and is thus assigned to be an intermediate in the heterolytic
cleavage of molecular hydrogen. For the Ni(I) in Ni-C a 3d
!/
ground state is sometimes discussed
[65,69,70]. As shown here, a hydride axially bound to a Ni 3d
!/
orbital would lead to a much larger
1
H
hyperfine coupling than the one observed in hydrogenase (16-20 MHz [69,70]). Such a bonding situation
seems therefore to be unrealistic in the Ni-C state [12]. A hydride ion bound to nickel in the xy-plane
can, however, not be excluded.
4.4 Conclusion 59
4.4 Conclusion
The calculation of magnetic resonance parameters from first principles offers a straight forward route to
the comparison of experimental and theoretical values for transition metal complexes. The detour via
atomic spin populations is no longer required.
The accuracy of the ZORA formalism to calculate the magnetic resonance parameters of nickel con-
taining model complexes both in the Ni(III) and Ni(I) oxidation states was demonstrated. The hyperfine
tensors can be computed relatively accurately, whereas the agreement in g-tensors is less good. Effects
of spin-orbit coupling may be large for both the calculated isotropic and the calculated anisotropic metal
hyperfine interactions. The effects on the ligand hyperfine interactions are in general much smaller.
In the case of Ni(mnt)
, the calculations helped to resolve ambiguities in the choice of signs of the
8
1
Ni and
:
S nuclei. The unpaired electron was found to reside in the 5b
D
orbital consisting mainly
of the Ni 3d
E
orbital and S 3p
orbitals. The covalent bonding leads to a delocalization of 64% of the
spin population into sulphur ligand orbitals. This large Ni–S bond covalency is an important result and
has to be taken into consideration in the interpretation and analysis of ENDOR data from the [NiFe]
hydrogenases.
In Ni(CO)
H, a hydride ion is bound axially to a hybrid Ni 3d
!/
, 4p
orbital. The large hyperfine in-
teraction of the hydrogen rules out such a bonding situation for the Ni-C state of the [NiFe] hydrogenase.
An in-plane bound hydride can, however, not be ruled out.
The ZORA formalism’s accuracy and computational efficiency holds great promise for the elucida-
tion and interpretation of EPR and ENDOR data of Ni complexes in biological systems and other active
centres in metalloenzymes.
60
Chapter 5
The Electronic Structure of the
Paramagnetic States of [NiFe]
Hydrogenase
5.1 Introduction
The active centre of the [NiFe] hydrogenase consists of a heterobimetallic Ni-Fe cluster. The Ni and
Fe atoms are bridged by sulphur atoms of two cysteine amino acids. In addition, there are two further
cysteines as terminal ligands to the Ni atom (see Fig. 5.1). D. gigas and D. vulgaris Miyazaki F [NiFe]
hydrogenases display identical EPR spectra [39]. The details of their active centres [27,28,171] with
regard to the nature of the bridging ligand X and the identification of the three non-protein ligands to the
Fe atom are controversely discussed. The electron density peak in the oxidized states between Ni and Fe
was tentatively assigned to an oxygen species in D. gigas [27] and to a sulphur species D. vulgaris [28].
Recently, liberation of H
S upon reduction of D. vulgaris was reported [172] indicating the presence of
a sulphur ligand in this species. Furthermore, there are three diatomic, non-protein ligands terminally
bound to the Fe. In the case of the [NiFe] hydrogenase from Allochromatium vinosum they have been
identified to be 1 CO and 2 CN ligands by FTIR spectroscopy [51] and chemical analysis [173]; and
by FTIR spectroscopy for D. gigas [27]. In D. vulgaris Miyazaki F two CO, and one SO ligand were
postulated from X-ray crystallography [28].
Recently, a high resolution X-ray structure (1.4 ˚
A resolution) of the reduced enzyme from D. vul-
garis Miyazaki F was published [174] in which removal of the bridging ligand in the reduced state was
reported. There were no significant changes in the bonding parameters associated with this reduction.
61
62 5. The Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase
Density Functional Theory (DFT) calculations have already been applied to [NiFe] hydrogenases by
Pavlov et al. [71] who have proposed a reaction mechanism for the dissociation of molecular hydrogen
by [NiFe] hydrogenases. The emphasis in this work was on the activation of H
by the enzyme. The Fe
was proposed to be the site of H
binding. In their work, the electronic ground state was not correctly
calculated, making a comparison with experimental data difficult. In a subsequent publication [72], the
initial reaction mechanism was slightly revised. The first attempt to describe the redox states of the
enzyme was recently addressed by De Gioia et al. [74]. These authors obtained the correct (S=1/2)
ground state but the reported spin populations were not in good agreement with experimental data (see
below). Later, Niu et al. [75] characterized the intermediate states of the [NiFe] hydrogenase by their
CO stretching frequencies but no atomic spin populations were reported. Amara et al. suggested atomic
compositions for the Ni-A and Ni-C paramagnetic states based on QM/MM calculations [76]. The
obtained spin populations, however, seem questionable due to large contributions from higher spin states
(see below).
In this chapter DFT investigations performed on the different paramagnetic states of the active centre
(Ni-A, Ni-B, Ni-C) are reported. Several candidates for the bridging ligand are suggested and the differ-
ent paramagnetic states are traced back mainly to modifications of this bridging ligand. Some aspects of
the non-protein ligands at the Fe atom are also discussed. The proposed atomic structures of the active
centre in the different paramagnetic states are in agreement with experimental results derived from EPR
and ENDOR spectroscopy. This yields an understanding at the atomistic level of the Ni-A, Ni-B and
Ni-C states. The obtained data for these states form the basis for establishing a reaction mechanism for
the activation of hydrogen by [NiFe] hydrogenases.
Fe
Ni
S
Cys
S
S
S
Cys
Cys
Cys
CN
CO
CN
X
Figure5.1: Schematic picture of the active centre of [NiFe] hydrogenase from D. gigas. The diatomic ligands
are 1 CO and 2 CN as shown [27], in D. vulgaris 1 CO, 1 CN, and 1 SO are postulated [28]. The bridging
ligand X is either an oxygen (D. gigas [27]) or a sulphur species (D. vulgaris [28]).
5.2 Computational Details 63
5.2 Computational Details
The efficiently parallelized density functional code DGauss4.0 [175] was used and run on a Cray T3E
computer using up to 128 processors. Large cluster models (42 atoms for Ni-B, 41 atoms for Ni-A/Ni-C)
of the active site of [NiFe] hydrogenase were completely geometry optimized imposing no constraints
on the structure. Due to the absence of point group symmetry and the open-shell nature of the species
considered here, typical CPU usage times for a geometry optimization were 50 - 100 h . Cysteine amino
acids were represented by a S–CH
–CH
moiety leading to a realistic description of the active site of the
enzyme (see below). Smaller cluster models lead to erroneous results and are insufficient to describe the
spin density distribution correctly. Two CN and one CO ligands were chosen as prosthetic groups to the
Fe atom but also 1 SO, 1 CN, and 1 CO ligand were alternatively considered.
The DFT-optimized DZVP basis set of Godbout et al. [176] was applied. The atomic basis set was
of the following contraction scheme: H 41, C 621/41/1, N 621/41/1, O 621/41/1, S 6321/521/1, Ni
63321/531/41, Fe 63321/531/41. The auxiliary basis set for the exchange-correlation and coulomb part
was of the following type: H 4, C 6/3/3, N 7/3/3, O 7/3/3, S 9/4/4, Ni 10/5/5, Fe 10/5/5. This basis set
was successfully used in the description of the electronic structure of blue-copper proteins [177]. The
Becke exchange functional and the Lee-Yang-Parr gradient-corrected correlation functionals were used
(BLYP) [91,92]. The BLYP functional was shown to yield structural parameters (bond lengths and vi-
brational harmonic frequencies) virtually identical to the hybrid B3LYP functional and to sophisticated
post-HF techniques in case of neutral and positively charged transition metal hydrides [178]. All struc-
tures reported here converged to doublet (S = 1/2) states as experimentally observed. The deviation of
the expectation value of
FHG
JI
from the theoretical value of 0.75 were
K
0.008.
5.3 Results and Discussion
5.3.1 Structural Parameters for The Oxidized States
One of the aims of the calculations was to elucidate the nature of the bridging ligand X between the Ni
and Fe atoms in the oxidized states that was postulated to be an oxygen [27] or a sulphur species [28].
O
, OH
, S
and SH
were tested as plausible candidates for this bridging ligand X. A protonation
of an oxygen or sulphur bridge would not be detectable by X-ray crystallography.
In Table 5.1 data from the two X-ray structures of the oxidized enzyme are collected. In the D.
gigas X-ray structure refined to 2.5 ˚
A an electron density peak between the Ni and Fe atoms was discov-
ered [27] and assigned to an oxygenic species. The crystals consist of enzyme that is predominantly in
64 5. The Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase
the “unready“ Ni-A state (85% Ni-A, 15% Ni-B) [171]. The structure of the homologous [NiFe] hydro-
genase from D. vulgaris Miyazaki F [28] (1.8 ˚
A resolution) differs from that of D. gigas. The Ni
LLL
Fe
distance is significantly shorter (2.55 ˚
A) and so are nearly all Ni–S and Fe–S bond lengths. A sulphur
species is postulated to occupy the bridging position. In D. vulgaris [28] the diatomic ligands to the Fe
atom are given as 2 CO and 1 SO ligand. The assignment of S as bridging ligand and SO as terminal Fe
ligand is based on higher temperature factors and electron density peaks of these atoms. It was shown by
EPR that the enzyme of D. vulgaris Miyazaki F was crystallized in the “ready” form Ni-B (70% Ni-B,
30% Ni-A) [179].
Table 5.1: Comparison of selected structural parameters from X-ray and BLYP/DZVP optimized structures
of the oxidized active centre of [NiFe] hydrogenase. In the calculations 2 CN and 1 CO ligands were chosen
as diatomic ligands to the Fe. Bond lengths in ˚
A, bond angles (
M
) in degrees.
Exp. Calc.
D. gigas D. vulgaris Bridging Ligand
distances/angles [27] [28] X= O
X= OH
X= S
X= SH
Ni
LLL
Fe 2.90 2.55 2.96 3.05 3.22 3.19
Ni
LLL
SCys533 2.62 2.37 2.49 2.51 2.50 2.48
Ni
LLL
SCys68 2.58 2.38 2.41 2.36 2.40 2.38
Ni
LLL
SCys530 2.27 2.33 2.40 2.31 2.39 2.32
Ni
LLL
SCys65 2.16 2.22 2.44 2.29 2.46 2.31
Ni
LLL
X 1.74 2.16 1.84 1.98 2.26 2.36
Fe
LLL
SCys533 2.20 2.37 2.61 2.47 2.56 2.48
Fe
LLL
SCys68 2.23 2.14 2.50 2.46 2.52 2.46
Fe
LLL
X 2.14 2.22 1.97 2.09 2.40 2.44
N
Ni-X-Fe 96.5 71.0 102.1 96.8 87.3 83.5
N
Ni-SCys533-Fe 73.6 64.1 71.0 75.5 79.1 82.5
N
Ni-SCys68-Fe 73.9 66.2 74.1 78.3 81.8 80.1
The error in the X-ray coordinates is estimated to be 0.27 ˚
A at 2.5 ˚
A [27] and 0.2 ˚
A at 1.8 ˚
A [28] resolution.
Table 5.1 compares selected features of the BLYP/DZVP optimized structures with the X-ray data. 1
1The offset in enumeration of amino acid residues between [NiFe] hydrogenases from D. gigas and D. vulgaris is +16
residues but in the following only the D. gigas enumeration of amino acid residues will be used for reasons of consistency.
5.3 Results and Discussion 65
In the calculations the Ni
LLL
Fe distance is larger when a sulphuric species occupies the bridging position
(3.22 ˚
A for S
and 2.96 for O
). The same holds for a protonated bridging ligand (3.19 ˚
A for SH
and
3.05 ˚
A for OH
). The angle between Ni, the bridging cysteines Cys533 and Cys68 and the Fe is about
7-8
O
larger with a sulphur atom. The Ni
LLL
X and Fe
LLL
X distances react most drastically upon sulphur
substitution. The distances increase by as much as 0.4 ˚
A when a sulphur is in the bridging position. The
increase in bond length between the metal and the bridging atom is partly compensated by a decrease of
the Ni–X–Fe bond angle from 102.1
O
(96.8
O
) for O
(OH
) to 87.3
O
(83.5
O
) for S
(SH
). The overall
increase of the Ni
LLL
Fe distance is modest with 0.26 ˚
A (O
vs. S
). The metal-cysteine bond lengths
are almost independent of the nature of the bridging ligand (see Table 5.1). Slightly larger values are
obtained for a doubly negatively charged bridge (e.g. O
and S
) than for singly negatively charged
bridges (OH
and SH
). The excess negative charge of the bridging ligand X leads to a weakening of
the Ni–S and Fe–S bonds, i.e. an elongation of the metal–S bonds. This indicates a charge transfer from
the Ni–X (X = sulphur or oxygen species) towards all coordinating four sulphur atoms of the cysteine
residues.
The optimized geometries for the four different bridging ligands are compared with the experimental
geometrical data obtained from the X-ray structure analysis in Table 5.1. The best agreement between the
calculated structures and those from X-ray crystallography is obtained for the structure of D. gigas [27]
and an oxygenic species, O
or OH
, occupying the position of the bridging ligand. The differences
between calculated bond lengths and those from X-ray coordinates are at most 0.1-0.2 ˚
A and thus within
the range of error of the X-ray structure coordinates. Bond angles agree within 2-4
O
(see Table 5.1).
In particular the Ni
LLL
X, Fe
LLL
X, Ni
LLL
Fe bond lengths and Ni–SCys(bridging)–Fe bond angles agree
favourably with the data from D. gigas. A discrimination between either an OH
or an O
bridge can,
however, not be made on the basis of structural parameters alone. This can be derived from features of
the electronic structure (see below).
According to the calculations a sulphur bridging ligand would lead to Ni
LLL
Fe distances of 3.22 ˚
A
(S
) and 3.19 ˚
A (SH
) which does not agree with the heavy atom distance of 2.55 ˚
A in the crystal
structure from D. vulgaris [28] (see Table 5.1). Considering a bond length error of 0.2 ˚
A for the X-ray
structure at 1.8 ˚
A resolution, the deviation is clearly outside the range of error. The discrepancy between
calculated structural parameters and those from the X-ray analysis is most striking for parameters asso-
ciated with the sulphur bridging ligand (Ni
LLL
X, Fe
LLL
X bond lengths,
N
Ni-X-Fe bond angle, see Table
5.1). Ni–SCys and Fe–SCys bond lengths are well reproduced, but these are nearly independent of the
nature of the bridging ligand. The deviation between calculated and measured Ni–Cys–Fe bond angles
is about 15
O
.
66 5. The Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase
To conclude, BLYP/DZVP calculations are able to describe the structural parameters of the active
centre of [NiFe] hydrogenase from D. gigas quite accurately. The cluster model chosen in the calculation
can therefore be used for elucidation of the electronic structure of the active centre and a comparison with
experimental data.
5.3.2 Electronic Structure of the Oxidized States
The spin density distribution of a molecule embedded in a protein environment is obtained from the
measured and assigned hyperfine coupling constants which are available from EPR and ENDOR spec-
troscopy [66]. In particular, the isotropic hyperfine coupling constants are directly proportional to the
spin density at the nucleus whereas the anisotropic part is related to the spin density in non-spherically
symmetric orbitals.
The observation of large hyperfine splittings in EPR spectra from
8
1
Ni (I=3/2) labelled hydrogenases
[45,59] the Ni atom has been recognizedto bear the largest part of the unpaired spin density. Furthermore,
EPR of
:
S substituted hydrogenase showed that one sulphur atom has a large hyperfine splitting [62].
This indicates that spin delocalization occurs predominantly onto one sulphur, probably from a cysteine
residue ligated to the Ni atom. Experiments on
P
?
Fe enriched hydrogenase showed virtually no line
broadening in the EPR spectra.
P
?
Fe-ENDOR experiments revealed a small hyperfine interaction of
1 MHz in Ni-A, whereas for Ni-B and Ni-C no coupling was detectable [61]. This indicates that the Fe
remains in a S = 0 (Fe(II) low spin) state in all paramagnetic intermediates of the enzyme. The low spin
state of the iron was also confirmed by M¨ossbauer spectroscopy [180].
When Ni-C is reoxidized with
1?
O
, a line broadening is observed in samples of Ni-B (increase in
line width of 0.0, 0.4, 0.7 mT for the
QA
,
QR
and
QS
components, respectively) and of Ni-A (increase
by 0.5, 0.5, 0.55 mT at
QA
,
QA
,
QS
, respectively) [63]. This implies that an oxygen species binds in the
vicinity of the Ni atom and that a small amount of unpaired spin density is transfered to this oxygen. It
has been discussed that this oxygen occupies the bridging position between the Ni and Fe [171]. This
cannot explicitly exclude the possibility of a sulphur atom as a bridging ligand in a different organism
and/or spin state.
The existence of a sulphur bridging ligand was supported by the reported release of H
S [172] upon
reduction of the D. vulgaris Miyazaki F enzyme and the simultaneous removal of the bridging ligand.
There are, at present, no further magnetic resonance data which might support or contradict this hypoth-
esis.
A reliable model of the active site of oxidized [NiFe] hydrogenase must be able to reproduce all of
the above mentioned experimental findings. This strict condition could not be fulfilled by any of the
5.3 Results and Discussion 67
theoretical studies so far [71,72,74–76]. Clearly, Ni and S must bear the largest part of the unpaired
spin density because they are the only nuclei leading to large hyperfine splittings in EPR and ENDOR
spectra. The spin density at the Fe atom can only be estimated to be very small. 2
Table 5.2 gives calculated atomic spin populations for the four different bridging ligands investigated.
The spin population at the nickel atom is nearly independent of the bridging ligand (0.52 for O
, OH
and SH
, 0.56 in the case of S
) and is in agreement with the experimental finding of
8
1
Ni hyperfine
splitting. The insensitivity of the Ni spin density to the type of bridging ligand (OH
or O
) is in
agreement with the experimental finding that the electron density at the Ni remains unchanged between
Ni-A and Ni-B [181].
The spin population at the Fe atom is small and negative. The negative sign may be due to spin
polarization effects of spin density from the nickel via the bridge to the Fe site. When a singly negatively
charged bridge (OH
, SH
) is present the spin population is only -0.002; it is about a factor of ten larger
(-0.02) when a doubly negatively charge bridge (O
, S
) is present. This small spin population is
in good agreement with the results from
P
?
Fe-ENDOR studies [61]. In Ni-B no
P
?
Fe-ENDOR effect
is observed, whereas Ni-A gives a small but detectable hyperfine interaction of
1 MHz. Thus, it is
proposed that Ni-B is associated with either OH
or SH
leading to a vanishing spin density at the
Fe site. Ni-A might possess either an O
or S
as bridging ligand which might give rise to a small
hyperfine interaction.
When going from a singly to a doubly negatively charged bridging ligand, the spin population at the
Cys533 sulphur atom is reduced (from 0.34 for OH
to 0.24 for O
and from 0.33 for SH
to 0.28 for
S
, see Table 5.2). Since no complete hyperfine tensors for
:
G
are available for the two forms Ni-A and
Ni-B, neighbouring
T
-CH
protons of the cysteine amino acid can be used to probe the magnitude of the
spin density at the sulphur atom itself. The reduction of atomic spin density at the sulphur of Cys533 is
in agreement with the decrease of isotropic hyperfine couplings by about 2-3 MHz of the
T
-CH
protons
of that cysteine residue [182]. In addition, the spin density at the terminal cysteine Cys530 is reduced by
a factor of two (from 0.06 in Ni-B to 0.03 in Ni-A, see Table 5.2).
The atomic spin populations presented here were used in the analysis of the deviation of the
anisotropic hyperfine tensors from axiality of the two
T
-CH
from Cys533 in the Ni-B state [169]. The
2The atomic spin populations are usually derived from experimentally determined hyperfine couplings by relating them to
the values expected for a free ion from Morton and Preston [159]. The situation is complicated due to the fact that the sign of
the hyperfine splittings is not known. One thus has to make a plausible choice of signs of the hyperfine splitting and a priori
assume an atomic ground state and a specific orbital occupancy. The situation is hopeless for heavy atoms where spin-orbit
coupling significantly contributes to the hyperfine interaction, i.e. Ni, Fe and S.
68 5. The Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase
experimentally obtained anisotropic hyperfine tensors could be explained by a coupling of the protons to
the adjacent sulphur atom with an atomic spin population of
0.3 and to the central nickel atom with
0.5.
Table 5.2: BLYP/DZVP calculated atomic spin populations for oxidized [NiFe] hydrogenase
De Gioia et al. Amara et al.
Nucleus Ni-B [74] Ni-A [76]
X = O
OH
S
SH
empty O
(Ni) 0.52 0.52 0.56 0.52 0.43 1.17
(Fe) -0.02 -0.002 -0.02 -0.002 0.19 -0.12
(S
U V4
P
:
) 0.24 0.34 0.28 0.33 0.006/-0.003
W
0.19
(S
U V4
P
.
) 0.03 0.06 0.03 0.06 0.172/0.217
W
0.07
(X) 0.18 0.003 0.08 0.02 / -0.48
No assignment to a specific cysteine is made. They are only classified as bridging or terminal cysteines.
The recent theoretical work by Pavlov et al. [71,72] has focused on the activation process of [NiFe]
hydrogenase. However, in their work the enzyme’s paramagnetic states were not accurately described,
i.e. structural parameters and atomic spin populations for Ni-A or Ni-B were not given. Thus, these
data cannot be compared with the results in this chapter. De Gioia et al. [74] were the first to attempt
a description of the paramagnetic states of oxidized [NiFe] hydrogenase. Ni-A was not considered but
atomic spin populations for Ni-B were given. Their values are included in Table 5.2. De Gioia et al. do
not place a bridging ligand between the Ni and Fe atoms. The spin population at the Ni (0.43) is only
slightly smaller than the result here (0.52). The spin population at the Fe is, however, too large and in
clear disagreement with the
P
?
Fe-ENDOR results.
Calculations on a cluster model with an empty bridging position yield a spin density distribution
which is not in agreement with the measured
Q
-tensor orientation and
1
H-ENDOR results (see below).
In this bonding situation, the sulphur atoms of the terminally bound cysteine amino acids (Cys65 and
530) would bear a significant amount of unpaired spin population (0.23 and 0.20, respectively). These
results also do not agree with the finding that the spin is localized along the Ni–SCys533 bond. Further-
more, the calculated Ni
LLL
Fe distance of 3.10 ˚
A is not in good agreement with the one from the X-ray
crystallographic analysis (see above). Such a model can therefore be ruled out for the oxidized states of
[NiFe] hydrogenases. 3
3BLYP calculations also rule out a water molecule as bridging ligand. The calculated Ni
XXX
Fe distance is 3.25 ˚
A and the
5.3 Results and Discussion 69
Figure 5.2 summarizes the findings for the Ni-B state. The figure (top) displays the calculated atomic
spin populations which are in good agreement with the data derived from EPR and ENDOR spectroscopy.
The lower figure shows a contour plot of the spatial spin density distribution in Ni-B. The spin density
is oriented along the Ni–S(Cys533) bond, as was also found in single crystal EPR studies [179,183].
This also explains the large isotropic hyperfine interactions of
T
-CH
protons of the cysteine Cys533
observed in pulsed-ENDOR investigations of protein single crystals [184] and orientation-selected cw-
ENDOR of frozen solution of A. vinosum [169] in the Ni-B state. The calculated isotropic hyperfine
coupling constant for the two protons
T
-CH
1:@
from the bridging cysteine Cys533 are 10.1 and 10.5
MHz, respectively, and compare well the experimental ones of 12.5 MHz for these protons [169].
Figure 5.3 shows the unpaired spin density distribution at a contour value of 0.005 e/a
.
when there
is a
Y
-oxo bridge between the Ni and Fe atoms. This is a model for the Ni-A state. Amara et al. recently
also suggested a Ni-A state with a
Y
-oxo bridging ligand based on the X-ray structure of the [NiFe]
hydrogenase from D. gigas [76] (see Table 5.2). Their B3LYP/ECP QM/MM calculation for the Ni-A
form suffered from a major spin-contamination (
FZG
[I
= 1.37 vs. a theoretical value of 0.75 for a S=
1/2 state). The given high spin population at the Ni of 1.17 (see Table 5.2) therefore seems unrealistic.
The BLYP/DZVP calculations presented in this chapter do not exhibit such a high spin-contamination
(see Computational Details). The results by Amara et al. agree with the data presented here that the
unpaired spin density in the Ni-A form is primarily on the Ni and SCys533 atoms. Furthermore, Amara
et al. also found that the bridging ligand O
in the Ni-A state may acquire a significant amount of
spin density. They report a spin population of -0.48 for the
Y
-oxo bridge for their S = 1/2 solution with
high spin contamination. This large value seems questionable. The
Y
-oxo bridge in the BLYP/DZVP
calculations exhibits a smaller spin population of 0.18 which appears more realistic when experimental
findings are considered [63]. In the work by Amara et al., the magnitude of spin population at the Fe is
also large (see Table 5.2).
5.3.3 Structural Parameters for the Reduced Enzyme (Ni-C)
The recent X-ray structure analysis of [NiFe] hydrogenase crystallized under H
atmosphere [174] in-
dicated a vacant bridging position between the Ni and Fe atoms. In the case of the Ni-C state the place
of the bridging ligand may be taken by a hydride species and not be detectable by X-ray crystallogra-
phy [34]. This assumption was here investigated by further DFT BLYP/DZVP calculations.
water molecule is only loosely coordinated to the Ni (at a distance of 3.23 ˚
A) and the Fe (at a distance of 2.27 ˚
A). The spin
populations are (Ni) = 0.45, (Fe) = 0.02 and nearly equal on the terminal cysteines (SCys65) = 0.22 and (SCys530) = 0.20. This
is not in agreement with experimental findings.
70 5. The Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase
Cys533
Fe
Fe
Ni
Cys68
Cys68
Cys65
Cys533
C
C N
C O
N
Cys533
Fe
Fe
Ni
Cys68
Cys68
Cys65
Cys533
C
C N
C O
N
C
0.06
OC
C N
N
-0.002
Ni
0.52
Cys65
0.04
0.34
0.03
Cys530
Cys530
Fe
Fe
Figure 5.2: Top: BLYP/DZVP calculated Mulliken spin populations for the active centre of [NiFe] hydro-
genase in the Ni-B state. Bottom: BLYP/DZVP contour plot at 0.005 e/a
&
3
of the unpaired spin density
distribution
Table 5.3 compares selected structural parameters of the reduced enzyme from the X-ray structure
[174] with those obtained from DFT BLYP/DZVPcalculations where a hydride ion bridges Ni and Fe and
the position of the bridging ligand is vacant. The results from X-ray analysis of the reduced [NiFeSe]
hydrogenase from Desulfomicrobium baculatum [185] are also included in Table 5.3. The [NiFeSe]
hydrogenase contains a selenocysteine in the position of the Cys530 in D. gigas and the bond distance to
5.3 Results and Discussion 71
Figure 5.3: BLYP/DZVP calculated spin density distribution in the Ni-A state at a contour value of 0.005e/a
&
3
this residue is elongated because of the larger van der Waals radius of selenium compared to sulphur. A
vacant position of the bridging ligand can be ruled out since the Ni
LLL
Fe distance is too large by 0.5 ˚
A in
the calculations.
The calculated structural parameters agree very well with those from the high-resolution (1.4 ˚
A)
X-ray structure of D. vulgaris [174] and D. baculatum [185] when a hydride ion occupies the bridging
position. The agreement in bond lengths and angles is better for the reduced state than for the oxidized
states which is probably due to the higher resolution of the X-ray analysis in the reduced enzyme. There
is less heterogeneity in the reduced state. The oxidation state of the active Ni-Fe cluster in the reduced
crystals, however, could not be determined yet. It thus remains not clear whether the paramagnetic state
Ni-C or the completely reduced state Ni-R is present in the crystal. When a further electron is added to
the model for the Ni-C state, and a diamagnetic, closed-shell cluster is obtained, the structural parameters
do not change significantly (less than 0.01 ˚
A in bond distances). This may be a model for the Ni-R state
which structurally would be very similar to the Ni-C form.
The Ni
LLL
Fe distance is 2.60 ˚
A in the crystal structure of the reduced [NiFe] hydrogenase from D.
vulgaris and hardly differs from that in the oxidized form (2.55 ˚
A). In contrast, the calculations suggest
that the heavy atom distance shortens by approximately 0.4-0.5 ˚
A upon replacement of the bridging
ligand (O or S) by a hydride ion (cf. Tables 5.1 and 5.3). One reason for this discrepancy between
experiment and calculation may be that the oxidation state for which the X-ray structure of the oxidized
72 5. The Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase
Table 5.3: Comparison of selected structural parameters from X-ray and BLYP/DZVP optimized structures
of the reduced active centre of [NiFe] hydrogenase. Bond lengths (r) in ˚
A, bond angles (
M
) in degrees.
Exp. Calc.
D. vulgaris D. baculatum
W
distances/angles [174] [185] X=H
empty
Ni
LLL
Fe 2.60 2.53 2.67 3.10
Ni–SCys533 2.45 2.62 2.43 2.23
Ni–SCys68 2.37 2.33 2.35 2.28
Ni–SCys530 2.21 2.46
W
2.27 2.22
Ni–SCys65 2.30 2.25 2.31 2.24
Ni
LLL
X / / 1.69 /
Fe–SCys533 2.34 2.37 2.44 2.33
Fe–SCys68 2.29 2.29 2.39 2.36
Fe
LLL
X / / 1.73 /
N
Ni-X-Fe / / 106.3 /
N
Ni-SCys533-Fe 65.7 60.7 66.5 85.4
N
Ni-SCys68-Fe 67.8 66.5 68.7 83.6
Note that the [NiFeSe] hydrogenase from Desulfomicrobium baculatum contains a selenocysteine at the position
530. This explains the large bond length to this residue.
form was solved predominantly corresponds to a different, e.g. Ni-Si, species.
5.3.4 Electronic Structure of the Reduced Enzyme (Ni-C)
The calculated spin populations for the situation where either a hydride ion occupies the position of the
bridging ligand or it is empty are given in Table 5.4. For the reduced Ni-C state, less experimental data
are available than for the oxidized states. The hyperfine tensors of
8
1
Ni or
:
S were not fully obtained;
the absence of a
P
?
Fe ENDOR effect [61], shows that the Fe is kept in its Fe(II) low spin state. The
calculations show that only 1
\
of the unpaired spin resides on the Fe atom when the two metal are
Y
-hydrido bridged and 3% when the bridge is absent. Furthermore, the calculations show that the spin
density distribution does not drastically change in Ni-C when a hydride occupies the bridging position
(compare Tables 5.2 and 5.4). The situation where the bridging position is empty appears unrealistic.
5.3 Results and Discussion 73
Table 5.4: BLYP/DZVP calculated atomic spin populations for reduced [NiFe] Hydrogenase
Nucleus De Gioia et al. Pavlov
]
et al. Amara et al.
X=H
empty Ni-C [74] Ni-C [72] Ni-C [76]
(Ni) 0.51 0.41 0.53 1.39 0.90
(Fe) 0.01 0.03 0.08 0.14 0.03
(S
U V4
P
:
) 0.29 0.05 0.14/0.14
W
0.00 0.00
(S
U V4
P
.
) 0.10 0.20 0.001/0.19
W
0.69 0.02
No assignment to a specific cysteine is made. They are only classified as bridging or terminal cysteines.
^
The calculations by Pavlov et al. were done on a S = 3/2 state.
It would be associated with a redistribution of spin density from the bridging cysteine Cys533 in the
oxidized states to the terminal cysteine Cys530 in the reduced state (compare Tables 5.2 and 5.4). In
addition, such a bonding situation could not explain the large, D
O-exchangeable
1
H-ENDOR coupling
in the Ni-C state [69,70].
When a hydride ion bridges the Ni and Fe atoms, the largest part of the unpaired spin density still
resides along the Ni–SCys533 bond as also found in the oxidized states. Figure 5.4 shows a plot of
the unpaired spin density at a contour value of 0.005 e/a
.
. The spin population at the sulphur atom of
the bridging cysteine Cys533 is slightly reduced from 0.34 in Ni-B (X=OH
) to 0.29 in Ni-C (X=H
).
The sulphur atom of the terminal cysteine Cys530 acquires 10
\
of the spin which may lead to small
additional hyperfine splittings of the
T
-CH
protons in ENDOR.
In X-ray absorption spectroscopy (XAS) experiments it was found that the electron density at the Ni
atom does only slightly change between Ni-A/Ni-B/Ni-C [186]. In this work, it was concluded that the
Ni atom would not the redox active metal. This is in agreement with the finding that the atomic spin
population at the Ni remains nearly constant (Ni-A/B 0.52, Ni-C 0.51). The conclusion [186] that Ni is
not the redox active metal, however, is not quite correct.
Results for the proposed Ni-C were also obtained from earlier calculations [72,74,76] (Table 5.4).
In the work by De Gioia et al. [74], the presence of a
Y
-hydrido ligand leads to a decrease of atomic
spin population at the Fe from 0.19 (no bridge in Ni-B) to 0.08 (Ni-C). Pavlov et al. also reported
an atomic spin population at the Fe of 0.08 in Ni-C (bearing in mind their S= 3/2 ground state this
comes close to the experimental value) [72]. Amara et al. suggested a
Y
-hydrido bridge and a protonated
74 5. The Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase
Figure 5.4: BLYP/DZVP calculated spin density distribution in Ni-C at a contour value of 0.005 e/a
&
3
.
cysteine Cys530 [76]. This explains the vanishing spin population on the sulphur nucleus of that cysteine
amino acid in their calculations (see Table 5.4). Their results also agree with the findings here that the
spin population at the Fe atom is small. In their work, however, the spin density is almost exclusively
localized at the Ni nucleus. This cannot explain the large hyperfine couplings of
T
-CH
protons in the
Ni-C state [69,70] and the similar
8
1
Ni hyperfine couplings in the Ni-B and Ni-C states [45].
The BLYP/DZVP calculated isotropic
1
H hyperfine splittings of the
T
-CH
protons from Cys533 are
8.0 and 8.3 MHZ, respectively, which agree well with the experimental values [69,70]. The calculated
1
H isotropic hyperfine interaction for a Ni–
Y
-hydrido–Fe bridge is -8.5 MHz and in good agreement with
the experimental value of -11 MHz for the solvent-exchangeable proton in the Ni-C state [69]. It was
argued that the sign is negative due to a hydride directly bound to the Ni atom in the nodal plane of a d
!/
orbital. The isotropic hyperfine coupling may arise from a 3d
!/`_
3d
a/
E/
spin polarization [69].
In the model suggested for the Ni-C form, Ni is still in its formal Ni(III) oxidation state. Possibly, a
reduction takes place in the ligand sphere for which the bridging ligand is a potential candidate.
5.3.5 Influence of the Small Ligands at the Iron on the Electronic Structure
In D. vulgaris Miyazaki F the diatomic ligands to the Fe were initially assigned to two CO and one SO
molecule in the X-ray structure [28]. These ligands, however, cannot explain the IR vibrations detected
above 2000 cm
1
which are characteristic for CN stretching vibrations. They were also observed for
5.4 Summary and Conclusion 75
D. vulgaris so at least one CN must be present (Y. Higuchi, K. Bagley, personal communication). The
model of the oxidized D. vulgaris Miyazaki F enzyme chosen here incorporates one CO, one CN and one
SO ligand as prosthetic group to the Fe. Although a sulphur species was postulated in this enzyme [28]
to constitute the bridging ligand a OH
instead of SH
/S
bdc
was chosen. The spin density distribution
is rather independent of the nature of the bridge.
The calculated spin density distribution (Figure 5.5) is remarkably different from the D. gigas model.
The terminal SO withdraws spin density from SCys533 and leads to a spin population at the Fe of -0.08.
In this case, atomic spin populations are (Ni) = 0.44, (Fe) = -0.08, (SCys533) = 0.24, (SCys530) = 0.01,
(SO) = 0.16, (SO) = 0.11. The calculations cannot positively rule out a terminal SO ligand. Its influence
on the spin density distribution, however, makes it an unlikely candidate for a non-protein ligand in
[NiFe] hydrogenase. The issue should easily be clarified by FTIR experiments.
D. gigas and D. vulgaris have very similar hyperfine interactions and
Q
-factors. If D. vulgaris would
have SO instead of CN one would expect, according to the calculations,
e
25 % of the spin population at
the SO ligand, and a reduction of the same amount at the other positions (Ni, S). Furthermore, a deviation
of the
Q
-tensor principal values would be expected. Since this is not observed in the experiments, a SO
ligand seems to be unlikely – although it cannot be completely ruled out because no direct hyperfine
coupling for
:
SO or S
1?
O have been measured (
S
1
8
O contains no magnetic isotope and shows no
hyperfine splittings).
5.4 Summary and Conclusion
DFT calculations of the heterobimetallic centre of [NiFe] hydrogenases yielded structural parameters,
atomic spin populations and spin density distributions that are in good agreement with the existing re-
lated experimental data for the paramagnetic states Ni-A/Ni-B/Ni-C. The differences between the para-
magnetic states can be primarily attributed to a modification of the bridging ligand.
With regard to the so far unassigned bridging ligand X, a OH
ligand in the case of Ni-B and a
O
in the case of Ni-A seem to be plausible. Ni-B would be described as a Ni(III)-
Y
OH-Fe(II) and
Ni-A as a Ni(III)-
Y
O-Fe(II) system. A bulkier sulphur SH or S
species are unlikely since they would
lead to a significant elongation of the Ni
LLL
Fe distances. The calculated spin density distribution is in
agreement with the experimentally determined
Q
-tensor orientation in the Ni-A and Ni-B forms. A vacant
bridging position would lead to a spin density distribution which is not in agreement with experimental
findings. When the bridge is occupied by an OH
ligand, the calculated isotropic hyperfine couplings of
the
T
-CH
protons of cysteine Cys533 agree well with available experimental data.
76 5. The Electronic Structure of the Paramagnetic States of [NiFe] Hydrogenase
Figure 5.5: Top: BLYP/DZVP calculated Mulliken spin populations for the active centre of [NiFe] hydroge-
nase from D. vulgaris (1 CO, 1 CN, 1 SO ligand) in the Ni-B state (OH
f
bridging ligand).
Bottom: BLYP/DZVP contour plot at 0.005 e/a
&
3
of the unpaired spin density distribution in the Ni-B state.
The replacement of the bridging ligand in the oxidized states (O
and OH
) by a hydride ion in the
reduced Ni-C state leads to a decrease of the Ni
LLL
Fe distance by 0.4 ˚
A. The Fe(II) is kept in its low spin
state in all intermediates. The calculated isotropic hyperfine interaction for the hydride ion is in good
agreement with the respective experimental value.
As to the nature of the non-protein diatomic ligands of the Fe atom, the proposed 2 CN and 1 CO
ligands appear most realistic. A terminal SO ligand would act as a sink of spin density and lead to
Q
-
5.4 Summary and Conclusion 77
values and spin density distribution which is not in agreement with experimental findings. The detection
of H
S upon reduction of the hydrogenase from D. vulgaris Miyazaki F [172] may still originate from
a degradation product of the cysteine amino acids which coordinate the active centre or one of the Fe-S
clusters.
When a possible mechanism is discussed, experimental findings must be taken into account. It is
known that bridging ligand is liberated upon reduction and might possibly take up the proton from the
heterolytic dissociation of H
. The difference between Ni-A and Ni-B (O
vs. OH
bridging ligand)
might reflect their different kinetics upon reductive activation. An OH
would be easier to activate and
liberate than an O
ligand.
Now that an understanding of the atomic composition of the active centre in the Ni-A, Ni-B and
Ni-C states evolves, the first principles calculation of magnetic resonance parameters from a Kohn-Sham
wavefunction and the comparison with experimental data is required.
78
Chapter 6
ENDOR Crystallography of the Oxidized
States
6.1 Introduction
The ‘as-isolated’, oxidized [NiFe] hydrogenase is a mixture of two paramagnetic states Ni-A and Ni-
B. From the similarities of the
Q
-values of Ni-A (2.32, 2.24, 2.01) and Ni-B (2.33, 2.16. 2.01) a drastic
change in the electronic structure in the Ni-A state compared to Ni-B can be ruled out. The two, however,
differ in their rates of activation. Ni-B (or ‘ready’) is reduced within minutes under an H
atmosphere
while Ni-A (or ‘unready’) requires incubation for several hours.
