TESE DE DOUTORAMENTO
P og ama Ciencia e ecnoloxía química
DEPARTAMENTO DE QUÍMICA-FÍSICA
FACULTADE DE CIENCIAS
LUGO
SETEMBRO 2014
Alba Campo Cacha ón
ON THE INTERACTION BETWEEN IONS
AND COMPLEX AROMATIC SYSTEMS:
amino acid side chains, ion channels, and buckybowls
On he in e ac ion be ween ions
and complex a oma ic sys ems:
amino acid side chains, ion channels, and buckybowls
Alba Campo Cacha ón
Depa amen o de Química-Física
Facul ade de Ciencias
LUGO, SETEMBRO 2014
Au o ización dos di ec o es da ese
D. En ique Manuel Cabalei o Lago
P o eso /a do Depa amen o: Química-Física (Lugo)
D. Jesús Rod íguez O e o
P o eso /a do Depa amen o: Química-Física (CIQUS)
Como Di ec o es da Tese de Dou o amen o i ulada: “On he in e ac ions be ween ions
and complex a oma ic sys ems: amino acid side chains, ion channels and buckybowls”.
P esen ada po Dna. Alba Campo Cacha ón
Alumna do P og ama de Dou o amen o en Ciencia e Tecnoloxía Química (D1121)
Au o izan a p esen ación da ese indicada, conside ando que eúne os equisi os esixidos
no a igo 34 do egulamen o de Es udos de Dou o amen o, e que como Di ec o da
mesma non incu e nas causas de abs ención es ablecidas na lei 30/1992.
Lugo a 20 Se emb o de 2014
Asdo: En ique M. Cabalei o Lago Asdo: Jesús Rod íguez O e o
Ag adecemen os
Quixe a ace uns b e es ag adecemen os pos o que me gus an máis as
demos acións con ab azos que con palab as, e máis, se es as hai que i buscalas a lib os
an pouco ape ecibles pa a le como es e.
En p imei o luga aos di ec o es de ese, Quique e Jesús. En especial a Quique, que
máis que un di ec o é un amigo. G acias pola úa paciencia, os eus consellos e pola úa
p eocupación. Fas que odo pa eza ácil e sinxelo e semp e poñendo un oque de
humo .
A O iguei a, po que a ese sen esos ca és e c ucig amas dia ios ben segu o non
hoube a saído adian e.
A meus pais, polo seu apoio cons an e, os seus ánimos e sob e odo o seu sac i icio
pa a que eu puide a con inua e acaba es a ese aínda sen con a o. Son o meu
exemplo.
A meu i mán, que aínda que non alemos an a miúdo como debe amos sei que con o
co seu apoio incondicional an e calque a das miñas decisións.
A meus ios e p imos, po que son a mello amilia que un pode e , semp e pensando
en come e en xoga o enis.
As miñas amigas, po que sen elas non se ía quen son. Tamén a Raquel, pa e
undamen al des os anos en Lugo es udiando, po que sei que le o unha amiga pa a a
ida.
A Tama a e a Ma i e e, po ese du o pe o an ás ico ano aballando á ez que acía a
ese. Polos nosos co illeos a a al as ho as da mad ugada, polos chocola es e pola osa
p eocupación pola miña ida amo osa. G acias, po que sei que le o dúas amigas pa a
semp e.
Po úl imo a Miguel, que aínda que oi o úl imo en en a na miña ida con e iuse
nun dos máis impo an es, semp e alen ándome a es udia , a mello a , a emp ende ,
semp e co seu apoio e ca iño in ini o.
INDEX
RESUMEN ................................................................................................................................. I
1. INTRODUCTION ................................................................................................................... 1
1.1. SUPRAMOLECULAR CHEMISTRY ................................................................................................... 3
1.2. INTERMOLECULAR INTERACTIONS ................................................................................................ 4
1.3. INTERACTION INVOLVING AROMATIC SYSTEMS ............................................................................... 9
1.4. INTERACTIONS WITH BUCKYBOWLS ............................................................................................ 17
1.5. REFERENCES.......................................................................................................................... 21
2. OBJECTIVES ........................................................................................................................ 25
3. METHODOLOGY ................................................................................................................. 31
3.1. INTERACTION ENERGY ............................................................................................................. 33
3.1.1. Basis Se Supe posi ion E o ..................................................................................... 34
3.1.2. Many-body e ec s ..................................................................................................... 36
3.2. WAVEFUNCTION-BASED METHODS ........................................................................................... 37
3.2.1. The Ha ee-Fock me hod .......................................................................................... 37
3.2.2. Many Body Pe u ba ion Theo y (MPn)..................................................................... 39
3.2.3. Coupled Clus e .......................................................................................................... 41
3.2.4. E o s in Wa e unc ion-based Me hods .................................................................... 43
3.2.4.1. Ex apola ing o basis limi ................................................................................................ 45
3.2.4.2. Ob aining benchma king alues........................................................................................ 47
3.3. DENSITY FUNCTIONAL THEORY METHODS ................................................................................... 49
3.3.1. Kohn-Sham p ocedu e ............................................................................................... 50
3.3.2. Func ional ypes ........................................................................................................ 52
3.3.3. Dispe sion-co ec ed DFT me hods ............................................................................ 54
3.3.3.1. DFT-D2 .............................................................................................................................. 55
3.3.3.2. DFT-D3 .............................................................................................................................. 56
3.4. REDUCING COMPUTATIONAL COST ............................................................................................. 57
3.5. INTERACTION ENERGY PARTITIONING ......................................................................................... 59
3.5.1. Ene gy Decomposi ion Analysis (EDA) Me hods ........................................................ 59
3.5.2. Symme y-Adap ed Pe u ba ion Theo y Me hods (SAPT) ........................................ 61
3.5.2.1. SAPT(DFT) ......................................................................................................................... 65
3.6. ELECTRON DENSITY ANALYSIS .................................................................................................... 66
3.6.1. NCI index .................................................................................................................... 67
3.7. SOLVATION EFFECTS ............................................................................................................... 71
3.7.1. Con inuum models ..................................................................................................... 72
3.8. REFERENCES.......................................................................................................................... 75
i
menos es ables, y de hecho no se han localizado en complejos con enol debido a la
endencia de es a especie a omá ica a in e acciona median e enlaces de hid ógeno.
En esumen, los íme os es án p incipalmen e condicionados po la in ensidad de los
con ac os ca ión···π, pe o in e acciones secunda ias en e especies a omá icas puede
modula su compo amien o, especialmen e cuando se o man enlaces de hid ógeno en
complejos con enol e indol. A pesa de es o, el balance de las di e en es con ibuciones
a la ene gía (π···π, X-H···π y M+···π) es muy delicado dependiendo de la na u aleza y de la
o ien ación ela i a de los agmen os.
El segundo bloque de es a esis es á dedicado al es udio de las in e acciones no
co alen es donde in e ienen especies a omá icas y aniones. Así como las in e acciones
ca ión···π han sido es udiadas desde hace iempo, el campo de las in e acciones en e
moléculas a omá icas y aniones es de ecien e desa ollo. Es o es p obablemen e
debido a que en una p ime a ins ancia la in e acción en e un anión y una molécula
a omá ica no pa ece posible debido a la capacidad de dona elec ones de ambas
especies. Sin emba go, p on o se hizo e iden e que es e ca ác e dado podía se
modulable en las moléculas a omá icas a a és de la sus i ución del anillo con g upos
elec oa ayen es. Así, se pueden de ini las in e acciones anión···π como las
in e acciones a o ables en e aniones y sis emas a omá icos de icien es en elec ones.
Las in e acciones anión···π han cob ado g an ele ancia debido a su posible
pa icipación en impo an es á eas como po ejemplo en bioquímica, ya que el ADN es
un polianión y muchos co ac o es y sus a os de las enzimas son aniónicos. Además, se
han p opues o nue as aplicaciones empleando es e ipo de in e acciones pa a ac ua en
ecep o es aniónicos. Po an o, cua o capí ulos en es a esis se co esponden con el
es udio de la in e acción anión···π: uno de ellos dedicado a las ca ac e ís icas de la
in e acción en un canal aniónico sin é ico y o os es cen ados en las ca ac e ís icas de
las in e acciones en e especies a omá icas cu as y aniones, p incipalmen e pa a
de e mina su posible uso como ecep o es aniónicos.
El capí ulo 6 es á dedicado al p ime canal aniónico sin é ico basado en in e acciones
anión···π, que ha sido p opues o ecien emen e. Las posibilidades de es e canal y su
no edosa es uc u a compues a po un mo i o geomé ico con anillos a omá icos
de icien es en elec ones epe ido a lo la go del canal lo hacen pe ec o pa a el es udio
de las in e acciones anión···π. Así, se han es udiado complejos o mados po modelos
simpli icados del canal iónico in e accionando con cua o aniones di e en es (B -, Cl-, F-,
y OH-) a los que se les han añadido has a es moléculas de agua de o ma explíci a. Los
esul ados ob enidos mues an que la in e acción de las unidades que o man el canal
con los aniones es in ensa en ase gas, dando luga a complejos muy es ables. Sin
emba go, la p esencia de un pequeño núme o de moléculas de agua que pueda
acompaña al ion den o del canal al e a de o ma signi ica i a las ca ac e ís icas de los
complejos, especialmen e los más es ables, o mados con los aniones más pola izan es.
Los esul ados indican que el papel de las moléculas de agua más p óximas al anión
puede se ele an e en el uncionamien o del canal iónico, disminuyendo los cos es
asociados a la deshid a ación del ión pa a en a en el canal. Además, si algunas
moléculas en an con el ion en el canal pueden con ibui a acili a el p oceso
es ableciendo in e acciones a ac i as con el p opio canal iónico.
Una úl ima sección, o mada po los es capí ulos inales, es á dedicada a las
in e acciones anión···π en las que pa icipan los sis emas a omá icos cu os llamados
buckybowls. Los buckybowls son hid oca bu os a omá icos policíclicos o mados po
una se ie de anillos usionados de cinco y seis miemb os que dan luga a una es uc u a
cu ada en o ma de cuenco. La cu a u a iene su o igen en la p opia es uc u a de
es as moléculas, ya que no es posible o ma una es uc u a plana combinando
pen ágonos y hexágonos. Es e ipo de especies ambién son denominadas agmen os
de ule enos, ya que su esquele o ca bonado se co esponde con pa es de las
es uc u as de los ule enos. Los buckybowls más sencillos que se pueden p oyec a
sob e el ule eno C60 son el co anuleno C20H10 (seis anillos hexagonales odeando un
anillo pen agonal cen al) y el sumaneno C21H12 ( es anillos hexagonales y es
pen agonales al e nos en o no a un anillo hexagonal cen al). En es a esis se
conside a án de i ados sus i uidos de ambas especies. Los buckybowls mues an
di e en es p opiedades dependiendo de la ca a cónca a o con exa en la que iene luga
la in e acción. Tan o sumaneno como co anuleno o man complejos con ca iones y
me ales de ansición, undamen almen e po la ca a con exa del bowl. Al igual que
o as especies a omá icas, pod ía se posible modula las ca ac e ís icas de es os bowls
median e sus i uyen es ap opiados, de modo que pudie an coo dina aniones
p e e en emen e po la ca a cónca a y ac ua como ecep o es aniónicos. Es e aspec o
es uno de los obje i os a a a en la p esen e esis.
En el capí ulo 7 se in en a de e mina cómo la sus i ución de g upos en el bo de de
los buckybowls a ec a a sus p opiedades. Conc e amen e, se a a de de e mina si se
p oduce la in e sión del po encial elec os á ico molecula (MEP) de los bowls,
pudiendo se así adecuados pa a un con ac o a o able con aniones. Además, median e
es e es udio se ha comp obado qué g upos sus i uyen es son los más adecuados pa a
a o ece la in e acción buckybowl···anión.
Se ha de e minado el po encial elec os á ico del co anuleno sus i uido con 5 o 10
g upos luo u o, clo u o y ni ilo. La cu a u a del co anuleno apenas su e cambios al
se sus i uido, excep o en los de i ados decasus i uidos con clo u o y ni ilo, en lo que
se ap ecia una pé dida de cu a u a del bowl. T as comp oba que se consigue la
in e sión del po encial elec os á ico (especialmen e con CN), se op imizan los
complejos o mados po dichos buckybowls sus i uidos y es aniones di e en es, Cl-, B -
y BF4-. En dichos complejos se p ueban di e en es egiones pa a la in e acción con los
aniones, comp obando así las di e encias ene gé icas en e complejos o mados po las
ca as cónca a y con exa. Los con ac os con el anión si uado en la pa e cónca a del
i
bowl son los más es ables con ene gías de coo dinación que siguen ap oximadamen e
los alo es ob enidos pa a los MEPs, siendo los más es ables aquellos o mados po el
co anuleno sus i uido comple amen e con 10 g upos CN y el anión clo u o po la ca a
cónca a. Además, se ha es imado el e ec o de a ios disol en es empleando modelos de
con inuo, que mues an impo an es pé didas de es abilidad de los complejos en
disolución. Aún así, los esul ados animan a segui in es igando es e ipo de sis emas, ya
que pa ecen apun a que los buckybowls sus i uidos pod ían ac ua como ecep o es
de aniones.
El capí ulo 8 es á más cen ado en aspec os me odológicos. Se ha de ec ado que la
in e acción con buckybowls es bas an e compleja de desc ibi , y que los dis in os
mé odos de cálculo p opo cionan esul ados dispa es. Como no exis en alo es de
e e encia pa a es e ipo de sis emas, en es e capí ulo se han ealizado cálculos con una
ba e ía de mé odos de di e en e ni el, pa a pode de e mina alo es de e e encia así
como pa a es ima qué mé odos de meno cos e compu acional pueden o ece una
desc ipción acep able de es os sis emas. En es e es udio se han conside ado complejos
con aniones y ca iones, pa a pode es ablece una compa ación di ec a de sus
ca ac e ís icas usando los mismos mé odos con los mismos buckybowls.
Se han conside ado complejos o mados po bowls pa cialmen e sus i uidos con
CH3, F y CN basados en co anuleno y sumaneno, e iones Cl- y Na+. En el caso del
co anuleno se han sus i uido cinco á omos de hid ógeno al e nos en el bo de del bowl.