Details of the structure of the active centre of [NiFe] hydrogenase have been revealed by X-ray
structure analysis of protein single crystals [28,32,36]. Figure 6.1 displays the active centre of the [NiFe]
hydrogenase from Desulfovibrio vulgaris Miyazaki F. The Ni atom is coordinated by four cysteinyl
sulphur atoms (Cys80, 84, 546, and 549), two of which (Cys84 and Cys549) form a bridge to the Fe atom.
In addition, three electron density peaks in the vicinity of the Fe were observed. They were identified by
FTIR measurements to be 2 CN
and one CO ligand in D. gigas and A. vinosum [27,51]. An unidentified
electron density peak ‘X’ between the Ni and Fe atoms of the active centre was tentatively assigned to an
oxygenic species in D. gigas and to a sulphur atom in D. vulgaris. In the hydrogenase from D. vulgaris,
the diatomic ligands of the Fe have been modeled as 1 CO, 1 CN
or CO and one SO ligands (due to a
larger electron density) [28]. The symmetry of the ligand sphere of the Ni is close to square-pyramidal
and that of the Fe is close to octahedral.
The coordination of the active centre in the two oxidized states is similar (the crystallized [NiFe]
hydrogenase from D. gigas is predominantly in the Ni-A state [27], that of D. vulgaris Miyazaki F in
79
80 6. ENDOR Crystallography of the Oxidized States
Cys84
Ni
Fe
Cys84
Ni
Fe
Cys549
X
Cys546
Cys81
Figure 6.1: Details of the active centre of the [NiFe] hydrogenase from D. vulgaris Miyazaki F [28].
the Ni-B state [28]). One difference between the two forms may lie in their proton environment - a
modification of which would not be detectable by X-ray crystallography.
In hydrogenases and other transition-metal containing enzymes, the large EPR linewidth prevents
the detection of proton hyperfine splittings. Thus Electron Nuclear Double Resonance (ENDOR) spec-
troscopy must be used to obtain further information about the interaction of the unpaired electron with
nuclear spins, In frozen solution, the determination of complete hyperfine coupling tensors Ais pos-
sible by stepping the magnetic field over the range of EPR absorption, i.e. taking advantage of the
orientational dependence of the molecules with respect to the magnetic field [187–189]. The analysis
of orientation-selected ENDOR spectra in frozen solution is difficult and sometimes it is not possible
to follow hyperfine interactions over the complete EPR envelope. Recently, an orientation-selected EN-
DOR study of the Ni-B state of the [NiFe] hydrogenase from A. vinosum has been published and three
hyperfine tensors were reported [169]. Earlier ENDOR investigations of the active site of [NiFe] hydro-
genases have been limited to one or a few field positions only and were primarily concerned with the
Ni-C state [69,70]. No hyperfine tensors were given and no spatial assignment to protons in the active
centre was done since no information about the ligand environment was available at that time.
A challenging alternative to the investigation of proteins in frozen solution (powder) is the EPR and
ENDOR study of protein single crystal if these are available. The
Q
- and hyperfine tensor magnitudes
and orientations can independently be obtained. EPR investigations of single crystals of D. vulgaris
Miyazaki F hydrogenase [179,190] have recently revealed the orientation of the principal
Q
-tensor axes
6.1 Introduction 81
in the crystal for Ni-A and Ni-B. It was shown that the structure of the active site remained unaffected
by freezing the protein single crystal and the orientation of the
Q
-tensor persisted [190]. The ENDOR
investigation of protein single crystals of the [NiFe] hydrogenase will reveal isotropic, anisotropic hy-
perfine contributions and spatial information about the unpaired spin density distribution in the ligand
environment of the active centre. Both continuous wave (cw) and pulsed-ENDOR can, in principle, be
used.
Pulsed-ENDOR has the advantage of being essentially free from the restrictions of balancing re-
laxation and induced transition rates [83,191]. To the best knowledge, there is only one application of
pulsed-ENDOR spectroscopy to protein single crystals in the literature so far [192].
Of the two common pulse sequences of pulsed-ENDOR (Mims- [193] and Davies-ENDOR [194]),
Davies-ENDOR provides a ”blind-spot”-free determination of nuclear spin-electron spin interactions.
Doan et al. [195] showed that Mims-ENDOR is most useful for observing nuclei with hyperfine inter-
actions smaller than 5 MHz while Davies-ENDOR is more sensitive to larger couplings. In the catalytic
cycle changes in the proton environment of [NiFe] hydrogenases are expected to be associated with large
hyperfine interactions since the Ni atom is believed to be the catalytically active transition metal and
either bind the substrate (H
) or one of its dissociation products. A large hyperfine interaction with a
hydrogen species is detected in the Ni-C state (approx. 20 MHz [70]). Thus Davies-ENDOR is the
method of choice to investigate [NiFe] hydrogenases. Here, results of pulsed-ENDOR spectroscopy of
single crystals of the oxidized enzyme in the ‘ready’ Ni-B and ‘unready’ Ni-A states are presented. The
enzyme is characterized prior to catalytic activity and subsequent comparative investigations on the re-
duced form may reveal changes in the proton environment and contribute to the understanding of the
reaction mechanism of the enzyme. Since protons are usually not detectable in the X-ray structures of
proteins, the detection of the position of protons in the active centre gives information which are not
accessible by X-ray crystallography.
First principles, in particular Density Functional Theory (DFT), calculations can provide additional
insight into the electronic structure of transition metal complexes [90,101]. Evidence is here presented
that the ground state of the unpaired spin distribution in the active centre of [NiFe] hydrogenase in
the oxidized states can be described as a Ni 3d
!/
orbital overlapping with a sulphur p
g
orbital to yield a
delocalized S =
1
state. A natural bond orbital (NBO) analysis yields mutually orthogonal atomic orbitals
which are familiar to a chemist’s point of view. The resulting natural atomic orbitals (NAOs) recover the
picture of a Lewis (valence bond) structure concept. The isotropic and anisotropic hyperfine tensors
can be obtained directly from a DFT (Kohn-Sham) wavefunction. The isotropic hyperfine interaction is
related to the value of the wavefunction at the nucleus, the anisotropic hyperfine interaction is obtained
82 6. ENDOR Crystallography of the Oxidized States
by integrating over the spatial distribution of the spin density. This is the first application to systems as
complex as the active centre of a transition metal enzyme and supports the assignment of experimental
proton hyperfine tensors in the Ni-A and Ni-B oxidation states.
6.2 Materials and Methods
6.2.1 Protein Purification and Crystal Mounting
The membrane-bound hydrogenase from D. vulgaris Miyazaki F was isolated and purified according to
the published procedure [37]. By means of vapour diffusion, orthorhombic single crystals belonging to
space group P2
1
2
1
2
1
with four sites in the unit cell could be obtained which diffracted to more than 2.5
˚
A. Recently, an X-ray structure at 1.8 ˚
A resolution was published and revealed details of the active site
and its protein environment [28]. Protein single crystals of the approximate dimensions 1 mm
h
0.5 mm
h
0.5 mm were transfered to a Wilmad
K
4 mm o.d. quartz EPR tube in a sealed quartz container [196].
Care was taken to avoid an orientation along one of the crystal axes.
6.2.2 Computational Details
Geometry optimizations were performed with DGauss4.0 [175] on a Cray T3E supercomputer using
up to 128 processors. The DFT-optimized DZVP basis set of Godbout et al. [176] was applied. This
basis set was already successfully applied to the description of the electronic structure of blue-copper
proteins [177]. The Becke exchange functional and the Lee-Yang-Parr gradient-corrected correlation
functionals were used (BLYP) [92]. The recently developed HCTH functional [94] (also a ‘pure’, non-
hybrid functional) was shown to yield improved energetics for reaction barriers and significantly im-
proved geometries for transition metal compounds compared to the BLYP functional. The HCTH func-
tional was also used to validate the sensitivity of the results with respect to the optimized structures.
Starting from the X-ray structure, 42 and 41 atom cluster models (Ni-B and Ni-A, respectively) were
completely geometry optimized imposing no constraints on the structure. Cysteinyl amino acids were
represented by ethanethiolate (-S-CH
-CH
) groups. At the BLYP/DZVP and HCTH/DZVP geometry,
property analyses were done with Becke’s three parameter hybrid functional (B3LYP [95, 96]) in the
GAUSSIAN94 [165] suite of programs. A sufficiently large Pople-type basis set with added diffuse
and two sets of polarization functions (6-311*G(2d,2p)) was used. Essentially, it is a Wachters-Hay
all-electron basis set for first row transition metals [197,198] using the scaling factors of Raghavachari
and Trucks [199] and a McLean-Chandler [200,201] basis set for second row atoms. The polarization
6.2 Materials and Methods 83
functions are from [202]. This basis set was shown to yield accurate hyperfine parameters. Reviews of
the calculation of hyperfine coupling parameters from DFT are given in [122–124]. The isotropic Fermi
contact hyperfine interaction is related to the unpaired spin density at the corresponding nucleus by [78]
i
,546Rjlknmpo
qsr
t
QSu2TCu:QsvwTxvzy{|a}
1
0
4
j~vm
(6.1)
in which
T%u
is the Bohr magneton,
T%v
the nuclear magneton,
QAu
the free electron
Q
-value and
QSv
the
nuclear
Q
-value and
y{a}
is the expectation value of the
"
-component of the total electron spin. The spin
density at the nucleus
0
4
j~ vm
can be expressed as
0
4
j~vmo
@
@
y
j~Rvm
%s}
(6.2)
where
~v
is the position of the nucleus,
@
is the spin density matrix. The formula for the anisotropic
(dipolar) component is derived from the classical expression of two interacting dipoles [123]
,jlkmpo
b
QAu2TCu:QsvTxvy{|a}
1
@
@
y
|
~
CP
v
j~
v
,@ c
t
~Rvp@ ,l~v@ am
%s}
(6.3)
where
~
vo~c~v
. The integration was performed following [122,123]. The thus obtained hyper-
fine parameters are non-relativistic and of first-order only and may only be applied to ligand hyperfine
interactions where second-order effects are expected to be small. A natural bond orbital (NBO) analy-
sis [203,204] was performed to derive atomic spin populations which are less sensitive to the choice of
the basis set than Mulliken atomic spin populations. The transformation from the molecular basis set to
the minimal atomic basis is done by a occupancy-weighted symmetric orthogonalization. The resulting
natural atomic orbitals (NAOs) recover the picture of a familiar Lewis (valence bond) structure concept.
The occupation numbers of core orbitals is close to two, that of non-participating orbitals close to zero
while bonding orbitals have an occupation number close to unity. The electronic ground state was also
derived from a NAO analysis.
6.2.3 EPR and ENDOR Setup
All experiments were performed on a Bruker ESP 380 E FT-EPR spectrometer [205] equipped with a
dielectric ring cavity (ESP 380-1052 DLQ-H) and an Oxford cryostat (helium gas flow system).
One of the advantages of pulsed-ENDOR compared with cw-ENDOR is the fact that the length of
the pulse sequence can be shorter than relaxation effects in the sample. Also, the ENDOR effect of
pulsed experiments is much higher than that of continuous wave studies. In Davies-ENDOR the first soft
r
pulse (preparation) burns a hole with a width of
1oZ u!¡1
in the inhomogeneously broadened EPR
84 6. ENDOR Crystallography of the Oxidized States
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
mw
rf
preparation polarization transfer detection
¢ ¢d£2¤ ¢
¥
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
mw
rf
112 56 112
0 1000 12000 12600 t [ns]
8000
Figure 6.2: Davies-ENDOR.
line. The population of electronic sublevels is inverted with respect to an initial equilibrium state. When
the (mixing) radio frequency (RF) pulse is in resonance with one of the NMR transitions, the population
change of the electronic levels is detected as an increase of the echo amplitude. Davies-ENDOR signals
in the frequency range
p1
around the free nuclear Larmor frequency are suppressed. Mims-ENDOR
provides higher sensitivity for small hyperfine interactions which are centred around the free nuclear
frequency but suffers from the drawback of containing ”blind-spots” for certain pulse distances
¦
. Mims
thus can be considered as complementary to Davies type ENDOR. In the Davies-ENDOR experiment
the separation between first and second microwave pulses was 12
Y
s, the width of the first
r
-pulse was
112 ns (see Figure 6.2). The mixing radio frequency pulse was applied for 8
Y
s covering a range from
0.5-25.5 MHz. The echo was detected after a traditional Hahn-echo sequence (
r¨§
b
—
r
pulses).
6.2.4 EPR Data Analysis
The analysis of EPR spectra of single crystals of the [NiFe] hydrogenase of D. vulgaris Miyazaki F has
already been described elsewhere [179,183,196].
The transformation matrices between the three axes systems
©
the laboratory axes system (
Aª
b
ª
t
)
«
the crystal axes system (
i
ª!¬aª
) with crystallographic axes
i
ª!¬ª
®
the intrinsic coordinate system (
#
ª
$
ª
"
) in which
Q
and
Q
tensors are diagonalized to yield their prin-
cipal values
6.2 Materials and Methods 85
B0
3
12
a
b
c
x
y
z
IV
III
II
I
φ
θ
Laboratory axes system
Crystal
Figure 6.3: Definition of the laboratory axes system L, the crystal axes system Cand the intrinsic coordinate
system I.
have to be determined (see Figure 6.3).
¯
is the rotation matrix between the intrinsic coordinate axes
system
®
and the crystal axes system
«
. The columns of
¯
then are the direction cosines of the
Q
-tensor
axes
#
ª
$
ª
"
with respect to the crystal axes
i
ª!¬ª
. The four sites in the unit cell of space group symme-
try P2
1
2
1
2
1
are related by symmetry operations
°²±
(corresponding to 180
O
rotations around the crystal
axes).
The relation between the diagonal
Q
-tensor of one site
³S´¶µ
and those of the four sites per unit cell
is then
·
´
µ
o¸°¹±LB¯ºL
³
´
µ
La¯
³
LB°
³
±
ª »
o¸¼
ªBAª
b
ª
t
(6.4)
With
½
being the transformation matrix between crystal and laboratory axes systems and
¾jl¿
ª
|m
the
unit vector along the magnetic field
ÀÁ
the
Q
-values of the four sites can be calculated according to
QA,:jl¿
ª
xmÂoÃjl¾ÄLa½ÅL
·
´
µ
±
LR½
³
LB¾ÂmSÆ
Ç
(6.5)
or, explicitly,
Q,jl¿
ª
xmÂoÃjl¾ÄLa½ÅLB°²±CLB¯ÈL
³
´
µ
±
LB¯
³
°
³
±
LR½
³
LB¾ÂmSÆ
Ç
(6.6)
6.2.5 ENDOR Data Analysis
The total hyperfine tensor is accessible from ENDOR single crystal studies. If the g-tensor is assumed to
be isotropic, the spin Hamiltonian can be written as
É
oHQÊT¨ÀËLS̶cÍ
,
QAÎ,lTÎR,lÀËL
®
±ÏÑÐ
,
̹LÒ²±L
®
±
(6.7)
86 6. ENDOR Crystallography of the Oxidized States
where
,
is the hyperfine coupling tensor for the
»
th nucleus. In the high field approximation (elec-
tron Zeeman (
ÉÔÓ¨Õ
)
Ö
nuclear Zeeman (
É
v
Õ
), hyperfine interaction (
ÉÔ×ÙØ
)) the orientation-dependent
hyperfine splitting is observed in the principal axis system
#
ª
$
ª
"
of the hyperfine tensor
Ò
6
]
4
oÚj
SÛ
Ï
! Û
Ï
VÛ
m
1ÜAÝ
(6.8)
Here,
,,
are the principal values of the hyperfine tensor and the
Û
,
are the direction cosines of the
orientation of the hyperfine tensor axes with respect to the crystallographic axes. The energy expression
for ENDOR transitions with selection rules
+ßÞàÔo¸¼
and
+ßÞÍáâo
reads [206]
+ßãäoZåÞ
à
j
®
LaÒÈLÒÈL
®
mÏÍ
¡
.
cæbSÞ à¡
.
j
®
LRÒçL
®
m!è
1Ü
(6.9)
Since ENDOR transitions are usually given in frequency units one obtains
é
o
é
v
Ï
Þ
à
Ð
j
®
LÒÈLaÒL
®
mêc
bSÞà
é
v
Ð
j
®
LaÒL
®
m
(6.10)
where
Ð
é
v¸oH ¡
.
Ý
(6.11)
When restricting to the
{æo
1
case, the two ENDOR frequencies are
é
ë
o
é
v
Ïq
Ð
j
®
LÒÈLÒÈL
®
mì
é
v
Ð
j
®
LaÒÈL
®
m
(6.12)
with the upper sign referring to
ÞàoÚÏ
1
and lower signs to the
Þàoc
1
transitions. The spectrum
is no longer symmetric with respect to the free nuclear frequency
é
v
since the vector of the applied
magnetic field B
.
and the hyperfine field Aare not collinear. The expression reduces to a symmetric
splitting only if the hyperfine coupling Ais purely isotropic, or if the magnetic field lies along a principal
direction of A. The elements of Acan be directly determined from a fit of both transitions
é
and
é
(here shown for a special orientation in the xy plane with an angle
¿
to the magnetic field axis) [206]
Ð
b
é
v
j
é
c
é
mpo
îíVïsð
¿âÏ
2 ñðòôó
¿âÏõb
êðò5ó ¿íVïsð ¿
Ý
(6.13)
This approach still implies an isotropic
Q
-tensor but was already successfully applied to fit the ENDOR
transitions in
-irradiated artificial Fe-S clusters [207]. In [NiFe] hydrogenases, the anisotropy of the
Q
-tensor in Ni-B (
QA@ a@
= 2.31, 2.16, 2.01) is still modest with
ö
7% around
Q
W
, i.e. (
QcæQ
)/
Q
W
. In
analogy to Equation 6.5 the following approach was applied to fit the ENDOR spectra of all four sites
simultaneously
,jl¿
ª
|m
1Ü
oÚjl¾ÄL½÷La°²±øLa¯L
³
Ò²±øLB¯
³
°
³
±
La½
³
La¾Âm
ª »
où¼
ªBAª
b
ª
t
(6.14)
6.3 Results 87
The tensor is then diagonalized, and the principal values of
Ò²±
are determined in its principal axes
system. The experiments only give the square of the elements of the hyperfine coupling tensor, the
absolute signs of the hyperfine coupling constants therefore can not be deduced.
The total hyperfine coupling tensor
Ò
is composed of isotropic and anisotropic (dipolar) components
Òú,¨o
iÊûýüþ
ÿ
Ï Ò
ûýüþ
,
(6.15)
where
ÿ
is the unity matrix. The isotropic part is given by
iûýüþ
o
t
Òß,,¨o
tj
Ï
2 Ï
am
Ý
(6.16)
The anisotropic contributions are obtained from
Ò
ûýüþ
,,
oùÒú,,xc
iûýüþ
ÿª »
o #
ª
$
ª
"
(6.17)
6.3 Results
6.3.1 cw-EPR
Initially, rotation angle-dependent cw-EPR spectra (in steps of 5 deg) were recorded at T = 80 K in
order to determine the quality of the single crystal and its orientation in the laboratory axes system.
The orientation of the
Q
-tensor in the crystal axes system was already determined before and checked
again [179,183]. Below T = 77 K the Ni EPR signal is superimposed by an intense signal at
Q
= 2.02
from a [3Fe-4S] cluster [39,208]. This prevented ENDOR measurements of some EPR signals below
Q
2.03. Figure 6.4 shows the angular dependence of the EPR signals with an arbitrary rotation angle
¿
in steps of 5 degrees.
The ratio of Ni-B to Ni-A is approximately 70
\
to 30
\
as determined from dissolved single
crystals [179,196]. For the space group
b1b1b1
there are four sites of the protein molecule in the unit
cell. Depending on the orientation of the crystal with respect to the magnetic field
ÀÁ
one expects a
varying number of EPR transitions. In an arbitrary orientation, four EPR signals corresponding to the
four sites per unit cell are to be seen. If the magnetic field is along one crystal plane, two EPR signals are
expected (the two are pairwise degenerate). In the special case when the magnetic field is exactly along
one of the crystal axes, only one EPR transition can be observed (all four sites are degenerate).
In the angular-dependent EPR spectra (Figure 6.4) between three and seven lines are observed which
correspond to the presence of two paramagnetic species (Ni-A and Ni-B) in the crystal. The EPR spectra
of both forms show the periodicity of 180
O
which is expected from the space group symmetry of the
88 6. ENDOR Crystallography of the Oxidized States
Θ
90
0
10
20
30
50
40
60
Rotation Angle
70
190
100
110
120
130
140
80
150
160
170
180
Figure 6.4: Angular-Dependence of the EPR line positions of protein single crystals of the [NiFe] hydroge-
nase from D. vulgaris Miyazaki F. Parameters: T = 80K, microwave frequency 9.728 GHz, field modulation
100 kHz, modulation amplitude 0.5 mT, microwave power 0.4 mW.
crystal. Initially, the more intense EPR signals were fitted. They were shown to originate from the Ni-B
form. Next, the weaker EPR signals (from Ni-A) were analyzed. For each form, all four sites were fitted
simultaneously, taking into account the symmetry operations between each site. EPR is used here to
distinguish between the Ni-A and Ni-B forms in the single crystal and assign sites I-IV to each form.
Details of the assignment of specific sites and the discussion of the
Q
-tensor orientation can be found
in [190,209] and are not repeated here. The most plausible assignment of the
Q
-tensor principal axes
system to the molecular structure is such that the
QA
-axis in both forms Ni-A and Ni-B is oriented along
the Ni–S(Cys549) bond (deviation 6
O
in Ni-A and 11
O
in Ni-B) and that
Q
- and
Q
-axes are rotated by
6.3 Results 89
3
O
. The ground state for both forms was determined to be
!/
based on a ligand field analysis [66,196]
with an orientation of the special
"
-axis along the Ni–SCys549 bond.
6.3.2 Pulsed-EPR
Pulsed-EPR spectroscopy (T = 10 K) with the same pulse lengths later used in the ENDOR experiments
(56 ns and 112 ns for
r
/2- and
r
-pulses, respectively) was applied (see Figure 6.5, top). The orientation
of the crystal in the EPR tube was reconfirmed and it was ensured that site separation and Ni-A/Ni-B
separation was still achieved under the chosen conditions. It was possible to show that the excitation
= 120 degreesΘ
Rotation Angle
297
307
317
327
B [mT]
Ni−B
2x Ni−B
Ni−B
Ni−A
Ni−A
Ni−A Ni−A
4th site
2nd site
3rd site
2nd site 1st site
4th site
1st site
3rd site
Figure 6.5: Pulsed-EPR of the single crystal of the [NiFe] hydrogenase from D. vulgaris Miyazaki F. Top:
pulse sequence and pulse lengths; bottom: pulsed-EPR spectrum at the rotation angle of
= 120
. (centre
field at 312 mT, sweep-width 30 mT, T = 10 K) Arrows indicate the contribution of each paramagnetic species
(Ni-A and Ni-B) to the EPR signal. The enumeration of each site in the unit cell (1-4) is arbitrary and used
only in order to differentiate their individual contributions to the pulsed-EPR and subsequent pulsed-ENDOR
spectra at the chosen field value.
bandwidth (8.9 MHz) is small enough to ensure site separation. Inhomogeneous line broadening did
not affect the site separation and separation of Ni-A/Ni-B species. Angular-dependent pulsed-EPR (field
swept echo) of the paramagnetic species in the crystal were recorded at T = 10 K in steps of 10 degrees
90 6. ENDOR Crystallography of the Oxidized States
prior to ENDOR experiments (complete data set not shown). The field position of each EPR resonance
transition was measured and chosen for a subsequent Davies pulsed-ENDOR experiment. Only one
typical example is shown here.
Figure 6.5 (bottom) shows the pulsed-EPR spectrum that was recorded at an rotation angle of 120
O
(see Figure 6.4). The assignment of the Ni-A and Ni-B forms and the four sites in the unit cell for
each species to the pulsed-EPR signals was done on the basis of the single crystal cw-EPR spectra. The
analysis of the
Q
-tensor magnitudes and orientations allowed a distinction between the different species
and sites. The EPR signal at 310 mT corresponds to one site (labelled 4th site) of Ni-B only (see Figure
6.5). Thus, an ENDOR spectrum recorded at this rotation angle and this field value is expected to exhibit
features of one site of Ni-B only. The pulsed-EPR spectrum at 314 mT is a superposition of two sites
from the Ni-B species (site 2 and 3) and one site from the Ni-A form (site 1). In an ENDOR experiment,
one would thus expect contributions according to this composition. In addition, contributions from the
neighbouring 1st site of Ni-A (peak at 316 mT) are also expected. At this rotation angle, pulsed-ENDOR
spectra at five different field values were subsequently collected (see trace at 120
O
in Figure 6.6).
6.3.3 Pulsed-ENDOR
Figure 6.6 shows the field positions selected for pulsed-ENDOR measurements. Since the crystal con-
tained predominantly Ni-B, the ENDOR effect was more pronounced for this form and the spectra dis-
played a better signal to noise ratio. Figure 6.7 shows the rotational angular-dependent pulsed-ENDOR
spectra of the four separate sites of Ni-B. The numeration is only used to label the four magnetically
distinguishable sites in the unit cell. Angular-dependent ENDOR spectra (Figure 6.7) could be followed
over a complete range of 180
O
. The spectra were adjusted to the free nuclear frequency which is also
field-dependent, and plotted centred around
é
×
. No spectra are shown (straight line is given) for a few
field values below g = 2.03 since the ENDOR spectra contained contribution of the paramagnetic [3Fe-
4S] cluster. At some field positions, a superposition of different Ni-B sites is obtained, furthermore
overlap with spectra from Ni-A could not always be avoided. Via the cw- and pulsed-EPR experiments
and the subsequent fit of the EPR spectra, the composition of each ENDOR spectrum at each field posi-
tion could, however, be accurately determined.
Starting from the field positions where only Ni-B and only one specific site was selected (‘single-site
ENDOR’), the ENDOR lines could be followed over the complete range of rotation angle. In Figure 6.7
clearly two hyperfine split line pairs at
ö
5-6 MHz around the free proton frequency can be detected.
They vary only slightly with the rotation angle and thus indicate a large isotropic hyperfine coupling
with a small anisotropic contribution. There is a further hyperfine interaction which appears outside the
6.3 Results 91
Θ
Rotation Angle
20
10
60
70
80
90
120
130
140
150
160
170
180
190
0
30
100
110
40
50
Figure 6.6: Selection of field positions for ENDOR in the angular dependent EPR spectra of single crystals
of [NiFe] hydrogenase. The positions of subsequent pulsed-ENDOR measurements are marked by arrows.
matrix and shows a significant angular dependence (ranging from a hyperfine coupling of
1-2 MHz at
= 0
to 8-9 MHz near 100
for site 1 of Ni-B). Here, isotropic and anisotropic hyperfine interactions
are of similar magnitude. The proton matrix range is very broad and a number of peaks can still be
detected in the
1-2 MHz range around
. The large number of hyperfine interactions, however,
makes it impossible to follow them over the complete rotation angle. The analysis and interpretation of
the angular-dependent pulsed-ENDOR spectra which correspond to the Ni-A form (see Figure 6.8) is
more complicated. The spectral resolution is not as good as for Ni-B since the ENDOR resonances are
broader. The two largely isotropic hyperfine interactions at
5-6 MHz around the free proton frequency
92 6. ENDOR Crystallography of the Oxidized States
are also present but not completely be resolved and appear as one broad signal. The angular dependence
of the ENDOR transitions could, however, not be fitted with the approach given above. This might be
due to the following reasons:
Ni-A is only the minority species in crystal of D. vulgaris Miyazaki F which complicates the
analysis.
Relaxation characteristics might be different for Ni-A and the pulse experiments were not specifi-
cally optimized for this species.
Ni-A could also possess a more heterogeneous environment; this is indeed indicated by higher
temperature factors of some cofactors in the Ni-A containing single crystals of D. gigas [27,32].
Despite these difficulties several statements about the Ni-A form can be made. The large couplings of
the Ni-B form are also present in Ni-A. The third hyperfine coupling of Ni-B with significant angular
dependence is absent in the Ni-A spectra. Where peaks of such a coupling can be seen in Figure 6.8 they
stem from a contribution of the Ni-B form to the Ni-A spectra (superposition of Ni-A and Ni-B sites).
6.3 Results 93
Figure 6.7: Pulsed-ENDOR spectra of Ni-B in protein single crystals from D. vulgaris Miyazaki F.
94 6. ENDOR Crystallography of the Oxidized States
Figure 6.8: Pulsed-ENDOR spectra of Ni-A in protein single crystals from D. vulgaris Miyazaki F.
6.3 Results 95
6.3.4 Analysis of ENDOR Spectra
Initially, the matrix
relating laboratory and crystal axes systems, was held fixed in the fits of the
ENDOR spectra since it was already determined in the analysis of the cw-EPR spectra. The crystal
orientation was not changed between the cw-EPR and pulsed-ENDOR experiments and thus
had to
remain constant within error. In this way, the number of fitting parameters was reduced from 9 to 6 and
facilitated the analysis. After satisfying fits were achieved, also the values of
were allowed to vary
but did not change drastically (at most a deviation of 3
was observed).
Figure 6.9 shows the results of the obtained fits for the three hyperfine interactions in Ni-B. All three
hyperfine tensors were simultaneously fitted for all four sites of Ni-B. The colour code distinguishes
the four magnetically inequivalent sites in the unit cell. The agreement between measured ENDOR
transitions (points) and fitted curves (solid lines) is very good. The deviation of fitted curves from
experimental data was less than 100 kHz, i.e. smaller than the linewidth. The largest coupling A
ranges
from 11-13 MHz (top of Figure 6.9) , the second coupling A
covers a range from 10-11 MHz (middle
of Figure 6.9) and the third coupling A
ranges from 2-8 MHz (bottom of Figure 6.9) . The results
of the fitted hyperfine tensors are given in Table 6.1.
are the obtained principal values of the total
hyperfine tensor and the direction cosines
!#"%$'& ()$'& *+$-,/.10324,/56,%7
describe the orientation of the hyperfine
tensor principal axes
2,/58,%7
in the crystal axes system
9:,<;=,%>
.
A
and A
both exhibit a large isotropic hyperfine interaction of 12.85 MHz and 10.67 MHz, respec-
tively. This indicates that the protons associated with these hyperfine tensors must be connected to an
atom which bears unpaired spin density. The values correspond to the range of ENDOR couplings (A
11-13.5 MHz, A
10.1-11.1 MHz). This provides evidence thatthe signs ofthe hyperfine principal values
of these coupling must all be positive or negative yielding the maximum isotropic hyperfine contribu-
tion. The possibility that all principal values of the hyperfine tensor have negative signs (this would yield
isotropic hyperfine interaction with opposite, negative signs) can be ruled out (see Discussion, below).
The anisotropic traceless contribution labelled A
?
$@$
in Table 6.1, in some cases deviates from axiality
(A
?
$@$
(axial) = ( -A
A/$CB
, -A
A/$CB
, 2 A
A%$ B
). Very often, the interpretation of ENDOR hyperfine couplings is
done under the assumption of axial hyperfine tensors in which the ‘dipolar’ axis is the special axis. For
A
A
?
$@$
= (4.19, -1.71, -2.47) axiality is not fulfilled, indicating a more complex hyperfine interaction than
that of classic expansionless spins. In the case of A
, axiality is nearly fulfilled A
?
$@$
= (1.09, -0.54, -0.55)
which might be explained by a larger distance between the coupled nuclear and electron spins. This is
also reflected in the lower values of the elements of the anisotropic hyperfine tensor since that indicates
a larger distance between electron spin and nuclear spin.
96 6. ENDOR Crystallography of the Oxidized States
30 60 90 120 150 180
2
3
4
5
6
7
8
9
30 60 90 120 150 180
11
11.5
12
12.5
13
13.5
HFC A [MHz]HFC A [MHz]
30 60 90 120 150 180
10
10.2
10.4
10.6
10.8
11
HFC A [MHz]
Θ
A1 11-13 MHz
A2 10-11 MHz
A3 2-8 MHz
Rotation Angle
Figure 6.9: Fit of three hyperfine tensors of angular dependent pulsed-ENDOR spectra of Ni-B in protein
single crystal of D. vulgaris Miyazaki F. The colour code refers to the four magnetically distinguishable sites
in the unit cell.
A
exhibits a smaller isotropic hyperfine contribution which is only half of that of A
and A
(a
$EDGF
=
5.20 MHz). Again, this value is the isotropic part estimated from the angular dependence of the complete
hyperfine tensor from 2.5-8.1 MHz. The signs of the complete hyperfine tensor A
must again be chosen
to be all positive or negative to yield this isotropic value. The resulting anisotropic hyperfine tensor A
?
$H$
= (3.07, 2.14, -5.20) also significantly deviates from axiality.
6.3 Results 97
Table 6.1: Hyperfine tensor principal values and direction cosines of hfccs for Ni-B (‘ready‘-state) in [NiFe]
hydrogenase from D. vulgaris Miyazaki F (T = 10 K)
x y z
A
A
$H$
17.04 11.14 10.38
l
"%$
0.511 -0.410 0.755
l
()$
-0.308 -0.908 -0.285
l
*+$
0.803 -0.087 -0.590
a
$IDJF
12.85
A
?
$H$
4.19 -1.71 -2.47
A
A
$H$
11.76 10.13 10.12
l
"%$
0.605 0.723 -0.335
l
()$
0.023 0.404 0.915
l
*+$
0.796 -0.561 0.227
a
$IDJF
10.67
A
?
$H$
1.09 -0.54 -0.55
A
A
$H$
8.27 7.34 0.00
l
"%$
0.110 0.738 -0.666
l
()$
-0.977 -0.041 0.208
l
*+$
-0.181 0.674 0.716
a
$IDJF
5.20
A
?
$H$
3.07 2.14 -5.20
A
KHK
: HFC-tensor principal values (i = x,y,z);
l
LK
: Direction cosines of HFC-tensor principal axes (i = x,y,z) in the crystal axes system (k = a,b,c) for one of the
four magnetically inequivalent sites.
6.3.4.1 Assignment of
NM
and
O
In the rotation-dependent pulsed-ENDOR pattern (Figure 6.7) of the Ni-B state, signals which were
later labeled A
and A
appear pairwise and exhibit a similar angular dependence. Consequently, it
can be assumed that the signals stem from a pair of protons of the same residue in close proximity to
each other. The large isotropic contributions of 12.85 MHz and 10.67 MHz, respectively, indicate that
they are either bound directly to a spin-bearing atom or they are bound in the vicinity of the spin-bearing
atom and aquire isotropic hyperfine interaction via hyperconjugation. The anisotropic contribution of the
98 6. ENDOR Crystallography of the Oxidized States
hyperfine tensor A
?
$H$
was used in order to assign A
and A
. Protons were added to the X-ray structure of
the D. vulgaris hydrogenase [28] by means of the INSIGHTII software [210] and an algorithm based on
standard bond lengths, bond angles and dihedral angles. From the anisotropic hyperfine interaction the
component with the largest value was considered to be along the dipolar axis. The deviations between
the corresponding direction cosines and Ni–H vectors of possible candidates were calculated. The results
are given in Table 6.2.
Table 6.2: Deviation [degree] Between Dipolar Axes and Ni–Proton Vectors for Ni-B in [NiFe] Hydrogenase
of D. vulgaris Miyazaki F
Hyperfine Tensor
Proton A
A
A
Cys81 H1 56 69 19
Cys81 H2 89 83 17
Cys84 H1 51 54 63
Cys84 H2 47 59 80
Cys546 H1 29 41 43
Cys546 H2 52 68 27
Cys549 H1 38 18 89
Cys549 H2 16 6 82
X553 H 80 85 14
Minimum deviations are given in bold and correspond to most probable assignments (see text for details).
For A
QP
-CH
protons of cysteines Cys81, Cys84, Cys546 can be excluded since the deviations are
56, 89, 51, 47, 29, and 52 degrees, respectively. Also, a protonated bridging ligand X533 can be ruled
out since the angle between dipolar axis and Ni–X553 H vector is 80 degrees. The minimum deviation
for A
is obtained for one of the
P
-CH
protons of cysteine Cys549 (Cys549 H2 with angle of 16
).
The same also holds for A
for which deviations of less than 20
were only obtained for the two
P
-
CH
protons of cysteine Cys549 (18 and 6 degree, respectively). Since Cys549 H2 was already assigned
to A
, the hyperfine tensor A
must be assigned to the second proton Cys549 H1. This is in agreement
with the cw-ENDOR orientation-selected study of the Ni-B form in Allochromatium vinosum [169].
The two large hyperfine interactions exhibited isotropic contributions of 12.5 and 12.6 MHz. From
comparison of the dipolar axes with Ni–proton vectors in the molecular structure they were shown to
originate from
P
-CH
protons of the bridging cysteine Cys533 (Cys549 in D. vulgaris enumeration of
6.3 Results 99
amino acids).
The assignment of A
and A
to
P
-CH
protons of cysteine Cys549 has to be considered to be on
firm grounds. The
R
-tensor of Ni-B was shown to have its
RTS
-axis along the Ni–S(Cys549) bond [183].
In the oxidized states, the Ni atom is assumed to be in a formal Ni(III) oxidation state with the unpaired
electron in a 3d
S
orbital. The five-fold coordination of the Ni is square-pyramidal in the oxidized forms
(four cysteinyl sulphur atoms and the bridging ligand bind to the Ni atom). The open coordination site
is opposite the Ni–S(Cys549) bond which makes that Ni–S bond a special axis. The spin bearing orbital
was assumed to be along the Ni–S(Cys549) bond. The isotropic hyperfine contributions of A
and A
indicate a significant spin delocalization into the sulphur p
S
orbitals of Cys549. The
P
-CH
protons thus
couple directly to the fraction of spin on the sulphur atom of Cys549 and also to that at the Ni atom (see
Figure 6.10).
Ni
U
C
V
H
H
Cys
V
549/533
S
W
Figure 6.10: Bonding situation for the
X
-CH
Y
protons from cysteine Cys549. They may couple to both the
fraction of unpaired spin at the cysteinyl sulphur atom and that at the Ni central atom.
This complicated coupling scheme may explain the rather large deviations of 16 and 18 degrees
between the dipolar axes and the corresponding Ni–H vectors for the cysteine Cys549. The deviation
from axiality and the large deviation of the direction cosines from the Ni–H vectors in Ni-B of the [NiFe]
hydrogenase from Allochromatium vinosum were analyzed [169]. The anisotropic hyperfine tensor was
simulated for the situation where the
P
-CH
protons couple simultaneously to a nickel atom and a sulphur
atom or to one of them alone. The spin populations at the Ni was varied from 1 to 0.5 and that on the
sulphur atoms was increased from 0 to 0.5. Both the X-ray coordinates from the D. gigas structure
and the DFT optimized cluster model were used. Best agreement with the experimentally determined
hyperfine tensors was found for the case where the spin density
Z
at the Ni is 0.5 and at the sulphur is
0.3. The remaining 0.2 were delocalized over the complete cluster. This is also in good agreement with
the calculated atomic spin populations (see Chapter 5).
The isotropic hyperfine interactions of 12.9 and 10.7 MHz indicate dihedral angles between the
P
-
CH
protons and the sulphur p
[
orbital of equal magnitude (see Figure 6.11).
100 6. ENDOR Crystallography of the Oxidized States
CH
H
Cys549/533
Φ
Figure 6.11: Newman projection and definition of the dihedral angle
\
of
X
-CH
Y
protons with respect to the
3p
]
orbital of the cysteinyl sulphur atom
In general, the angular dependence is of the form
9$EDGF 0_^`Zbadcfehgi^kjmlonqp
qrts
jvuxwGy
with
s
the
dihedral angle and
u
=
z
/2 [177].
e
and
^
are system-specific constants and not known for hydrogenase.
The largest coupling arises when one C-H bond is collinear with the sulphur p
[
orbital and minimum
coupling is achieved when the C-H bond is perpendicular to the lobes of the
{
-orbital. The positive sign
of the isotropic hyperfine interaction of the
P
-CH
protons can be explained by an analogy to organic
radicals where the sign of the spin density at the proton nucleus next to a C
|
carbon atom is determined
by hyperconjugation.