Con sumaneno hay dos posibles sus i uciones, una que a ec a a los á omos de hid ógeno
de los g upos CH de los anillos hexagonales, y o a en la que se sus i uyen los á omos de
hid ógeno de los g upos CH2 de los anillos pen agonales. Se han ob enido las ene gías de
in e acción de los complejos a lo la go de una línea que pasa po el eje cen al del
buckybowl a iando las dis ancias a las que se si úan los iones.
Los esul ados ob enidos con los di e en es mé odos p obados mues an un g ado de
co espondencia a iable. Compa ando con los alo es ob enidos con el mé odo de
e e encia empleado (MP2.X) se obse a que el mé odo SCS-MP2 ex apolado a base
comple a es el que mejo es esul ados o ece a un cos e de cálculo azonable, aunque
o as opciones de meno cos e como el uncional M06-2X ambién p opo cionan una
desc ipción acep able. En gene al, el sumaneno in e acciona más ue emen e que el
co anuleno con ambos iones. Además, en el sumaneno el e ec o de la sus i ución es más
p onunciado en los g upos CH que en los CH2. De o ma gene al las in e acciones siguen
el mismo pa ón que el obse ado pa a los MEPs, aunque pueden ap ecia se lige as
des iaciones. Los esul ados indican que la na u aleza de la in e acción es di e en e en
complejos ca iónicos y aniónicos. Así, la in e acción con aniones es á con olada po la
in e acción elec os á ica con con ibuciones signi ica i as de la dispe sión, mien as
que en los complejos con ca iones son las con ibuciones de inducción las que
desempeñan un papel p edominan e.
ii
Po úl imo en el capí ulo 9 se es udia el e ec o que la na u aleza del anión y la
p esencia de disol en e eje cen sob e las ca ac e ís icas de los complejos con
buckybowls. Se han conside ado una se ie de a iables y e ec os a es udia ales como:
es ipos de buckybowls sus i uidos con g upos ni ilo, uno basado en co anuleno y dos
basados en sumaneno; cua o líneas de ap oximación del anión con espec o al bowl;
dis in as o ien aciones de los iones con espec o al bowl; seis aniones di e en es
ag upados en pa es de dis in o ipo: monoa ómico (Cl-, B -), igonal plano (NO3-, CO2H-)
y e aéd ico (BF4-, ClO4-). Las ene gías de in e acción se han ob enido empleando los
mé odos SCS-MP2 y M06-2X, al como suge ían los esul ados del capí ulo 8.
Los esul ados indican que en odos los casos los complejos se o man po la ca a
cónca a del bowl, siguiendo su eje cen al. Igualmen e, las dis in as o ien aciones del
anión no pa ecen ene demasiado e ec o sob e la in e acción, aunque se a o ecen
o ien aciones con el mayo núme o de egiones nega i as o ien adas hacia la pa ed
in e na del bowl. Los complejos más es ables en ase gas son los o mados con CO2H-,
seguidos po los monoa ómicos, NO3-, y inalmen e los e aéd icos como los menos
es ables. Es e compo amien o cambia adicalmen e al inco po a el e ec o del
disol en e. Todos los complejos su en impo an es pé didas de es abilidad, pe o los
más a ec ados son los o mados con CO2H- que pasan a es a en e los menos es ables
en disol en es con cons an es dieléc icas ele adas. Los complejos más es ables en esas
condiciones son los o mados con B -.
Los esul ados conjun os de es os es abajos indican que se ía plausible que los
aniones ue an a apados po los buckybowls, dando luga a complejos que pod ían se
es ables incluso en disolución, ab iendo nue as posibilidades pa a el diseño de
ecep o es aniónicos basados en es e ipo de especies an a ac i as.
1. In oduc ion
1. In oduc ion
3
1.1. Sup amolecula Chemis y
Sup amolecula chemis y is a ield o science ha deals wi h he ela ionship be ween
molecula s uc u e and unc ion; i is he chemis y o he nonco alen bond, which
o ms he basis o highly speci ic ecogni ion, anspo , and egula ion e en s ha ac in
biological p ocesses. Sup amolecula chemis y a ises om he na u al esul o he
cu iosi y o humans, who ha e imi a ed phenomena o he na u e du ing cen u ies. This
subjec was ini ia ed wi h he pionee ing wo ks o Jean-Ma ie Lehn in 1969 abou he
idea o molecula ecogni ion and led him o ob ain he Nobel P ize in 1987 oge he
wi h Donald J. C am and Cha les J. Pede sen.[1, 2]
A en a i e de ini ion o Sup amolecula Chemis y p o ided by Lehn is he
ollowing:[1,3]
“Sup amolecula chemis y di ec s o he de elopmen o big complex
chemical sys ems om he componen s ha in e ac be ween hem by means
o in e molecula nonco alen o ces”
and has opened a new ield whe e he in e es o a ious disciplines o Chemis y
con e ge, including O ganic and Ino ganic Chemis y, Physical Chemis y,
Biochemis y, Ma e ials Science and Nano echnology.
As men ioned abo e, he objec i e o Sup amolecula Chemis y is o o m an
agg ega e o molecula en i y cons i u ed by species ha a e no linked co alen ly
among hem, bu associa ed by hei geome ic o /and elec onic a ini y; ha is, hey
a e molecula ly ecognized. Th ee concep s a e essen ial o unde s and hese p ocesses:
ixa ion, ecogni ion and coo dina ion. These concep s we e es ablished a he end o
XIX cen u y by Paul Eh lich (1898), Emil Fische (1894) and Al ed We ne (1893),
espec i ely.[1, 2]
Eh lich ecognized ha a molecule canno ac i i does no bind o he neighbo hood
o o he s. On he o he hand, Fische in oduced he key-lock concep o explain he
pe o mance o enzimes. Acco ding o his concep , he enzyme selec i ely ecognizes
he subs a e because i p esen s a speci ic geome y in i s ac i e si e, he same way a
key i s wi h i s lock. The be e hey i oge he he mo e e icien he complexa ion
will be. This ecogni ion is no only geome ic; bu i also implica es a chemical
in e ac ion and a con o ma ional ea angemen hus explaining he no able speci ici y
o enzyme ca alysis. This kind o nonco alen in e ac ion can be ela ed o he idea o
coo dina ion as in oduced by We ne .
Following he same line, C am was he i s one o in oduce he e ms hos -gues .[4, 5]
Thus, one sup amolecule is ob ained om he p ocess in which one molecule ac s as
ecep o (hos ) and ano he one as subs a e (gues ), binding o he i s one o ob ain a
ecep o -subs a e complex. No mally, he ecep o is a big molecule o agg ega e, as an
Alba Campo Cacha ón
10
Figu e 1.2. A oma ic g oups in amino acid side chains.
When a oma ic species a e p esen in complex sys ems, i is usual o he s uc u e o
show π···π con ac s, XH···π in e ac ions and in e ac ions be ween ions and he π cloud,
being any o hese con ac s ele an o de e mining he s uc u al cha ac e is ics and
ene gy o he sys em. Following he e is a b ie desc ip ion o hese in e ac ions.[13]
X-H···π in e ac ions
This in e ac ion is based on he a ac ion be ween X-H g oups, no mally C-H, N-H o
O-H g oups, and he π elec on cloud o an a oma ic ing.[13, 17-21] No mally, he ange o
dis ances be ween he hyd ogen a om and he cen oid o he ing is 2.4-3.2 Å, la ge
han he dis ance in a ypical hyd ogen bond (a ound 2 Å).
The C-H···π in e ac ion was i s pos ula ed by Tam es in 1952, who no ed ha
dissol ing benzene in chlo o o m was exo e mic.[22] Quali a i ely, he s eng h o he C-
H···π in e ac ion a ises mainly om cha ge ans e , gi ing ise o in e ac ion geome ies
whe e he CH bond lies di ec ly in line wi h a p-o bi al on he ing. O-H···π and N-H···π
in e ac ions show simila cha ac e is ics and ha e been equen ly ecognized as a mo i
con ibu ing o he s abili y in di e en sys ems. Besides, despi e he weakness o hese
indi idual con ac s, hei e ec s can be addi i e and in mac omolecula sys ems hei
in luence can be p onounced. This has been show in many cases by Nishio, who has
compiled an ex ensi e li e a u e da abase on C-H··· π in e ac ions and hei e ec s on
ene ge ics, eac i i y and con o ma ional changes o di e en species.[17, 23]
Theo e ical s udies and expe imen al esul s in he gas phase seem o indica e ha he
na u e o C-H···π in e ac ion is o ally di e en o con en ional hyd ogen bonds. While
he hyd ogen bonds a e mainly due o elec os a ic in e ac ions, he elec os a ic
componen in he C-H···π in e ac ions is minimum, being dispe sion in e ac ions he
main cause o o ma ion. O he undamen al di e ence is he di ec ionali y ha bo h
in e ac ions exhibi . While he undamen al hyd ogen bond ea u e is i s high
Phenylalanine
(benzene)
Hys idine
(imidazole)
T yp ophan
(indole)
Ty osine
(phenol)
1. In oduc ion
11
di ec ionali y due o he elec os a ic con ibu ion, he C-H···π in e ac ion does no
depend so d ama ically on he o ien a ion o he in e ac ing g oup. Thus, i is equen
o ind X-H···π con ac s clea ly depa ing om he ypical linea a angemen o
hyd ogen bonds.[17, 19]
π···π in e ac ions (s acking)
This ype o in e ac ion akes place be ween he π elec on clouds o s acked a oma ic
sys ems[11-13, 24, 25] No mally, one o he ings is elec on- ich, while he o he is elec on
poo , al hough cases ha e been desc ibed whe e bo h ings ha e he same elec on
weal h. This co esponds in p inciple o a weak in e ac ion (bonding ene gy a ound 0-10
kcal/mol) bu wi h a global e ec o g ea impo ance om a biological and
sup amolecula poin s o iew, as well as in c ys allog aphy. π···π in e ac ions, like in
benzene dime , a e usually go e ned by dispe sion e ec s, since hese a e he unique
o ces ac ing in he case o nonpola molecules ( he quad upole-quad upole in e ac ion
be ween benzene molecules is weake ).
π···π in e ac ions play an impo an ole in he s abiliza ion o DNA, oge he wi h
hyd ogen bonds, esul ing in he s acking o bases pai s and gene a ing i s
cha ac e is ics helicoidal s uc u e.[11, 12] Based on his, a numbe o in e cala ing d ugs
ha e been designed exploi ing π···π s acking in e ac ions. On he o he hand, π···π
s acking in e ac ions ha e a lo o applica ions in Sup amolecula Chemis y, especially
o hos -gues sys ems. A ema kable case is he one desc ibed by Sygula e al., who
ha e syn hesized a buckyca che based on a mul i ude o conjuga ed a oma ic ings ha
adop a conca e con o ma ion ma ching pe ec ly wi h a ulle ene C60 molecule, ac ing
as ecep o o his molecule h ough π···π s acking in e ac ions.[26]
The e has been con o e sy conce ning he physical na u e o his kind o in e ac ion.
In 1990, Hun e and Sande s p oposed a simple model based on he compe i ion
be ween he elec os a ic and he an de Waals o ces o explain he a ie y o
geome ies obse ed o hese in e ac ions and o quan i a i ely p edic hei
in e ac ion ene gies.[27] These au ho s pos ula e he exis ence o an a ac i e o e lap in
an de Waals in e ac ions, which a e p opo ional o he su ace con ac a ea be ween
bo h π sys ems. This o e lap is due o an a ac ion be ween he π elec onic cloud
nega i ely cha ged o one o he ings and he elec onic cloud posi i ely cha ged om
he o he . The ela i e o ien a ion o bo h ings is de e mined by elec onic epulsions
be ween bo h π sys ems nega i ely cha ged. Fo his eason, when an a oma ic sys em
is s acked in a pa allel way, i is no mally obse ed ha he ings a e no o ally aligned,
wi h one sligh ly displaced wi h espec o he o he , minimizing he π···π epulsion and
maximizing he π··· a ac ion. In ac , ew examples exis whe e he a oma ic ings a e
a anged o ally o e lapping.[28, 29] The mos common a angemen s a e he pa allel-
displaced and T-shaped disposi ions, because π··· a ac ions p edomina e in bo h. The
h ee disposi ions ha e been usually employed in his kind o complexes o s udy he
Alba Campo Cacha ón
12
e ec o he a angemen on he in e ac ion ene gy and s abili y o he complexes.
These a angemen s a e shown in Figu e 1.4 wi h a benzene dime as example.[24, 25]
I can be obse ed ha in he case o benzene dime ( he mos s udied π···π
in e ac ion), he s acking in e ac ions a e compe i i e wi h o he possible a angemen s
as he C-H···π in e ac ion in T-shaped s uc u es.[24, 25] This can be obse ed in Figu e 1.4,
which shows how bo h s uc u es a e i ually isoene ge ic. I is wo h men ioning ha
he s eng h o hese in e ac ions is highly a ec ed by di e en ac o s, such as he
p esence o elec on-dono o elec on-accep o subs i uen s in he ings, he exis ence
o he e oa oms o ming pa o he ing and he deg ee o annela ion o he ings
in ol ed in he s acking. The eby, he highe he numbe o used ings, he mo e
a o able he s acking.[13] Rega ding subs i u ion e ec s, i has been shown ha he
p esence o elec on-a ac o subs i uen s in he ing inc eases he s eng h o his kind
o in e ac ions since he elec onic densi y o he π cloud o he ing dec eases,
minimizing he π···π epulsions be ween he ings. In ac , s udies by She ill and
cowo ke s ha e shown ha subs i u ion always leads o s onge in e ac ion
un ega dingly o he dono o accep o cha ac e o he subs i uen s.[30, 31]
Figu e 1.4. Types o π···π con ac s o benzene dime wi h hei co esponding
in e ac ion ene gies.