6.3.4.2 Assignment of
~}
The third proton with the hyperfine tensor A
is only present in Ni-B (see Figure 6.7) and absent in Ni-A
(Figure 6.8). The hyperfine interaction A
in Ni-B exhibits an isotropic contribution of 5 MHz (Table
6.1) which is only half of that of A
and A
. A proton directly bound to a nucleus with a significant
amount of unpaired spin density in the active centre of [NiFe] hydrogenase can thus be excluded. One
therefore has to find the proton that is associated with an isotropic coupling of that magnitude in the Ni-B
form but absent in Ni-A.
The anisotropic hyperfine tensor A
?
$@$
= (3.07, 2.14, -5.20) has its large component along the A
S
axis
but also deviates from axiality. From a comparison of the dipolar axis of the hyperfine tensor A
with
that from Ni–H vectors in the X-ray structure of D. vulgaris, two possibilities remain (see Table 6.2).
The angle between the dipolar axis and Ni–H vectors is small for
P
-CH
protons of the terminal cysteine
Cys81 (19 and 17 degrees), large for all other
P
-CH
cysteinyl protons in question and minimum for a
possibly protonated bridging ligand X (deviation between dipolar axis and X553 H 14
) spanning Ni and
Fe in the active centre. It was investigated whether DFT calculations could contribute to the resolution
of this ambiguity in the assignment of
}
.
6.3 Results 101
6.3.5 DFT Calculations of the Electronic Ground State
DFT calculations can accurately reproduce the structural parameters of [NiFe] hydrogenase (see Chapter
5). Good agreement between experimental and BLYP/DZVP calculated bond lengths and angles was
found for the X-ray structure of D. gigas when the bridging ligand was an oxygen species, e.g. a OH
for Ni-B and a O
for Ni-A. The consideration of a sulphur bridging ligand led to bond distances,
especially Ni
Fe distances, that were significantly larger than those obtained from X-ray analysis (see
Chapter 5). 2 CN and 1 CO ligand were chosen as non-protein ligands to the iron atom since a SO ligand
did not lead to a reasonable spin density distribution (see Chapter 5).
Table 6.3 gives structural data for the cluster models of the Ni-A and Ni-B state which were used here
in the calculation of the
H hyperfine couplings. The structures were re-optimized from those in Chapter
5 using a finer integration grid and tight convergence criteria (5
10
in gradient, 1
10
6
in energy). The
obtained BLYP/DZVP and HCTH/DZVP optimized geometries are very similar (see Table 6.3). Usually,
the HCTH functional leads to bond lengths that are shorter than those of the BLYP functional. This was
also found in [94]. The difference in bond lengths can be as much as 0.05 ˚
A for the Fe–S distances and
0.04 ˚
A for the Ni
Fe distance. Bond angles agree to within 0.5 degrees between the two functionals.
The calculated structural parameters which were obtained with the HCTH functional, especially the Ni
Fe and Ni
X bond distances and the Ni–X–Fe bond angle, agree slightly better with those from
X-ray analysis for D. gigas [27] than those calculated with the BLYP functional. One has to bear in
mind the experimental uncertainties in structural parameters from X-ray structures (ca. 0.2 ˚
A at 2.0 ˚
A
resolution). The calculated structural parameters do not agree with those from the X-ray structure of the
[NiFe] hydrogenase from D. vulgaris Miyazaki F [28] (for a Discussion see Chapter 5).
Single point calculations at the optimized geometries and subsequent analyses of the Kohn-Sham
wavefunction provide insight into the electronic structure of the active site. It was shown by crystal field
analysis that the ground state of the oxidized enzyme may correspond to a Ni(III) with a 3d
S<
ground
state [66]. This assumption was the basis for the assignment of the
R
-tensor orientation in the oxidized
states [179,183]. In the calculations, the Ni is in its formal Ni(III) oxidation state, coordinated by four
cysteine amino acid residues. The iron atom is in its formal Fe(II) oxidation state and ligated by one
CO and two CN
. The position of the bridging ligand is occupied by either an OH
(Ni-B) or an O
(Ni-A) ligand leaving the Ni in a five-fold, square-pyramidal coordination sphere. A natural atomic
orbital (NAO) analysis was performed in order to determine the orbital occupancy of the Ni atom and
gain insight into the electronic structure of the active site.
Table 6.5 gives the total atomic spin densities as obtained from the NAO analysis, the orbital occu-
102 6. ENDOR Crystallography of the Oxidized States
Table 6.3: Comparison of selected structural parameters from X-ray and DFT optimized models of the oxi-
dized active centres of [NiFe] hydrogenase.
exp. BLYP/DZVP HCTH/DZVP
D. gigas [27] D. vulgaris [28] X= O
Y<
X= OH
X= O
Y<
X= OH
Ni
<
Fe 2.90 2.55 2.94 3.04 2.90 3.00
Ni–SCys549(533) 2.62 2.37 2.48 2.53 2.48 2.50
Ni–SCys84(68) 2.58 2.38 2.40 2.36 2.35 2.33
Ni–SCys546(530) 2.27 2.33 2.40 2.31 2.39 2.28
Ni–SCys81(65) 2.16 2.22 2.46 2.29 2.46 2.27
Ni
<
X 1.74 2.16 1.85 1.98 1.81 1.96
Fe–SCys549(533) 2.20 2.37 2.62 2.46 2.57 2.40
Fe–SCys84(68) 2.23 2.14 2.52 2.46 2.47 2.41
Fe
<
X 2.14 2.22 1.94 2.08 1.93 2.07
Ni-X-Fe 96.5 71.0 101.7 96.8 101.5 96.1
Ni-SCys549(533)-Fe 73.6 64.1 70.2 75.0 69.9 75.4
Ni-SCys84(68)-Fe 73.9 66.2 73.4 78.0 73.8 78.5
The enumeration of amino acid residues corresponds to that of D. vulgaris Miyazaki F. The related sequence
number of D. gigas is given in parentheses.
pation of the unpaired spin and the natural orbital configuration for the Ni-B form.
63% of the unpaired spin rest on the Ni atom, this is qualitative agreement with the
Ni hyperfine
splitting of isotope-enriched hydrogenases [59]. The difference to the results of the spin population
presented in Chapter 5 (0.52) may originate from the use of different functionals, basis set, integration
schemes etc.. The Fe atom only possesses 1% of the spin density which agrees with the absence of
any
Fe-ENDOR effect in isotope-enriched samples of Ni-B [61]. One of the sulphur atoms bears
significant spin density (23%, the sulphur atom of the bridging cysteine 533). This agrees well with the
observed hyperfine splitting in EPR due to one
/
S nucleus [62]. The spin density at the remaining other
three cysteinyl sulphur atoms is 0.02, 0.03, 0.07, respectively (data not included in Table 6.5) and is thus
significantly smaller than that of the cysteine 533. 86% of the unpaired spin density resides alone in the
bond Ni–S
8 D
%
. A closer inspection of the orbital occupancies of the unpaired spin at the two nuclei
gives the following picture: The largest fraction of the unpaired spin density is in the Ni 3d
S<
orbital, but
6.3 Results 103
Table 6.4: B3LYP/6-311G NAO analysis of the Ni-B state.
Total Atomic Natural Orbital Natural
Atom Spin Population Spin Occupancy Electron Configuration
3d
0.027
3d
S
0.204
Ni 0.63 3d
S
0.055 [core] 4s
3d
4p
5s
3d
0.003
3d
S<
0.341
3d
0.001
3d
S
0.001
Fe 0.01 3d
S
0.001 [core] 4s
3d
5s
4d
3d
o
0.005
3d
S<
0.007
3p
0.076
SCys549 0.23 3p
0.000 [core] 3s
3p
4s
4d
3p
S
0.149
also a significant amount in the 3d
S
orbital. The 3d
S
, 3d
3d
orbital occupancies are smaller. At
the sulphur atom of cysteine 533, the largest fraction of unpaired spin density resides in the 3p
S
orbital,
about half as much in the 3p
and zero in the 3p
orbital. This shows that the ground state of the nickel
atom in the Ni-B state is indeed composed of mainly a 3d
S
orbital with a slightly smaller contribution
from the 3d
S
orbital.
If the Ni orbital occupation were purely 3d
S<
(
= 0) then one could not explain the deviation of the
R
- and
RT
-values from
R
by 0.33 and 0.16, respectively. For a pure 3d
S
ground state,
R
-values much
closer to
RT
are expected (for an example see Chapter 4, Ni(CO)
H). The admixture of 3d
S
character
(
Q0
0) can contribute to the
R
-tensor via spin-orbit coupling and induce
R
-values larger than
R
.
The bonding situation of the Ni atom is characterized by a NBO analysis as follows: The sulphur
nuclei of Cys81 and Cys530 form two single bonds with the Ni atom. The bonds are S
Ni donor
bonds with a contribution of 76% from the sulphur (of which 5% are from s- and 95% from p-orbitals)
and 24% from the Ni (of which are 44% from s-, 0.6% from p- and 55% from d-orbitals). Furthermore,
there are two anti-bonding orbitals with reversed contributions (24% from S and 76% from Ni atoms).
For the
-spin, there is an additional single bond between the sulphur from Cys549 (71% S, 29% Ni)
and the corresponding anti-bonding (25% S and 75% Ni) interaction. This bond is not present for
P
-spin
104 6. ENDOR Crystallography of the Oxidized States
orbitals and thus shows that the unpaired spin resides in that bond. This is an a posteriori justification of
the assumptions made in the analyses of experimental
R
-tensor orientations [179,190].
A Ni(0) has the electron configuration [core] 4s
3d
, Ni(I) [core] 4s
3d
, Ni(II) [core] 4s
3d
and
Ni(III) [core] 4s
3d
. From the natural atomic configuration (Ni [core] 4s
3d
) it becomes obvious
that the oxidation state, however, is not a formal Ni(III) but due to sulphur–Nickel donation its charge
is reduced. The nickel atom can be described as a Ni(+1.2). The relation between the formal oxidation
state and the actual charge on an atom is not straight forward. Nevertheless, the discussion of formal
oxidation states is frequently done in the field of bioinorganic chemistry. The stabilization of high Ni
oxidation states by sulphur ligands can be explained by a favourable energetic proximity of S 3p- and
Ni 3d-orbitals. The covalency of S–Ni bonds then leads to a compensation of the charge on the central
metal atom.
The same argumentation also holds for the Ni-A state (see Table 6.5).
Table 6.5: B3LYP/6-311G NAO analysis of the Ni-A state.
Total Atomic Natural Orbital Natural
Atom Spin Population Spin Occupancy Electron Configuration
3d
0.235
3d
S
-0.167
Ni 0.88 3d
S
0.042 [core] 4s
3d
4p
5s
3d
o
0.175
3d
S<
0.591
3d
-0.008
3d
S
-0.009
Fe -0.05 3d
S
-0.009 [core] 4s
3d
5s
4d
3d
o
-0.012
3d
S
-0.012
3p
0.018
SCys549 0.12 3p
0.003 [core] 3s
3p
4s
4p
3p
S
0.084
The atomic spin population at the Ni is increased to +0.88, that of the bridging sulphur of the cysteine
533 decreased to 0.12. The Fe still bears only a small amount of spin density (5%) possibly due to spin
6.3 Results 105
polarization from the Ni atom via the O
bridge. The bridging ligand O
would acquire itself unpaired
spin density (0.3) and transfer it from the Ni to the Fe atom. This might explain the small but detectable
Fe-ENDOR signal in Ni-A [61] and an increased hyperfine splitting in
O
treated samples in Ni-
A compared to Ni-B [63] . The numbers given here must be critically discussed. The atomic spin
populations significantly differ from those given in Chapter 5. The B3LYP functional has a bias towards
higher spin contaminations compared to the pure GGA functionals since more ‘ionic’ contributions are
considered from the Hartree-Fock exchange. As a result, the expectation value of the S
operator differs
from that expected for a S = 1/2 state (S(S+1) = 0.75), for the B3LYP/6-311G calculation the
t
value
was 1.0001. This indicates contributions from spin states different from S = 1/2 to the Kohn-Sham
wavefunction.
The natural orbital configurations do not change on the Ni and Fe atoms (cf. Tables 6.4 and 6.5).
The Ni atom remains in its Ni(+1.2) state in agreement with results from EXAFS experiments [55,186]
which do not point to a change of electron density at the Ni.
6.3.6 DFT Calculated Hyperfine Tensors
Table 6.6 gives the calculated isotropic and anisotropic hyperfine coupling constants for the Ni-B case in
which the bridging ligand is OH
and 2 CN and 1 CO are the non-protein ligands to the Fe atom. The 6-
311+(2d,2p) basis set was used with a diffuse function on all heavy atoms and two sets of d-functions for
S,C,O,N (respectively f-functions for Ni and Fe) and two sets of p-functions for hydrogen atoms (1231
basis functions for a Ni-B, 1220 basis functions for a Ni-A cluster model). A single point calculation at
the BLYP/DZVP optimized geometry was carried out. The B3LYP functional is known to yield good
agreement between experimental and theoretical hyperfine coupling constants for organic radicals (for a
review, see [124,125]). Calculations with the Becke exchange and Perdew correlation functional (BP86)
were also performed using the same geometry and basis set.
Despite recent arguments against the classification of ‘spin contamination’ in DFT methods [211],
the term will be used here in the same context as in HF theory (see for example [212]). The effect of
spin-contamination on the calculated hyperfine coupling parameters is pronounced since the expectation
value of the
S
operator enters the formulae for the isotropic (Eq. 6.1) and anisotropic (Eq. 6.3) hyper-
fine interactions. The spin contamination for the B3LYP calculation is significantly larger (0.8153) than
in the BP86 case (0.7589). For a doublet, the exact expectation value
t
is 0.75. The deviation origi-
nates from the contribution of spin states of higher multiplicity. The isotropic (Fermi contact) hyperfine
interaction is most sensitive to the choice of basis set and functional. The largest value is obtained for
the two
P
-CH
protons of cysteine Cys549 (Cys533 in D. gigas nomenclature) 12.65 and 13.69 MHz
106 6. ENDOR Crystallography of the Oxidized States
Table 6.6: DFT Calculated Isotropic and Anisotropic
H-Hyperfine Coupling Parameters [MHz] in Ni-B
Functional/Basis B3LYP/6-311+G(2d,2p) BP86/6-311+G(2d,2p ) B3LYP/6-311+G(2d,2p)
Geometry BLYP/DZVP BLYP/DZVP HCTH /DZVP
¡£¢
/¤
0.8153 0.7589 0.7988
a
¥§¦'¨
A
©ª¥§¦'¨
a
¥ ¦'¨
A
©/ª¥ ¦'¨
a
¥§¦'¨
A
©/ª¥§¦'¨
Proton
Cys81(65) H1 terminal -0.40 -1.85,-1.17,3.02 1.02 -1.39,-0.96,2.34 -0.48 -1.79,-1.18,2.97
Cys81 H2 0.80 -1.83,-1.74,3.57 2.98 -1.74,-1.06,2.80 1.32 -1.73,-1.68,3.41
Cys84(68) H1 bridge 1.09 -1.00,-0.93,1.93 3.80 -0.87,-0.74,1.61 1.70 -1.00,-0.92,1.92
Cys84 H2 1.57 -2.59,-2.29,4.89 3.94 -1.99,-1.56,3.55 2.09 -2.50,-2.16,4.66
Cys546(530) H1 terminal -2.19 -2.45,-1.82,4.26 1.57 -1.61,-1.45,3.06 -1.21 -2.25,-1.8 0,4.05
Cys546 H2 3.77 -1.32,-1.06,2.38 5.99 -1.08,-0.93,2.01 4.59 -1.30,-1.10,2.40
Cys549(533) H1 bridge 13.69 -1.80,-1.06,2.85 17.53 -1.86,-0.97,2.83 16.40 -1.88,-1.10,2.89
Cys549 H2 12.65 -2.82,-1.60,4.42 16.72 -2.44,-1.02,3.46 13.97 -2.69,-1.46,4.15
X=OH 1.31 -4.42,-4.11,8.53 0.31 -3.24,-2.49,5.72 1.45 -4.35,-4.09,8.44
The enumeration of amino acid residues corresponds to that of D. vulgaris Miyazaki F. The related sequence
number of D. gigas is given in parentheses.
with the B3LYP and 16.72 and 17.53 MHz with the BP86 functional. The calculated isotropic hyperfine
couplings of the
P
-CH
protons of the terminal cysteine Cys546 (Cys530) are about a factor of three
smaller. The hyperfine interactions for
P
-CH
protons of the cysteines Cys81 and Cys84 (Cys65 and
Cys68 in D. gigas nomenclature) are also given in Table 6.6. The isotropic
H hyperfine interaction of
the
«
-hydroxo ligand is calculated to be 1.31 MHz with the B3LYP functional and 0.31 MHz with the
BP86 functional. In general, the hybrid functional B3LYP gives smaller isotropic and larger anisotropic
hyperfine interactions compared to the ‘pure’ BP86 functional. This may originate from the admixture of
‘exact’ Hartree-Fock exchange in the B3LYP calculations. Hartree-Fock is biased towards ionic solutions
of the wavefunctions. This may lead to an increase of spin density at the nuclei (thus larger isotropic
values) and therefore also to a larger anisotropic hyperfine interaction. Pure functionals, on the other
hand, tend to favour a more covalent, delocalized spin density distribution (the isotropic and anisotropic
values therefore decrease). The overall picture, however, given by the two calculations is similar.
For means of comparison and in order to test the sensitivity of the results with respect to the chosen
geometry, geometry optimization using the recently developed HCTH functional [94] were also per-
formed. HCTH is a ‘pure’ functional without admixture of Hartree-Fock contributions and was shown
to yield structural parameters, vibrational frequencies and energetics of superior quality to those of other
6.3 Results 107
pure functionals, the results are sometimes comparable in quality to those of the hybrid B3LYP func-
tional. In addition, also transition metal complexes were part of the training set from which the HCTH
functional was derived [94]. A B3LYP/6-311+G(2d,2p) single point calculation at the HCTH/DZVP
optimized geometry was performed. The
t
value of 0.799 is intermediate between that of the BP86
and the B3LYP functionals. The influence of the geometry becomes obvious when comparing B3LYP
calculations which were performed at the BLYP and HCTH optimized geometries (see Table 6.6). The
isotropic hyperfine interactions are generally large for the HCTH functional. This may originate from
the fact that the bond lengths with the HCTH functional are shorter than those with the BLYP functional
(see Table 6.3) or that the HCTH functional shows the same trend towards delocalization as the BLYP
functional (see above).
Table 6.7: DFT Calculated Isotropic and Anisotropic
H-Hyperfine Coupling Parameters [MHz] in Ni-A
Functional/Basis B3LYP/6-311+G(2d,2p) BP86/6-311+G(2d,2p ) B3LYP/6-311+G(2d,2p)
Geometry BLYP/DZVP BLYP/DZVP HCTH /DZVP
¡£¢
/¤
0.9204 0.7625 0.8645
a
¥ ¦'¨
A
©ª¥§¦'¨
a
¥§¦'¨
A
©/ª¥ ¦'¨
a
¥§¦'¨
A
©/ª¥§¦'¨
Proton
Cys81(65) H1 terminal 0.21 -1.90,-1.67,3.57 0.14 -1.31,-1.16,2.47 0.17 -3.84,-1.13,4.97
Cys81 H2 -0.10 -2.22,-1.82,4.04 -0.17 -1.61,-1.22,2.83 -0.17 -1.25,-1.14,2.29
Cys84(68) H1 bridge 1.71 -3.52,-2.19,5.71 4.08 -2.35,-1.95,4.30 3.28 -3.05,-2.20,5.25
Cys84 H2 4.90 -1.27,-0.72,1.99 5.43 -1.07,-0.73,1.80 4.96 -1.21,-0.84,2.04
Cys546(530) H1 terminal -2.37 -5.60,-0.44,6.05 0.63 -2.41,-2.15,4.56 -1.78 -1.86,-1.61,3.48
Cys546 H2 2.76 -1.26,-1.12,2.39 4.68 -1.06,-0.94,1.99 3.03 -1.93,-1.57,3.50
Cys549(533) H1 bridge 9.78 -1.79,-0.62,2.41 12.27 -1.77,-0.66,2.43 8.48 -1.64,-0.79,2 .43
Cys549 H2 5.07 -3.34,-1.45,4.81 8.74 -2.43,-1.46,3.89 7.76 -3.06,-1.72,4.78
X=O
J¬
-16.44 80.71,-31.89,-48.83 -3.89 32.74,17.05,-49.78 -16.22 70.24,-20.07,-50.18
The enumeration of amino acid residues corresponds to that of D. vulgaris Miyazaki F. The related sequence
number of D. gigas is given in parentheses.
Table 6.7 gives the DFT calculated hyperfine coupling constants for a model of Ni-A where an
O
ligand is assumed to occupy the bridging position. Again, the spin contamination (deviation from
the theoretical
t
value 0.75) increases in the range BP86//DZVP (0.76)
B3LYP//HCTH (0.86)
B3LYP//BLYP (0.92). The isotropic hyperfine interactions of the
P
-CH
protons of cysteine Cys549 are
again the largest. Their magnitudes are reduced compared to the Ni-B form by 3-8 MHz.
The hyperfine tensor of the bridging
«
-oxo atom reacts most sensitively to the choice of functional.
108 6. ENDOR Crystallography of the Oxidized States
While B3LYP//BLYP and B3LYP//HCTH yield very similar isotropic and anisotropic hyperfine interac-
tions, the BP86//BLYP calculations yield an isotropic hyperfine interaction reduced by 12 MHz and a
strongly changed anisotropic contribution (see Table 6.7).
6.4 Discussion
In [NiFe] hydrogenases, it has been shown that the EPR signal arises from the nickel atom (
Ni sub-
stitution and subsequent hyperfine splitting in EPR [59]) and one sulphur atom (
/
S substitution and
subsequent hyperfine splitting in EPR [62]). There are, however, at least four sulphur atoms ligating the
nickel ion (two terminal cysteines Cys81 and Cys546, and two bridging cysteines Cys549 and Cys84,
see Figure 6.1). 1
NMq,<O
: Frozen solution Q-Band cw-ENDOR experiments were performed on samples of D.gigas
hydrogenase by Fan et al. [69]. Ni-A and Ni-B were taken as a reference for Ni-C and no assignment of
hyperfine couplings in the oxidized states was made. The largest hyperfine interactions were A
= 12.8
MHz (Ni-A) and A
= 15 MHz (Ni-B). No estimate of isotropic and anisotropic contributions was given
but this range is also obtained in the pulsed-ENDOR experiments presented here.
DFT calculations are in agreement with the experimental assignment of the hyperfine tensors A
and
A
to the
P
-CH
of Cys549 in the Ni-B form. The calculated isotropic hyperfine coupling constants
for the
P
-CH
protons are in in good agreement with experiment (compare Table 6.1 and Table 6.6).
Best agreement for the
P
-CH
protons of Cys549(Cys533 in D. gigas) is obtained with the calculations
using the B3LYP functional at the BLYP optimized structure (B3LYP//BLYP). The calculated isotropic
hyperfine interactions are larger than the experimental (by ca. 5 MHz at BP86//BLYP, ca. 4 MHz at
B3LYP//HCTH and ca. 1 MHz at B3LYP//BLYP). The agreement between the calculated and experi-
mental anisotropic hyperfine interaction is very good (deviations less than 0.5 MHz) for the slightly more
remote proton Cys549 H2. For Cys549 H1 the deviation is up to 1.8 MHz for the largest anisotropic
hyperfine tensor component. This may originate from the complete neglect of relativistic effects (scalar-
relativistic and spin-orbit coupling) in the calculations. They may be important for the description of the
electronic structure of the Ni atom and likewise influence ligands in the surrounding of the Ni. At this
point, it cannot be decided whether the agreement of the B3LYP results is only a fortuitous cancellation
of errors and the BP86 results could be systematically improved by consideration of second-order effects
(i.e. spin-orbit coupling, see Chapter 4). The reduced spin-contamination of the BP86 results suggests
1A possible fifth sulphur atom was assigned to an electron density peak in D. vulgaris Miyazaki F [28] but considered to be
an oxygen species in D. gigas [27].
6.4 Discussion 109
that work along that line is promising.
In the Ni-A state, the two large couplings seem to be also present although no complete analysis is
done for the single-crystal spectra. The assignment of the two large coupling to the
P
-CH
protons of
cysteine Cys549 for Ni-A is supported by the following arguments:
the
RS
-axis is along that Ni-SCys549 bond in both Ni-B and Ni-A [190]
the oxidation state of the Ni is unchanged compared to Ni-B
there is no drastic spin reorientation in the active centre and the spin density resides mainly on Ni
and the sulphur of Cys549
the isotropic hyperfine interaction is reduced by approximately 2 MHz in the Ni-A case compared
to Ni-B (compare Figures 6.7 and 6.8) and the two couplings exhibit very similar isotropic hyper-
fine interaction and cannot be separated.
DFT calculations yield isotropic hyperfine interactions for the two
P
-CH
of 9.8/5.1 MHz
(B3LYP//BLYP), 12.3/8.7 MHz (BP86//BLYP) and 8.5/7.8 MHz (B3LYP//HCTH) (see Table 6.7). The
calculation at the HCTH geometry seems to give best results since the difference between the two pro-
tons is only marginal (0.7 MHz) while it is approximately 4 MHz at the BLYP optimized geometry.
Experimentally, the protons appear so similar that they cannot be separated.
~}
: Fan et al. [69] reported a hyperfine interaction in Ni-B of A = 4.4 MHz which was obtained
after solvent-exchange to D
O in the reduced Ni-C state and subsequent re-oxidation. The hyperfine
interaction was tentatively assigned to either a H
O or OH
molecule bound to the nickel site. Chipman
et al., by means of 2-pulse ESEEM spectroscopy, showed that there is no D
O exchangeable proton in
the vicinity of the Ni atom in the Ni-A state [119]. Consequently, the difference between the Ni-A and
Ni-B states can either lie in a different protein conformation which allows solvent accessibility in the
Ni-B but not in the Ni-A state or an additional, solvent-exchangeable proton in the active centre in the
Ni-B state. Deprotonation of the bridging ligand OH
in Ni-B to give a O
ligand in Ni-A is a plausible
model. According to the calculations, a protonated bridging ligand (i.e. OH
) in the Ni-B state would
lead to an isotropic hyperfine interaction of
0.31 - 1.45 MHz (see Table 6.6) and can be ruled out as
a candidate for A
. It may, however, correspond to the solvent-exchangeable proton observed by Fan et
al. [69].
The second possible assignment is that to a
P
-CH
of the terminal cysteine Cys81. In the Ni-B
model, the calculated isotropic hyperfine interaction for the two
P
-CH
protons are -0.40/0.80 MHz
(B3LYP//BLYP), 1.02/2.98 MHz (BP86//BLYP) and -0.48/1.32 MHz (B3LYP//HCTH) for H1 and H2,
110 6. ENDOR Crystallography of the Oxidized States
respectively, and smaller than the experimental value. As stated above, the BP86 values appear reliable
due to its lower spin-contamination. In the model for the Ni-A state, the isotropic hyperfine interaction
is reduced for these two
P
-CH
protons and close to zero in all calculations. Thus a deprotonation of the
bridging ligand also leads to a vanishing unpaired spin density at the terminal cysteine Cys81 (from 3
MHz isotropic coupling in Ni-B to 0.2 MHz in Ni-A). According to the calculations, the
«
-oxo bridge
in the Ni-A form might acquire significant spin density and withdraw it from the sulphur ligands i.e. the
bridging cysteine Cys549 and the terminal cysteine Cys81. There is, still, ample room for improvement
of the calculation of the isotropic hyperfine interactions, e.g. the inclusion of second-order effects or
the use of Slater-type orbitals (STOs) which give a better description of the core region of the electron
distribution. This is done in Chapter 7. 2
Experimentally, the anisotropic hyperfine tensor component seems to be overestimated. The fitted
ENDOR transitions range from 2-8 MHz (see Figure 6.9 bottom). With an isotropic value of 5 MHz, the
anisotropy can be estimated to be 3 MHz at most. Thus, a dipolar tensor of the order of magnitude (-1.5,
-1.5, 3.0) MHz appears plausible. Due to numerical instabilities of the fit routines, it was not possible to
fit the hyperfine tensors A
with these values.
The cw-ENDOR orientation-selected study by Geßner et al. [169] also revealed a third hyperfine
interaction. The measured isotropic part was, however, significantly smaller than the one reported here
(0.5 MHz) and assigned to either one
P
-CH
proton from Cys81 or a directly protonated cysteine Cys84.
The first possibility is in agreement with the finding in this work since a protonated Cys84 seems very
unlikely. A fourth hyperfine interaction was also reported but could not be analyzed because of its
maximum near the
RS
component [169]. It was labelled ‘
®
‘ and only tentatively assigned to either a
protonated bridging ligand or a
P
-CH
proton of the terminal cysteine Cys546 [169].
6.5 Conclusion and Outlook
The complete hyperfine tensors A
,A
,A
of three protons in Ni-B in the active centre of the [NiFe] hy-
drogenase from D. vulgaris Miyazaki F have been determined from Davies pulsed-ENDOR experiments
on protein single crystals. Figure 6.12 depicts the assigned proton hyperfine tensors.
A
and A
showed the same angular dependence and both exhibited a large isotropic contribution
(13 and 11 MHz, respectively). From the direction of the anisotropic contribution, the protons were
2Calculations using a STO basis set in the ADF99 program support the results obtained here. The BP86 calculated isotropic
hyperfine coupling constants are +13 and +12 MHz for the two
¯
-CH
protons of the bridging cysteine Cys549 in Ni-B and
+9.5 and +6 MHz in Ni-A. One of the
¯
-CH
protons of the terminal cysteine Cys81 exhibits an isotropic coupling of +3 MHz
in the Ni-B cluster model but it is absent in the Ni-A cluster model (reduced to +0.2 MHz).
6.5 Conclusion and Outlook 111
AA
A2
A
3
1
Figure 6.12: Assigned Hyperfine Tensors in the Ni-B State
shown to be
P
-CH
protons of the bridging cysteine Cys549. This assignment is in agreement with
previous work of orientation-selected cw-ENDOR measurements [169], the interpretation of the
R
-tensor
in single crystals with its
RTS
-axis along the Ni–S(Cys549) bond [179,190] and DFT calculations. In the
Ni-A form, the environment of the active site is more microheterogeneous and the ENDOR transitions
could not be completely analyzed. The hyperfine tensors A
and A
are also present in Ni-A but show a
reduced isotropic hyperfine interaction (8-9 MHz). This was also confirmed by DFT calculations. The
sensitivity of the DFT calculated hyperfine tensors with respect to the optimized geometry and functional
was investigated.
The third hyperfine interaction A
is only present when the enzyme is in the Ni-B form and absent in
Ni-A. It can originate from a either protonated bridging ligand, i.e. X = OH
or SH
, or from a
P
-CH
proton of the terminal cysteine Cys81 . The isotropic hyperfine interaction of 5 MHz makes it unlikely
to come from an OH
bridging ligand. The DFT calculations support an assignment according to the
second possibility that of a
P
-CH
of Cys81.
For the first time, the difference between the Ni-A and Ni-B forms of the [NiFe] hydrogenase is
given, i.e. a O
bridge in Ni-A and an OH
in Ni-B. The accumulation of spin density on the
«
-oxo
bridge in the Ni-A form leads to a withdrawal of spin population from the sulphur ligands to the bridging
atom. This modification of the bridging ligand might reflect the different activation kinetics of Ni-A and
Ni-B. The OH
ligand in the Ni-B state may be more easily liberated upon activation than the
«
-oxo
bridge in Ni-A.
Pulsed-ENDOR investigations on the reduced crystal will reveal changes in the proton environment
of the active site during the catalytic cycle and thus help to elucidate the reaction mechanism of this
enzyme. Neither the electronic structure nor the hyperfine interaction with protons is accessible from
112 6. ENDOR Crystallography of the Oxidized States
X-ray crystallographic studies. ENDOR crystallography in conjunction with DFT calculations therefore
are indispensable for the investigation of the intermediate states in hydrogenase catalysis.
Chapter 7
Relativistic DFT Calculations of the
Paramagnetic Intermediates of [NiFe]
Hydrogenase
7.1 Introduction
The paramagnetic states of the enzyme are experimentally well-characterized and are subject of intense
research [12,65]. Their electronic or geometrical structures have, however, not been understood on an
atomic level. In the ‘as-isolated‘ oxidized statesthe [NiFe] hydrogenase is a mixtureof two paramagnetic
forms (Ni-A and Ni-B). The two only slightly differ in their
R
-values (Ni-A
RT
&&S
= 2.32, 2.24, 2.02; Ni-
B
R
&&S
= 2.32, 2.16, 2.01, see Table 7.1). In these states, the enzyme is catalytically inactive. It can be
activated by reductive incubation under an H
atmosphere. Ni-B (or ‘ready’) is reduced within minutes
while Ni-A (or ‘unready’) requires incubation for several hours. During reduction, an EPR-silent state
Ni-Si is passed before a third paramagnetic state of the active centre (Ni-C) is reached. Ni-C is believed to
be a catalytic intermediate in the H
dissociation and may bind either H
, H
or H
°
. Upon illumination,
the Ni-C state is converted into a fourth paramagnetic state Ni-L. CO is an inhibitor of the enzyme
yielding a paramagnetic CO-bound state Ni-CO. The completely reduced state Ni-R is EPR-silent and
believed to be in equilibrium with H
[57]. The sequence of redox states reads
±³²µ´·¶
g
±³²´·¸º¹»¼±½²´
²:¹»¾±³²µ´À¿Á¹»¾±³²´·Â Ã
(7.1)
Table 7.1 collects the
R
-values for the paramagnetic states of the [NiFe] hydrogenase from Allochro-
matium vinosum for which the most complete set of data is available.
113
114 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
Table 7.1: g-Values of the paramagnetic states of the [NiFe] hydrogenase from Allochromatium vinosum.
State
RT
g
RS
Ref.
Ni-A 2.32 2.24 2.02 [63]
Ni-B 2.33 2.16 2.01
Ni-C 2.19 2.15 2.01 [67]
Ni-L 2.29 2.13 2.05
Ni-CO 2.12 2.07 2.02 [40,213]
Previous quantum mechanical studies [71–74] have addressed the question of H
activation by [NiFe]
hydrogenases but were not aimed at a description of intermediate states based on experimental observ-
ables. Niu et al. [75] and Amara et al. [76] obtained good agreement between calculated and experi-
mental IR CO and CN stretching frequency bands of the non-protein ligands but no attempt was made
to correctly describe the electronic structures of the paramagnetic states. In order to characterize the
paramagnetic states, it is necessary to calculate observables of magnetic resonance experiments directly
from relativistic DFT wavefunctions.
Here, the first relativistic description and calculation of magnetic resonance parameters (
R
- and
Ä
-
tensors) of a transition metal containing enzyme is presented. By correlating the
R
-values to structural
parameters and observing their changes between the different paramagnetic states, a possible reaction
mechanism may be suggested later.
7.2 Computational Details
We use the ‘zero-order regular approximation‘ for relativistic effects [112, 113,214,215], the efficient
implementation of the four-component wavefunction in a two-component picture. Recently, the calcula-
tion of
R
-tensors [146], hyperfine tensors [131] and quadrupole tensors [216] including scalar relativistic
effects and spin-orbit coupling have become available. The Amsterdam Density Functional (ADF) pack-
age was employed [160] which has the advantage of an efficient numerical integration scheme developed
by te Velde and Baerends [161]. Slater-typer orbitals (STOs) are used throughout. The calculations are
single-point calculations at non-relativistic BP86 [91,93,163,164] geometry-optimized structures. The
BP86 functional has been shown to yield good structural and magnetic resonance parameters for tran-
sition metal complexes (see Chapter 4). A double-zeta Slater-type basis set with polarization functions
(basis II in ADF nomenclature) was used. A triple-zeta basis set is used for the 3d shells of the first
7.3 Results 115
transition metals. The following orbitals were frozen during geometry optimizations : C 1s, N 1s, O 1s,
S up to 2p, Ni up to 2p, Fe up to 2p. The calculations of magnetic resonance parameters were performed
in an all-electron basis. For
R
-tensor calculations, a double-zeta Slater-type basis set with polarization
functions (basis II in ADF nomenclature) was used. A triple-zeta basis set is used for the 3d shells of
the first transition metals. This basis set produced reliable results for Ni model complexes (see Chapter
4) and an increase of basis set did not lead to an improvement of the results. For the calculation of A-
tensors, a larger basis set is needed. In particular the isotropic hyperfine interaction a
ÅCÆ#Ç
is most sensitive
to the quality of basis set. Basis IV in ADF nomenclature was shown to produce rather accurate results.
Hyperfine tensors using the smaller basis set (basis II in ADF nomenclature) were also obtained but are
not presented here. The difference between the two basis sets was
1 MHz or less for light nuclei but
up to 5 MHz for heavy elements.
For reasons of comparison, the ‘quasi-relativistic’ (QR) Pauli-Hamiltonian of Schreckenbach and
Ziegler [142] was also used. It is a modification of the ADF program and employs the same BP86
exchange-correlation functional, the same integration routines and the same basis set. Differences in
the results may therefore only originate from a different treatment of relativistic effects (i.e. spin-orbit
coupling). Scalar relativistic effects are treated self-consistently and spin-orbit coupling and thus the
R
-tensor are treated as a first order perturbation. Although, the Pauli-Hamiltonian is not bounded from
below, the use of an all-electron basis set was not a problem in these cases. The QR
R
-tensor calculations
allow the use of a spin-unrestricted DFT wavefunction which is important for the description of the Ni-A
state (see below).
7.3 Results
7.3.1 Ni-B
7.3.1.1 g-Tensor
In preparations of the [NiFe] hydrogenase from Desulfovibrio vulgaris Miyazaki F, Ni-B is the largest
constituent in solution and single crystals [179, 190]. Its
R
-tensor orientation in the active centre was
determined from angular-dependent EPR spectra of protein single crystals [179,190]. From the fact that
the smallest
R
-value is close to the free electron value
R
(see Table 7.1) a 3d
S<
ground state was deduced.
In the X-ray structure of the [NiFe] hydrogenase from D. vulgaris Miyazaki F, a sulphur species
was found to occupy the position of the bridging ligand [28] which could either be a S
, SH
or H
S
ligand. These possibilities were first tested in the calculations. After complete geometry optimizations
116 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
the Ni–Fe distances are 3.15 ˚
A for H
S, 3.11 ˚
A for SH
and 3.19˚
A for S
. The experimental Ni–Fe
distances from the X-ray structures are 2.55 ˚
A (D. vulgaris Miyazaki F [28]) and 2.90 ˚
A (D. gigas [27]).
Clearly. the calculated values are outside the error margin of the X-ray structure analyses.
Table 7.2: Comparison of experimental and calculated
È
-tensor principal values using the ZORA Hamiltonian
for the oxidized states of [NiFe] hydrogenase.
State/
Bridging ligand
RRi RTS
Ref.
exp. Ni-A 2.32 2.24 2.01 [63]
Ni-B 2.33 2.16 2.01
calc. H
S 2.19 2.06 2.01
SH
2.19 2.15 1.99
S
2.31 2.07 1.92
H
O 2.22 2.09 2.01
OH
2.21 2.17 1.98
O
2.36 1.95 1.84
The calculated
R
-values also do not agree with the experimental values for either oxidized state Ni-A
or Ni-B (see Table 7.2). A H
S ligand gives calculated
R
-values g
&&S
= 2.19, 2.06, 2.01; a SH
ligand
yields g
&&S
= 2.19, 2.15, 1.99 and a S
ligand yields g
&&S
= 2.31, 2.07, 1.91. Together with the
deviation in structural parameters, these discrepancies make a sulphur species an unlikely candidate for
the bridging ligand in the paramagnetic oxidized states of [NiFe] hydrogenase.
A sulphur species (i.e. S
or SH
) in the position of the bridging ligand can also not explain the
O hyperfine coupling in the Ni-A and Ni-B states observed by van der Zwaan et al. [63]. In the X-
ray structure, Volbeda et al. [27,32] also suggested an oxygenic species as a candidate for the bridging
ligand. This was investigated next. When an OH
ligand occupies the position of the bridging ligand,
the calculated Ni–Fe distance is 3.00 ˚
A which agrees with the experimental value of 2.90 ˚
A for the
hydrogenase from D. gigas [27].1The calculated
R
-tensor principal values
Ri
&&S
= 2.21, 2.17, 1.98 for
an OH
bridging ligand agree with the experimental values
R
&&S
= 2.33, 2.16, 2.01 for the
RT
- and
RS
-components. The deviation of the calculated g
-value from the experiment value is not unusual for
1The experimental value of the hydrogenase from D. vulgaris Miyazaki F could not be reproduced (see above). One reason
might be that the X-ray structures collected for the two hydrogenases refer to different oxidation states, e.g. the data collected
from D. vulgaris Miyazaki F could belong to an EPR-silent Ni-Si species.
7.3 Results 117
the ZORA approach (see Chapter 4 on model complexes).
Ni-C
z
x
yy x
Ni-C
z
x
yy x x
zzy
Ni-BNi-A
Figure 7.1: ZORA calculated
È
-tensor orientations of the Ni-A, Ni-B and Ni-C paramagnetic states in [NiFe]
hydrogenase.
Also, the experimental
R
-tensor orientation was reproduced when a OH
ligand occupies the position
of the bridging ligand (see Figure 7.1). Experimentally, the
RTS
-axis was shown to be approximately
oriented along the Ni–SCys533 bond (deviation 16
). The
Ri
axis pointed towards the bridging ligand X
and
RT
was oriented along the Ni–SCys65 bond. When the experimental
R
-tensor orientation in the active
centre is superimposed onto the geometry-optimized cluster with a OH
bridging ligand such that the
heavy atoms show minimal deviations, the difference in the axes orientations is 10
for g
, 12
for
Ri
and
14
for
RS
. Due to the absence of any symmetry elements in the active center of this metalloenzyme, the
agreement can be considered satisfactory. The orientation of the
RTS
-axis is in agreement with structural
information from orientation-selected
H cw-ENDOR of frozen solution of A. vinosum [169] and the
pulsed-ENDOR spectroscopy of protein single crystals from D. vulgaris Miyazaki F [184] (see Chapter
6). In these experiments, large isotropic
H hyperfine couplings were measured and assigned to
P
-CH
protons of the bridging cysteine Cys533. This shows that the unpaired spin density is localized along
that Ni–S bond.
For means of comparison, also spin-unrestricted QR calculations of the
R
-tensor were performed
(see Table 7.2). Identical geometry, basis set and exchange-correlation functional (BP86) compared to
the ZORA calculation were used. The QR values for the
R
and
Ri
components are smaller than the
corresponding ZORA results. This may be due to the different treatment of spin-orbit coupling in the
two approaches. In the QR calculations the spin-orbit coupling is treated as a perturbation while in the
ZORA case it is treated variationally. The
RS
value of the QR calculation is larger than the corresponding
ZORA value and closer to experiment. This may be due to an effect of spin-polarization along the
RS
axis which is taken into account in the QR calculation. The QR calculated
R
-tensor orientation is very
similar to the ZORA results. The
RT
- and g
-axes are rotated by 14
while the
RS
-axis remains nearly
118 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
unchanged (3
difference).
Table 7.3: Comparison of spin-restricted ZORA and spin-unrestricted QR results for the Ni-B state.
ROKS ZORA UKS QR
x y z x y z
R
-value 2.209 2.173 1.984 2.187 2.148 2.028
!E
$
0.65786 0.16489 -0.73487 0.69707 0.02767 -0.71647
!£ $
-0.40064 0.90284 -0.15609 -0.16520 -0.96617 -0.19804
!£S $
0.63773 0.39711 0.66000 0.69771 -0.25640 0.66892
ÈÉ
,
ÈÊ
,
È]
are the
È
-tensor principal values;
ËIÉK
,
ËIÊ%K
,
Ë]K
i = x, y, z are the
È
-tensor eigenvectors. The eigenvectors
of the ZORA Hamiltonian represent an orthonormal, right-handed coordinate axes system (the triple product of
the eigenvetors is +1); the eigenvectors of the QR calculation represent a left-handed coordinate axes system (the
triple product of the eigenvetors is -1).
7.3.1.2 Hyperfine Interaction
Table 7.4 gives the ZORA calculated hyperfine parameters for the Ni-B state when a hydroxo group
bridges the Ni and Fe atoms. The effect of spin-polarization on the hyperfine tensors can be rationalized
when comparing the results from scalar-relativistic spin-restricted (SR ROKS) calculations with those
from spin-unrestricted (SR UKS) calculations (cf. columns 1 and 2 in Table 7.4). The influence of spin-
orbit coupling becomes clear when one compares scalar-relativistic spin-restricted (SR ROKS) with spin-
orbit-coupled spin-restricted (SR+SO ROKS) results (cf. columns 1 and 3 in Table 7.4). The isotropic
hyperfine interaction a
ÅCÆ'Ç
is to be taken from spin-unrestricted scalar-relativistic (SR UKS) calculations,
except for hydrogen atoms for which also SO+SR ROKS results are reliable (see Chapter 4).
Ni: The isotropic
Ni hyperfine interaction is calculated to be small and positive (+5 MHz). in
the SR UKS calculation. The influence of spin-polarization is not large when going from SR ROKS to
SR UKS values. However, there is a striking effect of spin-orbit coupling when comparing SR ROKS
and SO+SR ROKS results. The anisotropic hyperfine interaction is reduced by a factor of two when
SO coupling is considered. Although there is no experimental data for the
Ni hyperfine tensor in the
Ni-B state (see Table 2.5), the SO coupled values seem unrealistically low. Ni-A and Ni-C display a
total
Ni hyperfine interaction along A
S
of 76 MHz (see Table 2.4) and Ni-B would be expected to
exhibit a hyperfine interaction of the same order of magnitude. Such a value was recently obtained from
hyperfine splitting of
Ni enriched protein of the [NiFe] hydrogenase from D. vulgaris Miyazaki F (S.
7.3 Results 119
Foerster, personal communication). The SR UKS values, in particular for the A
S
component, appear
more realistic.
Fe: The
Fe hyperfine interaction is calculated to be small at all levels of the calculations due to
the strong CN and CO ligands which keep the iron in its formal Fe(II) low spin (S = 0) state. A weak
spin polarization via the bridging hydroxo bridge leads only to a small
Fe hyperfine interaction. The
effect of spin-polarization (cf. SR ROKS and SR UKS values) reduces the hyperfine coupling by about
1 MHz for A
and A
S
. Spin-orbit coupling (cf. SR ROKS and SR+SO ROKS values) further reduces A
and A
S
components by 0.3 and 0.9 MHz, respectively. The A
components is also reduced in magnitude
and even inverts the sign. An extrapolated spin-polarized, spin-unrestricted
Fe hyperfine coupling then
is very small indeed. Despite a reported absence of
Fe-ENDOR couplings [61] in the Ni-B state, there
is new evidence that this result has to be revised. A value of 0.8 MHz was reported (J. Moura, B. M.
Hoffman, personal communication). The calculated small
Fe hyperfine interaction is thus in agreement
with most recent experimental findings.
/
S: In the Ni-B cluster model, only the sulphur atom of the bridging cysteine Cys533 exhibits a
significant hyperfine interaction (15 MHz isotropic hyperfine interaction). The isotropic hyperfine inter-
actions from the sulphur atoms of cysteine Cys530, Cys65 and Cys68 are 2.4 MHz, 0.3 MHz and 3.0
MHz and thus much smaller. Therefore these sulphur atoms are not included in Table 7.4. The cal-
culated
/
S coupling of the bridging cysteine Cys533 agrees with the experimental findings that there
is hyperfine splitting due to one sulphur nucleus only [62] in Ni-B, that the
RS
-axis (associated with a
3d
S
orbital) is along the Ni–SCys533 bond [190] and there is large hyperfine interaction of the
P
-CH
protons of cysteine Cys533 [169, 184]. Neither spin-polarization. nor spin-orbit coupling largely in-
fluence the calculated anisotropic
/
S coupling. The isotropic hyperfine interaction is about +15 MHz
and the anisotropic part very close to uniaxiality with A
A%$ B
= -27 MHz. Albracht et al. report a
/
S
hyperfine splitting of 27 MHz and 39 MHz along the
R
and
RT
components [62]. A splitting along
RS
was not reported. Reasons for the differences between experimental and calculated hyperfine splitting
may come from the number of simulation parameters that enter the analysis of the experimental split-
ting (e.g. number of sulphur nuclei, degree of enrichment,
R
- and
Ä
-tensor relative orientation). The
excellent agreement between measured and calculated
<Ì
hyperfine splitting of the
P
-CH
protons of
that SCys533 nucleus gives confidence that the spin density at the sulphur atom and thus the hyperfine
interaction are well described by the calculations (see below).
O: The
O coupling of the hydroxo oxygen exhibits an isotropic coupling of -7 MHz (SR UKS
results) and a small anisotropic contribution at all levels of the calculations. The total hyperfine tensor of
[-6 , -6, -10] MHz is in approximate agreement with the reported experimental
O hyperfine broadening
120 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
of EPR linewidth of 11 and 20 MHz for
R
and
RS
[63]. The experimental data must be critically regarded,
i.e. the use of an EPR modulation amplitude of 1 mT and the detection of line-width broadenings of the
order of 0.4-0.7 mT seem not reliable.
H: In the Ni-B cluster model, the
P
-CH
protons from the bridging cysteine Cys533 exhibit a
large hyperfine interaction. The agreement between calculated and experimental data from cw-ENDOR
of frozen solution (isotropic couplings +12.5 MHz) [169] and pulsed-ENDOR experiments of protein
single crystals (+13 and +11 MHz) (Chapter 6) is very good. The isotropic hyperfine interaction of
the two
P
-CH
of cysteine Cys533 is overestimated by 3 and 7 MHz in the spin-polarized SR ZORA
calculations, but reproduced to within 1 MHz when spin-orbit coupling (SR+SO ROKS) is considered.
The effect of spin-orbit coupling on the anisotropic hyperfine tensor is small (comparing SR ROKS with
SO+SR ROKS data). One of the
P
-CH
protons of the terminal cysteine Cys65 displays a hyperfine
coupling of +2.2 MHz (SR UKS value), respectively +2.6 MHz at the SO+SR ROKS level of calculation.
This would correspond to the third hyperfine coupling
Í}
assigned in Chapter 6. The calculations also
give an isotropic hyperfine interaction of +5 MHz for one
P
-CH
proton from the terminal cysteine
Cys530. This can either originate from the coupling
Ľ
in single crystals or the one labelled ‘
®
’ in
frozen solution [169]. The hyperfine interaction of the hydroxo bridge is rather small. The proton
exhibits a very small isotropic hyperfine interaction of about 1 MHz and a larger anisotropic coupling.
This may correspond to the solvent-exchangeable coupling of +4.4 MHz at
R
resported by Fan et al. for
the Ni-B state [69]. It was tentatively assigned by the authors to originate from a OH
or H
O bound in
the vicinity of the Ni atom.
7.3 Results 121
Table 7.4: ZORA calculated hyperfine interaction in Ni-B in MHz.
hf
Nucleus component SR ROKS SR UKS SO+SR ROKS
Î
Ni a
KHÏ
-17.28 +5.46 -55.19
A
Ð
É
+56.15 +55.67 +24.26
A
Ð
Ê
+21.10 +21.20 +9.58
A
Ð
]
-77.26 -76.86 -33.85
ÑJÒ
Fe a
KHÏ
+0.08 -1.00 +0.78
A
Ð
É
-3.07 -1.95 -2.72
A
Ð
Ê
-0.32 -0.44 +0.13
A
Ð
]
+3.41 +2.41 +2.58
ÓJÓ
S
ÔÊ<Ï
ÑJÓ-Ó
a
KHÏ
+13.13 +15.30 +12.52
A
Ð
É
-25.88 -27.54 -26.24
A
Ð
Ê
-25.79 -26.64 -26.08
A
Ð
]
+51.68 +54.18 +52.33
Ò
O
Õ6ÖØ×
a
KHÏ
-4.85 -7.26 -4.68
A
Ð
É
+1.77 +1.63 +2.38
A
Ð
Ê
+1.41 +1.38 +1.48
A
Ð
]
-3.19 -3.00 -3.81
H
ÔÊ<Ï
Ñ-ÓJÓ
Ö
a
KHÏ
12.60 15.06 12.54
A
Ð
É
-2.39 -2.41 -2.54
A
Ð
Ê
-0.40 -1.12 -0.43
A
Ð
]
+2.78 +3.52 +2.92
H
ÔÊ<Ï
Ñ-ÓJÓ
Ö
Y
a
KHÏ
12.42 13.92 12.34
A
Ð
É
-1.84 -1.68 -1.89
A
Ð
Ê
-0.80 -1.07 -1.89
A
Ð
]
+2.62 +2.76 +2.67
H
ÔÊ<Ï
Ñ-ÓGÙ
Ö
a
KHÏ
+2.16 +1.26 +2.23
A
Ð
É
-1.56 -1.59 -1.71
A
Ð
Ê
-0.87 -1.58 -1.02
A
Ð
]
+2.42 +3.15 +2.73
H
ÔÊ<Ï
Ñ-ÓGÙ
Ö
Y
a
KHÏ
+4.70 +4.89 +4.69
A
Ð
É
-0.95 -1.10 -1.02
A
Ð
Ê
-0.90 -0.91 -0.96
A
Ð
]
+1.85 +2.02 +1.99
H
ÔÊ<Ï
ÎJÑ
Ö
Y
a
KHÏ
+2.60 +2.22 +2.60
A
Ð
É
-1.84 -1.89 -1.99
A
Ð
Ê
-0.64 -1.15 -0.65
A
Ð
]
+2.48 +3.04 +2.64
H
Õ6Ö ×
a
KHÏ
+1.21 +0.30 +1.33
A
Ð
É
-2.70 -3.37 -3.25
A
Ð
Ê
-1.51 -2.34 -1.06
A
Ð
]
+4.20 +5.71 +4.84
122 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
7.3.2 Ni-A
7.3.2.1 g-Tensor
The
R
-tensor orientation of the Ni-A form was determined from angular-dependent EPR of single crystals
[179,190] in which Ni-A was the minor compound in the protein. From the similarity of the
R
-values
a drastic change in the electronic structure of the active site could be ruled out. Indeed, the
R
-tensor
orientation was experimentally found to be very similar to that of Ni-B [190]. Only a slight reorientation
of about 3-4
was detected. A modification of the bridging ligand or one of the terminal cysteines
was discussed which would cause a shift in the
RT
-value [190]. These hypotheses were tested with the
following results (see also Table 7.2).
1. A protonation of the terminal cysteine Cys530 leads to a
R
-tensor of g
&&S
= 2.29, 2.14, 1.92 which
appears implausible because of its low
RS
-value. Such a modification also could not explain the
different activation kinetic of Ni-A and Ni-B and their similarities in the
R
-tensor orientations (data
not shown).
2. Also, a doubly protonated bridging ligand H
O can be ruled out (the calculated
R
-tensor principal
values are 2.22, 2.09, 2.01).
3. ZORA calculations with a deprotonated bridging ligand, e.g. leaving a O
bridge, gave
R
-values
of g
&&S
= 2.36, 1.95, 1.84 which appear unrealistic.
In a next step, it was investigated whether the unrealistic values below
R
derive from the spin-restricted
nature of the wavefunction. Spin-unrestricted quasi-relativistic (QR) calculations using the Pauli-
Hamiltonian [142] but otherwise the same basis set, exchange-correlation functional and integration
scheme yielded values of g
&&S
= 2.187, 2.148, 2.028 when X = OH
and g
&&S
= 2.183, 2.159, 2.046
for X = O
. The QR-values are generally smaller than the corresponding ZORA results but the trends
are reproduced: the
R
component of Ni-B (OH
) is slightly larger than for Ni-A (O
), the
RT
value
for Ni-A is larger than for Ni-B. The QR
RTS
values are larger than the ZORA results perhaps due to the
perturbative treatment of spin-orbit coupling. In any case, the consideration of spin-polarisation drasti-
cally improves the description of the Ni-A state. If one assumes that the trends can be extrapolated to the
ZORA values for Ni-B, (i.e. Ni-A - Ni-B shifts
Ú`R
= -0.004,
Ú`RT
= 0.011,
Ú`RT
= 0.018) one arrives
at reasonable
R
-values of 2.20, 2.19, 2.02. The ZORA calculated
R
-tensor orientation is given in Figure
7.1. The tensor orientation is very similar to that of Ni-B as was also found experimentally [190]. The
g
S
axis is along the Ni–SCys533 bond and the
R
-axis roughly points to the bridging ligand.
7.3 Results 123
Table 7.5: Comparison of spin-restricted ZORA and spin-unrestricted QR results for the Ni-A state.
ROKS ZORA UKS QR
x y z x y z
R
-value 2.357 1.948 1.846 2.183 2.159 2.046
!
$
0.49499 -0.18690 -0.84856 -0.01959 0.41151 -0.91120
!$
-0.85012 -0.30610 -0.42848 -0.77154 -0.58585 -0.24799
!£S $
-0.17966 0.93347 -0.31040 0.63588 -0.69817 -0.32897
ÈÉ
,
ÈÊ
,
È]
are the
È
-tensor principal values;
ËÉK
,
ËÊ%K
,
ËI] K
i = x, y, z are the
È
-tensor eigenvectors. The eigenvectors
of the ZORA Hamiltonian represent an orthonormal, right-handed coordinate axes system (the triple product of
the eigenvetors is +1); the eigenvectors of the QR calculation represent a left-handed coordinate axes system (the
triple product of the eigenvetors is -1).
The difference between the spin-restricted ZORA and the spin-unrestricted QR
R
-tensor orientations
is also quite large. The
RS
-axes agree to within 11
while
R
- and
Ri
-axes differ by 57
and 58
, re-
spectively. From a comparison of the signs of the eigenvectors it becomes clear that the
2
- and
5
-axes
interchange when going from the spin-restricted ZORA to the spin-unrestricted QR calculations. The
7
-axis is retained. It is found that the axes orientation of the ZORA calculation is in better agreement
Figure 7.2: Comparison of ROKS ZORA and UKS QR
È
-tensor orientations for the Ni-A state.
with the experimental assignment of the Ni-A form. It is the
R
axis that points to the bridging ligand
124 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
in the ZORA calculation but the
RT
axis in the QR calculation and vice versa for the other axes. Ex-
perimentally, the exact orientation of the
R
-tensor axes with respect to the crystal axes was determined
from X-ray scattering experiments [179,196]. The Ni-B species is the major constituent of protein single
crystals from D. vulgaris Miyazaki F. Strictly speaking, the confirmed orientation of
R
- and crystal axes
orientation only holds for the Ni-B form. The orientation of a and b crystal axes with respect to the
corresponding
R
-tensor axes may be different for Ni-A but it was assumed to be similar to that of Ni-B.
Unless a protein single crystal from D. vulgaris Miyazaki F which is predominantely in the Ni-A form
is investigated first by room temperature EPR and then by X-ray scattering, a definite answer about the
experimental
R
-tensor orientation in Ni-A cannot be made.
The potential assignment of an O
bridging ligand in the Ni-A form is supported by the following
experimental facts.
O
line broadening was observed for Ni-A and Ni-B EPR signals which suggests that an oxygen
species binds in the vicinity of the Ni [63].
In the active centre, no D
O exchangeable proton could be detected in the Ni-A state [68,70].
Ni-A requires prolonged exposure to H
to be activated compared to Ni-B. An OH
ligand would
be more easily removable upon protonation than the proposed O
ligand.
7.3.2.2 Hyperfine Interaction
Table 7.6 gives the results of ZORA calculations of the hyperfine interaction in the model for the Ni-A
state.
Ni: The scalar-relativistic (SR UKS) calculated isotropic
Ni hyperfine interaction is positive (+13
MHz). The value of the SR UKS anisotropic A
Û
S
component agrees rather well with the experimental val-
ues by Albracht et al. [59] and Moura et al. [45] (see Table 2.5) of 76 MHz. The sign of the experimental
hyperfine coupling could not be determined. According to the calculations, it is negative. Experimen-
tally, however, a smaller
Ä
hyperfine interaction (21 MHz) was detected [59]. When comparing SR
ROKS and SR UKS calculations, the effect of spin-polarization can be seen: upon consideration of spin-
polarization A
Û
increases by 2 MHz, A
Û
is reduced by 4 MHz and A
Û
S
increases by 2 MHz. The effect
of spin-orbit coupling (cf. columns 1 and 3 in Table 7.6) reduces A
Û
by 14 MHz, A
Û
S
by 4 MHz but A
Û
increases by 9 MHz.
Fe: The isotropic
Fe hyperfine coupling is calculated to be very small (-0.5 MHz) from the SR
UKS calculation. The anisotropic hyperfine interaction is also very small (less than 1 MHz) at all levels
7.3 Results 125
of the calculations and neither spin-polarization nor spin-orbit coupling are of drastical influence. This
is in agreement with a small experimental
Fe-ENDOR hyperfine splitting of
1 MHZ in the Ni-A
state [61].
/
S: The calculated
/
S coupling of the sulphur of Cys533 shows a larger isotropic (+29 MHz in the
SR UKS calculation) and smaller anisotropic hyperfine coupling compared to the Ni-B state. The total
hyperfine tensor, however, remains about constant. All other cysteinyl sulphur nuclei exhibit smaller
isotropic hyperfine interactions of the order of 1/3 or less than that of the bridging cysteine Cys533; they
are not included in Table 7.6. The large hyperfine interaction of the sulphur atom of that bridging cysteine
supports the consistency between the Ni-B and Ni-A
R
-tensor orientations and the hyperfine interaction
of the
P
-CH
protons of the residue (see below and Chapter 6).
O: The calculated isotropic
O coupling (-8.8 MHz) is very similar to that in the Ni-B state (-
7.3 MHZ) while there is a drastic increase in the anisotropic hyperfine interaction compared to Ni-B.
The experimental
O hyperfine coupling that increases the EPR linewidth in Ni-A (14, 11, 13 MHz
for A
, A
, A
S
) does not show this large anisotropy [63] (see Table 2.5). One reason for that might
be an unfavourable orientation of
R
- and
Ä
-tensors which would make the determination of the
O
tensor principal values more difficult. The experimental study by van der Zwaan et al. [63] only aimed
at a characterization of the environment of the nickel nucleus but not at an accurate determination of
the
O hyperfine tensor principal values. Under the experimental conditions chosen by these authors
(see above), the reported increase in line-width can only serve as proof of an oxygenic species in the
vicinity of the nickel atom in the Ni-A state.
O-ENDOR experiments are in progress (J. Moura, B.
M. Hoffman, personal communication) and will provide a more sensitive tool to address the question of
oxygen binding in the oxidized states of [NiFe] hydrogenase.
H: The calculated isotropic hyperfine splittings of the
P
-CH
protons from the bridging cysteine
Cys533 (SR UKS values of +11 and +7 MHZ) are in agreement with experimental findings by Fan
et al. of a total hyperfine splitting of 12.8 MHz at
RT
in the Ni-A form (see Table 2.6) and pulsed-
ENDOR of protein single crystals (see Chapter 6). Neither spin-polarization nor spin-orbit coupling
have a large influence on the
H hyperfine tensor components (at most 1 MHz). Experimentally, the
two
P
-CH
protons appear closer to equivalence than in the calculation. The reason for this might be a
slight torsional change with respect to the sulphur 3p
S
orbital. The deprotonation of the hydroxo bridge
in the Ni-B form leads to a
«
-oxo bridge in Ni-A. The ENDOR spectra of Ni-A in H
O and D
O are
identical while a small D
O-exchangeable coupling was detected in Ni-B [69] which supports this model
(see above). One of the
P
-CH
protons of the terminal cysteine Cys65 displayed an isotropic hyperfine
interaction of 2-3 MHz in the Ni-B model cluster (see above). This hyperfine interaction is in the Ni-A
126 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
model cluster reduced to almost zero (-0.15 MHz at the SR UKS level of calculation) and would no
longer be easily detectable by ENDOR. This is in angreement with the postulated difference between the
Ni-A and Ni-B forms in Chapter 6.
7.3 Results 127
Table 7.6: ZORA calculated hyperfine interaction in Ni-A in MHz.
hf
Nucleus component SR ROKS SR UKS SO+SR ROKS
Î
Ni a
KHÏ
-17.05 +12.98 -85.10
A
Ð
É
+75.75 +77.44 +62.18
A
Ð
Ê
+0.95 -3.06 +10.06
A
Ð
]
-76.71 -74.38 -72.24
ÑJÒ
Fe a
KHÏ
0.08 -0.47 0.80
A
Ð
É
-0.78 -0.52 -0.79
A
Ð
Ê
+0.23 +0.13 -0.23
A
Ð
]
+0.55 +0.39 +1.02
ÓJÓ
S
ÔÊ<Ï
ÑJÓ-Ó
a
KHÏ
+29.83 +28.72 +30.17
A
Ð
É
-19.54 -19.48 -14.30
A
Ð
Ê
-19.51 -19.43 -19.75
A
Ð
]
+39.06 +38.90 +34.06
Ò
O a
KHÏ
-0.05 -8.83 -0.33
A
Ð
É
+21.89 +29.94 +28.27
A
Ð
Ê
+20.19 +14.08 +18.33
A
Ð
]
-42.19 -44.03 -46.61
H
ÔÊ<Ï
Ñ-ÓJÓ
Ö
a
KHÏ
+9.56 +10.61 +9.47
A
Ð
É
-1.79 -1.75 -1.70
A
Ð
Ê
-0.58 -0.61 -0.76
A
Ð
]
+2.38 +2.37 +2.46
H
ÔÊ<Ï
Ñ-ÓJÓ
Ö
Y
a
KHÏ
+6.10 +7.41 +6.22
A
Ð
É
-2.43 -2.47 -2.53
A
Ð
Ê
-0.90 -1.57 -1.10
A
Ð
]
+3.33 +4.06 +3.64
H
ÔÊ<Ï
Ñ-ÓGÙ
Ö
a
KHÏ
+1.88 +0.31 +1.56
A
Ð
É
-2.61 -2.44 -2.81
A
Ð
Ê
-1.69 -2.25 -2.30
A
Ð
]
+4.30 +4.70 +5.12
H
ÔÊ<Ï
Ñ-ÓGÙ
Ö
Y
a
KHÏ
+4.39 +4.20 +4.13
A
Ð
É
-0.98 -1.09 1.14
A
Ð
Ê
-0.90 -0.94 -1.08
A
Ð
]
+1.88 +2.03 +2.22
H
ÔÊ<Ï
ÎJÑ
Ö
Y
a
KHÏ
+0.24 -0.15 +0.17
A
Ð
É
-1.52 -1.71 -1.20
A
Ð
Ê
-0.98 -1.30 -1.13
A
Ð
]
+2.50 +3.01 +2.33
128 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
7.3.3 Ni-C
7.3.3.1 g-Tensor
In the X-ray structure analysis of the reduced enzyme, the position of the bridging ligand is vacant
[172,185]. This indicates that the bridging ligand
Ü
must be liberated upon activation when going from
the oxidized Ni-A/Ni-B states to the reduced Ni-C (or Ni-R) state. However, either the substrate H
or
the dissociation products H
°
and H
may still be bound to the active centre in the Ni-C state and not be
detectable by X-ray analysis.
Table 7.7: Comparison of experimental and calculated
È
-tensor principal values using the ZORA Hamiltonian
for the reduced Ni-C state of [NiFe] hydrogenase.
Bonding Sit.
RRi RTS
Ref.
exp. 2.19 2.15 2.01 [67]
2.20 2.15 2.01 [209]
calc. Ni(III) empty bridge 2.28 2.03 1.99
Ni(III) H
axial 2.13 2.06 2.02
Ni(III) H
°
axial, H
bridge 2.13 2.02 1.96
Ni(III) H
bridge 2.20 2.10 2.00
Ni(I) H
bridge 2.09 2.03 2.03
First, calculations with a formal Ni(III) oxidation state were performed. Calculations with an empty
bridging position yield
R
-values g
&&S
= 2.28, 2.03, 1.99 which are in poor agreement with experiment
(see Table 7.7). When one assumes that the hydride occupies the position opposite to Cys533 at the
vacant coordination site in the active centre (axially coordinated to the Ni 3d
S
orbital, see Figure 7.3), the
calculated
R
-values are g
&&S
= 2.13, 2.06, 2.02 which are not in agreement with experimental values (see
Table 7.7). Likewise, under the assumption that both products of the heterolytic cleavage of H
(H
°
and
H
) remain in the active site (one in the position of the bridging ligand and one at the open coordination
site) the calculated
R
-values are g
&&S
= 2.13, 2.02, 1.96. They also do not support this bonding situation
(Table 7.7). When a hydride ion occupies the position of the bridging ligand and the Ni is in a formal
Ni(III) oxidation state, the calculated
R
-tensor principal values (
R
&&S
= 2.20, 2.10, 2.00) agree well with
those from frozen solution
R
&&S
= 2.20, 2.15, 2.01 (see Table 7.7). The calculated
R
-tensor orientation is
depicted in Figure 7.1. The orientation of the
RS
-axis remains unchanged as compared with the oxidized
states (along Ni–SCys533) whereas the axes in the x,y-plane change quite remarkedly. In Ni-C it is the
7.3 Results 129
Ni
Ý
H
Þ
Ni
ß
H
à
Figure 7.3: Modes of Hydride Binding to a Ni 3d
]-á
Orbital.
g
-axis that points approximately to the position of the bridging ligand H
while it is the
R
-axis in the
oxidized states. In Ni-C the g
axis roughly points to the terminal cysteine Cys65. For means of an
Table 7.8: Comparison of spin-restricted ZORA and spin-unrestricted QR results for the Ni-C state.
ROKS ZORA UKS QR
x y z x y z
R
-value 2.200 2.097 2.001 2.163 2.104 2.026
!E
$
-0.34837 0.63152 0.69269 0.40226 0.61099 0.68182
!£ $
0.93735 0.23761 0.25479 -0.91548 0.27569 0.29307
!£S $
-0.00368 0.73805 -0.67473 0.00891 0.74208 -0.67025
ÈÉ
,
ÈÊ
,
È]
are the
È
-tensor principal values;
ËIÉK
,
ËIÊ%K
,
Ë]K
i = x, y, z are the
È
-tensor eigenvectors. The eigenvectors
of the ZORA Hamiltonian represent an orthonormal, right-handed coordinate axes system (the triple product of
the eigenvetors is +1); the eigenvectors of the QR calculation represent a left-handed coordinate axes system (the
triple product of the eigenvetors is -1).
independent check of the results, a spin-unrestricted QR calculation was performed (see Table 7.8). The
spin-unrestricted QR values are again very similar to the spin-restricted ZORA results. This indicates
that spin-polarization does not play a major role for the electronic structure of the Ni-C state. Compared
to the ZORA results, the
R
- and
RT
-values are smaller in the QR calculation and the
RS
-value is slightly
larger (for a discussion see above). The QR
R
-tensor orientation is also very comparable to the ZORA
calculated one. The
R
-axes differ by 3
, the
Ri
-axes by 2
and the
RS
-axes by 2
(see Table 7.8).
The DFT calculations suggested a
R
-tensor orientation before experimental studies on protein single
crystals in the Ni-C state were performed. Recent experimental findings indicate that there is indeed
the possibility for an agreement with the theoretical result. Here, the theoretically proposed
R
-tensor
orientation helped to resolve an ambiguity with respect to the orientation of the
2
- and
5
-axes with
respect to the crystal axes
9
and
;
( [209] and S. Foerster, personal communication).
130 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
The assumption of a hydride bridge in-plane bound to the Ni 3d
S
orbital (see Figure 7.3) is in
agreement with the observation of a rather large, D
O-exchangeable
H hyperfine coupling in the Ni-C
state [69,70] (see below).
Formally, Ni-C is two electrons more reduced than the oxidized Ni-A/Ni-B states. Recent EXAFS
results, however, do not report a large shift in electron density at the Ni atom [186]. This is in agreement
with our model that Ni-C formally contains Ni(III) which implies that an oxidation in the ligand sphere
or one of its cofactors or Fe-S clusters must take place upon Ni-A/B
Ni-C conversion. A formal Ni(I)
oxidation state with a hydride bridge yields calculated
R
-values g
&&S
= 2.09, 2.03, 2.03 and does not
agree with experimental data.
7.3.3.2 Hyperfine Interaction
The bonding situation when a hydride is bound axially to the Ni(III) 3d
S<
orbital (see Figure 7.3) does
not lead to satisfying
R
-values (see above). The proton hyperfine tensors are also not in agreement with
experimental findings, i.e. the
P
-CH
protons from Cys533 show isotropic hyperfine interactions of -0.7
and 1.7 MHz and the axial hydride displays a hyperfine tensor of [-16, -11, 14] MHz. Such a situation
seems unrealistic for the Ni-C state in particular because of the small calculated couplings of the
P
-CH
protons from the bridging cysteine (see below).
Table 7.9 gives the ZORA calculated hyperfine parameter for the Ni-C state when a hydride occupies
the position of the bridging ligand and is in-plane bound to the Ni 3d
S<
orbital.
Ni: The isotropic
Ni hyperfine interaction from the SR UKS calculation is small and of negative
sign (-2 MHz). The effect of spin-polarization (obtained when one compares SR ROKS and SR UKS
calculations) on the anisotropic hyperfine tensor is small and increases A
Û
by 3 MHz, A
Û
is reduced by
the same amount and A
Û
S
remains nearly unchanged. The anisotropic hyperfine tensor exhibits a large
effect upon consideration of spin-orbit coupling. SO coupling reduces the anisotropic components by a
factor of two compared to the SR ROKS case. This drastic reduction seems unrealistic since the spin-
polarized tensor is in good agreement with the experimental value for the hyperfine splitting along
RTS
by
Moura et al. (76 MHz) [45]. Values for the splitting along the
R
and
RT
components were not given.
Fe: The isotropic
Fe hyperfine splitting is very small (-0.9 MHz in the SR UKS calculation).
The anisotropic hyperfine tensor shows only a small effect upon consideration of spin-polarization (A
Û
increases while A
Û
and A
Û
S
slightly decrease; cf. columns 1 and 2). Spin-orbit coupling slightly decreases
A
Û
by 0.5 MHz and increases A
Û
by 1 MHz (compare columns 1 and 3). This small value of the
Fe
hyperfine coupling is in agreement with the experimental finding by Huyett et al. [61] who reported an
absence of any
Fe-ENDOR signal in the Ni-C state.
7.3 Results 131
/
S: Of the four cysteinyl sulphur atoms only that of the bridging cysteine Cys533 shows a significant
hyperfine interaction (isotropic hyperfine interaction +14 MHz). The isotropic hyperfine couplings of the
remaining three sulphur nuclei are smaller (+0.9 MHz for Cys65, +6 MHz for Cys68 and +1.9 MHz for
Cys530). The
/
S coupling of Cys533 is very similar to the Ni-B case and is in agreement with the
R
-tensor orientation which has its
RS
axis along the Ni–SCys533 bond.
H: The
P
-CH
protons of the Cys533 display isotropic and anisotropic hyperfine couplings of the
same order of magnitude as in the Ni-B state. The isotropic part is slightly reduced by 1-2 MHz which
was also found experimentally [70]. Whitehead et al. assigned this reduction to a slightly different
torsional angles of the
P
-CH
protons with respect to the sulphur 3p
S
orbital [70]. According to the cal-
culations, it is a shift of unpaired spin density away from the bridging cysteine to the terminal cysteine
Cys530 that is responsible for this reduction. The two
P
-CH
protons from Cys530 exhibit nearly identi-
cal hyperfine interactions with
9$EDJF
= +7 MHz and +6 MHz. These may correspond to the unassigned
H
hyperfine splitting
â
5 MHz in the Ni-C state which were shown not to be solvent-exchangeable [70].
The bridging hydride exhibits a rather unusual hyperfine interaction. The isotropic contribution is
positive in both SR ROKS and SO+SR ROKS calculations but negative when spin-polarization is con-
sidered. The hydride is bound to the unpaired spin density in a Ni 3d
S
orbital (see Figure 7.3). In case
of an axial binding (see Figure 7.3, left) a large isotropic hyperfine interaction is expected. If the analogy
to an
proton bound to an unpaired spin in a carbon 2p
S
orbital holds, the sign of the isotropic hyper-
fine interaction may be negative in case of a hydride bound in the nodal plane of a Ni 3d
S<
orbital (see
right hand side of Figure 7.3). Spin-polarization also increases the anisotropic hyperfine interaction by 3
MHz. The effect of SO coupling on the anisotropic hyperfine interaction, however, is small. The calcu-
lated hyperfine tensor is in good agreement with experiments where a total hyperfine tensor of [+15, -22,
-25] MHz was reported [69] which gives an isotropic hyperfine interaction of -11 MHz. The value for
the
ĽS
component given by Fan et al. [69] cannot be rationalized since no spectra near the
7
-component
were measured. From the spin-polarized calculation one arrives at [-20, -16, +10] MHz with a
ÅCÆ#Ç
= -9
MHz which is in good agreement with experiment. This large hyperfine coupling was shown to be D
O
exchangeable and the corresponding
H coupling was detected [69,70,196]. A nickel hydride species
would be easilysolvent-exchangeable due to the acidity of the hydrogen. Furthermore, the large coupling
was also lost upon photoillumination and conversion to the Ni-L form for which photodissociation of a
proton ligand was discussed [70]. When such a removal of either the hydride bridge or a proton from
the bridging position is investigated in the conversion to the Ni-L species, one also has an a posteriori
confirmation or falsification of the electronic structure of the precursor Ni-C form.
132 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
Table 7.9: ZORA calculated hyperfine interaction in Ni-C in MHz.
hf
Nucleus component SR ROKS SR UKS SR+SO ROKS
Î
Ni a
KHÏ
-20-20 -2.16 -55.11
A
Ð
É
+62.14 +65.43 +31.72
A
Ð
Ê
+16.63 +13.89 +7.83
A
Ð
]
-78.78 -79.33 -39.55
ÑJÒ
Fe a
KHÏ
+0.04 -0.93 +0.23
A
Ð
É
-2.81 -1.88 -3.38
A
Ð
Ê
+0.51 +0.24 +1.15
A
Ð
]
+2.29 +1.65 +2.23
ÓJÓ
S
ÔÊ<Ï
ÑJÓ-Ó
a
KHÏ
+11.35 +14.45 +10.70
A
Ð
É
-24.70 -25.21 -24.94
A
Ð
Ê
-24.58 -24.20 -25.22
A
Ð
]
+49.28 +49.43 +50.16
H
ÔÊ<Ï
Ñ-ÓJÓ
Ö
a
KHÏ
+10.56 +11.85 +10.48
A
Ð
É
-1.74 -1.66 -1.75
A
Ð
Ê
-0.89 -1.03 -0.88
A
Ð
]
+2.63 +2.69 +2.65
H
ÔÊ<Ï
Ñ-ÓJÓ
Ö
Y
a
KHÏ
10.55 12.90 10.50
A
Ð
É
-2.60 -2.49 -2.76
A
Ð
Ê
-0.09 -0.96 -0.05
A
Ð
]
+2.70 +3.44 +2.80
H
ÔÊ<Ï
Ñ-ÓGÙ
Ö
a
KHÏ
+7.01 +7.25 +6.98
A
Ð
É
-1.68 -1.63 -1.79
A
Ð
Ê
-0.47 -1.00 -0.51
A
Ð
]
+2.13 +2.62 +2.30
H
ÔÊ<Ï
Ñ-ÓGÙ
Ö
Y
a
KHÏ
+5.68 +5.62 +5.66
A
Ð
É
-1.18 -1.26 -1.18
A
Ð
Ê
-0.85 -0.97 -0.97
A
Ð
]
+2.02 +2.22 +2.14
H
bridge a
KHÏ
+10.04 -8.65 +10.89
A
Ð
É
-8.00 -11.12 -9.77
A
Ð
Ê
-4.19 -7.46 -4.88
A
Ð
]
+12.15 +18.57 +14.65
7.3 Results 133
7.3.4 Ni-L
7.3.4.1 g-Tensor
The reduced Ni-C state is light-sensitive [67,217]. Upon illumination at low temperatures
±³²´À¿äãæå´
±½²µ´·ç
(7.2)
a new rhombic signal evolves with g
&&S
= 2.29, 2.13, 2.05 (see Table 7.1). In the oxidized Ni-A and
Ni-B states and the reduced Ni-C state
RTS
was always close to the free electron value from which a
3d
S
ground state was deduced. In Ni-L, the
RS
-value argues for a d
or d
ground state [66].