When he s acking is p oduced be ween a oma ic he e ocycles he s eng h o hese
in e ac ions inc ease. The subs i u ion o a ca bon a oms o he ing by a ni ogen a om
in a six-membe ed ings (like in py idine o example) causes a dec ease o he elec onic
π densi y in he ca bon a oms o he ing, which leads o a s abiliza ion o he sys em
and dec eases he π···π epulsion o ces as men ioned abo e.[32] In any case, his
in e p e a ion o subs i uen e ec has been ecen ly e iewed by Wheele .[33, 34]
1. In oduc ion
13
Ca ion···π in e ac ions
A ca ion···π in e ac ion a ises om he elec os a ic in e ac ion o a ca ion wi h a ace
o a π sys em, as could be a benzene ing and i s de i a i es o π sys ems as e hylene.
The i s e idence o his ype o in e ac ion in he gas phase came ou om he wo k by
Keba le in 1981.[35] In a sys ema ic s udy o ion sol a ion by a ious sol en s, Keba le
obse ed ha benzene s abilizes K+ ions be e han wa e in he gas phase. Keba le
p oposed ha his was a esul o he ion in e ac ing wi h he quad upole momen o
benzene. A molecule wi h a dipole momen , such as wa e , expe imen s a a o able
elec os a ic in e ac ion wi h an ion i he ion is posi ioned nea he app op ia e end o
he dipole. Benzene, o cou se, has no dipole momen , bu i does ha e a subs an ial
pe manen quad upole momen .[36] A quad upole can be hough o as wo dipoles
aligned in such a way so ha he e is no ne dipole. Thus, he e is a pe manen
nonsphe ical cha ge dis ibu ion in benzene, wi h egions o ela i e nega i e and
posi i e cha ges. Jus as an ion can be a ac ed o he app op ia e end o a dipole, so
can an ion expe ience a a o able in e ac ion wi h app op ia e egions o a quad upole.
This is an elec os a ic in e ac ion and does no equi es adjus men o he elec onic
dis ibu ion a ound he ion o he molecule. Impo an ly, he e is no a p io i eason o
expec ha such in e ac ions will be inhe en ly weake when he molecule con ibu es a
quad upole a he han a dipole as demons a ed by Reisse and Williams.[37, 38]
Mos neu o ansmi e s ha e a ca ionic g oup ha pe mi s hem a selec i e ancho age
o hei ecep o s by ca ion···π in e ac ions.[39-41] The ca ion···π in e ac ion has impo an
applica ions in he ield o Sup amolecula Chemis y. [41-49] Nume ous s udies ha e
epo ed he occu ence o ca ion···π in e ac ions in p o ein s uc u es and in p o ein-
ligand and p o ein-DNA complexes.[40, 41, 50, 51] These analyses ha e e ealed he
p e e en ial loca ion o amino g oups in he a ea o a oma ic ings.[39, 52] This in e ac ion
is calcula ed o be e en mo e s abilizing han an analogous sal b idge, and i is no so
s ongly a enua ed in wa e .[53] The side-chains o he a oma ic amino acid esidues,
Phe, Ty and T p, p o ide a su ace o nega i e elec os a ic po en ial han can bind o a
wide ange o ca ions h ough a p edominan ly elec os a ic in e ac ion. I has been
ound ha 50% o he A g esidues a e in con ac wi h an a e age o wo a oma ic side
chains. O pa icula in e es is he in e ac ion o he ca ionic A g esidue wi h a oma ic
side chains. Two limi ing geome ies a e possible, a pe pendicula a angemen in which
he NH o he A g poin s in o he ace o he a oma ic uni , and a pa allel o s acked
a angemen o he plana guanidinium o A g and he a oma ic moie y. The s acked
a angemen is mo e equen ly ound, bu he e seems ha his is ela ed o
en i onmen e ec s. Also, se ies o ca ion···π in e ac ions in ol ing bo h A g and Lys
appea in di e en s uc u es con aining se e al a oma ic and ca ionic side chains om
di e en s ands o he p o ein, in e cala ed o o m an ex ended a ay o ca ion···π
in e ac ions.[39, 51, 52] Ano he ema kable case is he ace ylcholine nico inamide ecep o
whose mechanism o molecula ecogni ion o hei subs a e is based only on ca ion···π
Alba Campo Cacha ón
14
in e ac ions.[40, 54] Fu he mo e, sys ems wi h molecula s uc u es simila o c own
e he s, wi h π sys ems s a egically placed, ha e shown o be e y e ec i e binding
places o alkali ca ions.[41, 55] Addi ionally, ca ion···π in e ac ions ha e also been used o
inc ease he π- ace selec i ely in ca alysis in asymme ic ca alysis.[41, 56]
The s eng h o he ca ion···π in e ac ion has been a ionalized on he basis o he
s ong elec os a ic in e ac ion be ween he posi i ely cha ged ca ion and he ing
nega i e molecula elec os a ic po en ial (MEP). Many s udies, especially o gas-phase
complexes, es ablished ha elec os a ic in e ac ions play a p ominen and usually
dominan ole in p o o ypical ca ion···π in e ac ions.[41, 57, 58] Elec os a ic easoning can
also explain a ia ions due o changes in he a oma ic ing. The mo e nega i e he
maximum in elec os a ic po en ial o e he cen e o he a oma ic molecule, he
s onge he ca ion···π in e ac ion. In ac , good co ela ion has been ound in many
cases be ween he MEP alue and he s eng h o he ca ion···π in e ac ion. [41, 59, 60] A
clea indica ion ha elec os a ics play an impo an ole in ca ion···π in e ac ions comes
om a compa ison o simple alkali me als binding o benzene. The obse ed end in
s abili y is Li+ > Na+ > K+ > Rb+, he classical elec os a ic sequence, and exac ly wha
would be seen i benzene we e eplaced by Cl- o i one was compa ing hyd a ion
ene gies.[41, 50, 61]
Howe e , his analysis neglec s he ole played by pola iza ion in e ac ion. The
elec os a ic con ibu ion does no ep esen he 100% o he ene gy o ca ion···π
in e ac ions; in ac , he ac ion o he o al binding ene gy ha comes om
elec os a ics a ies conside ably depending on he a oma ic molecule. The
“nonelec os a ic” componen o he ca ion···π in e ac ion, some imes he majo
componen , e lec s a combina ion o e ec s mos ly ela ed o he pola izabili y o he
a oma ic uni . P obably he mos impo an o hese o simple sys ems is he
in e ac ion o he ion wi h he induced dipole in he a oma ic molecule.[62, 63] As he
a oma ic species becomes la ge i is expec ed ha induc ion con ibu ion also becomes
la ge e lec ing he inc ease in pola izabili y. In ac , s udies show ha he e can be
ca ion···π complexes held by induc ion con ibu ions, whe eas he elec os a ic e m is
epulsi e.[64] Induc ion con ibu ions also explain he p esence o o -plane ca ion···π
s abilizing in e ac ions o example in benzene···Na+ complexes. The loca ion o he
ca ion in he ing plane is des abilized elec os a ically, bu also shows a s abilizing
induc ion con ibu ion leading o a global a ac i e ( hough weak) in e ac ion.[65]
Di e en s udies ha e been de o ed o de e mine he o igins o subs i u ion e ec s
upon he ca ion···π in e ac ion. Recen s udies p opose ha he o igin o he changes
has no hing o do wi h changes in he π cloud bu depend on ough-space in e ac ion
be ween he ca ion and he subs i uen s.[59] These esul s ha e been sligh ly co ec ed
by Quiñone o e al. indica ing ha induc ion e ec s a e also esponsible o such
changes.[66]
1. In oduc ion
15
In summa y, he ca ion···π in e ac ion is an in ense in e ac ion in he gas phase ha
can equen ly appea in sys ems o in e es and basically con olled by elec os a ic and
induc ion con ibu ions. Howe e , he p esence o sol en o o he uni s nea he
ca ion···π con ac can modula e signi ican ly he s eng h o he in e ac ions. I is usually
obse ed a dec ease on he in e ac ion s eng h, bu his can also be accompanied by
signi ican s uc u al changes in he geome y o he complex. Sol en molecules
compe e wi h he a oma ic componen o in e ac ing wi h he ca ion and, as a
consequence, a dec easing o he in ensi y o he ca ion···π in e ac ion in he p esence
o he sol en is no mally obse ed. This led o some con o e sy ega ding he ole o
ca ion···π in e ac ions in p o ein s abili y. While some s udies sugges a ele an
con ibu ion ano he s udies es ima e ha he con ibu ion is insigni ican .[15, 41, 53, 58, 61,
67] These di e ences a e no mally a ibu ed o he di e en deg ee o exposu e o he
ca ion···π con ac o he sol en . I he con ac is bu ied in a hyd ophobic egion, i can
p esen an app eciable in ensi y, while i he con ac is exposed o he sol en , i e en
canno ake place.
Anion···π in e ac ions
While coo dina ion o ca ions has been objec o s udy one cen u y ago, he
coo dina ion o anions has ecei ed li le a en ion un il sho ime ago. The ad en o
syn he ic molecules able o coo dina e ca ions and anions was almos simul aneous: in
1967, C. J. Pede sen p epa ed he i s syn he ic ligand able o coo dina e ca ions,[68] and
only one yea a e C. H. Pa k and H. E. Simmons syn hesized he i s sys em sui able o
coo dina e anions which was called “kapa ina o” ( om kapa inosis, which means
swallow in g eek).[69] Despi e o his almos simul aneous disco e y, he a ea o anion
coo dina ion was ela i ely unexplo ed in con as o he ca ion coo dina ion. The i s
disco e y o he concep anion···π in e ac ion in li e a u e is da ed om he yea 2000
by Schneide .[2]
F om ha momen on, a ious s udies we e ca ied ou o unde s and he na u e o
he in e ac ion be ween anions and a oma ic species.[70-81] The esul s o hose s udies
demons a ed ha , con a y as i could be expec ed, he in ensi ies o in e ac ions
be ween ca ions and anions wi h a oma ic species can be o simila magni ude as shown
in Table 1.5.
A p io i he idea o an in e ac ion be ween an a oma ic ing and an anion will be non-
iable due o he elec on dono capaci y o bo h molecules, bu he elec on dono
capaci y o he a oma ic ing can be modula ed so, i he a oma ic ing is comple ely
subs i u ed wi h g oups which a ac elec ons, i becomes an elec o-de icien
a oma ic cloud and hen an a ac i e in e ac ion wi h an anion is possible. Thus,
anion···π in e ac ions a e desc ibed as he a o able nonco alen in e ac ions be ween
elec on de icien a oma ic sys ems and an anion.[70, 72]
Alba Campo Cacha ón
16
Table 1.5. In e ac ion ene gies o di e en ypes o con ac s wi h he π cloud ob ained
a di e se le els o calcula ion in kcal/mol.
ΔE (kcal/mol)
C6H6···C6H6
-2,5
C10H8··· C10H8
-5,7
C6H6···H2O
-3,0
C6H5OH···CH3CN
-6,6
C6H6···Na+
-21,3
C6H6···K+
-17,0
C6F6···Cl-
-14,0
C3N3H3···Cl-
-6,9
S udies e ealed ha anion···π in e ac ions a e, in gene al, domina ed by he
elec os a ic and induc ion con ibu ions.[75, 78] The elec os a ic componen o he
in e ac ion is di ec ly ela ed wi h he pe manen quad upole momen o he elec on-
de icien a oma ic ing. As indica ed in Figu e 1.6, he quad upole o a benzene ing is
posi i e bu i can be modula ed h ough he subs i u ion o g oups on he im o he
ing. Fo ins ance, he quad upole momen o a benzene ing is -8.45 B while he
quad upole momen o he benzene ing subs i u ed wi h six luo ide g oups is posi i e
by 9.50 B.[70, 72]
The e o e, he p esence o elec on-wi hd awing subs i uen s (halogen, ni o o cyano
g oups) o ni ogen a oms in he ing (py idine, iazine, e azine, among o he s) a o s
he o ma ion o anion···π complexes.
Figu e 1.6. Schema ic ep esen a ion o he quad upole momen s o hexa luo obenzene
and benzene. Quad upole momen s (Qzz) in Buckingham and molecula pola izabili ies
pa allel o he main symme y axis (||) in a omic uni s a e gi en.
1. In oduc ion
17
A opological analysis o he elec os a ic po en ial in anion···π in e ac ions has
demons a ed ha he e exis s a co ela ion be ween he MEP alue o he a oma ic
ing and he elec os a ic con ibu ion o he anion···π in e ac ion.[70, 72] Thus, he
sys ems wi h a e y posi i e quad upole momen gi e mo e a o able in e ac ions.
O he s udies show ha o molecules wi h e y posi i e quad upole momen s he
anion···π in e ac ion is domina ed basically by he elec os a ic e m, while o
molecules wi h small quad upole momen s he pola iza ion con ibu ion induced by he
anion can be he domina ing one. Finally, conside ing he la ge pola izabili y o anions i
has also been ound ha dispe sion con ibu ions end o be la ge in anion···π
complexes han in simila ca ion···π ones.[70, 72]
The p ope ies o he anion a e also impo an o applica ions o anion···π
in e ac ions in Sup amolecula Chemis y.[70, 72, 82] Bo h he elec os a ic and pola iza ion
con ibu ions o he o al in e ac ion ene gy depend s ongly upon he ion-a ene
dis ance. Small anions a e mo e pola izing and show sho equilib ium dis ances and,
consequen ly, gi e ise o s onge in e ac ions. In addi ion, plana and linea anions
such as NO3- o N3- can also in e ac wi h he a oma ic ing ia π···π s acking.[70, 72, 79]
Finally, a commen mus be said on he in e play o he di e en in e ac ions
commen ed abo e, all o hem in ol ing a oma ic species. Di e en π in e ac ions a e
e y impo an and omnip esen in a g ea a ie y o biological sys ems, so he s udy o
he mu ual in luence o di e en in e ac ions is c ucial. The in e play be ween ion···π
and π···π in e ac ions, which can lead o s ong coope a i i y e ec s, has been shown.