The photoreaction is reversible and tempering at 180 K fully recovers the Ni-C signal [67,218]. After
photolysis, the large
H-ENDOR coupling is lost and photodissociation of a ligand was discussed [70].
When the hydride would be lost upon illumination, the Ni remains in its formal Ni(III) oxidation state.
±½²
r'è<è%è
w
´é¿
¬qê
¬
´
±³²
r'è%è%è
w
´·ç
(7.3)
The calculated
R
-values for this situation are g
&&S
= 2.28, 2.03, 1.99. They cannot explain the shift of
the
RS
value in the Ni-L state compared to the Ni-C state. Therefore, this configuration for the Ni-L state
appears implausible.
Upon removal of a proton from the bridging position, the Ni atom is left in its formal Ni(I) state
±³²
r'è%è%è
w
´À¿
¬qê8ë
´
±³²
r'è
w
´ìç Ã
(7.4)
In the protein, the dissociated proton might be taken up by a nearby amino acid, i.e. the arginine Arg463
residue which resides like a lid on top of the active site and might be protonated at the -NH
group.
The calculated ZORA values (g
&&S
= 2.26, 2.10, 2.05) for Ni-L are in excellent agreement with the
frozen solution values (Table 7.1). The difference between spin-restricted ZORA and spin-unrestricted
QR calculations is small and follows the trends discussed above (see Table 7.10).
The QR calculated
R
-tensor orientation is rotated by 18
in the
5b7
-plane compared to the ZORA
orientation. (The
R
-axes differ by 1
, the
RT
-axes by 18
and the
RS
-axes by 18
.) The orientation of the
R
-tensor in the Ni-L state is similar to that of the Ni-C state with the
R
-axis pointing to the position of
the empty bridge (see Figure 7.4).
7.3.4.2 Hyperfine Interactions
The calculated hyperfine parameters for the Ni-L state are collected in Table 7.11.
134 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
Table 7.10: Comparison of spin-restricted ZORA and spin-unrestricted QR results for the Ni-L state.
ROKS ZORA UKS QR
x y z x y z
R
-value 2.257 2.097 2.049 2.211 2.138 2.090
!
$
-0.32790 -0.86757 -0.37391 0.34651 -0.70001 -0.62443
!£ $
0.94351 -0.28079 -0.17589 -0.93742 -0.23415 -0.25771
!£S $
0.04761 -0.41046 0.91063 -0.03419 -0.67466 0.73734
ÈÉ
,
ÈÊ
,
È]
are the
È
-tensor principal values;
ËÉK
,
ËÊ%K
,
ËI] K
i = x, y, z are the
È
-tensor eigenvectors. The eigenvectors
of the ZORA Hamiltonian represent an orthonormal, right-handed coordinate axes system (the triple product of
the eigenvetors is +1); the eigenvectors of the QR calculation represent a left-handed coordinate axes system (the
triple product of the eigenvetors is -1).
Ni: The isotropic
Ni hyperfine interaction obtained from a SR UKS calculation is of positive sign
and small (+12 MHz). The influence of spin-polarization on the anisotropic hyperfine tensor (obtained
from a comparison of columns 1 and 2) lies in a reduction of the A
Û
component by 8 MHz, the A
Û
component is reduced in absolute values by 6 MHz and A
Û
S
by 2 MHz. Spin-orbit coupling further
reduces A
Û
by 45 MHz, A
Û
by 25 MHz and A
Û
S
by 20 MHz in absolute values (comparing SR UKS and
SR+SO ROKS calculations). The effect of spin-polarization is certainly overestimated and further work
on spin-orbit-coupled spin-polarized relativistic calculations is needed. Compared to the other states, the
A
Û
S
component is reduced by
25 MHz. A
Û
component increases by the same amount. Here, maximum
coupling is no longer obtained along the
7
- but along the
2
-direction. This indicates a redistribution of the
spin density from axiality with preference of the
7
-direction to a more evenly distributed unpaired spin in
the
2:5
-plane. This is in agreement with experimental findings for the soluble hydrogenase from Ralstonia
eutropha (SH) in the Ni-L state [60], in which hyperfine splittings of 56 MHz, 28 MHz and 14 MHz were
obtained at the
R
-,
RT
- and
RTS
-components, respectively, and recent results for the hydrogenase from D.
vulgaris Miyazaki F (S. Foerster, personal communication).
Fe: The isotropic hyperfine interaction (-0.8 MHz in the SR UKS calculation) is small and of the
same order as in the Ni-C, Ni-A and Ni-B states. In the case of a vacant bridging position, the anisotropic
Fe hyperfine interaction is larger than in the other paramagnetic states investigated so far. The con-
sideration of spin-polarization leads to an increase of the anisotropic hyperfine tensor components by
5 MHz in magnitude along A
Û
, 2.5 MHz along A
Û
and 3.5 MHz along A
Û
S
. The inclusion of spin-orbit
coupling, on the other hand, does not show this large effect. The SR+SO ROKS values are very similar to
7.3 Results 135
Ni-B Ni-C
Ni-L Ni-CO
z
x
y
z
x
yx
z
y
x
z
y
Figure 7.4: Comparison of the ZORA calculated
È
-tensor orientations for the Ni-B, Ni-C, Ni-L and Ni-CO
paramagnetic states of [NiFe] hydrogenase.
those obtained at the SR ROKS level of theory (compare columns 3 and 1). This shows that the hyperfine
interaction is now mostly through space with the electron spin at the Ni and that the direct transfer of
unpaired spin density in the Ni-A, Ni-B and Ni-C states is mediated by the bridging ligands. There are
no experimental
Fe-ENDOR data to compare with.
/
S: The sulphur nuclei also sense the more evenly distributed spin density. The sulphur nucleus of
Cys533 shows a reduced anisotropic hyperfine interaction, while the isotropic term (+16 MHz) remains
constant compared with the Ni-C form. The sulphur nuclei of the other three cysteines also exhibit
/
S
hyperfine splittings which are not drastically smaller than that of Cys533 (SCys530 +7 MHz, SCys68 +15
MHz, SCys65 +10 MHz). The isotropic component of Cys68 is comparable to that of Cys533 and only
differs in the smaller anisotropic part. The hyperfine interactions of the sulphur nuclei of Cys530 and
Cys65 are slightly smaller. Neither spin-polarization nor the consideration of spin-orbit coupling show
large effects on the anisotropic hyperfine tensors. The maximum effect of spin-polarization is obtained
for the sulphur nuclei of Cys533 and Cys530 in which spin-polarization reduces the A
Û
S
component by 3
MHz.
136 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
H: The largest hyperfine coupling of the hydride bridge in Ni-C is no longer present in the Ni-
L form. The decrease of the anisotropic hyperfine interaction of the sulphur nucleus of Cys533 is also
shown by the
P
-CH
protons of that residue. The isotropic parts are reduced by 3.5 and 3 MHz compared
to the Ni-C form. This was also observed experimentally by Whitehead et al. [70]. The couplings of 12.8
MHz in the Ni-C form reduce to
10 MHz in the Ni-L state. The latter protons were neither photolabile
nor D
O-exchangeable. As a consequence of the sulphur nuclei being closer to equivalence, the
P
-CH
protons of the respective cysteines also show hyperfine interactions of the order of 3-7 MHz isotropic
hyperfine interaction and may thus be detectable by
H-ENDOR of the Ni-L state.
Table 7.11: ZORA calculated hyperfine interaction in Ni-L in MHz.
hf
Nucleus component SR ROKS SR UKS SR+SO ROKS
Î
Ni a
KHÏ
-23.76 +12.22 -76.04
A
Ð
É
+97.27 +89.32 +45.63
A
Ð
Ê
-42.11 -36.30 -11.93
A
Ð
]
-55.16 -53.01 -33.69
ÑJÒ
Fe a
KHÏ
+0.05 -0.83 +0.10
A
Ð
É
-2.22 -7.16 -2.39
A
Ð
Ê
+0.33 +2.93 +0.64
A
Ð
]
+1.90 +4.24 +1.73
ÓJÓ
S
ÔÊ<Ï
ÑJÓ-Ó
a
KHÏ
+12.16 +15.98 +11.41
A
Ð
É
-14.26 -13.21 -14.33
A
Ð
Ê
-14.12 -10.98 -15.08
A
Ð
]
+28.39 +24.19 +29.40
ÓJÓ
S
ÔÊ<Ï
ÑJÓJÙ
a
KHÏ
+2.70 +7.22 +1.42
A
Ð
É
-8.51 -7.77 -10.74
A
Ð
Ê
-7.83 -6.69 -7.76
A
Ð
]
+10.23 +7.16 +10.75
Ó-Ó
S
ÔÊ<Ï
Î-í
a
KHÏ
+15.72 +15.49 +15.30
A
Ð
É
-5.17 -4.76 -5.09
A
Ð
Ê
-5.06 -2.40 -5.67
A
Ð
]
+10.23 +7.16 +10.75
Ó-Ó
S
ÔÊ<Ï
Î-Ñ
a
KHÏ
+5.32 +10.27 +5.22
A
Ð
É
-2.67 -3.75 -2.96
A
Ð
Ê
-2.65 -1.42 -2.26
A
Ð
]
+5.02 +5.17 +5.22
continued on next page
7.3 Results 137
hf
Nucleus component SR ROKS SR UKS SR+SO ROKS
H
ÔÊ<Ï
Ñ-ÓJÓ
Ö
a
KHÏ
+5.50 +6.53 +5.44
A
Ð
É
-1.35 -1.59 -1.38
A
Ð
Ê
-0.75 -0.49 -0.76
A
Ð
]
+2.09 +2.07 +2.15
H
ÔÊ<Ï
Ñ-ÓJÓ
Ö
Y
a
KHÏ
+6.04 +7.05 +5.95
A
Ð
É
-2.37 -2.77 -2.59
A
Ð
Ê
-0.75 -0.49 -0.76
A
Ð
]
+2.88 +4.25 +3.12
H
ÔÊ<Ï
Ñ-ÓGÙ
Ö
a
KHÏ
+6.21 +6.05 +6.15
A
Ð
É
-1.74 -1.95 -1.86
A
Ð
Ê
-0.65 -1.46 -0.77
A
Ð
]
+2.39 +3.40 +2.62
H
ÔÊ<Ï
Ñ-ÓGÙ
Ö
Y
a
KHÏ
+4.61 +4.65 +4.56
A
Ð
É
-1.18 -1.41 -1.20
A
Ð
Ê
-0.85 -1.21 -0.96
A
Ð
]
+2.04 +2.62 +2.17
H
ÔÊ<Ï
ÎJí
Ö
a
KHÏ
+3.45 +3.40 +3.44
A
Ð
É
-2.13 -2.92 -2.34
A
Ð
Ê
-0.91 -1.48 -1.02
A
Ð
]
+3.02 +4.40 +3.95
H
ÔÊ<Ï
ÎJí
Ö
Y
a
KHÏ
+6.32 +6.56 +6.27
A
Ð
É
-1.20 -1.20 -1.24
A
Ð
Ê
-0.60 -0.66 -0.61
A
Ð
]
+1.78 +1.86 +1.85
The calculated hyperfine interactions, in conjunction with the good results obtained for the
R
-tensor
principal values, lead to a model picture of the Ni-L state and, a posteriori, support the proposed Ni-C
binding situation.
7.3.5 Ni-CO
The [NiFe] hydrogenase is irreversibly inhibited by binding of exogenous CO. This is accompanied by a
dramatic change in EPR
R
-values (g
&&S
= 2.12, 2.07, 2.02) (see Table 7.1) and a large almost isotropic
G
C hyperfine coupling of 85 MHz [63] at the
R
-components. Initially, it was discussed that the Ni-C
state binds CO [40,213].
138 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
A number of possible CO binding possibilities to a Ni(III) species were investigated by relativistic
DFT calculations, the results of which (
R
-tensor principal values and
G
C isotropic hyperfine coupling
constant) are given in Table 7.12. With respect to the
R
-tensor principal values alone, the bonding situa-
Table 7.13: Results of investigated CO-binding to a Ni(III) species
Binding situation
R
-values
G
C a
$EDJF
[MHz]
Ni
î
Fe
ï
S
ð
S
C
ñ
O
ò
CO bridging 2.10, 2.04, 2.01 11.6
Ni Fe
S
S
H
C
O
CO axial @Ni; H
¬
bridge 2.07, 2.05, 2.01 183.9
Ni Fe
S
S
C
O
CO axial @Ni; no bridge 2.20, 2.03, 2.00 154.6
Ni
ó
Fe
ô
S
õ
S
C
ö
O
÷
CO@Fe 2.11, 2.06, 2.01 9.9
experiment 2.12, 2.07, 2.02 85
tion where CO binds at the Fe atom and points to the position of the bridging ligand shows best agreement
with the experimental values. The isotropic hyperfine interaction, in contrast, is far too small. When the
CO axially binds to the Ni(III), a bonding situation proposed by van der Zwaan et al. [63] due to the
largely isotropic hyperfine interaction, the calculated
G
C isotropic hyperfine interaction is by a factor of
two larger than the experimental value irrespective of the presence or absence of a bridging hydride (184
MHz and 155 MHz, respectively).
Only recently, Happe et al. [58] brought forward the hypothesis, that it could actually be the Ni-L
state that binds CO. This hypothesis was investigated by probing different CO bonding situations to a
Ni-L species (see Table 7.13). A possible binding place of exogenous CO is the position of the bridging
ligand. CO and H
would then be in competition for binding to the Ni and the stronger Ni-CO bond
would inhibit the enzyme. In order to achieve this bonding situation, photodissociation of the bridging
hydride or a proton is also required. The calculated
R
-values for a Ni(I) with a CO molecule bridging
Ni and Fe are g
&&S
= 2.09, 2.05, 1.99 which are somewhat too small. The calculated isotropic
G
C
hyperfine interaction is also too small (26 MHz) compared with experimental data and such a bonding
situation for Ni-CO may therefore be ruled out. For the same reasons, a Ni(I) with CO binding on the Fe
atom and the CO pointing towards the Ni atom, may be excluded, too.
If one assumes that the Ni(I)-L cluster model binds CO in an axial position at the Ni, the calculated
R
-tensor principal values are g
&&S
= 2.11, 2.06, 2.00 and agree very well with the experimental data
7.3 Results 139
Table 7.14: Results of investigated CO-binding to a Ni(I) species
Binding situation
R
-values
G
C a
$IDJF
[MHz]
Ni
î
Fe
ï
S
ð
S
C
ñ
O
ò
CO bridging 2.09, 2.05, 1.99 25.9
Ni
ó
Fe
ô
S
õ
S
C
ö
O
÷
CO@Fe 2.09, 2.05, 1.99 26.5
Ni
ø
Fe
ù
S
S
C
O
CO axial @Ni 2.11, 2.06, 2.00 72.3
experiment 2.12, 2.07, 2.02 85
(g
&&S
= 2.12, 2.07, 2.02). The spin-unrestricted QR results (see Table 7.14) are very similar both in
magnitude and orientation which indicates that spin-polarization is not of major importance for the Ni-
CO state. Also the isotropic
G
CO hyperfine interaction is well reproduced by spin-unrestricted SR
ZORA calculations (72 MHz calculated vs. 85 MHz experimental, see Table 7.13). The proposed
R
-
tensor orientation from the ZORA calculation is shown in Figure 7.4. It quite drastically differs from that
of the other investigated paramagnetic states of the [NiFe] hydrogenase. In the CO-inhibited form, the
R
-axis points to the axially coordinated CO molecule and
Ri
points approximately to the vacant bridging
position. Compared to the formal Ni(III) Ni-B state the orientation in the Ni(I)-CO form corresponds to
an interchange of
2
´
and
7
-axes.
Table 7.15: Comparison of spin-restricted ZORA and spin-unrestricted QR results for the Ni-CO state.
ROKS ZORA UKS QR
x y z x y z
R
-value 2.112 2.056 2.000 2.108 2.070 2.016
!
$
-0.87738 0.01010 0.47969 0.89049 0.04804 0.45247
!£ $
-0.30734 0.75591 -0.57805 0.23208 0.80738 -0.54247
!S$
-0.36844 -0.65460 -0.66011 0.39137 -0.58808 -0.70781
ÈÉ
,
ÈÊ
,
È]
are the
È
-tensor principal values;
ËIÉK
,
ËIÊ%K
,
Ë]K
i = x, y, z are the
È
-tensor eigenvectors. The eigenvectors
of the ZORA Hamiltonian represent an orthonormal, right-handed coordinate axes system (the triple product of
the eigenvetors is +1); the eigenvectors of the QR calculation represent a left-handed coordinate axes system (the
triple product of the eigenvetors is -1).
140 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
The calculation was repeated using the large triple-
ú
basis set (basis IV in ADF nomenclature).
The isotropic
G
CO hyperfine interaction was slightly reduced to +67.61 MHz and A
"%ûi$EDGF
= [-6.04, -
1.61, 7.64] MHz. The agreement with the experimental values a
$EDJF
= 85 MHz and A
"<û=$EDJF
= [-4, 0, 5]
MHz [63] is more than satisfying. The assignment of the CO-treated enzyme to a Ni(I) species without
a hydride bridge is in agreement with the absence of any line broadening in EPR spectra upon H
O/
D
O solvent exchange of the Ni-CO EPR signal [213]. In Ni-C, there is such an effect [67] which can
be assigned, according to the calculations, to originate from the
H hyperfine coupling of the bridging
hydride. Furthermore, the carbon monoxide-treated hydrogenase is light-sensitive and upon illumination
the Ni-L EPR spectrum is fully recovered [213].
The proposed coordination of CO axially bound to the Ni is in agreement with most recent experi-
mental findings. The X-ray structure analysis of the CO-inhibited [Fe]-only hydrogenase from Clostrid-
ium pasteurianum CpI also showed axial binding of CO to one of the Fe atoms in the active site [219].
The recently obtained X-ray structure of the reduced, carbon monoxide treated [NiFe] hydrogenase from
D. vulgaris Miyazaki F contains two conformations of the bound CO (Y. Higuchi, personal communica-
tion). One shows a CO bound to the Ni atom opposite to Cys533 in an unusual bent mode, the other one
shows a CO molecule linearly bound to the Ni atom. At the moment, a statement about the oxidation
state of the Ni atom in the crystallized CO-treated enzyme cannot be made. It may be a product of the
active centre either in the Ni-Si, Ni-L or Ni-R form. Preliminary structural data for the bent CO coordi-
nation are for the Ni–CO distance 1.76 ˚
A, the C=O bond length is 1.22 ˚
A with a Ni–C–O angle of 118
(Y. Higuchi, personal communication). This bonding situation is discussed in Chapter 9.
Recent EXAFS investigations of the Ni-Si CO-treated enzyme gave a Ni–CO distance of 1.78 ˚
A, a
Ni–O distance of 2.90 ˚
A which led to a C–O bond length of 1.12 ˚
A [55]. The structural parameters from
the calculations are 1.74 ˚
A for the Ni–CO distance, 2.93 ˚
A for the Ni–O distance and 1.21 ˚
A for the C=O
bond length. The agreement is satisfying but the authors suggested a slightly different bonding situation
in which the CO would be bound to the Ni atom but would point towards the Fe atom [55].
The inhibition of the enzymatic cycle by CO binding in an axial position to the Ni atom suggests a
participation of this coordination site in the mechanism.
7.4 Discussion of Hyperfine Interactions
7.4.1
Ni Hyperfine Interaction
Figure 7.5 shows the relative orientations of the SO-coupled ZORA calculated
R
-tensors and the
Ni
hyperfine tensor. For Ni-A the angle between
RT
and
Äü
is 10
, between
R
and
Ä
10
, between
RS
7.4 Discussion of Hyperfine Interactions 141
and
ÄS
9
. For Ni-B, the angles are only 2
, 15
and 15
, respectively. For Ni-C, the hyperfine tensor
principal axes system is rotated by 42
away from
R
and
Ri
and by 18
from
RS
. For the Ni-L form, the
angle between
R
- and
Ä
-tensor principal axes system is 18
for the x-direction, 21
for the y-direction and
18
for the z-direction. Experimentally, only the
Ni hyperfine splitting along the
R
-tensor components
is known. The information gained from the theoretically postulated relative orientations of
R
- and
Ä
-
tensor principal axes systems may help to improve the analysis and simulation of experimental spectra
in frozen solution. Independently, the relative orientation of the
R
-tensor and
Ni
Ä
-tensor coordinate
axes systems could be determined from angular-dependent EPR spectra of
Ni enriched protein single
crystals.
Figure 7.5: Relative orientations of
È
- and
Î
Ni
ý
-tensors from SR+SO ZORA BP86/IV calculations
þHÿ
! "
#%$
&('
)(*
+(,
- .
/%0 1 2
3%4
5(6
7(8
9(:
; <
Ni-A Ni-LNi-B Ni-C
For Ni-A, Ni-B, and Ni-C the magnitude of the
ÄS
hyperfine interaction is almost unchanged (-61
MHz for Ni-A, -70 MHz for Ni-B, -81 MHz for Ni-C). This is in agreement with findings by Moura et
al. [45] for the Ni-A and Ni-C forms and Albracht et al. [59] for the Ni-A form. The authors obtained
hyperfine splitting of 76 MHz along the
RS
component and implicitly assumed
ijS
to be parallel to
RS
. According to the calculations, in the Ni-L state
ijS
reduces to -41 MHz. Ni-L is believed to be a
formal Ni(I) oxidation state with the unpaired spin in a 3d
orbital. As a consequence, the hyperfine
interaction is no longer largest along the z-axis associated with a 3d
S<
SOMO but along
Ä
. This is
supported by a recent analysis of
Ni enriched samples from the [NiFe] hydrogenase from D. vulgaris
Miyazaki F (S. Foerster, personal communication).
Spin-polarization effects seem to be very important for the description of hyperfine interaction along
the z-direction. Spin-orbit-coupled spin-restricted calculations underestimate the
ÄS
hyperfine interac-
tion by a factor of two. Spin-orbit coupling reduces the hyperfine interactions
Ä
and
Ľ
quite drastically
and brings them into the range of experimental values. In the Ni-A, Ni-B and Ni-C forms, the unpaired
spin density distribution is of spherical symmetry along the Ni–SCys533 bond. Therefore, one might
expect spin-polarization to be important for this direction. The hyperfine interactions perpendicular to
7
,
are obviously very sensitive to the effect of spin-orbit coupling. For the time being, one may not accu-
142 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
rately differentiate between the effects of spin-polarization and spin-orbit coupling. Once spin-polarized,
SO-coupled hyperfine tensors become available further insight is expected.
It is very difficult to comment on the signs and magnitudes of the isotropic
Ni hyperfine interac-
tions. They are calculated to be +13 MHz for Ni-A, +5 MHz for Ni-B, -2 MHz for Ni-C, and +12 MHz
for Ni-L. They are small and of the same order of magnitude for all four paramagnetic states. Due to the
absence of reliable experimental data, a definitive conclusion may not be drawn.
7.4.2
Fe Hyperfine Interaction
The calculated
Fe interaction is very small in all paramagnetic states. This indicates that the Fe is in
its formal Fe(II) oxidation state in a low spin configuration due to the strong ligand field caused by the
CO and CN ligands. Experimentally, there is only one value for the Ni-A state of
1 MHz from
Fe-
ENDOR measurements [61]. In the Ni-B and Ni-C states no
Fe-ENDOR signal could be detected but
a
Fe hyperfine coupling of 0.8 MHz for the Ni-B state was recently reported (J. Moura, B. M. Hoffman
personal communication). The signs of the
Fe hyperfine couplings are not known from experiment.
The calculated isotropic hyperfine interaction from spin-unrestricted ZORA calculations is smaller than
or equal to -1 MHz and makes a comparison with experimental data very difficult. The anisotropic part
of the
Fe hyperfine tensor is also generally very small. The anisotropic contribution in the Ni-L form
is a factor of 3-5 larger than that of the corresponding Ni-A, Ni-B and Ni-C states. In our model, the
Ni-L form exhibits a vacant bridging position while an O
, OH
, or a H
bridge is present in the other
forms, respectively. This may indicate that the presence of a bridging ligand significantly reduces the
anisotropic hyperfine interaction of the Fe atom. Unfortunately, there is no experimental
Fe coupling
for the Ni-L state which is predicted to be larger than in the other paramagnetic forms.
7.4.3
/
S Hyperfine Interaction
Experimentally, Albracht et al. concluded that there was hyperfine interaction due to one
/
S nucleus
only in the oxidized states [62]. This interpretation is supported by the ZORA calculations. The sulphur
nucleus of the cysteine Cys533 exhibits significant isotropic and anisotropic hyperfine interaction. The
isotropic hyperfine interaction is largest in the Ni-A form (
30 MHz), and about half of that in the
Ni-B, Ni-C, and Ni-L forms. The anisotropic part is almost of uniaxial symmetry. The decrease in
isotropic hyperfine interaction in the Ni-B, Ni-C and Ni-L forms with respect to Ni-A is compensated
by an increase in the anisotropic contribution. The total hyperfine tensor thus remains nearly unchanged
in the four paramagnetic states. Experimentally, there are only data available for the oxidized Ni-B
7.4 Discussion of Hyperfine Interactions 143
form in the hydrogenase from Wollinella succinogenes which is only remotely related to the ‘standard
hydrogenases’. The
/
S hyperfine tensor of [27, 39,–] MHz given by Albracht et al. [62] appears to be
too large for the x- and y- components. No value for the
ĽS
component could be obtained.
In the Ni-L form, the spin density is not only delocalized onto the bridging cysteine Cys533 but all
four Ni-coordinating cysteines may exhibit an appreciable
/
S coupling according to the calculations.
This is due to the formal Ni(I) oxidation state in Ni-L. The isotropic hyperfine interaction is largest for
the bridging Cys533 and Cys68 (both exhibit an isotropic coupling of +15 MHz). The terminal cysteines
Cys530 and Cys68 display +7 and +10 MHz isotropic couplings, respectively. This is in agreement with
the finding that the
Ni hyperfine interaction in Ni-L is no longer largest along the z-direction but in the
x,y-plane (see above). This leads to a more evenly distributed spin density onto all four sulphur atoms.
The sulphur nuclei are brought closer to equivalence and the coordination sphere of the Ni therefore
closer to being symmetric.
7.4.4
O Hyperfine Interaction
In order to explain the experimental
O hyperfine splitting in EPR spectra of the oxidized states, there
are potentially three candidates as ligands bridging the Ni and Fe atoms in the active centre: a water
molecule H
O, a hydroxo OH
or an oxo O
ligand. A water molecule leads to an isotropic
O
coupling of -23.50 MHz and an anisotropic coupling of [+1.94, +0.84, -2.79] MHz. Such a large isotropic
coupling is not observed experimentally and a water bridging ligand can be ruled out on the basis of
R
-
tensor calculations (see above) and the calculated hyperfine interaction. A
«
-oxo bridge and a hydroxo
bridge would both give very similar isotropic couplings of -9 and -7 MHz, respectively. The anisotropy,
however, would allow a discrimination between the two candidates. The anisotropy of a hydroxo ligand
[+2, +1, -3] MHz is very moderate compared to [+30, +14, -44] MHz for an oxo bridge. A definite
comparison with experimental data is very difficult. The experimental data by van der Zwaan et al. [63]
come from estimates of the increase of EPR line widths upon re-oxidation with
O
. The values are
all below the intrinsic EPR linewidth of typical [NiFe] hydrogenase samples and must be treated with
care. Here, orientation-selected
O-ENDOR would be of importance and contribute to a more profound
characterization of the bridging ligand in the oxidized states. Furthermore, from pulsed-ENDOR or
ESEEM spectroscopies the
O quadrupole tensor would also be accessible. These experiments are in
progress (J. Moura, B. M. Hoffman personal communication). Unfortunately, the calculated quadrupole
tensors of
O
[+0.29, +0.03, -0.32] MHz and
OH
[+0.31, +0.05, -0.36] MHz are very similar and
would make a definite assignment difficult.
144 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
7.4.5
H Hyperfine Interaction
In all four paramagnetic states Ni-A, Ni-B, Ni-C and Ni-L the
P
-CH
protons of the bridging cysteine
amino acid Cys533 exhibit a large hyperfine interaction. For these two couplings, the difference between
the Ni-A, Ni-B and Ni-C forms is small. This indicates that a major part of the spin density is oriented
along the Ni–SCys533 bond in all three states. There is no major spin density reorientation between the
three states.
The difference between the Ni-A and Ni-B forms lies in a protonation of the bridging oxo ligand for
Ni-B. This not only causes a massive
O coupling for Ni-A (see above) but also leads to an elongation
of all Ni–S bonds. This is responsible for the absence of a third
P
-CH
proton hyperfine interaction in
the Ni-A state. In the Ni-C form, the spin density slightly shifts to the terminal cysteine Cys530 and an
isotropic coupling of 5-6 MHz is predicted for the
P
-CH
of this amino acid residue. Furthermore, a
bridging hydride in the Ni-C state exhibits a large hyperfine interaction. In Ni-L, the largest hyperfine
interaction is lost upon illumination. The oxidation to a Ni(I) species results in a more evenly spread
spin density distribution in the
265
-plane (see above) away from the preferred axiality in the Ni-A, Ni-B
and Ni-C states. As a consequence, a larger number of hyperfine interactions from
P
-CH
protons is
predicted and the coupling of those from Cys533 are reduced by a factor of two compared to the other
states.
7.5
=?>
N Hyperfine and Quadrupole Interaction
Experimentally, hyperfine and quadrupole interactions due to one nitrogen nucleus were observed by
ESEEM spectroscopy. Chapman et al. measured ESEEM spectra of a frozen protein solution of the
[NiFe] hydrogenase from D. gigas in the Ni-A and Ni-C states [68]. A relatively small quadrupole cou-
pling (
@
ACBEDGFIH
= 1.9 MHz) was obtained for both forms and tentatively assigned to a directly coordinated
nitrogen of a weakly coupled imidazole [68].
Protein single crystals of the [NiFe] hydrogenase from D. vulgaris Miyazaki F were investigated by
3-pulse ESEEM spectroscopy. A set of quadrupole parameters for Ni-A (
@
ACBJDGFIH
= 1.98 MHz and
K
= 0.37) and for Ni-B (
@
ACBJDLFIH
= 1.90 and
K
= 0.37) were determined [184]. These values are almost
identical with those of Dikanov et al. who obtained
@
ABEDGFIH
= 1.87 and
K
= 0.39 for both Ni-A and Ni-B
states of frozen protein solution of the [NiFe] hydrogenase from D. gigas [220]. The isotropic hyperfine
interaction is about 2 MHz. Based on the magnitudes of the quadrupole parameters, both studies assign
the coupling to the N
M
nitrogen of a histidine, possibly that of His88 (His72 in D. gigas) which might be
hydrogen bonded to the bridging cysteine Cys533.
7.5
NPO
N Hyperfine and Quadrupole Interaction 145
This assignment was verified by ZORA calculations by adding a histidine protonated at the N
M
to the
bare active site cluster models. This hydrogen bond would allow the transfer of unpaired spin density
from the bridging cysteine Cys533 to the nearby histidine His72.
Complete geometry optimizations were carried out on the cluster models consisting of approx.
50 atoms. Hyperfine and quadrupole parameters were then calculated from a spin-polarized scalar-
relativistic BP86 DFT calculation using a double-
Q
basis set (basis II in ADF nomenclature). The
geometry-optimized structures are given in Figure 7.6.
2.33 2.45
2.31 2.23
Figure 7.6: Histidine coordination of the active centre of [NiFe] hydrogenase: BP86/DZP geometry opti-
mized structures Ni-A (top, left), Ni-B (top, right), Ni-C (bottom, left), Ni-L (bottom, right). Hydrogen bond
lengths in ˚
A.
The calculated parameters for the
NPO
N
M
for Ni-B are A
RTSUR
= [1.72, 1.74, 2.32] MHz with
VXWYZS
=
1.93 MHz. The calculated quadrupole tensor Q = [-1.02, +0.34, +0.68] leads to quadrupole parameters
@
ACBJDGFIH
= 2.04 MHz and
K
= 0.33 which agree nicely with the experimental values. The N
[
nucleus of
the histidine reveals a quadrupole tensor Q = [-1.86, 0.82, 1.04] which does not agree with experimental
findings. For Ni-A, a quadrupole tensor Q = [-0.96, +0.74, +0.22] was obtained which yielded
@
ACBJDLFIH
= 1.92 and
K
= 0.54. The calculated Ni-C
NPO
N
M
quadrupole tensor Q = [-1.09, +0.38, +0.71] leads to
146 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
@
ACBJDGFIH
= 2.18 MHz and
K
= 0.30. For Ni-L the
NPO
N
M
quadrupole tensor is Q = [-0.92, 0.21, 0.71]
which gives
@
ABJDLFIH
= 1.84 MHz and
K
= 0.54. The calculated quadrupole parameters agree well with
experimental data where those are available. They are rather untypical for a N
M
coordinated histidine.
The increase of both quadrupole parameters in the Ni-A and Ni-L forms may originate from the reduced
hydrogen bond distances in these models (2.33 ˚
A in Ni-A, 2.23 ˚
A in Ni-L).
To conclude, based on the DFT calculations the experimentally observed quadrupole interaction can
be assigned to the N
M
nucleus of histidine His72. The
NPO
N quadrupole parameters are of the same order
of magnitude in all paramagnetic states since the hyperfine interaction along the Ni–SCys533–His72
direction does not change drastically. In the geometry-optimized cluster models, the hydrogen bond
lengths (Ni-A 2.33 ˚
A, Ni-B 2.45 ˚
A, Ni-C 2.31 ˚
A, Ni-L 2.23 ˚
A) slightly varies with the oxidation state.
One reason might be the different total charges of the cluster models in the different states. In vivo the
histidine ligand may be held in place by the protein environment.
7.6 The Influence of the Protein Matrix
One point of criticism with respect to the ab initio or DFT calculation of the active centres of proteins
is the complete neglect of the protein environment. One tries to compare in vacuo model cluster cal-
culations with experimental data obtained in liquid or frozen solution or single crystals of the complete
protein. The aim of this section is to investigate whether the satisfying agreement between experimen-
tal and calculated
\
-tensor magnitudes and orientations were a mere artefact of the model and due a
fortuitous cancellation of errors.
All covalently bound cofactors of the active site (namely the four cysteine amino acids) were already
considered. Further interaction of the protein might be mediated by hydrogen bonds. The arguments for
a potential hydrogen bond are
]
the proximity of a potential hydrogen bond donor (-OH,-NH, -CH) and acceptor (CN,CO,O),
]
a heavy atom distance smaller than 3.5 ˚
A,
]
an approximate linear arrangement of hydrogen bond donor and acceptor.
There are, potentially, three hydrogen bond interactions of nearby amino acids with the active centre (see
Figure 7.7). Possibly, there are more van der Waals, neither covalent nor hydrogen bonding interactions
but they were not considered here. The histidine His72 can form a hydrogen bond to the bridging
cysteine Cys533 (see above) and transfer unpaired spin density from the cysteinyl sulphur to the N
M
7.6 The Influence of the Protein Matrix 147
Ser L 486
His L 72
Cys L 68
Arg L 463
Cys L 533
Cys L 530
Cys L 65
X
Ni
C
NCCN
O
Fe
Ser L 486
His L 72
Cys L 68
Arg L 463
Cys L 533
Cys L 530
Cys L 65
Figure 7.7: Protein-cofactor interactions in the active centre of the [NiFe] hydrogenase from D. gigas [27].
nitrogen of that residue and account for the
NPO
N quadrupole interaction measured in [NiFe] hydrogenases
[68, 184, 220]. Furthermore, the inorganic ligands at the Fe site can also form hydrogen bonds. The
assignment of the three non-protein ligands in the X-ray structure of D. gigas was done by their ability
to form hydrogen bonds [27]. From FTIR measurements and chemical analysis one knows that there
were 2 CN and 1 CO ligand coordinating the Fe atom [51,54,173]. Two of the inorganic ligands point
towards polar neighbouring amino acids and the third is directed towards an unpolar protein pocket. It
was concluded that the two cyanides would be more efficient hydrogen bond acceptors than CO while
the carbon monoxide would sit in the unpolar pocket (see Figure 7.7) [27,54]. The arginine Arg 463
sits like a lid on top of the active site and may enter into one or more hydrogen bonds to one of the CN
ligands. Serine Ser486 could form a hydrogen bond to the other CN ligand (see Figure 7.7).
It was investigated whether the consideration of these hydrogen bonding partners would significantly
change the calculated
\
-values. Successively, the cluster was enlarged by first considering the histidine
residue and then also the arginine and serine amino acids. Each cluster was again completely geometry-
optimized using frozen core orbitals (see Computational Details) and the
\
-tensors were calculated in
an all-electron basis. The number of atoms increased from 40 for the bare active site to 50 when the
histidine was added to 90 when all three amino acids were taken into account. This posed a significant
challenge on the computational side. For a picture of the clusters optimized with coordinating His 72,
please refer to Figure 7.6. The geometry-optimized structures of Ni-A, Ni-B and Ni-C with all potential
hydrogen bonding partners are given in Figure 7.8.
In the Ni-A state where a O
A_^
occupies the position of the bridging ligand, there are in total five
hydrogen bonds formed. The amino acids surrounding the active site are hydrogen bond donors and
148 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
1.9
SER 486
HIS 72
ARG 463
2.2
1.7 2.4
1.7
2.2
2.4
2.0 2.0
1.7
2.1
2.1
2.1
2.4
2.2
2.3
Figure 7.8: BP86 geometry-optimized clusters considering protein-cofactor interactions in the Ni-A(left),
Ni-B(middle) and Ni-C (right) states. Hydrogen bond lengths in ˚
A.
the sulphur of Cys533 and the CN groups act as hydrogen bond acceptors. Histidine His72 is hydrogen
bonded to the bridging cysteine Cys533 in all three states. The hydrogen bond length is slightly shorter in
the Ni-A form, possibly due to the increased negative charge in that cluster model compared to the Ni-B
and Ni-C clusters. Serine Ser486 forms two hydrogen bonds to one of the cyanide groups. A strong one
from the -OH group (1.7 ˚
A) and a weaker one from the -NH group (2.2 ˚
A). Arginine Arg486 coordinates
the second cyanide group via two hydrogen bonds, one of 1.9 ˚
A length, the other of 2.3 ˚
A length. This
picture is retained in all three states. The hydrogen bonds from the serine residue are unchanged in length
and those by the arginine residue shorten and become equivalent in length (2.0 ˚
A) in the Ni-C state. This
may imply a participation of the latter residue in the reaction cycle of the [NiFe] hydrogenase, i.e. in the
transfer of a proton from the active site to the protein surface.
In addition to the five hydrogen bonds described above, there is an additional sixth hydrogen bond
in the Ni-B state. Arginine 463 resides on top of the active site like a lid. The proton of the bridging
hydroxo group may form a donator bond to the arginine Arg463 residue. The hydrogen bond length is
rather long with 2.4 ˚
A but it may assist the release of that ligand upon activation of the enzyme. This
may explain the different activation kinetics for ‘ready’ Ni-B and ‘unready’ Ni-A.
The structural parameters do not change significantly when the hydrogen bonds are considered. The
Ni–Fe distances remain constant to within 0.01 ˚
A and the C
`
N triple bonds are only marginally ex-
panded by 0.002 ˚
A upon hydrogen bond formation.
7.7 Conclusion 149
Table 7.16: ZORA calculated
a
-tensor principal values upon successive consideration of protein-cofactor
interactions
Oxidation State
Cluster Ni-A Ni-B Ni-C
Active Site No. of Atoms 41 42 41
\
-values 2.36,1.95,1.85 2.20,2.17,1.98 2.20,2.10,2.00
+His72 No. of Atoms 53 54 53
\
-values 2.69,0.58,0.41 2.19,2.12,2.00 2.23,2.10,1.99
+Arg463 No. of Atoms 91 92 91
+Ser486
\
-values 2.35,1.99,1.90 2.20,2.18,1.98 2.19,2.10,1.99
experiment 2.32,2.24,2.02 2.33,2.16,2.01 2.19,2.15,2.01
The protein environment considered so far does not significantly influence the calculated magnetic
resonance parameters (see Table 7.16). The calculated
\
-values do not drastically change when hydrogen
bonding is considered. A caveat, however, must be issued that a balanced description of the protein
environment is important. The largest changes in the calculated
\
-tensor principal values are found,
when only His72 is considered (along the
\Eb
direction of the
\
-tensor). In particular, the
\Ic
component
is affected when only this residue is taken into account, e.g. for Ni-B the
\Ic
value changes from 2.17 in
the bare active site to 2.12 when the histidine is added and back to 2.18 when all three amino acids are
considered. The same effect is observed for Ni-C where the
\ed
value is mostly affected (bearing in mind
the suggested interchange the x- and y-axes orientations in the Ni-C form compared to Ni-B, the effect
is comparable).
7.7 Conclusion
With the ability to correlate a shift of
\
-values with structural changes, one has a powerful tool at hand
to discriminate different paramagnetic states and intermediates in the reaction mechanism of the hy-
drogenase enzyme. There is, however, some systematic deviation between calculated and experimental
\
-values. The results obtained from DFT calculations for
\
- and hyperfine tensors therefor always need
a critical inspection and evaluation. The ZORA approach seems to give reliable results with the excep-
tion of the Ni-A state for which spin-polarization effects have to be considered in order to achieve a
reasonable description of the electronic structure.
150 7. Relativistic DFT Calculations of the Paramagnetic Intermediates of [NiFe] Hydrogenase
For Ni-B a
f
-hydroxo ligand gives best agreement with experimental values. For Ni-A, a
f
-oxo
bridge appears most plausible while for Ni-C a
f
-hydrido bridging ligand is suggested. In these forms,
the Ni is in its formal Ni(III) oxidation state. The model of the Ni-C form is supported by results for the
Ni-L form in which the bridging ligand would be lost upon illumination as a proton and leaves the Ni
in a formal Ni(I) oxidation state. For Ni-CO, best agreement with experimental data is obtained when it
axially binds to a Ni(I) originating from the Ni-L state. Since CO is an inhibitor of the enzyme, this may
suggest a participation of the open coordination site opposite to Cys533 in the reaction mechanism.
The size of the calculated cluster model was successively enlarged by considering some of the sur-
rounding amino acids, i.e. those which form hydrogen bonds with the active site. It was found that
the protein environment does not impose energetically unfavourable conformations on the active centre
since the structural parameters were nearly unchanged compared to the gas phase cluster models alone.
Neither did the three amino acids considered so far strongly influence the electronic structure. The calcu-
lated
\
-values were similar for all cluster sizes. A participation of the protein in the catalytic mechanism,
however, is still possible.
Further work will suggest a connection of the intermediate paramagnetic states via EPR-silent dia-
magnetic states and thus contribute to the unravelling of the enzymatic mechanism.
Chapter 8
Orientation-Selected ENDOR of the Ni-C
State
8.1 Introduction
The investigation of the reduced Ni-C state of the [NiFe] hydrogenase from Desulfovibrio vulgaris
Miyazaki F is complicated by the spin-spin interaction of the Ni centre with that of the S = 1/2 re-
duced form of the proximal [4Fe-4S]
g
cluster [209]. The shortest distance (edge to edge) between the
two cofactors is 13 ˚
A. The result of which is a complicated splitting of the Ni-C EPR signal at low tem-
peratures [209]. At temperatures above 70 K, due to the the fast relaxation of the [4Fe-4S]
g
spin, the
interaction averages out and the Ni-C EPR signal appears ‘unsplit’ Below 70 K, the spin-spin interaction
is detectable and some structural information can be gained about the relative orientations of the
\
-tensors
of the Ni centre and the proximal iron-sulphur cluster [46,47]. This interaction, however, leads to a fast
relaxation of the Ni spin and prevents the detection of any cw-ENDOR or Davies pulsed-ENDOR signal
from the Ni-C form (data not shown).
The regulatory hydrogenase (RH) from Ralstonia eutropha (formerly Alcaligenes eutrophus) does
not exhibit this spin-spin interaction between the Ni-Fe and [4Fe-4S]
g
cluster spins. The RH is a hy-
drogenase consisting of two subunits (HoxB, HoxC). HoxA and HoxJ are two additional proteins [221]
(see Figure 8.1). HoxB and HoxC share significant similarity [222] with the small and large subunits,
respectively, of the standard [NiFe] hydrogenases from Desulfovibrio gigas and Desulfovibrio vulgaris
Miyazaki F for which crystal structures are available [28,32]. The cysteine and histidine residues that
coordinate the three Fe-S clusters in the small subunit are well conserved in HoxB. However, the lack of
an N-terminal signal sequence indicates a cytoplasmic location of the RH. HoxC contains signal motifs
151
152 8. Orientation-Selected ENDOR of the Ni-C State
Histidine
Protein
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
hihihihihihihihih
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
jijijijijijijijij
Ni-Fe
Fe-S
Fe-S
kmlon_prqsl
Fe-S
lotvu_w
l
x
l
y
z
Kinase
lotvu_{
lsteu_q
lotvu}|
~v
tvZTv
~v
tv
Figure 8.1: Schematic drawing of the role of the regulatory hydrogenase (RH) from Ralstonia eutropha.
Upon hydrogen sensing in the large subunit (HoxC) and electron transfer to the small subunit (HoxB), con-
nection to the histidine protein kinase (HoxJ) is established via phosphorylation/dephosphorylation. The
transcriptional activator HoxA then induces the expression of the genes coding for the soluble hydrogenase
(SH) and the membrane-bound hydrogenase (MBH).
of the large subunit which harbours the active site. The two pairs of cysteines that coordinate both Ni
and Fe are also present in the RH. HoxC displays the conserved amino acid motifs which are considered
essential elements for the coordination of the NiFe cofactor. It is noteworthy, however, that the RH con-
tains slight modifications in the histidine motifs of the large subunit. HoxB has potentially three Fe-S
clusters similar to the small subunit of D. gigas. Four cysteines coordinate a proximal [4Fe-4S] cluster,
three cysteines and a histidine coordinate the distal [4Fe-4S] cluster. The intermediate cluster may also
be a [4Fe-4S] cluster since there are four instead of three conserved cysteine residues [222]. hoxJ shows
homologies to sensor kinases of bacterial two-component systems [221]. Lenz and Friedrich also showed
that HoxJ mediates RH regulation [221]. HoxJ inactivates the transcriptional activator HoxA by phos-
phorylation. This negative effect is released upon H
A
-sensing by the RH. The communication between
the RH and HoxJ is not clear yet. In its non-phosphorylated form HoxA activates the transcription of
genes coding for the other two, more efficient hydrogenases from R. eutropha, the soluble hydrogenase
(SH) and the membrane-bound hydrogenase (MBH) (see Figure 8.1).
8.1 Introduction 153
The active site of the hydrogen sensor was characterized by EPR and FT-IR spectroscopies [223].
The RH has an active site much like that of standard [NiFe] hydrogenases [32,51], i.e. a Ni-Fe site (Ni
was shown to be a requirement for hydrogen sensing by Kleihues et al. [222]) and two CN and 1 CO as
prosthetic ligands of the Fe atom. Pierik et al. showed that the uptake activity of H
A
is two orders of
magnitude lower than that of standard hydrogenases [223] but insensitive to the presence of oxygen and
carbon monoxide.
The EPR properties of the RH somewhat differ from that of standard hydrogenases, i.e. there is only
one paramagnetic state. The as-isolated RH only exhibits a faint signal with two components
\IdI c
=
2.29, 2.17 which resembles that of Ni-B. The
\Eb
edge was not observed [223]. After incubation with
H
A
a new EPR signal evolved with
\IdI c b
= 2.191, 2.133, 2.010 which resembles that of Ni-C. It is also
light-sensitive and converts into a Ni-L signal with g
dI c b
= 2.24, 2.09, 2.04. It is noteworthy that the g
d
value of Ni-L is lower than that of other hydrogenases (2.29). The FT-IR spectra of the RH also show
typical bands for the as-isolated (Ni-SI) and reduced (Ni-C) forms (see Table 8.1).
Table 8.1: Comparison of the high-frequency bands from RH with standard [NiFe] hydrogenases. The fre-
quencies of the two CN and one CO stretching modes are given in cm
o
.
RH [223] A. vinosum [50] D. gigas [54]
State
Es Eo Es Eo Es E
Ni-SI 2081 2073 1943 2086 2074 1932 2085 2075 1934
Ni-C 2084 2072 1962 2087 2074 1950 2086 2073 1952
Although the binding motifs for three Fe-S clusters in the small subunit are present in the RH, there
is no report of an Fe-S EPR signal [223]. Furthermore, there is no evidence for a spin-spin interaction
between the Ni-C spin and that of the proximal [4Fe-4S] cluster. The absence of that interaction and
the similarity of the RH Ni-C EPR signal with that of standard [NiFe] hydrogenases make it an ideal
candidate for ENDOR investigations of the Ni-C state. Since there are no protein single crystals available
for the RH yet, one has to resort to orientation-selected ENDOR in frozen solution.
Orientation-selected ENDOR, in principle, allows the complete determination of hyperfine coupling
tensors [224,225]. This method has been successfully applied to biological systems to study hemoglobin
[188], copper-enzymes [177] and to elucidate the reaction mechanism of enzymes, e.g. aconitase [189].
The method of orientation-selected ENDOR has been reviewed in [226,227]. Recently, an orientation-
selected cw-ENDOR study of the Ni-B state was reported and three hyperfine tensors were structurally
assigned [169]. Here, an orientation-selected
N
H-ENDOR study which allows the full determination and
154 8. Orientation-Selected ENDOR of the Ni-C State
assignment of the hyperfine tensors for several protons in the active center of [NiFe] hydrogenase in
the reduced Ni-C state is presented. For this method, the knowledge of the
\
-tensor orientation in the
molecular structure is a prerequisite. Since it was not reliably determined in [NiFe] protein single crystals
yet, the theoretically calculated
\
-tensor of the Ni-C state will be used. Based on this assignment, the
orientation of
N
H hyperfine coupling tensors with respect to the
\
-tensor axes will be used to characterize
the proton environment of the active NiFe center during catalytic activity and help to further elucidate
the reaction mechanism of [NiFe] hydrogenases.
8.2 Materials and Methods
8.2.1 Sample Preparation
The regulatory hydrogenase was overexpressed in the native host R. eutropha, grown, purified and as-
sayed as described previously [222]. The final protein concentration was 0.5 mM. The solution was
transferred to a Wilmad 707SQ, 4mm o.d. EPR tube. The enzyme was activated for 30 mins at room
temperature with 100% H
A
under frequent stirring and then rapidly frozen in liquid nitrogen.
8.2.2 EPR and ENDOR Setup
Pulsed-EPR and pulsed-ENDOR experiments were performed with a Bruker ESP 380 E FT-EPR spec-
trometer. A sapphire ring resonator (1052 DLQ-H, Bruker) was used. Resonator and sample were cooled
with a helium flow-cryostat (Oxford CF 935). The optimum ENDOR effect was found at T = 10 K. The
pulse lengths were 96 and 48 ns for
and
FI
pulses, respectively. The spectra taken at field values
of 3229 G, 3260 G, 3366 G, and 3430 G are from Davies-ENDOR experiments with selective
-
FI
-
microwave pulse sequence and a radiofrequency pulse of 8
f
s. The spectra that were recorded at field
values of 3165 G, 3208 G, 3235 G, 3245 G, 3255 G, 3288 G, 3310 G, 3337 G, 3385 G, 3390 G, and 3410
G are Davies-ENDOR experiments with an ‘optimized polarization transfer’ which exhibit an increased
ENDOR effect (for details see [84]) and thus decreased the accumulation time. The preparation phase
is also a
-microwave pulse of 96 ns length, the mixing period consists of a non-selective microwave
(16 ns)
-pulse sandwiched between two
-radiofrequency pulses of 8
f
s each. The detection is done
after a traditional
/2-
microwave pulse Hahn-echo sequence. Pulsed-ENDOR spectroscopy has been
extensively reviewed in [83,84,189,191].
8.2 Materials and Methods 155
8.2.3 Orientation-Selected ENDOR
The spin Hamiltonian used here for a system of one electron and several magnetic nuclei
E
}¢¡
¤£
¥
§¦¨©
\IªI«
¥
¬
(8.1)
includes electron Zeeman, electron-nuclear hyperfine interaction and nuclear Zeeman terms. Diagonal-
ization of the Hamiltonian yields the energy levels of the system. These levels can be labelled with the
magnetic quantum numbers of the electron
®°¯
and of the different nuclei
±²®´³µ
. Since nuclear-nuclear
interactions are much smaller than electron-nuclear interactions, it is sufficient to discuss the interactions
of the unpaired electron with one nucleus at a time.
In the ENDOR experiment, an EPR transition (
¶©®°¯
¸·
) is monitored, while transitions between
the nuclear sublevels within one
®¯
-manifold (
¶¹® ¯
»º½¼
¶©® ³
¾·
) are induced using an additional
radio frequency field with appropriate resonance frequency
I§¿À
. The detected EPR amplitude changes
whenever
IÁ¿À
matches a nuclear sublevel transition. The ENDOR transition frequency reflects the
interaction of the nuclear spin with the electron spin acting on the nucleus (second term in the Hamilto-
nian). The observed lines are centred around the free nuclear frequency
¦
.
In the case of an isotropic
\
-tensor and isotropic hyperfine interaction
Â
VXÃÄ(Å
, the interactions in
the Hamiltonian do not depend on the orientation of the molecular axis system in the external magnetic
field. The ENDOR transition energies are then simply the sum of the nuclear Zeeman frequency and the
additional contribution from hyperfine interaction, the sign of the latter being dependent on the electron
spin
®°¯
. In a system with electron spin
Æ
Ç·
FI
and nuclear spin
È
É·
FI
this leads to a pair of ENDOR
transitions spaced symmetrically about the free nuclear Zeeman frequency,
¦
.
oÊ
Ë
§ÌÍÎÀ
ÐÏ
¦ÒÑ
Â
ÏÔÓ
(8.2)
In the more general case of anisotropic
\
- and hyperfine tensors, the EPR and ENDOR transition ener-
gies depend on the orientation of the magnetic field relative to the molecular axes. Assuming that the
hyperfine interactions are small compared with the electron Zeeman term, the EPR resonance condition
is expressed as
H
\αÖÕ
¼Ø×
µ
ÚÙÜÛ¨¼
(8.3)
with the effective
\
-value defined as
\αÖÕ
¼Ø×
µ
ÇÝ ?Þ
±(\
ÞvßàÞ
µ
A
¼
(8.4)
156 8. Orientation-Selected ENDOR of the Ni-C State
where
\
Þ
±á
â·I¼
¼?ã
µ
are the
\
-tensor principal values.
ßÞ
±á
ä·I¼
¼?ã
µ
are the direction cosines of the
external field in the
\
-tensor principal axis system,
ß
N
»å}æJçÁ×èçêéTë
Õ
¼
ß
A
»çêéTëì×èçêéTë
Õ
¼
ß_í
å}æJç
Õ
Ó
(8.5)
Now at a given field value only the subset of molecules with appropriate orientations contributes to the
EPR intensity and thus to the ENDOR spectrum recorded at that field value. Also, the hyperfine field is
no longer parallel to the external field, it now depends on direction and magnitude on the electron spin
quantum number
®°¯
. This leads to a more complicated expression for the ENDOR frequencies, derived
from diagonalization of the Hamiltonian in Eq.(8.1) for an (
Æ
Ç·
FI
¼
È
Ç·
FI
)-system [224]:
Ê
Ë
ÁÌÍÎÀ
±ÖÕ
¼Ø×
µ
îï
ï
ï
ð
í
WTñ
N©òó
ß
W
¦ôÑ
í
Þ
ñ
N
\
ÞßàÞ
\Á±ÖÕ
¼Ø×
µ
ÂW
Þ_õö
A
(8.6)
Due to the effect of the hyperfine field on the ENDOR signal intensities [85], signals at
o÷
Ë
ÁÌÍÎÀ
usually
appear more intense in the ENDOR spectrum than the corresponding lines at
^
Ë
ÁÌÍÎÀ
. The determi-
nation of the complete hyperfine tensor
£
can, in principle, be obtained from ENDOR single crystal
measurements but in the case of protein molecules single crystals are often not available. When ap-
plied to frozen-solution samples, angle-selected ENDOR spectra of samples with anisotropic magnetic
interaction (non-axial
\
-anisotropy) in the EPR also allows the full determination of electron-nuclear
interaction tensors in favorable cases. The EPR spectrum of a polycrystalline sample is a superposition
of signals from a large number of molecules randomly oriented with respect to
©
.
Over the complete EPR envelope (Figure 8.2) ENDOR spectra are recorded at selected field positions
ÙÜÛ
from
\Id
to
\Eb
. Only the fraction of molecules that are oriented according to Eq.(8.3) are contributing
to the ENDOR spectrum at each field position. A subset of molecules is selected by stepping through
the EPR spectrum. At the EPR edges
\Id
and
\Ib
the selected subset is very small and single crystal-
like ENDOR spectra are observed. At intermediate field values the selection is less restrictive and the
resulting ENDOR spectra are superpositions of a larger number of molecular orientations.
8.2.4 Simulation of ENDOR Spectra
In the first step, the full EPR spectrum was simulated according to Eq.(8.3) (Figure 8.2 bottom). ENDOR
frequencies were then calculated for specific field values and orientations for a given number of hyperfine
tensors
±ÖÂ W
Þ
µ
using Eq.(8.6), the intensity of the ENDOR transition was assumed to be proportional to
that of the EPR transition. The ENDOR simulation program [196] allows the angle-dependent simula-
tion of ENDOR spectra using an arbitrary number of fully anisotropic hyperfine tensors with arbitrary
8.3 Results and Discussion 157
orientations relative to the
\
-tensor axes. Based on an algorithm by Mombourquette and Weil [228], a
uniformly distributed set of orientations was created by stepping on a spiral path, typically using 5160
different orientations. A more detailed description of the algorithm can be found in [196]. ENDOR spec-
tra with 1024 points each were simulated for each of the 15 field positions selected in the experiments.
The specific contribution of each orientation (
Õ
¼Ø×
) to the EPR spectrum is calculated, including
\
-
anisotropy and the hyperfine interactions. Contributions of this orientation to an ENDOR spectrum taken
at a given field value are then calculated according to Eq. (8.6), weighted with the EPR amplitude at this
field position and stored. In this way, a series of orientation-selected ENDOR spectra was simulated.
8.3 Results and Discussion
8.3.1 Characterization by EPR
The X-band (9.699 GHz) pulsed-EPR spectrum of the regulatory hydrogenase from R. eutropha at 10
K displays a Ni-C-like spectrum (Fig. 8.1, top). The
\
-tensor principal values were determined from
a simulation of the pulsed-EPR spectrum to be
\ed
= 2.192,
\ec
= 2.135,
\Eb
= 2.011 and are identical to
those obtained by Pierik et al.
\IdI c b
= 2.191, 2.133, 2.010 [223] within error. Furthermore, they are very
similar to those reported for the Ni-C signal of the ‘standard hydrogenase’ from D. gigas which exhibited
\IdI c b
= 2.19, 2.14, 2.02 [66,229]. This striking similarity indicates that the two active centres of the two
functionally different hydrogenases must be very closely related, if not identical.
8.3.2 Analysis of Orientation-Selected Pulsed-ENDOR Spectra
Figure 8.3 shows the collected field-dependent pulsed-ENDOR spectra. The spectra were normalized to
the free nuclear frequency
Eø
. From top to bottom the magnetic field increases going from 3165 G (g
= 2.189) to 3430 G (g = 2.020). Especially at the high-frequency side of the spectra (
÷
Ë
§ÌÍÎÀúù
Eø
)
several lines can clearly be distinguished. The splitting in the ENDOR spectra is nearly symmetric with
respect to the free proton frequency with a maximum deviation of 0.2 MHz. In general lines at the
÷
Ë
§ÌÍÎÀ
side are more intense than those at
^
Ë
§ÌÍÎÀ
. Three large hyperfine coupling can be directly
deduced. At
\
= 2.189 there are large couplings of
÷
= 8 MHz, 6 MHz and 3 MHz. The signals are
rather broad and may contain contributions from more than one proton. When stepping through the EPR
spectrum and going to larger field values, the intermediate signal splits and then becomes broader. Near
\Ic
(
\
= 2.136), one large broad ENDOR signal is detectable at
Êüû
9 MHz and a number of unresolved
smaller hyperfine couplings appear between
Ê
= 2 and 7 MHz. Here, the analysis is especially compli-
158 8. Orientation-Selected ENDOR of the Ni-C State
3000 3100 3200 3300 3400 3500 3600
B [G]
ý
0
Signal Intensity [a.u.]
þ
g
ÿ
xg
ÿ
yg
ÿ
z
Figure 8.2: Pulsed-EPR spectrum of the RH. Comparison of experimental pulsed-EPR spectrum of the RH
(top) and simulation (bottom), both in absorption mode. Experimental Details: T = 10 K, mw-frequency
9.699 GHz, (
/2-,
-pulses of 56 ns and 112 ns, respectively. Details of the simulation: centre field 3300 G,
field sweep 600 G, EPR linewidth 18 G,
a
= 2.192, 2.135, 2.011.
cated because a large number of orientations contribute to the ENDOR effect at
\c
. At field values larger
than
\Ic
, the unresolved signals coalesce into two pairs of doubly split ENDOR resonances. The large
and broad resonance signal moves to smaller hyperfine coupling values and a new very broad and flat
signal evolves at the high frequency side (see for example spectrum at
\
= 2.077). Near
\Eb
(
\
= 2.020),
one sharp signal at
Ê
= 3 MHz and two broad signals at
Ê
= 6 MHz and
Ê
= 9 MHz are observed.
Figure 8.4 shows a field-dependent plot of the ENDOR resonances. The hyperfine splitting with
respect to
Eø
is plotted versus the variation of the magnetic field. The situation is so complicated that
one cannot trace a hyperfine coupling continuously over the whole field range. There may be multiple
crossings of hyperfine interactions which complicate this procedure.
8.3.3 Simulations
For the analysis of the orientation-selected ENDOR spectra, the orientation of the
\
-tensor principal axes
in the molecular coordinate axes system is a prerequisite. For Ni-C, the experimental
\
-tensor orientation
is not yet unambiguously determined (S. Foerster, personal communication). The ZORA calculated
\
-
tensor orientations were shown to be in good agreement with experimental findings for the Ni-A and
Ni-B states [179,190].
When one assumes that the composition and structural parameters of the Ni-C form of the regulatory
8.3 Results and Discussion 159
−12
−10
−8 −6 −4 −2 0
2
4
6
8
10
12
νENDOR −νH [MHz]
Magnetic Field B0
3165 G
3430 G
2.189
2.077
g−value
2.136
2.020
3208 G
3222 G
3410 G
3390 G
3235 G
3245 G
3255 G
3385 G
3366 G
3337 G
3310 G
3288 G
3260 G
2.160
2.151
2.142
2.129
2.126
2.108
2.094
2.059
2.047
2.044
2.032
Figure 8.3: Orientation-selected pulsed-ENDOR spectra of the RH. The spectra are centred around the free
nuclear frequency
for each field position. T = 10 K, sweep width 1-26 MHz.
hydrogenase are similar if not identical to those suggested for the Ni-C state of standard hydrogenases
(e.g. D. gigas,D. vulgaris Miyazaki F), the dilemma can be resolved by resorting to magnitudes and ori-
entations of magnetic resonance parameters obtained from relativistic DFT calculations. The underlying
assumption of the analysis presented in this chapter is therefore that a Ni(III)-
f
hydrido-Fe(II) bridged
active centre exists with four coordinating cysteine ligands and two CN and one CO inorganic ligands at
the Fe atom.
The theoretically predicted
\
-tensor from the spin-orbit-coupled ZORA calculations in Chapter 7
may be a first starting point for the analysis of the orientation-selected ENDOR spectra. For protons,
the spin-restricted SO-coupled ZORA hyperfine tensors were shown to be in good agreement (within
û
1 MHz for both isotropic and isotropic contributions) with experiments (see Chapter 7). Thus knowing
the
\
-tensor orientation and the hyperfine tensors‘ magnitudes and orientations, one has a good starting
point for the analysis of the ENDOR spectra.
Tables 8.2 and 8.3 give the calculated magnetic resonance parameters for the Ni-C form. The values
come from spin-restricted spin-orbit-coupled ZORA calculations using a large basis set (basis IV in
ADF nomenclature [160]). The principal values of the
\
- and
Â
-tensors are given in their corresponding
160 8. Orientation-Selected ENDOR of the Ni-C State
3150 3200 3250 3300 3350 3400 3450
Magnetic Field B
0 [G]
−12
−10
−8
−6
−4
−2
0
2
4
6
8
10
12
νENDOR − νH
[MHz]
Figure 8.4: Field plot of ENDOR resonance positions
eigenvector systems.
For the simulations of the ENDOR spectra, the
\
-tensor orientation from ZORA calculations was
used but the
\
-tensor principal values from the simulation of the pulsed-EPR spectrum of the RH were
taken since the
\
-tensor principal values from DFT calculations are not accurate enough to allow a simu-
lation with these. Deviations of up to 0.1 in
\
-magnitude are sometimes found for the largest components
which is not tolerable for such a sensitive probe like orientation-selected ENDOR.
The total
Â
-tensors in Tables 8.2 and 8.3 are given in their individual principal axes systems. The
hyperfine tensors are then rotated to a common axes system, here the
\
-tensor principal axes system,
according to
£
^
N
£
^
N
!
(8.7)
where
£
"
is the diagonal hyperfine tensor in its own eigenvector system,
and
are the eigen-
vectors of the
\
-tensor (the
\
-tensor principal axes system).
£
is the resulting, non-diagonal hyperfine
tensor in the
\
-tensor principal axes system.
8.3.3.1 ENDOR Signals from
-CH
#
Protons
Figure 8.5 shows the simulated ENDOR transitions which are expected for the four
-CH
#
protons from
the bridging cysteine Cys533 (left) and the terminal cysteine Cys530 (right). The ZORA calculated
\
-
8.3 Results and Discussion 161
Table 8.2: Prinicpal values and orientations of the
a
-tensor and
$
-CH
%
hyperfine tensors in the Ni-C state.
Hyperfine couplings are given in MHz.
x y z
g-Tensor
\W
2.178 2.090 2.002
&
dW
-0.37047 -0.60913 -0.70122
&
cW
0.92801 -0.27462 -0.25174
&
bW
-0.03923 -0.74401 0.66702
A-Tensor
ÂW
+8.73 +9.60 +13.13
N
H Cys533-H1
&
dW
0.20484 -0.01154 -0.97873
&
cW
0.87856 -0.43863 0.18905
&
bW
-0.43148 -0.89859 -0.07971
A-Tensor
ÂW
+7.74 +10.45 +13.30
N
H Cys533-H2
&
dW
-0.09268 -0.41085 -0.90698
&
cW
0.99358 -0.09746 -0.05738
&
bW
0.06482 0.90648 -0.41725
A-Tensor
ÂW
+9.28 +5.19 +6.47
N
H Cys530-H1
&
dW
-0.68409 -0.58703 -0.43292
&
cW
0.53783 -0.80689 0.24426
&
bW
-0.49271 -0.06574 0.86771
A-Tensor
ÂW
+7.80 +4.69 +4.48
N
H Cys530-H2
&
dW
-0.25378 -0.43947 -0.86166
&
cW
0.71822 -0.68230 0.13646
&
bW
-0.64788 -0.58423 0.48880
The labelling of amino acid residues according to the standard [NiFe] hydrogenase from D. gigas was used for
which an X-ray structure is available [27]. The values are from relativistic SO ZORA BP86/IV calculations at
the BP86/II optimized geometry using very tight convergence criteria.
')(+*,(.-
are the
a
-tensor and
/
-tensor prin-
cipal values, respectively.
021 (.0 31 (.0 41
,
5768')(+*,(.-
, are the eigenvectors that diagonalize the
9;:
and
/
matrices,
respectively.
tensor orientation and the hyperfine tensors of the four
-CH
#
protons was used. The
-CH
#
protons of
cysteine Cys533 both exhibit an isotropic coupling of 10.5 MHz each (see Table 8.2). Near
\Id
the spectra
fall together to a splitting of A = 10-12 MHz, with increasing field value split into two components due
to slightly different orientations with respect to the magnetic field and coalesce to a single signal at
\b
at
162 8. Orientation-Selected ENDOR of the Ni-C State
A = 10 MHz (see Figure 8.5, left). The anisotropy is rather small.
−12
<
−10
<
−8
=
−6
>
−4
?
−2
@
0
A
2
@
4
?
6
>
8
=
10
A
12
@
νENDOR − νH
B
[MHz]
Magnetic Field B0
−12
C
−10
C
−8
D
−6
E
−4
F
−2
G
0
H
2
G
4
F
6
E
8
D
10
H
12
G
νENDOR − νH
I
[MHz]
Magnetic Field B0
Figure 8.5: Simulation of Ni-C orientation-selected ENDOR spectra using the theoretically calculated
a
-
tensor orientation and hyperfine tensors of
$
-CH
%
protons from cysteine residues Cys533 and Cys530.
Left: Simulations of the two
$
-CH
%
protons from the bridging cysteine Cys533
Right: Simulations of the two
$
-CH
%
protons from the terminal cysteine Cys530.
The
-CH
#
protons of the terminal cysteine Cys533 display a significantly reduced isotropic hyper-
fine interaction of 7 and 6 MHz, respectively (see Table 8.2). At
\Id
they show a single hyperfine splitting
of around 7 MHz. With increasing magnetic field, the two protons slightly split into a pair of 5 MHz and
8 MHz hyperfine splitting and at
\Ib
again fall together to a single resonance at
Êüû
3 MHz (see Figure
8.5, right).
This set of four protons can, in general, satisfactorily explain a number of features of the experimental
ENDOR spectra (Figure 8.3). At
\Id
the ENDOR resonances at
Ê
= 6 MHz can be assigned to the
-
CH
#
protons of cysteine Cys533 and those at
Ê
= 3 MHz to
-CH
#
protons of cysteine Cys530. The
same holds for
\Ib
. At intermediate field values the sets of pairs of protons split into individual splittings
and the experimental ENDOR resonances are broader (see Figure 8.3). The simulated spectra exhibit
an additional slight splitting of the pairs of protons at
\ed
which is not observed experimentally. It may
be not resolved in the broad ENDOR signals at
\Id
. Or alternatively, the splitting might be caused by a
slight deviation of the calculated
\
-tensor orientation from the experimental one along the x-axis. Since
the splitting is small, the difference between the
\
-tensor orientation can be assumed to be only a few
degrees.
8.3 Results and Discussion 163
8.3.3.2 ENDOR Signals from the Bridging Hydride Ion
The experimental ENDOR spectra (Figure 8.3) display an additional large hyperfine splitting of about 16
MHz at
\ed
, broad features of about 16-20 MHz near
\ec
and 17 MHz at
\Ib
. This large hyperfine splitting
cannot be explained by a coupling resulting from
-CH
#
protons. A candidate for this nucleus is the
bridging
f
-hydrido that may occupy the vacant bridging position in the Ni-C form [34]. Table 8.3 shows
the calculated hyperfine parameters for such a bonding situation. Scalar-relativistic, restricted open-shell
Table 8.3:
J
-tensor principal values in MHz and orientations for the bridging hydride in Ni-C
A
K
A
L
A
M
SR ROKS
A-Tensor +22.19 +2.07 +5.85
Eigenvectors
&
dW
+0.45327 -0.79855 -0.39607
&
cW
-0.89137 -0.40508 -0.20340
&
bW
-0.00199 -0.44524 +0.89541
SR + SO ROKS
A-Tensor +25.54 +1.12 +6.01
Eigenvectors
&
dW
-0.46165 -0.77852 -0.42518
&
cW
+0.88705 -0.40742 -0.21714
&
bW
-0.00418 -0.47740 +0.87868
SR UKS
A-Tensor +9.92 -19.77 -16.12
Eigenvectors
&
dW
+0.46001 -0.71084 -0.53206
&
cW
-0.88786 -0.37474 -0.26697
&
bW
+0.00961 -0.59521 +0.80351
The values are from ZORA BP86/IV calculations at the BP86/II optimized geometry using very tight convergence
criteria.
0N21O(.0N31O(.0N41
,
56P'Q(R*S(+-
are the eigenvectors that diagonalize the
/
matrix.
calculations (SR ROKS) yield all hyperfine tensor elements of positive sign. When spin-orbit coupling
(SO) is additionally considered (SR + SO ROKS), the sign of the hyperfine tensor principal values is
retained but A
d
increases by 3 MHz, A
c
decreases by about 1 MHz and A
b
remains nearly unchanged.
When spin-polarization is considered at the scalar-relativistic level (SR UKS), a completely different
picture is obtained: Compared to the SR ROKS results, A
d
is reduced by 55% upon consideration of
spin-polarization, A
c
and A
b
show inverse signs and significantly larger values.
164 8. Orientation-Selected ENDOR of the Ni-C State
A detailed discussion of the influence of spin-polarization and spin-orbit coupling can be done on the
basis of the decomposition into isotropic and anisotropic hyperfine tensor components done in Table 8.4.
One must bear in mind, that the discussion presented here deals with the influence of relativistic effects
(scalar relativistic effects and spin-orbit coupling) of the transition metals Ni and Fe on a
f
-hydrido
bridging ligand. For the bridging atom itself, the intrinsic effects are expected to be vanishingly small.
Changes in the electronic structure and the hyperfine parameters originate from the adjacent transition
metals.
Table 8.4: Influence of spin-polarization and spin-orbit coupling on the
H hyperfine tensor
of a Ni–
T
-hydrido-Fe bridge. All values are in MHz.
SR ROKS A
U
Å
U
+22.19 +2.07 +5.85
a
ÃÄ(Å
+10.04
A
V4W
}ÃÄ(Å
+12.15 -7.97 -4.19
SR + SO ROKS A
U
Å
U
+25.54 +1.12 +6.01
a
ÃÄ(Å
+10.89
A
V4W
}ÃÄ(Å
14.65 -9.77 -4.88
SR UKS A
U
Å
U
+9.92 -19.77 -16.12
a
ÃÄ(Å
-8.66
A
V4W
}ÃÄ(Å
+18.58 -11.11 -7.46
SR + SO UKS (extrapolated) A
U
Å
U
+11.6 -22.4 -17.7
a
ÃÄ(Å
-9.5
A
V4W
}ÃÄ(Å
+21.1 -12.9 -8.2
Spin-restricted calculations yield a positive isotropic hyperfine interaction for a hydride bridge. The
influence of spin-orbit coupling is small (9%) when comparing SR ROKS and SR + SO ROKS calcu-
lations. Spin-unrestricted calculations give a negative isotropic hyperfine interaction of about the same
magnitude. 1Since the hydride is bound to the Ni 3d
b
YX
orbital in the nodal plane (see Figure 7.3),
the isotropic hyperfine interaction may be of negative sign if the analogy to an
Z
-proton bound to a
spin-carrying carbon 2p
b
orbital holds (for discussion see for example [69]). The influence of spin-orbit
coupling on the anisotropic hyperfine tensor becomes clear when one compares SR ROKS and SR +
1For comparison a non-relativistic unrestricted B3LYP/6-311+G(2d,2p) calculation at the same geometry was performed.
The obtained values (a
[ \^]
= -41.74 MHz, A
_a`4[ \^]
= (-15.76, -12.23, 28.04) MHz) are unrealistically large.
8.3 Results and Discussion 165
SO ROKS calculations. Spin-orbit coupling increases the A
V4Wbdcfeg K
component by 2.5 MHz, the A
h4i bdcfeg j
component by 2 MHz and the A
h4i bdckeg l
component by 0.6 MHz. One reason for this effect might be the
relativistic contraction of the Ni p- and d-orbitals which would then lead to an increase of unpaired spin
density near the core of the Ni nucleus and likewise increase the anisotropic hyperfine interaction of the
neighbouring hydride.
It is difficult to calculate spin-polarization effects in spin-orbit coupled equations (see ref. [132]).
One therefore has to assume that the effect of spin-orbit coupling can be taken from the SR ROKS
m
SR
+ SO ROKS calculation and may be added to the spin-polarized scalar-relativistic (SR UKS) data. The
extrapolated values are also given in Table 8.4.
−14
n
−12
n
−10
n
−8
o
−6
p
−4
q
−2
r
0
s
2
r
4
q
6
p
8
o
10
s
12
r
14
q
νENDOR − νH [MHz]
Magnetic Field B0
−12
t
−10
t
−8
u
−6
v
−4
w
−2
x
0
y
2
x
4
w
6
v
8
u
10
y
12
x
νENDOR − νH
z
[MHz]
Magnetic Field B0
Figure 8.6: Simulation of Ni-C orientation-selected ENDOR spectra for the bridging hydride using theoreti-
cal data. Left: Simulations using the SO + SR ROKS ZORA hyperfine tensor (spin restricted).
Right: Simulations using the SR UKS ZORA hyperfine tensor (spin unrestricted).
Figure 8.6, left shows the field-dependent simulations for a bridging hydride using the calculated
spin-restricted spin-orbit-coupled ZORA hyperfine tensor. At
{}|
a very large hyperfine splitting of 25
MHz is obtained which then quickly splits into a pair of two weak ENDOR signals. At
{~
the signals
fall together to a single resonance signal at 6 MHz. This dependence is not in agreement with the
experimental ENDOR spectra for the following reasons:
i) experimentally, there is no such large splitting of 25 MHz at
{|
,
ii) the simulations cannot explain the large hyperfine splitting larger than 16 MHz for all field values.
Table8.4 shows that there is a drastic influence of spin-polarization on the hyperfine tensor magnitude
and orientation for the bonding situation of a hydride bound to a Ni 3d
~Y
orbital. Also, the
-tensor
orientation changes slightly. The eigenvectors of the
|
component in the SO ZORA calculation show
166 8. Orientation-Selected ENDOR of the Ni-C State
an inversion of sign in the SR spin-unrestricted calculation. The eigenvectors of the
component in
the SO ZORA calculation are rotated by 8
in the SR spin-unrestricted calculation. Those of the
~
component in the SO ZORA calculation are transformed to those in the spin-unrestricted calculation by
likewise rotation by 8
. The result of a simulation using the spin-unrestricted data is given in Figure 8.6
right. The hyperfine splitting at
{|
of A = 10 MHz is too small. Over the complete range of field values,
the general features of the spectra are well reproduced, i.e. an accumulation of an intense ENDOR signal
at about A = 20 MHz at
{
to about A = 16 MHz at
{~
. This indicates the importance of spin-polarization
for the description of the hyperfine interaction of a
-hydrido bridge as was suggested here.
The discrepancy between the simulated ENDOR spectrum (Figure 8.6, right) with the experimental
spectrum (Figure 8.3) for field values near
{|
may result from the neglect of spin-orbit coupling. From
the experimental spectra at
{|
(Figure 8.3, top trace) one expects a hyperfine interaction of the large
coupling of about 16 MHz at this field value. Fan et al. measured a hyperfine coupling of A = 16.8
MHz at the
{}|
-component of the Ni-C EPR spectrum of the [NiFe] hydrogenase from D. gigas [69] and
showed that the nucleus associated with this signal was D
O exchangeable and also belonged to the same
nucleus that exhibited a coupling of A = 20 MHz at
{
[70]. Upon illumination, this signal is lost [70].
The effect of spin-orbit coupling is most pronounced for the A
h4i bdcfeg
component, smaller for A
h4i bdcfeg j
,
and almost negligible for A
h4i bdcfeg l
(see Table 8.4). If spin-orbit coupling were considered along these
lines, an improvement of the simulations would be possible. Extrapolated values (SR + SO UKS) are
given in Table 8.4 and suggest this trend. The simultaneous treatment of spin-polarization and spin-orbit-
coupling might improve the agreement for the hyperfine interaction along the g
|
-component but such a
theoretical approach is currently out of reach.
There is such a large number of adjustable parameters in the simulations of orientation-selected
ENDOR spectra (e.g. the
{
-tensor orientation, the hyperfine tensor principal values and the hyperfine
tensor orientations) that a systematic improvement of the simulations is difficult.
8.4 Discussion and Conclusion
The orientation-selected pulsed-ENDOR spectra of the regulatory hydrogenase (RH) from R. eutropha
were recorded for a number of field positions between
{}|
and
{~
. Supported by the theoretically cal-
culated
{
-tensor orientation and the hyperfine tensor magnitudes and orientations from relativistic DFT
calculations in the ZORA approach, hyperfine tensors of five protons could be assigned to experimental
ENDOR signals.