The coope a i i y e ec s can be a o able o un a o able depending on he na u e o
he a oma ic ing and he sign o he ion.[41, 83-87] The heo e ical esul s on ion···π···π
complexes ha e also been used o explain an unexpec ed expe imen al inding ega ding
he pa allel s acking o pen a luo phenyl g oups in subs i u ed e ocenes.[88] Mos
o en, he in e ac ions a e no isola ed bu inse ed in long s uc u es whe e mul iple
in e ac ions o di e en ype a e possible. Thus, i is qui e ypical o ind π···π
in e ac ions a he same ime as ca ion···π o X-H···π in e ac ions in many p o eins and
amino acids. Some imes, hese in e ac ions a e combined o ming a la ge complex
whe e wo o mo e di e en kinds o in e ac ions a e es ablished wi h simul aneous
pa icipa ion o he a oma ic uni s.[11, 12, 41]
1.4. In e ac ions wi h buckybowls
Polycyclic a oma ic hyd oca bons (PAH) a e a amily o hyd oca bon molecules ha
ypically possess a s uc u e o med by a se ies o used benzene ings c ea ing a plana
s uc u e. In g aphene, ma e ial wi h po en iali ies s ill o disco e , his s uc u al
mo i e ex ends c ea ing la ge bidimensional laye s. Some o hese PAHs cons i u e
impo an a mosphe ic con aminan s wi h some implica ions o human heal h bu , on
he o he hand, some PAHs ha e been loca ed in he in e s ella medium and pos ula ed
as species ha could ac as basis o he mo e p imi i e ways o li e.[89]
Alba Campo Cacha ón
18
In 1966 Ba h and Law on p esen ed he i s syn hesis o he C20H10 PAH, called
co annulene, ha p esen s a non-plana s uc u e.[90] Con a y o o he PAH as helicenes
he non-plana i y o co annulene is no a consequence o he p esence o bulky g oups
ha o ce he loca ion o pa o he used ings ou o he plane. The o igin o he non-
plana i y o co annulene is he p ope s uc u e o he ca bon ings: co annulene is
o med by i e benzene ings g ouped a ound a pen agonal cen al ing. The p esence o
he i e ca bon cen al ing in oduces he cu a u e in he co annulene s uc u e
because i is no possible o build a plana laye using pen agons and hexagons.
Acco ding o his, he s uc u e is de o med c ea ing species wi h bowl shape ha ,
con a y o plana PAH, p esen wo aces, conca e and con ex, which can exhibi
di e en p ope ies. This is he mo i a ion why hese species a e denomina ed
molecula bowls, π-bowls o buckybowls.[91]
The ela i ely ecen disco e y o buckmins e ulle ene and o he ulle enes has
inc emen ed he in e es in buckybowls because hey a e conside ed as ulle ene
agmen s and hey could be a key piece in he syn hesis and design o new species
ela ed o ulle enes and ca bon nano ubes.[92, 93] The e is a comple e amily o
buckybowls ha has been iden i ied o syn hesized in he labo a o y, and i has been
obse ed ha hough hese species equen ly sha e as s uc u al mo i e hei bowl
shape, hei p ope ies change app eciably wi h size, cu a u e and subs i uen s.[91]
Figu e 1.7. Buckymins e ulle ene and he smalles buckybowls ela ed o i .
Co annulene
C20H10
Sumanene
C21H12
Buckymins e ulle ene
C60
1. In oduc ion
19
In any case, his a ea o s udy is ecen ly eme ging: while co annulene has been
syn hesized in 1966, he o he smalles buckybowl ela ed o C60, denomina ed
sumanene (C21H12), has been syn hesized so ecen ly as in 2003.[94] Sumanene p esen s a
s uc u e ha is o med by a hexagon as he cen al ing and al e na ing hexagons and
pen agons a ound i . Due o i s ecen disco e y, ela i ely ew s udies which desc ibe
p ope ies and cha ac e is ics o sumanene a e published.[94-99]
These ca bon a oma ic nanosys ems show sub le dependences be ween hei
s uc u e, dynamic and p ope ies, so hey a e a se o ma e ials wi h g ea po en iali ies
in a a ie y o a eas. One o he mos in e es ing aspec s is he possibili y o c ea ing
in e molecula complexes o di e en na u e employing one o bo h aces o he
buckybowls, c ea ing sup amolecula s uc u es bonded by nonco alen in e ac ions. In
his sense, he e is a g ea a ie y o possibili ies in which buckybowls could ac as
ecep o s in e ac ing wi h o he buckybowls o ulle enes, ansi ion me als, ions o
di e en na u e, e c.[91]
An in e es ing applica ion o hese species is ela ed o a conca e-con ex in e ac ion
be ween wo buckybowls by means o π···π con ac s, so hey ha can be employed as
weeze s o ca ching species o in e es , o ins ance ulle enes. In his case,
buckybowls can be used as one o he mos e icien buckyca che s, as p oposed by
Sygula.[26]
Whe eas s acking wi h plana hyd oca bons is limi ed o he egion nea by he bo om
o he bowl, he use o cu ed su aces allows ex ending he con ac a ea inc easing he
in e ac ion. Di e en modi ica ions o co anulenne and sumanene ha e been s udied as
possible ulle ene ecep o s based on π···π in e ac ions, hough o he e ec s as C-H···π
can also help s abilizing he complex as al eady shown o sumanene.[100-106]
Figu e 1.8. Tweeze s de eloped by Sygula e al. o ca ch ulle enes.
2. Objec i es
27
The main objec i e o his hesis is o gain mo e insigh in o he cha ac e is ics o
sys ems ha es ablish in e ac ions be ween a oma ic and cha ged species by applying
compu a ional chemis y me hods. The in e es on ion···π in e ac ions has g own in he
las decades wi h new e idences o hei impo ance in many ields co e ing om
biochemis y o ma e ials science. Mo e speci ically, he upcoming o anion····π
in e ac ions has p oduced a enewed in e es abou he cha ac e is ics and na u e o
he in e ac ions wi h a oma ic sys ems, as well as hei ela ionship wi h o he ypes o
in e ac ions.
Compu a ional chemis y has also ecen ly e ol ed wi h new me hods and unc ionals
speci ically designed o s udying in e molecula in e ac ions, especially ega ding he
ea men o dispe sion in e ac ions. These new app oaches, oge he wi h echniques
allowing signi ican educ ions o he compu a ional cos , ha e made possible he
applica ion o app op ia e me hods o sys ems o inc easing size, hus a oiding being
es ic ed o he simples cases as benzene complexes wi h alkaline o halogen ions.
The s udy o ion···π in e ac ions cons i u es a wide ield o esea ch, including e y
di e en sys ems and phenomena, so in his hesis he goal will be ocused on a se ies o
speci ic aspec s o he ca ion···π (chap e s 4 and 5) and anion···π (chap e s 6 o 9)
in e ac ions. Mo e p ecisely, he goals o he di e en chap e s a e summa ized in he
ollowing.
Chap e 4 is de o ed o phenol···ca ion (K+, Na+, Li+ and Mg2+) complexes. Though he
in e ac ion o simple a oma ic molecules, mos ly benzene, wi h simple ca ions as
alkaline ones has al eady been s udied in de ail, he e a e se e al aspec s o he
in e ac ion ha dese e mo e a en ion. Ca ion···π in e ac ions a e s ong in he gas
phase, bu he p esence o sol en molecules o o he dona ing g oups nea by can
modula e he s eng h and cha ac e is ics o he in e ac ion. Mic ohyd a ion o
complexes opens a ou e o isola ing he e ec s due o speci ic in e ac ions wi h he
sol en . Clus e s o med by phenol and simple ca ions will be subjec ed o s epwise
mic ohyd a ion in o de o de e mine he mos s able a angemen s o he hyd a ed
complexes. Tha way, he balance among he di e en a ac i e con ac s in he clus e s
can be analyzed and hei impac on clus e p ope ies de e mined. Mo eo e , sys ems
con aining a small numbe o molecules can be moni o ed by in a ed spec oscopy, so
he ib a ional spec a will be p edic ed o he complexes s udied. The esul s will be
compa ed o he expe imen al ones ob ained by Vaden and Lisy (J. Chem. Phys. 2004,
120, 721-730) o phenol complexes wi h K+ and Na+ and ou wa e molecules.
Chap e 5 deals wi h he analysis o ano he possible modula ing e ec in ca ion···π
complexes. Besides sol en molecules, o he elec on dona ing g oups can also in e ac
wi h he ca ion in a ca ion···π con ac . In his chap e , he e ec o a second a oma ic
Alba Campo Cacha ón
28
uni in e ac ing wi h a ca ion···π con ac will be analyzed. Te na y sys ems o med by
wo a oma ic molecules and one ca ion will be s udied in o de o quan i y he balance
be ween he di e en ca ion···π, X-H···π and π···π in e ac ions and hei mu ual
in luence. The sys ems a e o med by a ca ion and a oma ic ings selec ed as o
ep esen possible con ac s be ween amino acid side chains. Benzene, phenol and
indole a e employed as a oma ic uni s, whe eas guanidinium ca ion is selec ed as a
model o he ca ionic side chain o a ginine. The mos s able s uc u es o hese e na y
complexes will be de e mined and hei cha ac e is ics analyzed. Consequen ly, possible
speci ic in e ac ions, as hyd ogen bonds in phenol and indole complexes, o he ole
played by dispe sion in e ac ions would be e ealed. Also, a pai ene gy decomposi ion
will allow de e mining he magni ude o possible coope a i e e ec s in his kind o
complexes.
Chap e 6 is he i s one de o ed o anion···π in e ac ions. Recen ly, Ma ile e al. (J.
Am. Chem. Soc. 2006, 128, 14788-14789) syn hesized he i s anionic channel which is
supposed o be based on anion···π in e ac ions. This anion channel is cons uc ed by a
se ies o oligome s o naph halendiimides (NDIs), which a ange hemsel es as o c ea e
a po e h ough which anion anspo a ion has been e i ied. Howe e , se e al
ques ions emain unanswe ed abou how his channel wo ks. Speci ically, i has been
sugges ed ha sol en molecules can play an ac i e ole in anion anspo , maybe going
in o he channel and acili a ing he p ocess. Two simple models will be employed o
s udying he in e ac ion o anions wi h NDI, and he e ec o wa e molecules will be
es ima ed by explici ly inco po a ing a small numbe o wa e molecules in o he model
and also by using a con inuous ep esen a ion o he sol en . The esul s will help
unde s anding he ole o he sol en molecules closes o he anion in o de o a o
he in e ac ion wi h he channel uni s.
Chap e s 7 o 9 a e dedica ed o an eme gen ield in chemis y ela ed o he
p ope ies and in e ac ions o cu ed a oma ic sys ems (buckybowls). In hese chap e s,
he possible use o hese buckybowls as ion ecep o s will be analyzed by in oducing
di e en modi ica ions in he s uc u es o he bowls. Subs i u ed de i a i es o
co annulene and sumanene will be employed in hese s udies.
Chap e 7 is ou i s app oach o his subjec . Co annulene shows nega i e molecula
elec os a ic po en ial (MEP) by bo h aces o he bowl, bu p ope subs i u ion wi h
elec on-wi hd awing g oups can in e i s molecula elec os a ic po en ial and p o ide
a a o able in e ac ion wi h anions. Subs i u ion o co annulene wi h i e and en F, Cl
and CN g oups will be conside ed, and i s e ec upon he p ope ies o he bowls will be
analyzed, specially ega ding hei MEPs, seeking a s onge in e ac ion wi h anions. The
e ec o hese subs i u ions upon he in e ac ion wi h anions will be s udied in
2. Objec i es
29
complexes o med wi h Cl-, B - and BF4- anions, ob aining hei op imal geome ies and
in e ac ion s eng hs. I is in ended o o m ema kably s able complexes, looking o
inclusion s uc u es wi h he anion by he conca e side o he bowl, as opposed o he
con ex complexa ion al eady obse ed in ca ions.
Chap e 8 is mo e o ien ed o he pe o mance o di e en compu a ional me hods. I
has been obse ed ha in his kind o sys ems a eliable me hod is di icul o ind, he
e o s being qui e la ge in many cases. Since he e a e no e e ence alues, he me hod
employed is somewha blindly chosen. In o de o alle ia e his p oblem, a ho ough
s udy will be ca ied ou in complexes o Na+ and Cl- wi h buckybowls. Two ypical
buckybowls, co annulene and sumanene, will be conside ed and subs i u ed by CH3, F
and CN g oups o p omo e changes in he molecula elec os a ic po en ials.
Consequen ly, he in e ac ion will be modula ed a o ing ca ions o anions. Re e ence
alues o he in e ac ion will be ob ained by employing high-le el calcula ions, being
used a e wa ds o checking he pe o mance o a a ie y o mo e a o dable me hods.
A eliable accoun on how subs i u ion a ec s he in e ac ion in bo h anion and ca ion
complexes will be ob ained, allowing he di ec compa ison o ca ion···π and anion···π
in e ac ions in he same se o sys ems. The de ailed analysis o he cha ac e is ics o
he in e ac ion will hope ully e eal he in insic di e en na u e o he in e ac ion wi h
ca ions and anions in hese ex ended π sys ems.
Chap e 9 comple es he s udies on he in e ac ion be ween anions and buckybowls.
A e selec ing an app op ia e me hod in chap e 8, now his me hod will be applied in
o de o gain insigh abou how he shape, size and disposi ion o he anions a ec he
p ope ies o he complexes. CN-subs i u ed co annulene and sumanene will be
employed o s udy he in e ac ion wi h six di e en anions, going om monoa omic Cl-
and B -, o plana igonal NO3- and CO2H-, and o e ahed al BF4- and ClO4-. Se e al
o ien a ions o he polya omic anions as well as di e en app oaching lines o he bowl
will be conside ed. The cha ac e is ics o hese complexes will be analyzed in de ail in
o de o ind he key ac o s con olling he in e ac ion in each case and he possible
di e ences associa ed o he di e en anion’s na u e. Also, sol en e ec s as modeled
by a con inuum model will be e alua ed o check whe he he p oposed complexes
would be o med in solu ion. A se ies o sol en s wi h di e en dielec ic cons an will
be used o quan i y how he gas-phase in e ac ion is al e ed and o which ex en anion’s
na u e a o s o hinde s he o ma ion o complexes in solu ion.
3. Me hodology
3. Me hodology
33
3.1. In e ac ion Ene gy
Though in e ac ion ene gies a e se e al o de s o magni ude smalle han elec onic
ene gies, and usually signi ican ly smalle han bond ene gies, he usual app oxima e
me hods employed o sol ing he Sch ödinge equa ion in chemical sys ems can be
employed o s udying nonco alen in e ac ions.[1-3]
The concep o in e ac ion ene gy appea s na u ally wi hin he Bo n-Oppenheime
app oxima ion when a sys em o med by say, wo molecules, a oms o ions is
conside ed.[3] Quan um chemis y ea s he sys em as a whole so a e calcula ing wi h
a gi en me hod, he ene gy o he comple e sys em (supe molecule) is ob ained. As
indica ed in Figu e 3.1, a sys em de ined by a se o nuclei a gi en posi ions oge he
wi h he co esponding elec ons has o be di ided (a bi a ily o no ) in a se o
sepa able a oms, molecules o ions.
Figu e 3.1. A phenol···wa e dime . Le : he se o a oms o ming he sys em. Righ : he
di ision employed o s udying he in e ac ion be ween phenol and wa e .
Once his sepa a ion is done, he ene gy o he sys em can be exp essed as:[3-5]
in
ABBAAB EEEE
. (eq. 3.1)
The ene gy o he sys em is hen exp essed as a sum o he ene gies o he isola ed
agmen s plus a con ibu ion coming om hei in e ac ion. Following his line, he
in e ac ion ene gy could hen be ob ained wi hin he supe molecule app oach as:
)()()()(
in BAABAB EEEE
, (eq. 3.2)
whe e i has been highligh ed ha he same se o nuclea posi ions has been employed
in he calcula ion o he h ee quan i ies.[3, 6-8]
Howe e , i we a e in e es ed in s udying he p ocess o complex o ma ion, a new
e m has o be included, since he geome ies o he species o ming he complex can
change as a consequence o he in e ac ion and o ma ion o he complex.[6-8] The e o e,
a new e m has o be included desc ibing his e ec ,
Alba Campo Cacha ón
34
)()()()()( 00 BABAde EEEEE
. (eq. 3.3)
Along his wo k his e m will be called he de o ma ion ene gy,[9, 10] hough in
li e a u e o he names can be ound o his quan i y, such as elaxa ion ene gy (in he
sense ha i we hink o dissocia ion, he geome y has o elax o ha o he isola ed
agmen s)[6-8] o p epa a ion ene gy (in he sense ha his is he ene gy needed o
p epa e he agmen s in o de o o m he complex a he inal geome y).[4]
The sum o hese wo quan i ies de ines he complexa ion ene gy, he ene gy change
obse ed when a complex is o med om he isola ed, elaxed molecules ha o m i .
The nega i e o his quan i y is o en called he binding ene gy, ela ed o he ene gy
needed o sepa a ing he complex in o isola ed agmen s. O he e ec s such as ze o
poin ene gy co ec ions o he mal e ec a e added as usual o each o he ene gies
needed o ob aining he magni udes desc ibed abo e. In summa y, he complexa ion
p ocess can be o mally di ided in o wo s eps: de o ma ion plus in e ac ion, so he
complexa ion ene gy is ob ained as:
)()()( in de Ab
complex
AB EEE
(eq. 3.4)
o
)()()()(
)()()()(
00
BABA
BAAB
complex
AB
EEEE
EEEE
(eq. 3.5)
and:
)()()()( 00 BAAB
complex
AB EEEE
(eq. 3.6)
So, he complexa ion ene gy could be ob ained wi hou making any e e ence o he
in e ac ion and de o ma ion ene gies. Howe e , i could be in e es ing o sepa a e he
complexa ion p ocess in o hese wo con ibu ions in o de o ob ain a be e
in e p e a ion o he sys em, especially when la ge de o ma ion e ec s a e p esen as
consequence o impo an geome y changes. In such si ua ions, a e y la ge in e ac ion
could be hidden by opposing la ge de o ma ion e ec s.[7, 8, 11, 12] Also, he p ac ical
calcula ion o complexa ion ene gies aces some p oblems, which make ad isable o
sepa a e hem in o hese wo con ibu ions as i will be commen ed below.
3.1.1. Basis Se Supe posi ion E o
Any esea che dealing wi h he quan um chemis y calcula ion o in e ac ion ene gies
has aced he p oblem o Basis Se Supe posi ion E o (BSSE).[3, 5, 6, 13] The p oblems
appea when using (eq. 3.2) o ob aining he in e ac ion ene gy. Wi h his exp ession,
he in e ac ion ene gy o a dime is ob ained as a di e ence be ween h ee quan i ies.
3. Me hodology
35
As commen ed abo e, in e ac ion ene gies a e se e al o de s o magni ude smalle han
elec onic ene gies, so he in e ac ion ene gy, a small quan i y, is ob ained om he
di e ence among la ge quan i ies. The e o e, i has o be ensu ed ha all elec onic
ene gies a e ob ained cohe en ly, and ha any e o s coming om he me hod
employed will be p ope ly cancelled ou . Howe e , a p ac ical quan um chemis y
calcula ion is pe o med wi h a ini e basis se employed o cons uc ing he
wa e unc ion, and his is he o igin o he p oblem.
Conside a dime AB. When monome A app oaches monome B in o de o o m he
dime AB, he ene gy o he dime is a i icially lowe ed because monome A can employ
he basis se cen e ed on o he a oms o B in o de o imp o e he desc ip ion o i s
elec on dis ibu ion, and he same applies o monome B using basis unc ions
cen e ed in A. This ene gy lowe ing is no possible in he calcula ions in isola ed
monome s whe e only he basis se o each monome is p esen . As indica ed by an
Duijne eld ,[14] his ene gy lowe ing as ex a basis unc ions a e employed is no an e o
in i sel . The e o comes om an inconsis en ea men o he monome s, which
canno ake bene i om he basis se o he o he as he dis ance becomes la ge . This
inconsis en ea men o he monome s as he dis ances change is he o igin o he
BSSE. The e o e, BSSE depends on he geome y o he sys ems, and a di e en alue is
ob ained o each di e en a angemen o nuclei. I has o be aken in o accoun ha
e en i BSSE is emo ed comple ely, he e s ill emain o he e o s associa ed o he
me hod employed and he ini e basis se used.
The usual p ocedu e o co ec ing BSSE is he coun e poise me hod p oposed by Boys
and Be na di, explained below.[15, 16] The unco ec ed in e ac ion ene gy o a dime AB
would be ob ained as in eq 3.2, o :
)()()()( dime dime dime in BEAEABEABEBAABAB
, (eq. 3.7)
whe e now he e ms in pa en heses indica e he basis se employed in he calcula ions
and supe sc ip s he geome y employed. These quan i ies a e ob ained in h ee
sepa a e calcula ions o he dime , monome A wi h i s basis unc ions and monome B
wi h i s basis unc ions. As commen ed abo e, he di e en basis se s employed in he
calcula ions in oduce BSSE, so he coun e poise co ec ion consis s on ob aining he
h ee ene gies using he same basis se and ene gy in all calcula ions.
)()()()( dime dime dime in ABEABEABEABEBAABAB
. (eq. 3.8)
Now he ene gy o monome A is ob ained in a calcula ion wi h he basis se o B in he
same posi ions as in he dime , and he same applies o monome B. In ha way, he
same basis se is employed in all calcula ions and BSSE is co ec ed. The e o e, BSSE can
be de ined as:
)()()()( dime dime dime dime ABEABEBEAEBSSE BABA
(eq. 3.9)
Alba Campo Cacha ón
42
000 ˆ
. (eq. 3.30)
0
ˆ
is he wa e ope a o , ha in CI is a linea ope a o , bu in CC is an exponen ial one:
...
ˆˆˆ
1
ˆ3210 CCC
CI
(eq. 3.31)
...
ˆ
6
1
ˆ
2
1
ˆ
1)
ˆ
exp(
ˆ32
0 TTTT
CC
(eq. 3.32)
...
ˆˆˆˆ 321 TTTT
. (eq. 3.33)
Mo e explici ly, he expansion o he exponen ial will be (only singles and doubles
included):
...
ˆˆ
!2
1
ˆˆˆ
!2
1
ˆ
!4
1
ˆ
!3
1
ˆ
!2
1
ˆˆ
1
ˆ2
1221
2
2
4
1
3
1
2
1210 TTTTTTTTTT
. (eq. 3.34)
The C and T ope a o s a e exci a ion ope a o s ha change one, wo, …. occupied
spino bi als by i ual ones. Fo example:
s ba
s
ab
s
ab
T
02
ˆ
, (eq 2. 35)
whe e
s
ab
a e he coe icien s (o ampli udes) o be de e mined in CC calcula ions.
The g ea ad an age o CC me hods o e CI ones is ha he exponen ial an saz
employed in CC me hods ensu es ha he me hod will be size consis en , hus a oiding
he majo p oblem aced by CI calcula ions. Usually, CC me hods a e employed
unca ed up o a gi en exci a ion o de , ypically including single and double
exci a ions, CCSD. Though ampli udes a e only calcula ed o singles and doubles, he
exponen ial expansion in oduces es ima ions o highe -o de exci a ions exp essed as
p oduc s o singles and doubles. Fo example, quad uple exci a ions a e no included,
bu hei e ec is es ima ed by p oduc s o doubles. The e o e, o a gi en unca ion
le el CC beha es be e han CI since hese so-called disconnec ed clus e s include he
e ec o highe exci a ions. CI me hods, on he o he hand, only include exci a ions up
o he unca ion le el.
The mos common choice in p esen calcula ions is o employ CCSD me hod combined
wi h a sui ably lexible basis se . Including iple exci a ions implies a huge
compu a ional e o so CCSDT is only applicable o small sys ems. Mos o en, a e he
CCSD solu ion has been eached, a pe u ba i e es ima ion o he iples is added in he
so-called CCSD(T) me hod. Tha way he e ec o iple exci a ions (o en e y
impo an ) is included wi hou needing o sol e he ull CCSDT equa ions. In any case,
3. Me hodology
43
inclusion o iples is also a demanding ask, so CCSD(T) can only be used o sys ems
wi h mode a e size.
Nowadays, esul s ob ained a he CCSD(T) le el wi h a la ge basis se a e conside ed
as he golden s anda d o quan um chemis y calcula ions, especially in he case o
in e molecula in e ac ions domina ed by dispe sion e ec s. Ve y ecen ly, esul s
ob ained wi h CCSD(T) ha e been compa ed wi h hose ob ained wi h highe o de CC
calcula ions such as CCSDT[Q] o a se o complexes, con i ming he e y good beha io
o CCSD(T).[54-56]
3.2.4. E o s in Wa e unc ion-based Me hods
F om p e ious sec ions i is clea ha a ypical calcula ion wi h a wa e unc ion-based
me hod is a ec ed by wo sou ces o e o as depic ed in Figu e 3.2. When compa ing
he esul o an ac ual calcula ion employing a pos -HF me hod wi h he exac solu ion
(wi hin Bo n-Oppenheime app oxima ion and non- ela i is ic Hamil onian) an appa en
e o is obse ed coming om wo di e en sou ces.[21]
Figu e 3.2. Rep esen a ion o he e o s associa ed o elec onic s uc u e calcula ions.
Alba Campo Cacha ón
44
Conside ing ha FCI solu ion is he exac solu ion o a gi en basis se , an e o is
in oduced due o he de iciencies o ou me hod o desc ibing co ela ion. MPn and CC
me hods a e di e en app oaches o app oxima ing o he FCI solu ion, bu in ac ual
calcula ions bo h MPn and CC ha e o be unca ed somehow, hus in oducing an e o
as compa ed wi h he FCI esul ( he N-elec on e o in Figu e 3.2). In any case, he
me hods cu en ly employed o including elec on co ela ion al eady show a e y good
pe o mance, so he N-elec on e o can be educed including highe o de s o MPn o
CC, o cou se a he cos o much mo e expensi e calcula ions.
The o he sou ce o e o is ela ed wi h he se o one-elec on basis unc ions
employed o cons uc ing he N-elec on wa e unc ion. Tha is, o a gi en N-elec on
model (MP2, MP4, CCSD, …) he e is an e o associa ed wi h he basis o one elec on
unc ions employed, he basis se . When he esul o an ac ual calcula ion is compa ed
wi h he same calcula ion employing a comple e basis se , a di e ence is obse ed
co esponding o he basis se e o . In o de o educe his e o , la ge basis se s ha e
o be employed, ideally eaching he limi o comple e basis se . When his limi is
eached, he e s ill emains an e o ela ed wi h he de iciencies o ou N-elec on
model as commen ed abo e.
The e o e, in o de o ob ain accu a e esul s om a wa e unc ion based me hod, one
has o ake ca e in o de o educe bo h sou ces o e o s, hus ying o employ an
adequa e ep esen a ion o co ela ion by means o a good N-elec on model, combined
wi h a one-elec on basis se la ge enough in o de o educe he e o s associa ed o
incomple eness o he basis se . Tha is, one has o use he ob ious choice o a good
co ela ion me hod combined wi h a la ge basis se .
The choice o N-elec on model and basis se is o cou se condi ioned by he
compu ing esou ces since an inc emen in he quali y o any o hem has a deep impac
on he compu a ion ime. The cu en ly used N-elec on models pe o m qui e a good
job app oaching he FCI esul s, including co ela ion ene gy o a g ea ex en . In
p ac ical calcula ions, howe e , one is no mally educed o he use o MP2 i he size o
he sys em is mode a e, o o CCSD(T) i he size o he sys em and esou ces allow i . As
commen ed abo e, he use o CCSD(T) combined wi h a lexible basis se is nowadays
conside ed as he gold s anda d in quan um chemis y calcula ions. As indica ed in a
ecen pape , CCSD(T) o he basis limi is able o ep oducing he in e ac ion ene gies o
a se o complexes wi hin 1.5% e o .[54] In summa y, as o he N-elec on model, we a e
limi ed in he p ac ice o choose be ween he p ac ical and cheapes MP2 and he mo e
accu a e and demanding CCSD(T). O he in e media e op ions could be o in e es in
pa icula p oblems.
The e o associa ed o he one-elec on basis se dese es a li le mo e a en ion, so
i will be analyzed in he ollowing sec ion.