Given the number of approximations and parameters that enter the analysis of orientation-selected
8.4 Discussion and Conclusion 167
ENDOR spectra, the impact and accuracy of theoretical calculations must be considered satisfying. Fur-
ther work on spin-polarized spin-orbit-coupled DFT wavefunctions might improve the theoretically pre-
dicted
{
-tensor orientation and/or the calculated hyperfine tensors. Figure 8.8 displays the assigned
hyperfine tensors at the
side of the spectra.
−2
0
2
4
6
8
10
12
νENDOR −νH [MHz]
Magnetic Field B0
3165 G
3430 G
2.189
2.077
g−value
2.136
2.020
3208 G
3222 G
3410 G
3390 G
3235 G
3245 G
3255 G
3385 G
3366 G
3337 G
3310 G
3288 G
3260 G
2.160
2.151
2.142
2.129
2.126
2.108
2.094
2.059
2.047
2.044
2.032
Figure 8.7: Assigned hyperfine couplings in the Ni-C form of the RH from Ralstonia eutropha. At the high
frequencyside, the ENDOR signals originating from the bridging hydride (dotted line), the
-CH
protons of
Cys533 (dashed line), and the
-CH
protons of Cys530 (solid line) are marked.
The assignment of two
-CH
protons of the bridging cysteine Cys533 with isotropic values of
10.5 MHz each agrees well with orientation-selected cw-ENDOR measurements of the Ni-B form from
Allochromatium vinosum [169]. In the Ni-B form 12.6 and 12.5 MHz were found. This indicates that
the
{~
-axis should be close to the Ni–SCys533 bond in both redox states. A complete reorientation of
the
{
-tensor axes seems implausible and a reduction to a formal Ni(I) can therefore also be ruled out.
This results was also obtained in the ZORA calculations of the
{
-tensor orientation (see Chapter 7). The
decrease of the isotropic coupling might be explained by a slight reduction of spin density at the cysteine
sulphur atom. The values obtained for the
-CH
protons of Cys533 also agree with values reported by
Fan et al. [69] who measured a coupling of around 12 MHz at
{
for the [NiFe] hydrogenase from D.
gigas in the Ni-C state. The coupling was found to be rather isotropic and not solvent-exchangeable.
A tentative assignment was made to cysteinyl
-protons but a specific structural assignment was not
possible due to the lack of an X-ray structure at that time.
The signals assigned to
-CH
protons from the terminal cysteine Cys530 in this work may corre-
spond to those reported by Whitehead et al. [70] who observed a number of hyperfine coupling with
168 8. Orientation-Selected ENDOR of the Ni-C State
5 MHz in the Ni-C state of Thiocapsa roseopersicina. An assignment, however, was not done. In the
oxidized states Ni-A and Ni-B these couplings were not observed (see Chapter 6 and references [70,169].
The redistribution of spin density towards the terminal cysteine in the Ni-C state may explain the
Se
hyperfine interaction of the hydrogenase from Methanococcus voltae. This [NiFeSe] hydrogenase pos-
sesses a selenocysteine in the position of Cys530. In the oxidized state, there is no
Se hyperfine
interaction detectable in EPR while the Ni-C state exhibits a large
Se hyperfine splitting [230]. This
indicates that in the Ni-C form, unpaired spin density is transfered to the position of Cys530. Given the
ratio of the nuclear
{
-factors of
Se and of
S (1.0693/0.42911 = 2.49), a Se atom in place of the S
atom of Cys530 may display such an effect.
Se hyperfine interactions that are 2.5 times larger than the
corresponding
S are then expected.
The assignment of the large hyperfine coupling to a hydride ion in the position of the bridging ligand
is supported by a number of experimental findings. The value reported by Whitehead et al. of 16-20 MHz
agrees well with that found for the RH [70]. The coupling was shown to be solvent-exchangeable in D
O
and the corresponding deuterium-ENDOR signal was observed. Furthermore, upon photoillumination
this coupling was completely lost. Fan et al. reported a solvent-exchangeable coupling of 17 MHz at
{|
for the Ni-C form [69]. The authors also suggested a complete hyperfine tensor
= (+15, -22,
-25) MHz and argued in favour of a negative sign of the isotropic hyperfine interaction (-11 MHz) for an
in-plane bound hydride. From their work, it is not clear which
{
-tensor principal axes system and which
hyperfine tensor orientation was used by the authors. Furthermore, since no ENDOR spectrum near
{~
was reported, their estimate of the A
~
hyperfine interaction is not comprehensible. The spin-unrestricted
scalar-relativistic ZORA calculations yielded a complete tensor of (+10, -20, -16) MHz (a
bdcfe
= -9 MHz)
in its own principal axes system which agrees reasonably well with that postulated by Fan et al..
The regulatory hydrogenase from R. eutropha seems to possess an active centre that is very similar to
that of the ‘standard hydrogenases’. The composition of the Ni-Fe cluster with its three diatomic ligands
(2 CN and 1 CO) and fourcysteines coordinating the Ni and Fe atoms appearsto be very similar to that of
other ‘standard [NiFe] hydrogenases’. The role of the RH, however, is distinct from that of the ‘standard
hydrogenases’, i.e. its low activity, its resistivity towards oxygenation and the absence of S = 1/2 EPR
signals from Fe-S clusters cannot be explained by a modification of the active site. The modulation of
the function may result from a different protein environment or folding pattern. This issue cannot be
decided yet.
Further experimental investigations are necessary in order to characterize the active centre of the RH.
The determination of the
{
-tensor orientation from angular dependent EPR of protein-single crystals in
the Ni-C form (either in one of the standard hydrogenases or in the RH) may support or contradict
8.4 Discussion and Conclusion 169
the orientation obtained from relativistic DFT calculations. In frozen solution, D
O solvent exchange,
observation of the disappearance of certain ENDOR signals and subsequent
H-ENDOR or ESEEM
detection will shed more light on the hydrogen/deuteron binding site.
170
Chapter 9
Proposal of a Reaction Mechanism
Based on the findings in this thesis, the difference between the paramagnetic states of the [NiFe] hydro-
genase can be explained. Ni-A can be described as a Ni–
-oxo–Fe, Ni-B as a Ni–
-hydroxo–Fe and
Ni-C as a Ni–
-hydrido–Fe bridged cluster.
For the firsttime, a model of the oxidation states and ligand environment can be proposed: Ni remains
in its Ni(III) oxidation state in the Ni-A, Ni-B, and Ni-C forms. Ni-L originates from the Ni-C state by
photodissociation of the bridging hydride which leaves its two electrons at the Ni atom (then a formal
Ni(I) oxidation state). The CO-inhibited form Ni-CO is derived from the Ni(I)-L form; the agreement
with a CO bound to Ni-C were not satisfying.
By characterization of the paramagnetic states, one only has an incomplete picture of the complete
reaction cycle of the enzyme. The connection of the paramagnetic states isaccomplished via diamagnetic
and thus EPR-silent states Ni-Si
4g
and Ni-R. According to the above findings, a sequence of redox states
for the active site can be deduced (see Figure 9.1).
However, a number of open questions remain to be answered.
What is the role and function of the Ni and Fe metals, i.e. which of them is catalytically active?
Where does the substrate hydrogen bind?
What is the role of the Fe atom in the strong ligand field caused by the CO and CN ligands?
Does the bridging ligand facilitate or participate in the splitting of H
?
Are the cysteine amino acids likewise involved in the reaction mechanism?
Do the protein-cofactor interactions fine-tune the heterolytic splitting of hydrogen?
171
172 9. Proposal of a Reaction Mechanism
νh
- CO
hν
Τ > 120 Κ
Τ < 70 Κ + CO
Ni-A Ni-B
Ni-L Ni-CO
Ni-R
Ni-SINi-SI u r
Ni-C
Figure 9.1: Sequence of redox states in [NiFe] hydrogenase
The number of electrons that flow into the active centre and the number of protons associated with each
redox step were derived from redox titrations in the presence of dyes [40] (see Figure 9.2). These results
must be considered when a reaction mechanism is suggested. In the absence of artificial dyes, the redox
potential of the protein is controlled by the H
partial pressure in solution [12]. Then, the exact number
of redox equivalences (electrons and protons) that enter or leave the active site in each redox step cannot
be determined. Only the overall conversions of H
by all metallic cofactors can be monitored.
Ni-R
Ni-Si
Ni-C
Ni-A/B
4Fe-4S
Ni-Fe
-E/mV
3Fe-4S 4Fe-4S
∗
∗
∗
∗∗
∗ ∗
¡Y¢
¡£
¡£
¡¢
¡£
¡¢;¤
¤
¥
¥
¥
¤
Figure9.2: The redox equivalences that enter the active centre of [NiFe] hydrogenase. Symbols are explained
in the caption of Figure 2.6.
In a model for the heterolytic splitting of H
, Ni-L and Ni-CO are not considered since they do not
participate in the catalytic cycle. The investigation of those states, however, provides evidence for the
173
light-sensitivity and inhibition of this enzyme.
Ni
S
¦
Fe
Cys
§
S
¦
Cys
§
S
¦
Cys
S
¦
Cys
CO
§
CN
§
CN
§
O
¨
Ni
S
¦
Fe
Cys
§
S
¦
Cys
§
S
¦
Cys
S
¦
Cys
CO
§
CN
§
CN
§
O
¨
H
+e
©
-, +H+
Ni
S
¦
Fe
Cys
§
S
¦
Cys
§
S
¦
Cys
S
¦
Cys
CO
§
CN
§
CN
§
O
¨
HH
+e
©
-, +2H+
-H3O+
Ni
S
¦
Fe
Cys
§
S
¦
Cys
§
S
¦
Cys
S
¦
Cys
CO
§
CN
§
CN
§
H
Ni
S
¦
Fe
Cys
§
S
¦
Cys
§
S
¦
Cys
S
¦
Cys
CO
§
CN
§
CN
§
H
+e
©
-
Ni-A Ni-B
Ni-Si
Ni-C
Ni-R
+e
©
-, +2H+
+
©
H+
H
-H2
Figure 9.3: Reaction Pathway Proposed
Taking into account the results of the composition of the active centre in its paramagnetic states [Ni-A
(X = O
2ª
), Ni-B (X = OH
ª
), Ni-C (X = H
ª
)] and the redox equivalents that enter the active site in each
step (from Figure 9.2), the following picture is obtained (Figure 9.3): Upon activation of the enzyme,
first the bridging ligand may be protonated. The resulting H
O bridge would only be loosely bound and
open the coordination site at the Ni atom. H
could then be heterolytically split. The hydride remains in
the active centre as a Ni–Fe bridging ligand while the water molecule may take up the proton and leave
the active site as a H
O
. Alternatively, the proton may be released via an amino acid assisted proton
transfer chain. Formally, the completely reduced Ni-R state is one electron more reduced than Ni-C. The
axial coordination site is a possible candidate for binding of an additional proton.
This is a plausible connection of the alternating paramagnetic and diamagnetic redox states of the
active centre but there is no ultimate proof for the suggested mechanism.
All proposed intermediates 1were characterized by DFT calculations using the ADF99 [160] pro-
gram and the BP86 exchange correlation functional (for computational details see Chapter 7). A detailed
1The Ni-A, Ni-B, Ni-C and Ni-L cluster models were identified as minima on the potential energy surface by analytical
174 9. Proposal of a Reaction Mechanism
comparison of the structural parameters of the calculated paramagnetic intermediates was already done
in Chapters 5and 7and is not repeated here. Formally, the paramagnetic states correspond to Ni(III)
and the diamagnetic states to Ni(II) oxidation states. Figure 9.4 shows the obtained structures for the
intermediates. Only relevant structural parameters are given.
calculations of second derivatives. At the B3LYP/6-311+G level all harmonic frequencies were positive. Transition states
could not be obtained so far.
175
Ni
S
Fe
Cys
S
«
Cys
¬
SCys
SCys
CO
CN
¬
CN
¬
O
Ni
®
S
«
Fe
Cys
¬
SCys
S
«
Cys
S
«
Cys
CO
¬
CN
CN
¬
O
H
¯
Ni
®
S
«
Fe
Cys
SCys
S
«
Cys
S
«
Cys
CO
¬
CN
¬
CN
¬
O
H
H
Ni
®
S
«
Fe
Cys
¬
SCys
SCys
S
«
Cys
CO
¬
CN
¬
CN
¬
H
Ni
®
S
«
Fe
Cys
¬
SCys
SCys
S
«
Cys
CO
¬
CN
¬
CN
¬
H
Ni-A Ni-B
Ni-C
Ni-R H
Ni
S
Fe
Cys
S
«
Cys
¬
SCys
SCys
CO
¬
CN
CNO
H
H
¯
Ni-Si
Ni
S
Fe
Cys
S
«
Cys
¬
S
«
Cys
SCys
CO
¬
CN
CNO
H
H
H
H
Ni
®
S
«
Fe
Cys
¬
SCys
SCys
SCys
CO
¬
CN
CN
OH
H
H
¯
H
Ni
S
«
Fe
Cys
¬
SCys
SCys
SCys
CO
CN
CN
O
H
H
H
H
¯
III
IIa
III
IIIa IIIb
IIIc
IV
V
1.85 1.92
Ni-Fe 2.90
1.95 2.03
Ni-Fe 3.00
®
+ H
°
+
2.28 2.23
Ni-Fe 2.96
+ e-
3.07 2.19
Ni-Fe 3.32
+ H
°
2+
3.26
±
2.19
Ni-Fe 3.11
3.25
2.44
2.36
Ni-Fe 3.03
- H3O+
1.61 1.72
Ni-Fe 2.61
®
Ni-Fe 2.59
1.63 1.68 4.45
²
Ni-Fe 2.62
®
1.59 1.76
1.45
+ H
°
+ + e-
2.87
³
Figure 9.4: Calculated intermediates in the heterolytic splitting of H
by [NiFe] hydrogenase in the absence
of the protein environment. Selected bond distances in ˚
A.
176 9. Proposal of a Reaction Mechanism
Starting from the model for the Ni-B (II) form, a proton is added to the bridging OH
ª
ligand yielding
a S = 1/2 state with a water molecule bridging Ni and Fe (IIa). The bond distances to the water molecule
increase by 0.3 ˚
A and 0.2 ˚
A. The EPR-silent (S = 0) state Ni-Si is reached upon further adding an electron
to the cluster (III) in which the Ni–OH
bond is already broken (3.07 ˚
A). Next, molecular hydrogen may
enter the active site. It is believed to diffuse through a hydrophobic channel towards the Ni atom [231].
An axial coordination (IIIa), however, is very weak (at a distance of 3.26 ˚
A) but induces a decrease of the
Ni–Fe distance from 3.32 ˚
A to 3.11 ˚
A. When the substrate is located between the Ni and water molecule
(IIIb), a (local) minimum is reached. In an end-on coordination of the H
moiety, the Ni–H distance is
2.44 ˚
A and the shortest distance to the water molecule 2.36 ˚
A. This is accompanied by a decrease of the
Ni–Fe distance to 3.03 ˚
A. A proton transfer is only achieved when it is manually transfered to the water
molecule yielding a formal H
O
molecule (IIIc). The remaining hydride then occupies the position of
the bridging ligand. The H
O
is still hydrogen bound to the CN ligands. It may donate a proton to one
of the ligands and remain coordinated in the vicinity of the active site or diffuse as a whole H
O
away
from the active centre. Thereby, the Ni-C state (IV) is obtained. The Ni-R (V) state is diamagnetic and
contains one electron and one more proton than the Ni-C state (see [40] and references therein). An axial
coordination of a formal hydrogen atom seems most plausible.
Experimental support for the suggested structure of the Ni-R form comes from the carbon monoxide-
inhibited hydrogenase forwhich an axial coordination of theCO to the Ni was suggested (Y. Higuchi, per-
sonal communication). The crystallized reduced CO-inhibited hydrogenase from D. vulgaris Miyazaki
F shows an unusual bent form of a CO axially coordinated to the Ni atom. This is reproduced in the
calculations when the suggested Ni-R cluster model binds CO, the carbon monoxide molecule would
insert into the Ni–H bond and give the experimentally found bent coordination (see Figure 9.5).
Figure 9.6 displays the structures of the geometry-optimized intermediates.
In Chapter 7it was shown that protein environment did not have a large influence on the calculated
magnetic resonance parameters of the active centre of the [NiFe] hydrogenase. Next, it remained to be
investigated whether the protein surrounding would then participate in or assist the heterolytic cleavage
of H
. Furthermore, it was investigated whether the local minimum of H
coordination to the Ni atom
was an artefact of the cluster model approach. The suggested reaction path was then re-investigated using
a larger cluster model in which the coordinating amino acids histidine His72, serine Ser486 and arginine
Arg463 were explicitly considered. His72 forms a hydrogen bond to the bridging cysteine Cys533,
Ser486 coordinates to one of the CN ligands, and Arg486 coordinates the second CN ligand and, in the
Ni-B state, also the bridging ligand OH
ª
(see Chapter 7).
Schematically, the obtained intermediates are given in Figure 9.7.
177
r (Ni-CO)
r (C=O)
<(Ni-C-O)
r (Ni-Fe) 2.64
1.76
127
1.22
118
1.95
2.68
1.24
Figure 9.5: Comparison of Ni-R
´¶µ
structures. Left: X-ray structure of the CO-inhibited [NiFe] hydrogenase
from D. vulgaris Miyazaki F (Y. Higuchi, personal communication). Proton positions could not be deter-
mined. Right: BP86 calculated model cluster for Ni-R with CO inserted into the Ni–H
·R¸3¹ ·.º
bond. Bond
lengths (r) in ˚
A, bond angle (
»
) in degree.
178 9. Proposal of a Reaction Mechanism
Ni-A Ni-B
II
I
IIa
Ni-Si
III
IIIa IIIb
IIIc
Ni-R
V
IV
Ni-C
Figure 9.6: Geometry-optimized structures of the intermediates in the reaction cycle of [NiFe] hydrogenase
in the absence of the protein environment (for a schematic drawing see Figure 9.4).
179
Ni
SH
Fe
Cys
SCys
SCys
SCys
CO
CN
CN
ONi
SH
Fe
Cys
SCys
SCys
SCys
CO
CN
¼
CN
O
H
Ni
SH
Fe
Cys
SCys
SCys
SCys
CO
CN
CN
O
H
H
Ni
SH
Fe
Cys
SCys
SCys
SCys
CO
¼
CN
CN
H
Ni-A Ni-B
Ni-R
H
Ni
S
Fe
Cys
SCys
SCys
SCys
CO
CN
CN
O
H
H
Ni-Si
Ni
SH
Fe
Cys
SCys
SCys
SCys
CO
CN
CN
O
H
H
H
H
Ni
SH
Fe
Cys
SCys
SCys
SCys
CO
CN
CN
OH
H
H
H
Ni
S
Fe
Cys
SCys
SCys
SCys
CO
CN
CN
OH
H
H
H
III
IIa
III
IIIa IIIb
IIId
V
1.85 1.92
Ni-Fe 2.90
1.93 2.07
Ni-Fe 3.00
+ H+
2.10 2.31
Ni-Fe 2.98
+ e-
2.05 2.32
Ni-Fe 3.17
+ H2+
3.42
Ni-Fe 2.51
Ni-Fe 2.62
1.59 1.76
1.45
Arg463
His72
Ser486
Arg463
Ser486
His72
Arg463
His72
Ser486
His72
Ser486
Arg463
Ser486
2.25 2.14
Arg463
Arg463
Ser486
His72
His72
Arg463
His72
Ser486
½
Arg463
Ser486
His72
Ni
SH
Fe
Cys
SCys
S
H
Cys
SCys
CO
CN
CN
OH
H
H
Arg463
Ser486
His72
Ni
SH
Fe
Cys
SCys
SCys
SCys
CO
CN
CN
H
Ni-C
IV
1.61 1.72
Ni-Fe 2.61
Arg463
Ser486
His72
+ H+ + e-
IIIc
Figure 9.7: Calculated intermediates in the heterolytic splitting of H
by [NiFe] hydrogenase in the presence
of the protein environment. Selected bond distances in ˚
A.
180 9. Proposal of a Reaction Mechanism
When the bridging
-hydroxo ligand in the Ni-B form (II) is protonated, a paramagnetic state with a
bridging water molecule is generated (IIa). The hydrogen bond to the arginine Arg463 leads to a shorter
Ni–OH
bond distance (2.10 ˚
A) than in the absence of the arginine residue. Upon one-electron reduction,
the Ni-Si state (III) is reached. In the absence of protein interaction (Figure 9.4) the Ni–OH
bond was
already mostly broken and the water was only loosely coordinated to the Fe atom. Here, the picture
is different. The water is still firmly bound to the Ni atom (distance 2.05 ˚
A) and slightly more remote
from the Fe atom (distance 2.32 ˚
A). As in the previously suggested reaction cycle in the absence of the
protein environment, H
may approach the active centre through a hydrophobic protein channel and only
loosely coordinate the Ni atom at a distance of 3.4 ˚
A (IIIa). Still, the water molecule is held in place by
a hydrogen bond to the arginine Arg463 residue.
When the substrate comes into the vicinity of the bridging water molecule, the Ni–OH
bond breaks
and space is provided for the H
substrate (IIIb). Whereas an end-on coordination was found in the
absence of any protein environment (see Figure 9.4 IIIb), only a temporary side-on coordination of the
substrate to the Ni atom is found here. During the course of a very long geometry optimization (more
than 200 optimization steps for the 95 atom cluster model), without any bias or manual interference, the
H
substrate is split.
One hydrogen atom (the later hydride) quickly forms a bond to the neighbouring Fe atom and occu-
pies the position of the bridging ligand while the other hydrogen (considered to be a proton) is temporar-
ily taken up by the sulphur atom of the terminal cysteine Cys530 (IIIc). Finally, the cysteine donates
the proton to the approaching water molecule (IIId) and H
O
is formed. The H
O
moiety is still
hydrogen-bound to both the arginine residue and the terminal cyanides and may donate a proton to ei-
ther of these or diffuse away from the active site. Then the Ni-C state is obtained (IV) and finally the
completely reduced Ni-R state (V).
The optimized geometries of the cluster models with relevance to the splitting of H
(from IIIb to
IIId) are given in Figure 9.8
181
IIIc
IIIb
IIId
Figure 9.8: Snapshots of the geometry optimizations of the splitting of H
by [NiFe] hydrogenase. Top, left:
side-on coordination of H
(IIIb); top, right : splitting of H
; middle, right: protonation of Cysteine Cys530,
middle, left: reorientation of the protonated Cys530 (IIIc); bottom: proton transfer to the bridging ligand
(IIId).
182 9. Proposal of a Reaction Mechanism
Whereas the overall picture and the reaction products are the same in the two suggested mechanisms
with and without the consideration of the coordinating nearby amino acid residues, they strongly dif-
fer in the details. In the absence of the protein, the bridging ligand is easily removed and not directly
coordinated to the Ni atom. For the substrate, an end-on coordination to the Ni is obtained but no sponta-
neous dissociation of H
is found. The resulting hydride is found to occupy the position of the bridging
ligand while H
O
forms hydrogen bonds to the terminal cyanide ligands. The influence of the protein-
cofactor interactions is manifested in a tight coordination of the protonated bridging ligand. Arginine
Arg463 holds the bridging water molecule in close proximity to the Ni atom. For the substrate a side-on
coordination is found. In the reaction cycle, the substrate immediately dissociates and temporarily proto-
nates the terminal cysteine Cys530. This intermediate protonation of the terminal cysteine may explain
the higher activity of [NiFeSe] hydrogenases which possess a selenocysteine in the position of Cys530.
The role of the arginine residue, again, is to bring the water molecule in close contact with the protonated
cysteine and thus finally enable protonation of the water.
The suggested mechanism for the [NiFe] hydrogenase differs in some aspects from those suggested
by other authors [71–76]:
Ni was identified as the active metal site.
Ni-Si/Ni-C are the catalytically active states.
The experimentally determined number of electrons and protons that enter the active site was taken
into account.
Experimental data for the paramagnetic states were considered.
The number of experimentally determined D
O solvent-exchangeable protons is in agreement with
the suggested structures of the paramagnetic states.
The Ni atom shuttles between formal +III and +II oxidation states.
The bridging ligand is involved in the activation of the enzyme.
The Fe atom is not redox active; its role is of structural, not electronic nature.
Amino acid residues surrounding the active site have an important structural role in retaining the
position of the bridging ligand.
The terminal cysteine and the bridging ligand assist the heterolytic cleavage of H
.
183
A protonation of a cysteine residue is only short-lived and finally the protonated water molecule
may receive the proton.
To conclude, the work in this thesis has suggested structural details for the paramagnetic and dia-
magnetic states of the [NiFe] hydrogenase. In particular, care was taken to assure agreement with a vast
amount of experimental data where they were available. Many experimental data could be reproduced
within satisfying accuracy. Some experimental findings are predicted and may stimulate further work.
A plausible reaction mechanism which links the well-characterized paramagnetic states via diamag-
netic states is proposed. There is ample room to support or contradict the suggested enzymatic mecha-
nism both on the experimental and theoretical side.
The experimental determination of
{
- and hyperfine tensors in protein single crystals in the Ni-
C and Ni-L states will hopefully agree with the suggested
{
-tensor orientation from relativistic DFT
calculations. This work is in progress (S. Foerster, personal communication).
These days, very little is known about the EPR-silent states. Further characterization of these states,
e.g. additional parallel-mode detected EPR experiments on the energetic ordering of integer spin states
or time-resolved FTIR experiments which lead to more kinetic data would be helpful.
From the theoretical point of view, an efficient and reliable calculation of reaction profiles includ-
ing second derivatives and transition states on models that consist of 90-100 atoms, when the protein
environment is explicitly considered, is required in order to characterize the reaction mechanism. Fur-
thermore, there is a need for methodological extensions for simultaneously considering spin-polarization
and spin-orbit coupling in transition metal complexes.
The introduction of a mutagenesis system for the ‘standard hydrogenases’ and site-directed mutations
in the proton or electron transfer channels will further help to unravel the catalytic process of [NiFe]
hydrogenases.
184
Chapter 10
Zusammenfassung und Ausblick
In der vorliegenden Arbeit wurden [NiFe]-Hydrogenasen mit Methoden der magnetischen Reso-
nanzspektroskopie (EPR, ENDOR) und der Dichtefunktionaltheorie (DFT) untersucht. Hydrogenasen
katalysieren die reversible, heterolytische Oxidation von molekularem Wasserstoff
¾¿À ¾
ÂÁ
¾
ª
.
Das aktive Zentrum in der großen Untereinheit des Enzyms ist ein heterobimetallischer Ni-Fe-
Cluster, der von Cysteinaminos¨auren koordiniert wird. Drei anorganische Liganden sind zus¨atzliche
terminale Liganden des Eisenatoms. Ein bisher nicht eindeutig identifizierter Ligand verbr¨uckt die bei-
den Schwermetallatome. Drei Eisen-Schwefelcluster in der kleinen Untereinheit des Proteins sind am
Elektronentransfer von und zum aktiven Zentrum beteiligt. In einigen Redoxzust¨anden weist das aktive
Zentrum ungepaarte Elektronen auf und ist deshalb mit der EPR-Spektroskopie und verwandten Metho-
den untersuchbar.
Ziel dieser Doktorarbeit war es, Einsicht in die Funktionsweise dieses Metalloenzyms ¨uber die
Charakterisierung der paramagnetischen Intermediate zu erhalten.
Nickelmodellkomplexe
Die beiden anorganischen Modellkomplexe Bis(maleonitrildithiolat)-Nickelat(III) (Ni(mnt)
ª
) und Tri-
carbonylnickel(I)hydrid (Ni(CO)
H) weisen gewisse ¨
Ahnlichkeiten in der geometrischen und elektron-
ischen Struktur mit den [NiFe]-Hydrogenasen auf. F¨ur diesen beiden Komplexe wurde die Berechnung
von
Ã
- und
Ä
-Tensoren mit dem ZORA-Hamiltonoperator etabliert und kritisch mit vorhandenen exper-
imentellen Ergebnissen verglichen. Ein st¨orungstheoretischer Ansatz wurde als Vergleich ebenfalls ver-
wendet. Der Einfluß skalar-relativistischer Effekte auf die Bindungsparameter wurde diskutiert. Im De-
tail lassen sich die Einfl¨usse von skalar-relativistichen Effekten und der Spinbahnkopplung auf die Hyper-
feintensoren untersuchen. Die Ber¨ucksichtigung der Spinbahnkopplung erweist sich als unverzichtbar,
185
186 10. Zusammenfassung und Ausblick
wenn die elektronische Struktur (insbesondere die Hyperfeintensoren) von ¨
Ubergangsmetallkomplexen
mit DFT-Verfahren berechnet werden sollen. Die ¨
Ubereinstimmung mit experimentellen
Ã
-Tensoren ist
zufriedenstellend. Die Abweichung der berechneten von den experimentellen Daten ist proportional zu
der Abweichung der
{
-Werte von
{Å
. F¨ur die Hyperfeintensoren ist die ¨
Ubereinstimmung i.a. sehr gut
und die Gr¨oße der Abweichung ist wenige Prozent. Experimentelle Uneindeutigkeiten in der Bestim-
mung der Vorzeichen der Nickel- und Schwefelhyperfeintensoren in Ni(mnt)
ª
konnten mit Hilfe der
Rechnungen behoben werden.
Spindichteverteilung im aktiven Zentrum der [NiFe] Hydrogenase
F¨ur die paramagnetischen Zust¨ande Ni-A, Ni-B und Ni-C war die genaue atomare Struktur des ak-
tiven Zentrum bisher unklar. Insbesondere die Art des Nickel und Eisen verbr¨uckenden Liganden
war Gegenstand kontroverser wissenschaftlicher Diskussionen. Es konnte gezeigt werden, daß beste
¨
Ubereinstimmung mit den R¨ontgenstrukturdaten der Hydrogenase aus D. gigas erzielt werden kon-
nte, wenn der Br¨uckenligand ein O
2ª
oder OH
ª
war. Der Schwefelligand, der f¨ur die Hydrogenase
aus D. vulgaris Miyazaki F postuliert wurde, konnte nicht durch die Rechnungen best¨atigt werden,
da die berechneten strukturellen Parameter nicht in gutem Einklang mit experimentellen Ergebnissen
der R¨ontgenstrukturanalyse waren. Die berechnete Verteilung der ungepaarten Spindichte ist in guter
¨
Ubereinstimmung mit Daten der EPR- und ENDOR-Spektroskopie oder daraus abgeleiteten Ergeb-
nissen. Im Ni-C Zustand konnte gute ¨
Ubereinstimmung mit der R¨ontgenstruktur der reduzierten Hy-
drogenasen aus D. baculatum und D. vulgaris Miyazaki F erzielt werde, wenn die vakante Position
des Br¨uckenliganden in den R¨ontgenstrukturen durch ein Hydridanion besetzt wurde. Die berech-
nete Verteilung der ungepaarten Spindichte war ebenfalls in ¨
Ubereinstimmung mit vorhandenen exper-
imentellen Daten der magnetischen Resonanz. Es konnte gezeigt werde, daß die drei anorganischen,
prosthetischen Liganden am Eisenatom des aktiven Zentrums wahrscheinlich zwei Zyanidliganden und
ein Kohlenmonoxid sind. Ein f¨ur die Hydrogenase aus D. vulgaris Miyazaki F postulierter SO-Ligand
f¨uhrte in den Rechnungen zu einer großen Verschiebung der ungepaarten Spindichte. Dieser Ligand
erscheint daher wenig wahrscheinlich.
ENDOR-Kristallographie der oxidierten Zust¨
ande der [NiFe] Hydrogenase
Proteineinkristalle der [NiFe]-Hydrogenase aus D. vulgaris Miyazaki F wurden mit der gepulsten
ENDOR-Spektroskopie in den oxidierten Zust¨anden Ni-A und Ni-B untersucht. Eine Trennung der
beiden Spezies und der vier Molek¨ule in der Einheitszelle (Raumgruppe der Kristalle P2
Æ
2
Æ
2
Æ
) erfolgte
187
durch eine Analyse der rotationswinkelabh¨angigen EPR-Spektren. F¨ur den Ni-B Zustand konnten drei
Hyperfeintensoren aus den winkelabh¨angigen ENDOR-Spektren analysiert und zugeordnet werden. Die
beiden großen Kopplungen wurden
-CH
Protonen des verbr¨uckenden Cysteins Cys549 zugeordnet.
F¨ur die dritte Kopplung blieben zwei Zuordnungsm¨oglichkeiten: zu einem Proton am Br¨uckenliganden
oder zu einem
-CH
Proton des terminalen Cysteins Cys81. DFT Berechnungen der Hyperfeinten-
soren best¨atigten die Zuordnung der beiden großen Hyperfeintensoren und konnten die Uneindeutigkeit
bez¨uglich der dritten Kopplung beseitigen. Die Zuordnung zu einem
-CH
Proton des terminalen Cys-
teins Cys81 erschien am plausibelsten. Der Ni-A Zustand zeichnete sich durch eine Mikroheterogenit¨at
der Proteinumgebung aus. Die erhaltenen winkelabh¨angigen ENDOR-Spektren ließen sich nicht im De-
tail analysieren. Nichtsdestoweniger konnten die beiden großen Hyperfeinkopplungen, nicht aber die
kleinere, dritte Kopplung beobachtet werden. Dieser Befund wurden wiederum unterst¨utzt von DFT
Rechnungen.
Relativistische DFT Rechnungen an den paramagnetischen Zust¨
anden der Hydrogenase
In diesem Kapitel konnte erstmals eine Vorstellung der genauen atomaren Zusammensetzung und der
elektronischen Struktur der paramagnetischen Zust¨ande Ni-A, Ni-B, Ni-C, Ni-L und Ni-CO der [NiFe]-
Hydrogenase gewonnen werden. Im Rahmen des ZORA-Hamiltonoperators wurden eine Vielzahl von
m¨oglichen Bindungssituationen berechnet und die erhaltenen Ergebnisse mit experimentellen Daten ver-
glichen. Beste ¨
Ubereinstimmung bez¨uglich der Orientierung und Gr¨osse des
Ã
-Tensors mit den ex-
perimentellen Ergebnissen wurde erzielt, wenn der Br¨uckenligand ein OH
ª
im Ni-B Zustand ist. Die
berechneten Hyperfeinwechselwirkungen sind ebenfalls im Einklang mit experimentellen Befunden.
F¨ur den Ni-A Zustand (eine O
2ª
Br¨ucke erscheint am plausibelsten) konnte gezeigt werden, daß sich
Defizite des ZORA-Hamiltonoperators durch Ber¨ucksichtigung von Spinpolarisation im Pauli-Operator
teilweise beheben lassen. F¨ur Ni-C wurde beste ¨
Ubereinstimmung mit experimentellen Ergebnissen er-
halten, wenn ein Hydridanion die Bindungsstelle des Br¨uckenliganden einnimmt. Die vorgeschlagene
Ã
-Tensororientierung wurde sp¨ater experimentell best¨atigt. Nach den Rechnungen geht der Ni-L Zus-
tand aus dem Ni-C Zustand durch Photodissoziation des B¨uckenliganden hervor. Eine Reduktion zum
formalen Ni(I) wird vorgeschlagen. F¨ur alle Zust¨ande (Ni-A, Ni-B, Ni-C, Ni-L) wurden Hyperfeinten-
soren f¨ur
Ç
Æ
Ni,
È
Fe,
S,
Æ
O und
Æ
H berechnet und kritisch mit experimentellen Daten verglichen. Das
Enzyme wird durch Kohlenmonoxid irreversibel inhibiert. Verschiedene Bindungspositionen f¨ur das
zus¨atzliche CO-Molek¨ul wurden untersucht. Beste ¨
Ubereinstimmung mit experimentellen Ergebnisse
wurde f¨ur eine axiale Bindung an das aktive Zentrum im Ni-L Zustand erhalten. Zus¨atzlich wurden
ÆOÉ
N
Hyperfein- und Quadrupolkopplungen berechnet und diskutiert und der Einfluß der Proteinumgebung
188 10. Zusammenfassung und Ausblick
auf die elektronische Struktur des aktiven Zentrums untersucht.
Orientierungsselektierte ENDOR-Spektroskopie am Ni-C Zustand
Die regulatorische Hydrogenase (RH) aus R. eutropha weist im reduzierten Ni-C Zustand keine Spin-
Spin-Kopplung zwischen Elektronenspins des aktiven Zentrums und Fe-S Clustern auf. Dies macht
die RH eine ideale Kandidatin f¨ur die ENDOR-Charakterisierung des Ni-C Zustandes, die in der Stan-
dardhydrogenase aus D. vulgaris Miyazaki F aus dem obigen Grund nicht m¨oglich war. In gefrorener
Proteinl¨osung wurde von der Selektivit¨at der Anzahl resonanter Molek¨ule in Bezug auf das Magnet-
feld profitiert. Orientierungsselektierte gepulste ENDOR-Spektren an f¨unfzehn Feldpositionen wurden
so erhalten. Die Analyse der orientierungsselektierten Spektren erfordert eine a priori Kenntnis der
Lage des
Ã
-Tensors in der molekularen Struktur. Diese wurde aus den Rechnungen mit dem ZORA-
Hamiltonoperator gewonnen. Zusammen mit den berechneten Gr¨oßen und Orientierungen der Proto-
nenhyperfeintensoren im Ni-C Zustand konnten insgesamt f¨unf Protonen zugeordnet werden Vier davon
r¨uhren von den beiden
-CH
Protonen des terminalen Cysteins Cys530 und des verbr¨uckenden Cysteins
Cys549 her. Das f¨unfte Proton wurde dem verbr¨uckenden Liganden H
ª
zugeordnet.
Vorschlag eines Reaktionsmechanismus
Die oben erw¨ahnten Einblicke in die verschiedenen paramagnetischen Zust¨ande wurden in diesem Kapi-
tel zusammengef¨ugt, um einen plausible Reaktionsmechanismus des Enzyms vorzuschlagen. Ni-A und
Ni-B unterscheiden sich in ihren Aktivierungskinetiken unter reduzierenden Bedingungen. Die Freiset-
zung des Br¨uckenliganden und die Aufnahme eines Hydridanions in diese Bindungsposition scheinen die
Aktivierung des Enzyms darzustellen. Ein plausibler Reaktionsweg, der die gewonnene Einsicht in die
paramagnetischen Zust¨ande verbindet mit den Redox¨aquivalenten und Protonen, die das aktive Zentrum
in jedem Reaktionsschritt aufnimmt, wurde konstruiert. In der Abwesenheit der Proteinumgebung wird
ein Modelle f¨ur alle Zwischenzust¨ande vorgeschlagen. Das so gew¨ahlte Modell ist aber nicht von sich aus
katalytisch aktiv, d.h. H
-Spaltung setzte nicht spontan ein. Erst nach der expliziten Ber¨ucksichtigung
der Aminos¨auren Arginin Arg463, Histidin His72 und Serin Ser486 konnte ein Reaktionszyklus erhalten
werden, in dem die heterolytische Dissoziation von H
ein spontan ablaufenden Prozeß ist. Das termi-
nale Cystein Cys530 agiert demnach tempor¨ar als Base und nimmt das Proton aus der heterolytischen
H
-Spaltung auf. Das Proton wird an den modifizierten Br¨uckenliganden weitergegeben und kann als
H
O
oder ¨uber einen Protonentransferkanal das aktive Zentrum verlassen. In diesem vorgeschlagenen
Mechanismus ist das Nickelatom das katalytisch aktive Metall. Dem Eisenatom und der Proteinumge-
189
bung kommen demnach Rollen struktureller Natur zu, z. B. die Positionierung des Br¨uckenliganden, so
daß dieser an der Aufnahme des Protons beteiligt werden kann.
Ausblick
In dieser Arbeit konnte Einsicht in die paramagnetischen Zust¨ande und den Reaktionsmechanismus der
[NiFe]-Hydrogenase gewonnen werden. Die Resultate k¨onnen noch viele zuk¨unftige Experimente stim-
ulieren bzw. zur Analyse von experimentellen Befunden beitragen. Die experimentelle Bestimmung der
Lage der
Ã
-Tensoren in den Ni-C und Ni-L Zust¨anden k¨onnte durch die hier vorgeschlagenen vereinfacht
werden. Derzeit wird daran in der AG Lubitz gearbeitet (S. Foerster, pers¨onliche Mitteilung). Verglichen
mit den paramagnetischen Zust¨anden weiß man heute relativ wenig ¨uber die diamagnetischen Interme-
diate. Mit der zeitaufgel¨oste FTIR-Spektroskopie k¨onnte man wichtige Aussagen ¨uber Kinetiken der
Zustandsumwandlungen gewinnen. Mit der EPR-Spektroskopie in paralleler Detektion ließen sich noch
viele interessante Einzelheiten ¨uber diese Zust¨ande hervorbringen, d.h. die energetische Lage von ganz-
zahligen Spinzust¨anden k¨onnte bestimmt werden.