3. Me hodology
45
3.2.4.1. Ex apola ing o basis limi
The p oblem o he e o associa ed o he one-elec on basis se is ha i con e ges
e y slowly as he size o he basis se is inc eased, so e y la ge basis se s a e needed o
app oach he limi ing alue o comple e basis se (CBS). Figu e 3.3 ep esen s he
con e gence o he co ela ion ene gy o a wa e molecule as he size o he basis se is
inc eased. I can be obse ed ha he con e gence is e y slow, and e en wi h he
eno mous cc-pV6Z basis se he esul is s ill a om he limi . This bad con e gence
wi h espec o he one-elec on basis se is ela ed wi h he inabili y o he usual one-
elec on basis unc ion o ep oduce he elec on-elec on cusp.[21, 57, 58]
In any case, in p ac ical calcula ions he la ges basis se s o be employed as ou ine
a e cc-pVQZ o aug-cc-pVTZ o simila , so i can be obse ed om Figu e 3.3 ha he
esul s will be a om he CBS limi . I has o be aken in o accoun ha when
compu ing ene gy di e ences as o example in ob aining in e ac ion ene gies pa o
hese e o s can be cancelled and he esul s could be nea e he limi ing alue.
Figu e 3.3. Va ia ion o he co ela ion ene gy in wa e molecule as he size o he basis
se is inc eased.
X
0 2 4 6 8 10
Eco (a.u.)
-0.40
-0.38
-0.36
-0.34
-0.32
-0.30
-0.28
-0.26
-0.24
-0.22
-0.20
wa e molecule
cc-pXDZ
Alba Campo Cacha ón
46
The solu ions o his p oblem depend on using e y la ge basis se s, which is
imp ac ical o , mo e ecen ly, by using explici ly co ela ed me hods, which end mo e
quickly o he limi han he s anda d ones.[57, 58] Howe e , he e is an in e media e
solu ion used qui e o en which passes by ex apola ing he esul s ob ained wi h
mode a e-sized basis se in o de o ob ain an es ima ion o he limi ing alue.[59-65]
These ex apola ion schemes a e only applicable i he beha io o he ene gy as he
basis se g ows is smoo h so i can be i ed o a unc ion and hen ob ain he limi ing
alue. Thus, his kind o ex apola ion schemes a e mos ly limi ed o well-balanced basis
se as he co ela ion consis en cc-pVXZ amily p oposed by Dunning.[66] In his espec ,
one should dis inguish be ween he beha io o HF ene gies and he con ibu ions
coming om co ela ion.
In he case o HF ene gies, i has been ound ha in a oms he ene gies app oxima ely
ollow an exponen ial beha io .[20, 57, 67] Assuming ha his exponen ial decay can be also
employed in molecules, an o en-employed ex apola ion scheme assumes ha he HF
ene gy beha es as:
)exp( BXAEE HF
CBS
HF
X
. (eq. 3.36)
So, i h ee calcula ions a e pe o med wi h co ela ion consis en basis se o inc easing
X, he limi ing alue could be es ima ed as:
HF
X
HF
X
HF
X
HF
X
HF
X
HF
X
HF
CBS EE
EE
Bb
b
bEE
E
21
11 )exp(;
1
. (eq. 3.37)
Howe e , he need o h ee calcula ion o inc easing size is uncom o able, so o he
wo-poin ex apola ion schemes ha e been de ised. Fo example, Ka on and Ma in
p oposed he ollowing wo-poin p ocedu e:[68, 69]
)9exp()1( XXAEE HF
CBS
HF
X
. (eq. 3.38)
In any case, HF ene gies con e ge qui e quickly wi h he basis se , and especially when
ene gy di e ences a e conside ed, as in e ac ion ene gies. Thus, i is usually ound ha
ob aining he HF in e ac ion ene gies wi h a basis se o cc-pVTZ quali y is o en enough
since he e o s associa ed o co ela ion a e no mally la ge .
When dealing wi h co ela ion ene gies, he dependency on he basis se size is s ill
mo e impo an , so a good es ima ion o co ela ion ene gies o en demands e y la ge
basis se s. Fu he mo e, he con e gence o co ela ion ene gy wi h he basis se size is
e en slowe han in he HF case, so la ge basis se s would be needed, as ep esen ed in
Figu e 3.3. Fo una ely, he e a e ex apola ion schemes ha seem o pe o m
easonably well allowing a good es ima ion o he co ela ion ene gy a a mode a e cos .
In He a om i has been obse ed ha he e o in co ela ion ene gy a ies as
3. Me hodology
47
3
cNEN
, being N he p incipal quan um numbe .[57] Tha is, he e is a cubic decay o
he co ela ion ene gy as la ge basis se s a e included. Assuming a simila beha io in
molecules and iden i ying N wi h he X o dinal in Dunning basis se s,[59, 60, 63] i can be
assumed ha he co ela ion ene gy changes as:
3
AXEE XCBS
. (eq. 3.39)
This exp ession con ains only wo unknowns and he e o e can be sol ed i wo
calcula ions a e pe o med o ob aining he co ela ion ene gy,
3
AXEE XCBS
, (eq. 3.40)
3
AYEE YCBS
. (eq. 3.41)
So:
33
33
YX
EYEX
EYX
exac
. (eq. 3.42)
O cou se he esul will depend on he alues used o X and Y, bu i has been ound
ha a T-Q ex apola ion employing cc-pVXZ basis se s al eady gi es esul s be e han
he di ec calcula ion employing a cc-pV6Z basis se . In p ac ical calcula ions in sys ems
o mode a e size, one is usually limi ed o pe o m T-Q ex apola ions wi h he cc-pVXZ
basis se o D-T ones wi h he aug-cc-pVXZ basis se s.
3.2.4.2. Ob aining benchma king alues
In he p e ious sec ion i has been exposed how applying an ex apola ion scheme o
co ela ion ene gies he e is an a o dable ou e o ob aining co ela ion alues a he
CBS limi . Howe e , his kind o ex apola ion is s ill qui e demanding so i is usually
pe o med wi h MP2 es ima ions o he co ela ion ene gy. The e o e, e en when he
MP2 alues a e ob ained a he basis limi , he e s ill emains an e o associa ed o he
low quali y o he N-elec on model employed.
The s aigh o wa d solu ion would be employing a be e model, say CCSD(T), in
o de o ob ain be e es ima ions o he co ela ion ene gy, and hen apply an
ex apola ion scheme. This op ion, hough o mally app op ia e, is e y demanding, and
o sys ems o mode a e size canno be applied in ou ine calcula ions due o he high
cos o he CCSD(T) calcula ions wi h he la ge basis se . The e o e, o he app oaches
ha e been de ised in o de o es ima e he CCSD(T)/CBS alues bu wi h a educed
compu a ional cos , many o hem p oposed by Hobza. Hobza and collabo a o s
obse ed ha e en hough he co ela ion ene gy con ibu ions o he in e ac ion
ene gy o a dime a e e y di e en wi h MP2 and CCSD(T), he di e ences be ween
bo h me hods we e p e y independen o he basis se size.[52, 70, 71] The e o e, he
Alba Campo Cacha ón
48
CCSD(T)/CBS limi ing alue o he co ela ion con ibu ion o he in e ac ion ene gy
could be ob ained as:
smallbasisco
MP
smallbasisco YTCCSD
CBSco
MP
CBSco TCCSD EEEE ,
2
,)(
,
2
,)(
. (eq. 3.43)
In his exp ession, he MP2 con ibu ion o he co ela ion ene gy is es ima ed o basis
limi wi h he ex apola ion p ocedu es explained abo e, and he esul is co ec ed
om he ine iciencies o he N-elec on model, by using a CCSD(T) calcula ion wi h a
small basis se , and assuming ha he di e ence be ween CCSD(T) and MP2 is ai ly
cons an . An al e na i e way o unde s anding eq. 3.43 is by conside ing ha he
co ela ion con ibu ion is ob ained a he CCSD(T) le el wi h a small basis se , and he
basis se incomple eness e o is es ima ed a he MP2 le el, eq. 3.44.
smallbasisco
MP
CBSco
MP
smallbasisco YTCCSD
CBSco TCCSD EEEE ,
2
,
2
,)(
,)(
(eq. 3.44)
In any case, his p ocedu e is commonly used in o de o ob ain benchma k alues o
he in e ac ion ene gies o complexes. I should no be o go en howe e ha e o s
a e s ill p esen , depending on he size o he small basis se employed o he CCSD(T)
calcula ion. Applying his app oach, se e al da ase ha e been cons uc ed which a e
widely used as e e ence o de eloping app oxima e me hods.[72-75]
S ill wi hin his app oach, o mode a e-sized sys ems he bo leneck o he
calcula ions is he CCSD(T) calcula ion ha , e en wi h a basis se o aug-cc-pVDZ quali y
can be e y demanding. Thus, Hobza and Rezak p oposed an al e na i e way o
es ima ing he co ec ion o he MP2/CBS alue a oiding he expensi e CCSD(T)
calcula ion. The i s o hese p oposals (MP2.5)[76] and he subsequen e inemen
(MP2.X)[77] subs i u e he CCSD(T) calcula ion by cheape MP3 ones. Thus in he MP2.X
app oach, he co ela ion con ibu ion o he in e ac ion ene gy is ob ained as:
smallbasisco
MP
smallbasisco
MP
CBSco
MP
CBSco TCCSD EECEE ,
2
,
3
,
2
,)(
. (eq. 3.45)
Hobza and Rezak in oduced an empi ical scaling coe icien ob ained by i ing o he
CCSD(T)/CBS es ima es o a se o complexes o di e en na u e. Wi h his app oach i
has been obse ed ha he accu acy o he MP2.X esul s is almos independen o he
basis se employed o he MP3 calcula ion gi en a p ope C coe icien . Thus, modes
basis se s as 6-31G* can be employed gi ing esul s p e y simila o hose ob ained by
pe o ming an ac ual CCSD(T) calcula ion.[78, 79] As a consequence, he MP2.X p ocedu e
allows sa ing compu a ional esou ces by using he cheape MP3 me hod, bu also
allowing he use o smalle basis se in o de o es ima e he N-elec on co ec ion o
he MP2 limi .
3. Me hodology
49
3.3. Densi y Func ional Theo y Me hods
Densi y Func ional Theo y (DFT) is an al e na i e o me hods based on he calcula ion
o he wa e unc ion as he goal o he desc ip ion o he sys em and i s p ope ies. In
he las decades DFT has been de eloped in ensely because i becomes e y use ul o a
lo o di e en kind o sys ems due o i s ad an ageous ela ion be ween he quali y o
he esul s and compu a ional cos . Like pos -HF me hods, DFT includes he elec onic
co ela ion e m bu wi h a cos simila o HF calcula ions.[32, 80]
The ounda ion o DFT is based on he idea ha he in o ma ion ha can be ex ac ed
om he wa e unc ion can also be ob ained om he elec onic densi y. Whe eas he
ene gy in wa e unc ion-based me hod is a unc ional o he wa e unc ion (N spa ial
coo dina es + N spin coo dina es in a N-elec on sys em), which is dependen on he
numbe o a oms, in DFT he ene gy is a unc ional o he elec on densi y, so i only
depends on he h ee spa ial coo dina es
) ( E
, (eq. 3.46)
In o de o wo k wi h he densi y unc ional heo y i is necessa y o apply he i s
heo em o Hohenbe g and Kohn (1964).[32, 81]
“Any obse able o a s a iona y non-degene a e g ound s a e can be calcula ed,
exac ly in heo y, om he elec on densi y o he g ound s a e. In o he wo ds, any
obse able can be w i en as a unc ional o he elec on densi y o he g ound
s a e”.
In a sys em wi h M nuclei o cha ge Za loca ed in Ra, he in e ac ion o N elec ons o he
sys em wi h he M nuclei can be desc ibed h ough V ope a o .
d d
R
Z
R
Z
Vi
i
ai
a
i a ai
a
)()()(
||||
, (eq. 3.47)
whe e
)(
is he e ec i e po en ial o an elec on and
ii
)()(
is he
ope a o o he elec onic densi y. The es o he ope a o s in he Hamil onian depend
exclusi ely on he coo dina es o he elec ons, so hei exp essions a e equal in all
sys ems and only he numbe o elec ons changes. The e o e, he o al elec onic
ene gy depends only on he o al numbe o elec ons (N) and ex e nal po en ial
)(
.
In addi ion o his, o he essen ial cha ac e is ic o he i s Hohenbe g-Kohn heo em is
ha he ela ionship be ween ene gy and densi y is uni ocal. The e o e, i he e exis
wo di e en ex e nal po en ials ha gene a e he same elec onic densi y, hen bo h
po en ials mus be he same.
On he o he hand, he second Hohenbe g-Kohn heo em p o ides a a ia ional
p inciple:[32, 81]
Alba Campo Cacha ón
50
“The elec on densi y o a non-degene a e g ound s a e can be calcula ed,
exac ly in heo y, de e mining he densi y ha minimizes he ene gy o he
g ound s a e”.
The second Hohenbe g-Kohn heo em es ablishes he exis ence o a a ia ional p inciple
o he ene gy, e i ying ha o a es elec onic densi y
)(
, he ene gy o such
sys em is la ge han o equal o he ene gy o he eal g ound s a e o he sys em. So,
he ene gy eaches a minimum alue o he exac g ound s a e.
)()( 00 E E
. (eq. 3.48)
The e o e, he di e en ial equa ion
0
)(
)(
E
(eq. 3.49)
Is ul illed, in which he Lag ange mul iplie ensu es ha he elec onic densi y is
no malized o N elec ons. The e o e, he densi y can be a ia ionally op imized in
o de o app oach he eal g ound s a e densi y.
S a ing om hese wo undamen al heo ems, he main goal o he DFT me hods
consis s on designing unc ionals ha connec ene gy and elec onic densi y bu ,
un o una ely, Hohenbe g-Kohn heo ems do no es ablish how he exac connec ion
be ween bo h magni udes is. In o de o sol e his p oblem, Kohn and Sham de eloped
a p ac ical applica ion o his heo y h ough a me hod wi h a o mula ion simila in
s uc u e o he Ha ee-Fock me hod.