Von der theoretischen Seite ist die genaue Berechnung von Reaktionsbarrieren und die Lokalisierung
von ¨
Ubergangszust¨anden f¨ur Systeme von der Gr¨osse von 90-100 Atomen zwingend n¨otig, um zu-
verl¨assige Aussagen ¨uber einen m¨oglichen Reaktionsmechanismus machen zu k¨onnen. Weitere method-
ische Arbeit ist zur gleichzeitigen Behandlung von Spinbahnkopplung und Spinpolarisation notwendig,
um dadurch das Verst¨andnis der elektronischen Struktur von ¨
Ubergangsmetallkomplexen und -enzymen
zu vertiefen.
Bisher existieren nur ungenaue Vorstellungen ¨uber einen m¨oglichen Protonen- oder Elektronentrans-
ferweg in der [NiFe]-Hydrogenase. Die Etablierung eines Mutagenesesystems f¨ur ‘Standardhydroge-
nasen’ und ortsgerichtete Mutationen im Protonen- oder Elektronentransferweg (Austausch von poten-
tiell am Transfer beteiligten Aminos¨auren gegen andere und Beobachtung der Auswirkung der Mutatio-
nen auf die Transferraten) wird dazu beitragen, die Spaltung von molekularem Wasserstoff durch dieses
Metalloenzym bei Raumtemperatur zu verstehen.
190
Bibliography
[1] Hoppe-Seyler, F. Z. Physiol. Chem. 1887 11, 561.
[2] C.Pakes, W. C.; Jollyman, W. H. J. Chem. Soc. 1901 79, 386.
[3] Harden, A. J. Chem. Soc. 1901 79, 601.
[4] Stephenson, M.; Stickland, L. H. Biochem. J. 1931 25, 205.
[5] Tuner, J. A. Science 1999 285, 687.
[6] Carrette, L.; Collins, J.; Dickinson, A.; Stimming, U. Bunsen-Magazin 2000 2, 27.
[7] Appleby, A. J. Scientific American 1999, 74.
[8] Cammack, R. Nature 1999 397, 214.
[9] Maroney, M. J.; Davidson, G.; Allan, C. B.; Figlar, J. Struct. Bond. 1998 92, 1.
[10] Frausto Da Silva, J. J. R.; Williams, R. J. P. The Biological Chemistry of the Elements : The Inorganic Chemistry of Life
Clarendon Press, Oxford, UK, 1994.
[11] Fontecilla-Camps, J. C.; Volbeda, A.; Frey, M. Trends Biotechn. 1996 14, 417.
[12] Albracht, S. P. J. Biochim. Biophys. Acta 1994 1188, 167.
[13] Adams, M. W. W. Biochim. Biophys. Acta 1990 1020, 115.
[14] Thauer, R. K.; Klein, A. R.; Hartmann, G. C. Chem. Rev. 1996 96, 3031.
[15] Voordouw, G. In: Advances in Inorganic Chemistry Vol. 38, R. Cammack and A. Sykes (Eds.), Academic Press, London,
1992, pp. 397–422.
[16] Hedderich, R.; Klimmek, O.; Kr¨oger, A.; Dirmeier, R.; Keller, M.; Stetter, K. O. FEMS Microbiol. Revs. 1999 22, 353.
[17] Adams, M. W. W.; Mortenson, L. E.; Chen, J.-S. Biochim. Biophys. Acta 1981 594, 105.
[18] Przybyla, A. E.; Robbins, J.; Menon, N.; Peck Jr., H. D. FEMS Microbiol. Rev. 1992 88, 109.
[19] Wu, L.-F.; Mandrand, M. A. FEMS Microbiol. Revs. 1993 104, 243.
[20] Rakhely, G.; Colbeau, A.; Garin, J.; Vignais, P. M.; Kovacs, K. L. J. Bact. 1998 180, 1460.
[21] Dahl, C.; Rakhely, G.; Pott-Sperling, A. S.; Fodor, B.; Takacs, M.; Toth, A.; Kraeling, M.; Gy¨orfi, K.; Kovacs, A.; Tusz,
J.; Kovacs, K. L. FEMS Microbiol. Letts. 1999 180, 317.
[22] Volbeda, A.; Fontecilla-Camps, J. C.; Frey, M. Curr. Op. Struct. Biol. 1996 6, 804.
[23] Ermler, U.; Grabarse, W.; Shima, S.; Goubeaud, M.; Thauer, R. K. Curr. Op. Struc. Biol. 1998 8, 749.
191
192 BIBLIOGRAPHY
[24] Ragsdale, S. W. Curr. Op. Chem. Biol. 1998 2, 208.
[25] Maroney, M. Curr. Op. Chem. Biol. 1999 3, 188.
[26] Karplus, P. A.; Pearson, M. A.; Hausinger, R. P. Acc. Chem. Res. 1997 30, 330.
[27] Volbeda, A.; Garcin, E.; Piras, C.; de Lacey, A. L.; Fernandez, V. M.; Hatchikian, E. C.; Frey, M.; Fontecilla-Camps,
J. C. J. Am. Chem. Soc. 1996 118, 12989.
[28] Higuchi, Y.; Yagi, T.; Yasuoka, N. Structure 1997 5, 1671.
[29] Ermler, U.; Grabarse, W.; Shima, S.; Goubeaud, M.; Thauer, R. K. Science 1997 278, 829.
[30] Peters, J. W.; Lanzilotta, W. N.; Lemon, B. J.; Seefeldt, L. C. Science 1998 282, 1853.
[31] Nicolet, Y.; Piras, C.; Legrand, P.; Hatchikian, C. E.; Fontecilla-Camps, J. C. Structure 1998 7, 13.
[32] Volbeda, A.; Charon, M.-H.; Piras, C.; Hatchikian, E. C.; Frey, M.; Fontecilla-Camps, J. C. Nature 1995 373, 580.
[33] Fontecilla-Camps, J. C. J. Biol. Inorg. Chem. 1996 1, 91.
[34] Frey, M. Structure and Bonding 1998 90, 97.
[35] Garcin, E.; Montet, Y.; Volbeda, A.; Hatchikian, C.; Frey, M.; Fontecilla-Camps, J. C. Biochm. Soc. Trans. 1988 26,
396.
[36] Rousset, M.; Montet, Y.; Guigliarelli, B.; Forget, N.; Asso, M.; Betrand, P.; Fontecilla-Camps, J. C.; Hatchikian, E. C.
Proc. Natl. Acad. Sci. USA 1998 95, 11625.
[37] Higuchi, Y.; Yasuoka, N.; Kakudo, M.; Katsube, Y.; Yagi, T.; Inokuchi, H. J. Biol. Chem. 1987 262, 28823.
[38] Higuchi, Y.; Okamoto, T.; Fujimoto, K.; Misaki, S. Acta Cryst. D 1994 50, 781.
[39] Asso, M.; Guigliarelli, B.; Yagi, T.; Bertrand, P. Biochim. Biophys. Acta 1992 1122, 50.
[40] Cammack, R.; Patil, D. S.; Hatchikian, E. C.; Fernandez, V. M. Biochim. Biophys. Acta 1987 912, 98.
[41] Lancaster Jr., J. R. FEBS Lett. 1980 115, 285.
[42] Graf, E.-G.; Thauer, R. K. FEBS Lett. 1981 136, 165.
[43] Fernandez, V. M.; Hatchikian, E. C.; Cammack, R. Biochim. Biophys. Acta 1985 832, 69.
[44] Dole, F.; Fournel, A.; Magro, V.; Hatchikian, E. C.; Bertrand, P.; Guigliarelli, B. Biochemistry 1997 36, 7847.
[45] Moura, J. J. G.; Moura, I.; Huynh, B. H.; Kr¨uger, H.-J.; Teixeira, M.; DuVarney, R. G.; DerVartanian, D. V.; Ljungdahl,
P.; Xavier, A. V.; ad J. LeGall, H. D. P. Biochem. Biophys. Res. Comm. 1982 108, 1388.
[46] Guigliarelli, B.; More, C.; Fournel, A.; Asso, M.; Hatchikian, E. C.; Williams, R.; Cammack, R.; Bertrand, P. Biochem-
istry 1995 34, 4781.
[47] Betrand, P.; Camensuli, P.; More, C.; Guigliarelli, B. J. Am. Chem. Soc. 1996 118, 1426.
[48] Dole, F.; Medina, M.; More, C.; Cammack, R.; Bertrand, P.; Guigliarelli, B. Biochemistry 1996 35, 16399.
[49] Bagley, K. A.; Van Garderen, C. J.; Chen, M.; Duin, E. C.; Albracht, S. P. J.; Woodruff, W. H. Biochemistry 1994 33,
9229.
[50] Bagley, K. A.; Duin, E. C.; Roseboom, W.; Albracht, S. P. J.; Woodruff, W. H. Biochemistry 1995 34, 5527.
[51] Happe, R. P.; Roseboom, W.; Pierik, A. J.; Albracht, S. P. J. Nature 1997 385, 126.
BIBLIOGRAPHY 193
[52] Jonas, V.; Thiel, W. J. Chem. Phys. 1996 105, 3636.
[53] Jensen, F. Chem. Phys. Lett. 1990 169, 519.
[54] de Lacey, A. L.; Hatchikian, E. C.; Volbeda, A.; Frey, M.; Fontecilla-Camps, J. C.; fernandez, V. M. J. Am. Chem. Soc.
1997 119, 7181.
[55] Davidson, G.; Choudbury, S. B.; Gu, Z.; Bose, K.; Roseboom, W.; Albracht, S. P. J.; Maroney, M. J. Biochemistry 2000
39, 7468.
[56] Hsu, H.-F.; Koch, S. A.; Popescu, C. V.; M¨unck, E. J. Am. Chem. Soc. 1997 119, 8371.
[57] Coremans, J. M. C. C.; van Garderen, C. J.; Albracht, S. P. J. Biochim. Biophys. Acta 1992 1119, 148.
[58] Happe, R. H.; Roseboom, W.; Albracht, S. P. J. Eur. J. Biochem. 1999 259, 602.
[59] Albracht, S. P. J.; Graf, E. G.; Thauer, R. K. FEBS Letts. 1982 140, 311.
[60] Erkens, A.; Schneider, K.; M¨uller, A. J. Biol. Inorg. Chem. 1996 1, 99.
[61] Huyett, J. E.; Carepo, M.; Pamplona, A.; Franco, R.; Moura, I.; Moura, J. J. G.; Hoffman, B. M. J. Am. Chem. Soc. 1997
119, 9291.
[62] Albracht, S. P. J.; Kr¨oger, A.; der Zwaan, J. W. V.; Unden, G.; B¨ocher, R.; Mell, H.; Fontijn, R. D. Biochim. Biophys.
Acta 1986 874, 116.
[63] van der Zwaan, J. W.; Coremans, J. M. C. C.; Bouwens, E. C. M.; Albracht, S. P. J. Biochim. Biophys. Acta 1990 1041,
101.
[64] Lancaster Jr., J. R. Science 1982 216, 1324.
[65] Lancaster, Jr., J. R., ed. The Bioinorganic Chemistry of Nickel VCH, Weinheim, 1988.
[66] Moura, J. J. G.; Teixeira, M.; Moura, I.; LeGall, J. In: The Bioinorganic Chemistry of Nickel, J. R. Lancaster, Jr. (Ed.),
VCH, Weinheim, 1988, pp. 191–226.
[67] van der Zwaan, J. W.; Albracht, S. P. J.; Fintijn, R. D.; Slater, E. C. FEBS Lett. 1985 179, 271.
[68] Chapman, A.; Cammack, R.; Hatchikian, E. C.; McCracken, J.; Peisach, J. FEBS Lett. 1988 242, 134.
[69] Fan, C.; Teixeira, M.; Moura, J.; Moura, I.; Huynh, B.-H.; Gall, J. L.; Peck, H. D. J.; Hoffman, B. M. J. Am. Chem. Soc.
1991 113, 20.
[70] Whitehead, J. P.; Gurbiel, R. J.; Bagyinka, C.; Hoffman, B. M.; Maroney, M. J. J. Am. Chem. Soc. 1993 115, 5629.
[71] Pavlov, M.; Siegbahn, P. E. M.; Blomberg, M. R. A.; Crabtree, R. H. J. Am. Chem. Soc. 1998 120, 548.
[72] Pavlov, M.; Blomberg, M. R. A.; Siegbahn, P. E. M. Intern. J. Quant. Chem. 1999 73, 197.
[73] DeGioia, L.; Fantucci, P.; Guigliarelli, B.; Bertrand, P. Inorg. Chem. 1999 38, 2658.
[74] DeGioia, L.; Fantucci, P.; Guigliarelli, B.; Bertrand, P. Int. J. Quant. Chem. 1999 73, 187.
[75] Niu, S.; Thomson, L. M.; Hall, M. B. J. Am. Chem. Soc. 1999 121, 4000.
[76] Amara, P.; Volbeda, A.; Fontecilla-Camps, J. C.; Field, M. J. J. Am. Chem. Soc. 1999 121, 4468.
[77] Atherton, N. M. Principles of Electron Spin Resonance Ellis Horwood PTR Prentice Hall, New York, 1993.
[78] Weil, J. A.; Bolton, J. R.; Wertz, J. E. Electron Paramagnetic Resonance Wiley and Sons Inc., New York, 1994.
194 BIBLIOGRAPHY
[79] Abragam, A.; Bleaney, B. Electron Paramagnetic Resonance of Transition Ions Clarendon Press, Oxford, UK, 1970.
[80] Mabbs, F. E.; Collison, D. Electron Paramagnetic Resonance of d Transition Metal Compounds Elsevier, Amsterdam,
1992.
[81] Pilbrow, J. R. Transition Ion Electron Paramagnetic Resonance Clarendon Press, Oxford, UK, 1990.
[82] Feher, G. Phys. Rev. 1956 103, 834.
[83] Schweiger, A. Angew. Chem. Int. Ed. Engl. 1991 30, 265.
[84] Gemperle, C.; Schweiger, A. Chem. Rev. 1991 91, 1481.
[85] Kurreck, H.; Kirste, B.; Lubitz, W. Electron Nuclear Double Resonance Spectroscopy of Radicals in Solution VCH,
Weinheim, Germany, 1988.
[86] McConnell, H. M. J. Chem. Phys. 1956 24, 764.
[87] Harriman, J. E. Theoretical Foundations of Electron Spin Resonance Academic Press Inc., New York, 1978.
[88] Lowe, D. J. ENDOR and EPR of Metalloproteins R. G. Landes Co., UK, 1995.
[89] Parr, R.; Yang, W. Density-Functional Theory of Atoms and Molecules Oxford University Press, New Yorck, New Yorck,
1989.
[90] Koch, W.; Holthausen, M. C. A Chemist’s Guide to Density Functional Theory WILEY-VCH, Weinheim, Germany,
2000.
[91] Becke, A. D. Phys. Rev. A 1988 38, 3098.
[92] Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988 37, 785.
[93] Perdew, J. P. Phys. Rev. 1986 B33, 8822.
[94] Hamprecht, F. A.; Cohen, A. J.; Tozer, D. J.; Handy, N. C. J. Chem. Phys. 1998 109, 6264.
[95] Becke, A. D. J. Chem. Phys. 1993 98, 5648.
[96] Stevens, P. J.; Devlin, J. F.; Chabalowski, C. F.; Frisch, M. J. J. Phys. Chem. 1994 98, 11623.
[97] Ziegler, T. Chem. Rev. 1991 91, 651.
[98] Ziegler, T. Can. J. Chem. 1995 73, 743.
[99] Koch, W.; Hertweg, R. H. In: Encyclopedia of Computational Chemistry, P. von Ragu´e Schleyer (Ed.), Wiley and Sons
Inc., New York, 1998, pp. 900–920.
[100] C. W. Bauschlicher Jr. In: Encyclopedia of Computational Chemistry, P. von Ragu´e Schleyer (Ed.), Wiley and Sons Inc.,
New York, 1998, pp. 3084–3094.
[101] Siegbahn, P. E. M. In: Advances in Chemical Physics Vol. XCIII, I. Prigogine and S. A. Rice (Eds.), Wiley and Sons
Inc., New York, 1996, pp. 333–388.
[102] Jonas, V.; Thiel, W. J. Chem. Phys. 1995 102, 8474.
[103] Siegbahn, P. E. M.; Blomberg, M. R. A. Chem. Rev. 2000 100, 421.
[104] Pykk¨o, P. Chem. Rev. 1988 88, 563.
[105] Visscher, L.; Aerts, P. J. C.; Nieuwpoort, W. C. J. Chem. Phys. 1992 96, 2910.
BIBLIOGRAPHY 195
[106] Visscher, L.; Visser, O.; Aerts, P. J. C.; Merenga, H.; Nieuwpoort, W. C. Comp. Phys. Commun. 1994 81, 120.
[107] van W¨ullen, C. J. Comput. Chem. 1999 20, 51.
[108] Ziegler, T. J. Chem. Phys. 1981 74, 1271.
[109] Knappe, P.; R¨osch, N. J. Chem. Phys. 1990 92, 1153.
[110] Frenking, G.; Antes, I.; Boehme, M.; Dapprich, S.; Ehlers, A. W.; Jonas, V.; Neuhaus, A.; Otto, M.; Stegmann, R.;
Veldkamp, A.; Vyboishchikov, S. In: Rev. Comp. Chem. Vol. 8, K. B. Lipkowitz and D. B. Boyd (Eds.), Wiley and Sons
Inc., New York, 1996, pp. 63–143.
[111] Cundari, T. R.; Benson, M. T.; Lutz, L.; Sommer, S. O. In: Rev. Comp. Chem. Vol. 8, K. B. Lipkowitz and D. B. Boyd
(Eds.), Wiley and Sons Inc., New York, 1996, pp. 145–202.
[112] van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1993 99, 4597.
[113] van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1994 101, 9783.
[114] Chang, C.; P´elissier, M.; Durand, P. Phys. Scr. 1986 34, 394.
[115] Pople, J. A.; Beveridge, D. L.; Dobosh, P. A. J. Am. Chem. Soc. 1968 90, 4201.
[116] Plato, M.; Tr¨ankle, E.; Lubitz, W.; Lendzian, F.; M¨obius, K. Chem. Phys. 1986 107, 185.
[117] Karna, S. P.; Grein, F.; Engels, B.; Peyerimhoff, S. D. Int. J. Quant. Chem. 1989 36, 255.
[118] Feller, D.; Davidson, E. R. In: Theoretical Models of Chemical Bonding Vol. 3, Z. B. Maksic (Ed), Springer-Verlag,
Heidelberg, Germany, 1991, pp. 430–453.
[119] Chipman, D. M. In: Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy, S. R. Langhoff
(Ed.), Kluwer, Amsterdam, 1995, pp. 109–138.
[120] Eriksson, L. A.; Wang, J.; Boyd, R. J. Chem. Phys. Letts. 1993 211, 88.
[121] Barone, V.; Adamo, C.; Russo, N. Chem. Phys. Letts. 1993 212, 5.
[122] Barone, V. In: Recent Advances in Density Functional Methods Part I, D. P. Chong (Ed.), World Scientific, Singapore,
1995, pp. 287–304.
[123] Malkin, V. G.; Malkina, O. L.; Eriksson, L. A.; Salahub, D. R. In: Modern Density Functional Theory: A Tool for
Chemistry, J. M. Seminario and P. Politzer (Eds.), Elsevier, Amsterdam, 1995, pp. 273–347.
[124] Eriksson, L. A. In: Encyclopedia of Computational Chemistry, P. von Ragu´e-Schleyer (Ed.), Wiley and Sons Inc., New
York, 1998, pp. 952–958.
[125] Engels, B.; Eriksson, L. A.; Lunell, S. Adv. Quantum Chem. 1996 27, 297.
[126] Munzarova, M.; Kaupp, M. J. Phys. Chem A 1999 103, 9966.
[127] Hayes, R. G. Inorg. Chem. 2000 39, 156.
[128] Belanzoni, P.; Baerends, E. J.; van Asselt, S.; Langewen, P. B. J. Phys. Chem. 1995 99, 13094.
[129] Belanzoni, P.; Baerends, E. J.; Gribnau, M. J. Phys. Chem. A 1999 103, 3732.
[130] Swann, J.; Westmoreland, T. D. Inorg. Chem. 1997 36, 5348.
[131] van Lenthe, E.; van der Avoird, A.; Wormer, P. E. S. J. Chem. Phys. 1998 108, 4783.
196 BIBLIOGRAPHY
[132] van Lenthe, E.; Snijders, J. G.; Baerends, E. J. J. Chem. Phys. 1996 105, 6505.
[133] T¨orring, J. T.; Un, S.; K¨upling, M.; Plato, M.; M¨obius, K. J. Chem. Phys. 1997 107, 3905.
[134] Lushington, G. H.; Bundgen, P.; Grein, F. Int. J. Quant. Chem. 1995 55, 377.
[135] Engstr¨om, M.; Minaev, B.; Vahtras, O.; ˚
Agren, H. Chem. Phys. 1998 237, 149.
[136] Jayatilaka, D. J. Chem. Phys. 1998 108, 7587.
[137] Tachikawa, H. Chem. Phys. Lett. 1996 260, 582.
[138] Bruna, P. J.; Grein, F. J. Chem. Phys. 1998 109, 9439.
[139] Lushington, G. H. J. Phys. Chem. A 2000 104, 2969.
[140] Vahtras, O.; Minaev, B.; ˚
Agren, H. Chem. Phys. Lett. 1997 281, 186.
[141] Engstr¨om, M.; Himo, F.; Gr¨aslund, A.; Minaev, B.; Vahtras, O.; Agren, H. J. Phys. Chem. A 2000 104, 5149.
[142] Schreckenbach, G.; Ziegler, T. J. Phys. Chem. A 1997 101, 3388.
[143] Patchkovskii, S.; Ziegler, T. J. Chem. Phys. 1999 111, 5730.
[144] Patchkovskii, S.; Ziegler, T. J. Am. Chem. Soc. 2000 122, 3506.
[145] Schreckenbach, G.; Ziegler, T. Theor. Chem. Acc. 1998 99, 71.
[146] van Lenthe, E.; Wormer, P. E. S.; van der Avoird, A. J. Chem. Phys. 1997 107, 2488.
[147] Malkina, O.; Vaara, J.; Schimmelpfennig, B.; Munzarova, M.; Malkin, V. G.; Kaupp, M. J. Am. Chem. Soc. 2000 122,
9206.
[148] Halcrow, M. A.; Christou, G. Chem. Rev. 1994 94, 2421.
[149] Maki, A. H.; Edelstein, N.; Davison, A.; Holm, R. H. J. Am. Chem. Soc. 1964 86, 4580.
[150] Schmitt, R. D.; Maki, A. H. J. Am. Chem. Soc. 1968 90, 2288.
[151] Huyett, J. E.; Choudhury, S. B.; Eichhorn, D. M.; Bryngelson, P. A.; Maroney, M. J.; Hoffman, B. M. Inorg. Chem. 1998
37, 1361.
[152] Sano, M.; Adachi, H.; Yamatera, H. Bull. Chem. Soc. Jpn. 1981 54, 2636.
[153] Kraffert, C.; Walther, D.; Peters, K.; Lindqvist, O.; Langer, V.; Sieler, J.; Reinhold, J.; Hoyer, E. Z. Anorg. Allg. Chem.
1990 588, 167.
[154] Shiozaki, H.; Nakazumi, H.; Kitao, T. J. Jpn. Soc. Col. Mat. 1987 60, 415.
[155] Blomberg, M. A.; Wahlgren, U. Chem. Phys. 1980 49, 117.
[156] Hjalmars, I. F.; Henrickson-Enflo, A. I. J. Quant. Chem. 1980 18, 409.
[157] Zakharov, I. I.; Startsev, A. N.; Yudanov, I. V.; Zhidomirov, G. M. J. Struct. Chem. 1996 37, 201.
[158] Arca, M.; Demartin, F.; Devillanova, F. A.; Garau, A.; Isai, F.; Lelj, F.; Lippols, V.; Pedraglio, S.; Verani, G. J. Chem.
Soc. Dalton Trans. 1998 22, 3731.
[159] Morton, J. R.; Preston, K. F. J. Magn. Res. 1978 30, 577.
[160] Theoretical Chemistry Amsterdam Density Functional (ADF), Rev. 1999 Vrije Universiteit De Boelelaan 1083, NL-1081
HV Amsterdam, The Netherlands.
BIBLIOGRAPHY 197
[161] te Velde, G.; Baerends, E. J. Int. J. Quant. Chem. 1992 99, 84.
[162] van Lenthe, E.; Ehlers, A.; Baerends, E. J. J. Chem. Phys. 1999 110, 8943.
[163] Becke, A. D. J. Chem. Phys. 1986 84, 4524.
[164] Perdew, J. P. Phys. Rev. 1986 B34, 7406.
[165] Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.;
Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman,
J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong,
M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker,
J.; Stewart, J. P.; Head-Gordon, M.; Gonzalez, C.; Pople, J. A. Gaussian94, Revision D.2 Gaussian Inc., Pittsburgh PA
1995.
[166] Kobayashi, A.; Sasaki, Y. Bull. Chem. Soc. Jpn. 1977 50, 2650.
[167] Sch¨afer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992 97, 2571.
[168] W. E. Geiger, J.; Allen, C. S.; Mines, T. E.; Senftleber, F. C. Inorg. Chem. 1977 16, 2003.
[169] Geßner, C.; Stein, M.; Albracht, S. P. J.; Lubitz, W. J. Biol. Inorg. Chem. 1999 4, 379.
[170] Morton, J. R.; Preston, K. F. J. Chem. Phys. 1984 81, 5775.
[171] Volbeda, A.; Charon, M.-H.; Piras, C.; Hatchikian, E. C.; Frey, M.; Fontecilla-Camps, J. C. Nature 1995 373, 580.
[172] Higuchi, Y.; Yagi, T. Biochem. Biophys. Res. Com. 1999 255, 295.
[173] Pierik, A. J.; Roseboom, W.; Happe, R. P.; Bagley, K. A.; Albracht, S. P. J. J. Biol. Chem. 1999 274, 3331.
[174] Higuchi, Y.; Ogata, H.; Miki, K.; Yasuoka, N.; Yagi, T. Structure 1999 7, 549.
[175] DGauss4.0 Cray Res. Inc., San Diego 1995.
[176] Godbout, N.; Salahub, D. R.; Andzelm, J.; Wimmer, E. Can. J. Chem. 1992 70, 560.
[177] Neese, F.; Kappl, R.; H¨uttermann, J.; Zumft, W. G.; Kroneck, P. M. H. J. Biol. Inorg. Chem. 1998 3, 53.
[178] Barone, V.; Adamo, C. Intern. J. Quant. Chem. 1997 61, 443.
[179] Geßner, C.; Trofanchuk, O.; Kawagoe, K.; Higuchi, Y.; Yasuoka, N.; Lubitz, W. Chem. Phys. Lett. 1996 256, 518.
[180] Surerus, K. K.; Chen, M.; der Zwaan, W. V.; Rusnak, F. M.; Kolk, M.; Duin, E. C.; Albracht, S. P. J.; M¨unck, E.
Biochemistry 1994 33, 4980.
[181] Gu, Z.; Dong, J.; Allen, C. B.; Choudbury, S. B.; Franco, R.; Moura, J. J. G.; Moura, I.; LeGall, J.; Przybyla, A. E.;
Roseboom, W.; Albracht, S. P. J.; Axley, M. J.; Scott, R. A.; Maroney, M. J. J. Am. Chem. Soc. 1996 118, 11155.
[182] Stein, M.; Trofanchuk, O.; Brecht, M.; Lendzian, F.; Bittl, R.; Higuchi, Y.; Lubitz, W. manuscript in preparation 2001.
[183] Trofanchuk, O.; Stein, M.; Geßner, C.; Lendzian, F.; Higuchi, Y.; Lubitz, W. J. Biol. Inorg. Chem. 2000 5, 36.
[184] Brecht, M.; Stein, M.; Trofanchuk, O.; Lendzian, F.; Bittl, R.; Higuchi, Y.; Lubitz, W. In: Magnetic Resonance and
Related Phenomena Vol. II, D. Ziessow, F. Lendzian, W. Lubitz (Eds.), TU Berlin, 1998, pp. 818–819.
[185] Garcin, E.; Vernede, X.; Hatchikian, E.; Volbeda, A.; Frey, M.; Fontecilla-Camps, J. C. Structure 1999 7, 557.
[186] Bagyinka, C.; Whitehead, J. P.; Maroney, M. J. J. Am. Chem. Soc. 1993 115, 3576.
198 BIBLIOGRAPHY
[187] Rist, G. H.; Hyde, J. S. J. Chem. Phys. 1970 52, 4633.
[188] H¨uttermann, J. In: Biological Magnetic Resonance Vol. 13, L. J. Berliner and J. Reuben (Eds.), Plenum Press, New York,
1993, pp. 219–252.
[189] Hoffman, B. M.; DeRose, V. L.; Doan, P. E.; Gurbiel, R. J.; Houseman, A. L. P.; Telser, J. In: Biological Magnetic
Resonance Vol. 13, L. J. Berliner and J. Reuben (Eds.), Plenum Press, New York, 1993, pp. 151–218.
[190] Trofanchuk, O.; Stein, M.; Gessner, C.; Lendzian, F.; Higuchi, Y.; Lubitz, W. J. Biol. Inorg. Chem. 2000 5, 36.
[191] Dinse, K. P. In: Advanced EPR - Applications in Biology and Biochemistry, A. J. Hoff (Ed.), Elsevier, Amsterdam, 1989,
pp. 615–631.
[192] Coremans, J. W. A.; Poluektov, O. G.; Groenen, E. J. J.; Nar, G. W. C. H.; Messerschmidt, A. J. Am. Chem. Soc. 1996
118, 12141.
[193] Mims, W. B. Proc. R. Soc. London 1965 283, 452.
[194] Davies, E. R. Phys. Lett. A 1974 47A, 1.
[195] Doan, P. E.; Fan, C.; Hoffman, B. M. J. Am. Chem. Soc. 1994 116, 1033.
[196] Geßner, C. NiFe-Hydrogenasen: Beitr¨age der EPR-Spektroskopie zur Strukturaufkl¨arung des aktiven Zentrums Ph.D.
thesis Technische Universit¨at Berlin 1996.
[197] Wachters, A. J. H. J. Chem. Phys. 1970 52, 1033.
[198] Hay, P. J. J. Chem. Phys. 1977 66, 4377.
[199] Raghavachari, K.; Truck, G. W. J. Chem. Phys. 1989 91, 1062.
[200] McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980 72, 5639.
[201] Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980 72, 650.
[202] Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984 80, 3265.
[203] Reed, A. E.; Curtiss, L. A. Chem. Rev. 1988 88, 899.
[204] Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. NBO Version 3.1.
[205] BRUKER Analytische Messtechnik In: Pulsed EPR: A new field of applications, C. P. Keijzers, E. J. Reijerse and J.
Schmidt (Eds.), North Holland, Amsterdam, 1989, pp. 81-88.
[206] Atherton, N. M. Principles of Electron Spin Resonance Prentice Hall, New York, 1993.
[207] Mouesca, J.-M.; Rius, G.; Lamotte, B. J. Am. Chem. Soc. 1993 115, 4714.
[208] Teixera, M.; Moura, I.; Xavier, A. V.; Dervartanian, D. V.; LeGall, J.; Jr., H. D. P.; Huynh, B. H.; Moura, J. G. Eur. J.
Biochem. 1983 130, 481.
[209] Trofanchuk, O. Catalytic Center of [NiFe] Hydrogenases. EPR, ENDOR and FTIR Studies Ph.D. thesis TU Berlin 2000.
[210] Biosym Technologies Insight II Version 235 San Diego, 1994.
[211] Pople, J. A.; Gill, P. M. W.; Handy, N. C. Int. J. Quant. Chem. 1995 56, 303.
[212] Jensen, F. Introduction to Computational Chemistry Wiley and Sons Inc., Chichester, UK, 1999.
[213] van der Zwaan, J. W.; Albracht, S. P. J.; Fontijn, R. D.; Roelofs, Y. B. M. Biochim. Biophys. Acta 1986 872, 208.
BIBLIOGRAPHY 199
[214] van Leeuwen, R.; van Lenthe, E.; Baerends, E. J.; Snijders, J. G. J. Chem. Phys. 1994 101, 1272.
[215] Sadlej, A. J.; Snijders, J. G.; van Lenthe, E.; Baerends, E. J. J. Chem. Phys. 1995 102, 1758.
[216] van Lenthe, E.; Baerends, E. J. J. Chem. Phys. 2000 112, 8279.
[217] Cammack, R.; Fernandez, V. M.; Schneider, K. In: The Bioinorganic Chemistry of Nickel J. R. Lancaster, Jr. (Ed.), VCH,
Weinheim, 1988, pp. 167–190.
[218] R. Cammack, C. Bagyinka, K. L. K. Eur. J. Biochem. 1989 182, 357.
[219] Lemon, B. J.; Peters, J. W. Biochemistry 1999 38, 12969.
[220] Dikanov, S. A.; Patil, D. S.; Bowman, M. K. J. Inorg. Biochem. 1997 67, 427.
[221] Lenz, O.; Friedrich, B. Proc. Natl. Acad. Sci. USA 1998 95, 12474.
[222] Kleihues, L.; Lenz, O.; Bernhard, M.; Buhrke, T.; Friedrich, B. J. Bact. 2000 182, 2716.
[223] Pierik, A. J.; Schmelz, M.; Lenz, O.; Friedrich, B.; Albracht, S. P. J. FEBS Lett. 1998 438, 231.
[224] Hurst, G. C.; Henderson, T. A.; Kreilick, R. W. J. Am. Chem. Soc. 1985 107, 7294.
[225] Henderson, T. A.; Hurst, G. C.; Kreilick, R. W. J. Am. Chem. Soc. 1985 107, 7299.
[226] Kappl, R.; H¨uttermann, J. In: Advanced EPR - Applications in Biology and Biochemistry, A. J. Hoff (Ed.), Elsevier,
Amsterdam, 1989, pp. 501–540.
[227] Hoffman, B. M.; Gurbiel, R. J.; Werst, M. M.; Sivaraja, M. In: Advanced EPR - Applications in Biology and Biochem-
istry, A. J. Hoff (Ed.), Elsevier, Amsterdam, 1989, pp. 541–591.
[228] Mombourquette, M. J.; Weil, J. A. J. Mag. Res. 1992 99, 37.
[229] Teixeira, M.; Moura, I.; Xavier, A. V.; Huynh, B. H.; DerVartanian, D. V.; Peck Jr., H. D.; LeGall, J.; Moura, J. J. G. J.
Biol. Chem. 1985 260, 8942.
[230] Sorgenfrei, O.; Duin, E. C.; Klein, A.; Albracht, S. P. J. Eur. J. Biochem. 1997 247, 681.
[231] Montet, Y.; Amara, P.; Volbeda, A.; Vernede, X.; Hatchikian, E. C.; Field, M. J.; Frey, M.; Fontecilla-Camps, J. C. Nat.
Struct. Biol. 1997 4, 523.
200
Danksagung
Herrn Prof. Dr. Wolfgang Lubitz danke ich f¨ur die freundliche Aufnahme in seine Arbeitsgruppe und
die Betreuung bei der Bearbeitung eines spannenden Themas ¨ubergangsmetallhaltiger Enzymkatalyse.
Seine Kritik und Skeptik gegen¨uber den Aussagen theoretischer Verfahren waren immer eine Heraus-
forderung.
Herr Prof. Dr. Wolfram Koch hat freundlicherweise die Mitbegutachtung der Doktorarbeit
¨ubernommen. In der Anfangsphase der Arbeit waren einf¨uhrende Diskussionen ¨uber die elektronische
Struktur von ¨
Ubergangsmetallen sehr hilfreich. Den Mitarbeitern seiner Arbeitsgruppe danke ich f¨ur
technische Unterst¨utzung mit quantenchemischen Programmen.
I am very grateful to Prof. Dr. Yoshiki Higuchi (University of Kyoto, Japan) for an excellent co-
operation. Without his magnificent and beautiful protein single crystals, much of the work in this thesis
would not have been possible.
Herrn Dipl.-Chem. Thorsten Buhrke aus der AG von Frau Prof. Dr. B¨arbel Friedrich (Humboldt-
Universit¨at Berlin) danke ich f¨ur die Anzucht, Isolation und Reinigung der regulatorischen Hydrogenase.
Thorsten, mein angeheirateter Schwipp-Cousin, wir werden schon noch zusammen alt werden - und sei
es auf dem Spielplatz. Unvergessen sind unsere gemeinsamen Pantschereien in Unwissenheit vom 1.
Semester an bis zum heutigen Tag.
I enjoyed the co-operation with Prof. Dr. Evert Jan Baerends and Dr. Erik and Lenthe (VU Amster-
dam, Netherlands). I happily remember their hospitality during a short stay in Amsterdam. I learned a lot
from their carefulness in the interpretation of results from DFT. Erik, you are the most gifted theoretical
physicists I have ever met. Before I met you, I always thought relativistic effects were something for
anoraks.
Herrn Dr. Thomas Steinke vom Konrad-Zuse-Zentrum f¨ur Informationstechnik Berlin (ZIB) bin ich
dankbar f¨ur Hilfe und Unterst¨utzung mit den Großrechnern am ZIB.
I thank Prof. Dr. Tom Ziegler and Dr. Serguei Patchkovskii (University of Calgary, Canada) for
making the QR code by Dr. Georg Schreckenbach available to me. I was allowed to use their impressive
Cobalt cluster.
Herrn Dr. Friedhelm Lendzian und Herrn Priv.-Doz. Dr. Robert Bittl danke ich f¨ur Tag-und-Nacht
Hilfe mit den Spektrometern, wenn es mal nach Ampere riecht. Esc-Esc-Esc-p-p-r-e-i-a.
Den Mitgliedern der H2ase-Combo (Frau Dr. Olga Trofantschuk, Herrn Dipl.-Phys. Marc Brecht
und Frau Dipl.-Chem. Stefanie Foerster) verdanke ich eine Menge. Olga, unvergessen bleiben unsere
langen Messungen. Hannes, Herr der Pulse, ein Puls geht schon noch rein; was heißt das denn nun
biologisch? Stefanie, Frau mit den gl¨ucklichen H¨andchen, behandele die paramagnetischen Proben gut.
Alle Mitarbeiter der AG Lubitz haben eine angenehme, anregende Arbeitsatmosph¨are geschaffen.
Dem Fonds der Chemischen Industrie danke ich f¨ur ein Chemiefondsstipendium in der Anfangsphase
der Promotion.
Die Arbeit w¨are niemals vollendet worden ohne den Zuspruch, die Unterst¨utzung und die Ablenkung
durch meine Familie. Ich widme Kerstin und Jonas diese Arbeit.
Lebenslauf
Name Matthias Stein
Geburtsdatum 03.05.1971
Geburtsort Berlin
Familienstand verheiratet mit Kerstin Stein, geb. Bethge
seit 21.01.1998 freuen wir uns ¨uber unseren Sohn Jonas Paul
Ausbildung
1977 – 1983 Stechlinsee-Grundschule, Berlin
1983 – 1990 Rheingau-Gymnasium, Berlin
06/1990 Abitur
1990 – 1993 Chemiestudium an der TU Berlin
1992 Vordiplom mit der Note “sehr gut”
1993 – 1994 Auslandsstudienaufenthalt an der
University of Manchester, UK
1994 ‘Master of Science’ Abschluß der University of Manchester, UK
1994 – 1995 Chemiestudium an der TU Berlin
09/1995 Diplom in Chemie “mit Auszeichnung”
01/1997 Beginn der Dissertation an der TU Berlin
T¨
atigkeiten
1995-1996 wissenschaftlicher Mitarbeiter bei Prof. Dr. J. Sauer,
Arbeitsgruppe Quantenchemie der Max-Planck-Gesellschaft
1997 – 2000 wissenschaftlicher Mitarbeiter am Max-Volmer-Institut
f¨ur Biophysikalische Chemie und Biochemie der
Technischen Universit¨at Berlin
seit 01.01.2000 Gesch¨aftsf¨uhrer des Sonderforschungsbereiches 498