3.3.1. Kohn-Sham p ocedu e
A gene al exp ession o he ene gy aking in o accoun he Bo n Oppenheime
app oxima ion could be he nex one: [32, 80]
eene EETE
. (eq. 3.50)
The ene gy is di ided in o h ee pa s: kine ic ene gy
T
, a ac ion be ween he
nuclei and elec ons
ne
E
and elec on-elec on epulsion
ee
E
( he nuclea -nuclea
epulsion is a cons an wi hin he Bo n-Oppenheime app oxima ion). Fu he mo e,
simila ly as in Ha ee-Fock heo y, he
ee
E
e m may be di ided in o a Coulomb and
Exchange pa
J
and
K
, hough implici ly including co ela ion ene gy in all e ms.
The
ne
E
and
J
unc ionals a e gi en by hei classical exp essions, whe e he ½
ac o in
J
allows he in eg a ion o un o e all space o bo h a iables.
aa
a
ne d
R
Z
E
||
)(
][
, (eq. 3.51)
3. Me hodology
51
'
|'|
)'()(
2
1
][ d d
J
. (eq. 3.52)
The basic idea in he Kohn-Sham o malism is spli ing he kine ic ene gy unc ional
in o wo pa s, one which can be calcula ed exac ly and a small co ec ion e m. In he
eal molecula sys em, he elec onic densi y and he kine ic ene gy will be w i en as:
ii
ii
T
2
2
1
][
, (eq. 3.53)
ii
2
. (eq. 3.54)
Kohn-Sham o malism es ablishes hen he calcula ion o he kine ic ene gy unde he
assump ion o a e e ence sys em o non-in e ac ing elec ons S (in he same sense as
HF o bi als in wa e mechanics desc ibe non-in e ac ing elec ons) bu unde an ex e nal
po en ial such ha he densi y is he same as in he eal sys em. The solu ion, wi hin he
Bo n-Oppenheime app oxima ion, is p o ided by Sch ödinge equa ion, and he sys em
could be desc ibed by a Sla e de e minan o molecula o bi als
i which ha e he
ollowing exac kine ic ene gy:
ii
iiS
T
2
2
1
][
, (eq. 3.55)
iiS
2
. (eq. 3.56)
O cou se, he elec ons in e ac among hemsel es and he p e ious equa ions do no
p o ide he co ec o al kine ic ene gy. Howe e , jus as HF heo y p o ides ~99% o
he co ec answe , he di e ence be ween he exac kine ic ene gy and ha calcula ed
by assuming non-in e ac ing elec ons is small. The emaining kine ic ene gy no
included in
][
S
T
is abso bed in o an exchange-co ela ion e m, and a gene al DFT
exp ession o he ene gy can be w i en as:
xcneSDFT EJETE
. (eq. 3.57)
I
][
xc
E
is expanded up, i becomes easie o unde s and which a e he con ibu ions o
his exchange-co ela ion ene gy.
JETTE eeSxc
. (eq. 3.58)
The p oblem is simila o ha encoun e ed in wa e mechanics HF heo y: de e mining
a se o o hogonal o bi als ha minimize he ene gy. The elec on densi y is exp essed
Alba Campo Cacha ón
58
As i can be obse ed he in eg al can be exp essed as a p oduc o wo gene alized
densi ies. Then, hese densi ies can be app oxima ed by using a linea expansion
employing an adequa e auxilia y basis se :
)()(
Nbas
PP
pq
Ppq d
. (eq. 3.70)
The e a e di e en me hods o ob aining he expansion coe icien s, bu one o he
mos common op ions leads o he ollowing i ing coe icien s:
PPQ
pq
PPpqd])[|( 1
J
(eq. 3.71)
wi h
)(
1
)()()|( 2
12
1121 Pqp
ddPpq
(eq. 3.72)
and
)(
1
)( 2
12
121 QPPQ
ddJ
. (eq. 3.73)
Thus, making he p ope subs i u ions, he ou -index in eg al can be exp essed as:
)|(])[|()|()|( 1 sQPpq sQd spq
PQQ
pq
Q
J
. (eq. 3.74)
The impo an aspec in his exp ession is ha he ou -index in eg al has been
ac o ized in o an exp ession unning h ough h ee indexes. One ad an age o his
p ocedu e is ha he s o age equi emen s a e g ea ly educed when only h ee-index
in eg als a e needed a mos . Also, h ee- and wo-index in eg als a e mo e easily
e alua ed ha he co esponding ou -index ones, hus sa ing compu a ional ime.
This kind o app oxima ion exp essing ou -index in eg als in wo o h ee-index ones,
can be applied o di e en me hods, he compu a ional sa ing being di e en
depending on each case. This echnique has been applied e y success ully in o de o
speed up DFT calcula ions employing pu e unc ionals, whe e he ime o Coulomb
con ibu ion can be g ea ly educed. Also, MP2 calcula ions bene i om his app oach
since he co ela ion con ibu ion comes om wo-elec on in eg als in ol ing wo
occupied and wo i ual o bi als. Resolu ion o he Iden i y can also be applied o he
exchange con ibu ion (RI-JK), hough in his case he speedup is no as ad an ageous as
o he Coulomb pa .
3. Me hodology
59
The cen al poin in he esolu ion o he iden i y app oach is he design o p ope
auxilia y basis se s which a e capable o ep oducing he densi y in oducing negligible
e o s. Di e en se s o auxilia y basis unc ions a e a ailable in li e a u e speci ically
designed o applying he RI app oach o he Coulomb,[112] exchange[113] o
co ela ion[114] ene gy calcula ions.
3.5. In e ac ion Ene gy Pa i ioning
Applying he abo e-desc ibed supe molecule me hod wi h any o he wa e unc ion-
based o DFT me hods p o ides a magni ude o he in e ac ion ene gy o a gi en
geome y. Howe e , i would be desi able o ob ain mo e in o ma ion abou he na u e,
o igins and cha ac e is ics o he in e ac ion i sel , bu his kind o in o ma ion is no
p o ided by he supe molecule app oach.
Conside ing he classical and his o ical desc ip ion o in e molecula o ces, he
in e ac ion is usually a ionalized in e ms o con ibu ions om elec os a ics,
epulsion, pola iza ion and dispe sion. Thus, a me hod p o iding such a kind o physical
pa i ioning would be desi able, and i will be he subjec o his sec ion.[2, 3]
3.5.1. Ene gy Decomposi ion Analysis (EDA) Me hods
Wi h he common denomina ion o Ene gy Decomposi ion Analysis (EDA) he e is a
a ie y o me hods de ised o pa i ioning he in e ac ion ene gy ob ained om
a ia ional supe molecule HF and DFT me hods.[4, 115] Mos EDA me hods a e a ian s o
he o iginal pa i ioning scheme p oposed by Ki au a and Mo okuma.[116] In he o iginal
o mula ion he in e ac ion ene gy o a dime was decomposed in elec os a ic,
epulsion, pola iza ion and cha ge ans e con ibu ions as ob ained a he HF le el.
The e o e, no dispe sion con ibu ion was ob ained. EDA me hods ha e been la e
ex ended o many-body sys ems by Chen and Go don, hus allowing he pa i ioning in
ime s, e ame s o la ge clus e s.[117] In any case, he o iginal EDA pa i ioning posed
some p oblems, and he a emp s o sol ing hem gi e way o a a ie y o EDA me hods,
such as he na u al ene gy decomposi ion analysis (NEDA),[118-120] he educed a ia ional
space analysis (RVS),[117, 121] and he gene alized Kohn-Sham EDA (GKS-EDA)[122]
Following he e is a gene al desc ip ion o how mos EDA me hods wo k.[4] The
o ma ion o he complex is di ided in a se ies o s eps, each one associa ed wi h a gi en
physical con ibu ion. Conside a dime AB o med by wo sepa a e uni s A and B
al eady in he inal geome y hey ha e in he complex.
1. In he i s s ep o dime o ma ion acco ding o EDA, agmen s A and B wi h
ozen cha ge dis ibu ion a e aken om in ini e sepa a ion and b ough oge he
o he posi ion in he dime . The in e ac ion be ween he ozen cha ge densi ies
o A and B gi es he elec os a ic in e ac ion:
Alba Campo Cacha ón
60
12
21
)()(
)()()()(
d d d V d V
R
ZZ
EBA
A B BAABelec
. (eq. 3.75)
2. In he second s ep o EDA he p oduc wa e unc ion employed be o e,
no malized bu no an isymme ical, is an isymme ized. As a consequence o he
an isymme iza ion he ene gy changes, leading o a e m called Exchange o Pauli
epulsion.
3. The wa e unc ion is allowed o elax o gi e he inal s a e o he dime AB wi h
ene gy EAB. The ene gy lowe ing associa ed wi h his o bi al elaxa ion is he
o bi al elaxa ion con ibu ion.
The e o e, he in e ac ion ene gy is spli in o h ee con ibu ions as indica ed in eq.
3.76,
o bi alPauli icelec os aAB EEEE in
. (eq. 3.76)
This is he global amewo k, bu di e en EDA app oaches u he spli he in e ac ion
ene gy by di iding Pauli and o bi al elaxa ion e ms. Depending on he me hod
employed, Pauli epulsion can be spli as Exchange + Repulsion, and o bi al elaxa ion is
u he di ided in A pola iza ion, B pola iza ion and cha ge ans e e ms.
EDA pa i ioning has been employed in one chap e o his hesis. The LMO-EDA
me hod[123] used can be conside ed an ex ension and modi ica ion o he me hods
de eloped by Ki au a and Mo okuma[116], Ziegle and Rauk,[124] and Hayes and S one.[125]
The main ea u es o his pa i ioning a e lis ed as ollows:
1. The elec os a ic, exchange and epulsion e ms a e ob ained om he Hei le -
London in e ac ion ene gy as p oposed by Hayes and S one om an
an isymme ic p oduc o he monome HF spino bi als.
2. Pola iza ion ene gy is de ined as o bi al elaxa ion ene gy going om monome
o bi als o dime o bi als. Thus, no cha ge ans e e m is de ined.
3. A dispe sion con ibu ion can be compu ed ia a supe molecule calcula ion
wi h a pos -HF o DFT me hod. Dispe sion is de ined as he di e ence be ween
he sum o all con ibu ions and he in e ac ion ene gy ob ained wi h he pos -HF
me hod. Though his has been common p ac ice, i has o be aken in o accoun
ha using HF pa i ioning, he dispe sion con ibu ion eally co esponds o
co ela ion ene gy con ibu ion, con aining o he e ec s o e elec os a ic,
induc ion and epulsion e ms.
4. The pa i ioning can be applied simila ly o DFT me hods.
3. Me hodology
61
In summa y, LMO-EDA allows pa i ioning he global in e ac ion ene gy in o
con ibu ions ha can gi e hin s on he e ec s con olling he in e ac ion. Wi hin he
Ha ee-Fock amewo k he in e ac ion ene gy is exp essed as:
pol epexchelec
HF
AB EEEEE in ,
. (eq. 3.77)
Applying a pos -HF me hod as, say, CCSD(T), a dispe sion con ibu ion is de ined:
disppol epexchelec
TCCSD
AB EEEEEE )(in ,
, (eq. 3.78)
wi h dispe sion (co ela ion con ibu ion) de ined as:
HF
AB
TCCSD
ABdisp EEE )(
. (eq. 3.79)
In he case o employing a DFT me hod a simila pa i ion is employed, so
disppol epexchelec
DFT
AB EEEEEE in ,
. (eq. 3.80)
Dispe sion is ob ained as:
)(
in , pol epexchelec
DFT
ABdisp EEEEEE
. (eq. 3.81)
3.5.2. Symme y-Adap ed Pe u ba ion Theo y Me hods (SAPT)
Symme y Adap ed Pe u ba ion heo y me hods employ a o ally di e en app oach
in o de o di ec ly ob ain he in e ac ion ene gy.[126, 127] SAPT is based on pe u ba ion
heo y, whe e he in e ac ion i sel is ea ed as he pe u ba ion and i s magni ude is
di ec ly compu ed. Applying a pe u ba ional scheme (Rayleigh-Sch odinge ) o a
complex na u ally p o ides exp essions which can be iden i ied wi h con ibu ions om
elec os a ic, induc ion and dispe sion. The mos ob ious pa i ioning o he Hamil onian
ope a o o an in e ac ing pai o molecules A and B is he ollowing:
VHVHHH BA ˆˆˆˆˆˆ 0
, (eq. 3.82)
whe e
0
ˆ
H
is he solu ion o he unpe u bed sys em and
V
ˆ
is he ope a o o he
in e molecula in e ac ion. The e e ence sys em consis s on he isola ed non-
in e ac ing molecules and he pe u ba ion is he in e ac ion.
AAAA EH
and
equi alen ly o he monome B
BBBB EH
. As a consequence, he e e ence
wa e unc ion is he p oduc o he isola ed molecules’ wa e unc ions
BA 000
.
Applying Rayleigh-Sch ödinge pe u ba ion heo y unde hese assump ions, he
ypical exp ession can be ob ained o he di e en co ec ions o i s , second, …
o de .[3] Tha way, he i s o de co ec ion will be:
Alba Campo Cacha ón
62
BABA
el VE 0000
)1(
. (eq. 3.83)
This exp ession co esponds o he coulombic in e ac ion be ween he elec on densi y
o bo h monome s, and is he e o e associa ed o he elec os a ic ene gy. To second
o de , e ms appea depending on single and double exci a ions which can be associa ed
wi h induc ion and dispe sion con ibu ions. Thus:
00
2
000
mAA
m
BA
m
BA
A
ind EE
V
E
(eq. 3.84)
co esponds o single exci a ions wi hin monome A due o he p esence o he nea by
monome B, and he e o e is associa ed o he induc ion con ibu ion o monome A. An
equi alen exp ession is also ound o single exci a ions in ol ing B
00
2
000
nBB
n
B
n
ABA
B
ind EE
V
E
. (eq. 3.85)
Finally, o second o de ano he e m emains in ol ing double exci a ions which is
assigned as dispe sion con ibu ion.
0;0 00
2
00
nm BAB
n
A
m
B
n
A
m
BA
disp EEEE
V
E
. (eq. 3.86)
I is wo h no ing ha hese exp essions, oge he wi h he mul ipole expansion,
p o ide much o ou quali a i e and quan i a i e discussion on he ole o nonco alen
bonding o ces, allowing o desc ibe in e molecula in e ac ions as unc ions o
molecula p ope ies such as mul ipoles o pola izabili ies.[2, 3]
The pe u ba ion heo y o well-sepa a ed molecules desc ibed abo e ( he long- ange
app oxima ion o pola iza ion app oxima ion) is e y success ul i he molecules a e a
long dis ance apa , bu a sho ange ails comple ely.[3] Pa o he eason o he
ailu e o he heo y as usually o mula ed is ha he mul ipole expansion b eaks down.
A mo e undamen al ailu e is ha he epulsion be ween molecules ha occu s a
sho - ange is comple ely missed om he long- ange heo y. This ailu e a ises om he
ac ha i he molecules a e close enough o hei wa e unc ions o o e lap, exchange
canno be igno ed.
The sou ce o he di icul ies o Rayleigh-Sch ödinge pe u ba ion heo y o
desc ibing in e molecula in e ac ions a sho ange is he w ong symme y o he
e e ence wa e unc ion.[2, 3] The e e ence wa e un ion
BA 000
is an isymme ic
upon elec on exchange wi hin A o wi hin B, bu i is no upon exchange o elec ons
3. Me hodology
63
be ween A and B. The e o e, he e e ence wa e unc ion is physically unsound, hus
leading o he lack o p ope epulsion o ces as he molecules come oge he .
The e o e, he e e ence wa e unc ions should be p ope ly an isymme ized in o de o
sa is y he Pauli p inciple.
The e ha e been di e en app oaches o o e come he an isymme y p oblem, bu
he p e ailing one is he symme ized Rayleigh-Sch ödinge heo y, a nowadays
synonym o Symme y Adap ed Pe u ba ion Theo y (SAPT). Wi hin SAPT, an isymme y
is o ced in he ene gy exp essions, modi ying he elec on densi y in such a way as o
cause a epulsi e o ce on he nuclei. This is he o ce co esponding o he exchange-
epulsion ene gy.[126, 127]
The ou come o SAPT p ocedu e is a se ies o con ibu ions ha o low o de can be
associa ed o physical e ec s as in pola iza ion heo y. The main di e ence, howe e , is
ha each o he pola iza ion e ms is now accompanied by an exchange- epulsion e m
a ising om p ope an isymme y. The e o e, he in e ac ion ene gy is exp essed in
SAPT as:
...
)2()2()2()2()1()1(
in dispexchdispindexchindexchel EEEEEEE
. (eq. 3.87)
Thus, i can be seen ha an isymme iza ion p oduces new e ms ha a e comple ely
missed when a simple p oduc wa e unc ion is used. The mos impo an ac is ha
he e is a s ong epulsion be ween closed-shell molecules when hei wa e unc ions
o e lap signi ican ly.
The desc ip ion o SAPT p esen ed abo e assumed ha one knows he exac
wa e unc ions o monome s. In p ac ice, he wa e unc ions a e compu ed sepa a ing
he HF and he co ela ion con ibu ions. Since elec on co ela ion signi ican ly a ec s
molecula p ope ies equi ed as inpu o SAPT i is manda o y o accoun o
in amolecula elec on co ela ion. [52, 126, 127]
I he MP decomposi ion o he Hamil onians is used o monome s, SAPT becomes a
double-pe u ba ion heo y acco ding o he ollowing spli ing o he Hamil onian,
WVFH
(eq. 3.88)
so he sum o monome ’s Fock ope a o s
BA FFF
is now he unpe u bed
Hamil onian, whe eas V and he sum o MP po en ials o monome s
BA WWW
a e
he wo pe u ba ion ope a o s. Acco dingly, he in e ac ion ene gy can now be
exp essed as
0;1
in ji
ij
exch
ij
pol EEE
, (eq. 3.89)
Alba Campo Cacha ón
64
whe e ij is he o de in V-W. A la ge numbe o e ms in his expansion ha e been
de eloped up o i=3 and j om 0 o 4, depending on i and he physical componen . Thus,
SAPT allows desc ibing he in e ac ion wi h inc easing accu acy by including e ms o
highe o de s in bo h expansions. Depending on he con ibu ions included, di e en
models can be de ined, hough he se ies expansion is ypically unca ed a second-
o de in V, esul ing in a comple e neglec o hi d- and highe o de e ms. I has been
obse ed ha in pola sys ems highe o de e ec s can be impo an , o en associa ed
wi h induc ion e ec s. A co ec ion is ecommended in o de o a leas in oduce an
es ima ion o such e ec s. The co ec ion is de ined as
)20()20()10()10(
in indexchindexchel
HF
HF EEEEE
, (eq. 3.90)
whe e
HF
Ein
is he Ha ee-Fock in e ac ion ene gy calcula ed using he supe molecula
me hod.
The e o e, SAPT can pa i ion he in e ac ion ene gy a he HF le el as:
HFindexchindexchel
HF EEEEE
)20()20()10()10(
in
. (eq. 3.91)
O cou se, a he HF le el, he in e ac ion ene gy does no include dispe sion, bu
applying pe u ba ion heo y based on HF wa e unc ions he dispe sion e m can be
ob ained in SAPT. Thus, he Ha ee-Fock calcula ion can be co ec ed wi h he
dispe sion con ibu ion ob aining he HF+D me hod (in a simila way as he al eady
commen ed DFT-D me hods).
)20()20()20()20()10()10(
in dispexchdispHFindexchindexchel
DHF EEEEEEE
. (eq. 3.92)
The las exp ession con ains all SAPT con ibu ions o o de 2 ob ained employing HF
wa e unc ions. As commen ed abo e, highe -o de e ms in induc ion a e aken ca e o
by he
HF
con ibu ion.
The nex s ep would be including in amonome co ela ion e ec s, leading o a mo e
accu a e desc ip ion o he in e ac ions. Fo example, he so-called SAPT2 le el
co esponds o:
)22()22()12()11()12(
in in indexchindexchexchel
DHFSAPT EEEEEEE
, (eq. 3.93)
including co ec ions simila o MP2. Mo e accu a e models would include con ibu ions
o hi d o de bo h in he in e molecula pe u ba ion and he in amonome
co ela ion pe u ba ion. The p oblem o using such exp ession is i s high compu a ional
demand, which has led o o he app oaches o be commen ed in he ollowing sec ion.
In any case, i is wo h no ing ha , ecen ly, Hohens ein and She ill ha e de eloped a
SAPT scheme exploi ing he esolu ion o he iden i y app oach in o de o educe he
3. Me hodology
65
compu a ional cos , which could make SAPT calcula ions mo e easible.[52, 128, 129] This
app oach has been coded in o he PSI4 p og am.[130]
3.5.2.1. SAPT(DFT)
Despi e he successes o SAPT, he calcula ion o he in amonome co ela ion e ms
makes i compu a ionally p ohibi i e o la ge molecula sys ems. Williams and
Chabalowski sugges ed ha i a co ela ed desc ip ion o he monome s was used, he
cos ly co ela ion e ms can be a oided.[131] Due o compu a ional conside a ions,
Williams and Chabalowski sugges ed ha a DFT desc ip ion o he monome s would be
bes sui ed. This ac allows SAPT o be pe o med on much la ge sys ems han
p e iously allowed al hough he ini ial esul s we e a he poo . Thus, he idea was
simply changing he HF o bi als and ene gies by hei Kohn-Sham coun e pa s. This
way, a SAPT calcula ion including only he pe u ba ion on he in e molecula
in e ac ion will su ice, because in amonome co ela ion e ec s we e al eady aken
ca e o in he DFT calcula ions. [131]
The esul s ob ained ollowing his p ocedu e we e disappoin ing. I was obse ed ha
one o he easons o his inaccu acy was he inco ec asymp o ic beha io o he
exchange-co ela ion unc ions o ob aining he Kohn-Sham ene gies. While he
exchange-co ela ion po en ial should decay as 1/ o a neu al sys em, he s anda d
local o /and g adien -co ec ed DFT exchange-co ela ion po en ials decay oo quickly.
The me hod was soon imp o ed by Hesselmann and Jansen[132-136] and Szalewicz[137-140]
independen ly, leading o essen ially iden ical me hods. In bo h p oposals, a co ec ion
o he asymp o ic beha io is assumed. In Jansen’s p oposal he unc ional employed is
combined wi h he LB94 unc ional, which has a co ec asymp o ic beha io a long-
ange (bu ails a sho - ange).[136] This ac c ea es a new p oblem ha i is he
b eaking a in e media e dis ances be ween he beha io o he wo unc ionals.[141, 142]
In o de o a ange his, a g adien - egula ed connec ion me hod as de eloped by
G üning e al. was employed.[141] This scheme (Adiaba ic Co ec ion AC) equi es he sum
HOMO
IP
as he inpu pa ame e (which anishes in he case o exac KS DFT). The
alue o
HOMO
is ob ained om a calcula ion wi h he unco ec ed xc unc ional,
whe eas he ioniza ion po en ials can ei he be aken om expe imen o calcula ed
om he di e ence o KS DFT calcula ions o he neu al and he ionized sys ems,
espec i ely.
Once hese p oblems a ec ing accu acy a e sol ed, he equa ion ob ained o
SAPT(DFT) is he ollowing:
HFdispexchdisp espindexch espindexchel
DFTSAPT EEEEEEE
)20()20()20(,
)20(,
)10()10(
in
. (eq. 3.94)
The same co ec ion e m
HF
is included in he calcula ion in o de o ake in o
accoun highe -o de con ibu ions. Despi e o he di icul ies in he implemen a ion o
Alba Campo Cacha ón
66
DFT in a complica ed heo y like SAPT, SAPT(DFT) p esen s many ad an ages in
compa ison o SAPT. The main eason, and he o igin o his me hod, is he dec eased
compu a ional cos o he desc ip ion o in amonome co ela ion, which allows he
applica ion o SAPT pa i ioning o la ge sys ems ha could no be a o ded wi h SAPT
based in MBPT o CC. In addi ion o his, i is wo h no ing ha densi y i ing app oach
can be employed, g ea ly educing he compu a ional cos . Also, simpli ied ex apola ion
schemes ha e been p oposed in o de o each he comple e basis se limi in he
amewo k o SAPT(DFT) calcula ions.[143]
3.6. Elec on densi y analysis
A oms in Molecules quan um heo y (QTAIM), ha was de eloped by Bade , is a
heo y based on he opological analysis o he elec on densi y, which b ough quan um
mechanics in o applicabili y o an a om wi hin a molecule.[144] When a molecula
p ope y can be exp essed in e ms o a p ope y densi y, he con ibu ion o a gi en
a om o ha molecula p ope y can be ob ained by in eg a ing his densi y o e he
olume o he a om in he molecule. Thus, he heo y ela es concep s as bonding,
unc ional g oups o chemical eac i i y o he opology o he unde lying elec on
densi y, hough he aspec o he molecula densi y is always he same: la ge cups a he
nucleus and an exponen ial dec easing beha io in all di ec ions.
The cha ac e iza ion o c i ical poin s is based on he beha io o he g adien ec o in
he zone nea by. So, a c i ical poin in he elec on densi y can be de ined as a poin in
space a which he i s de i a es o he densi y anish,
kji
dz
d
k
dy
d
j
dx
d
izyx
, (eq. 3.95)
meaning ha each indi idual de i a i e in he g adien ope a o ,
, is ze o and no jus
hei sum. The g adien o a scala unc ion such as
)(
a a poin in space is a ec o
poin ing in he di ec ion in which
)(
unde goes he g ea es a e o inc ease and
ha ing a magni ude equal o he a e o inc ease in ha di ec ion.
Conside ing he second de i a i es, he elemen s o he enso
, one can
disc imina e be ween a local minimum, a local maximum, o a saddle poin . The e a e
nine second de i a i es o
)(
ha can be a anged in he so-called Hessian ma ix,
which when diagonalized a a c i ical poin c gi es:
3. Me hodology
67
3
2
1
'
2
2
2
2
2
2
00
00
00
00
00
00
c
z
y
x
. (eq. 3.96)
1
,
2
and
3
a e he eigen alues o he Hessian ma ix (o de ed as
321
) and
ep esen he cu a u es o he densi y wi h espec o he h ee p incipal axes x’, y’ and
z’.
The e a e ou ypes o s able c i ical poin s ha ing h ee non-ze o eingen alues:
1
,
2
,
3
<0 ; (3,-3): all cu a u es a e nega i e. ρ is a local maximum. This is
called a Nuclea C i ical Poin .
1
,
2
<0,
3
>0 ; (3,-1): wo nega i e cu a u es. ρ is a maximum in he plane
de ined by he co esponding eigen ec o s and a minimum along he hi d axis
which is pe pendicula o his plane. This is called a Bond C i ical Poin .
1
<0,
2
,
3
>0 ; (3,+1): wo posi i e cu a u es. ρ is a minimum in he plane
de ined by he co esponding eigen ec o s and a maximum along he hi d axis
which is pe pendicula o his plane. This is called a Ring C i ical Poin .
1
,
2
,
3
>0 ; (3,+3): Th ee cu a u es a e posi i e. ρ is a local minimum and
co esponds o a Cage C i ical Poin .
The collec ion o pa hs linking he nuclei o bonded a oms in an equilib ium geome y
wi h he associa ed c i ical poin s is known as he molecula g aph, which p o ides an
unambiguous de ini ion o he “molecula s uc u e” and can hus be used o loca e
changes in s uc u e along a eac ion pa h. Also, he s eng h o a chemical bond is
e lec ed on he elec on densi y a he bond c i ical poin
)( b
.
b
is g ea e han 0.20
a.u. in sha ed (co alen ) bonding and less han 0.10 a.u. in a closed-shell in e ac ion
(ionic, dW, hyd ogen bond, e c.).
b
has been shown o be s ongly co ela ed wi h he
binding ene gy o se e al ypes o bonding in e ac ion.
In conclusion, he analysis o he elec on densi y and i s de i a i es h ough i s main
opological ea u es p o ides much in o ma ion abou he cha ac e is ics o he sys em
and can be employed o analyze he mos ele an nonco alen in e ac ions p esen in
he sys ems unde s udy.
3.6.1. NCI index
As commen ed in he p eceding sec ion, A oms in Molecules Theo y can be employed
o analyze in de ail he cha ac e is ics o he in e ac ion in in e molecula sys ems.
Howe e , in la ge sys ems, QTAIM p o ides an o e whelming amoun o in o ma ion: a
la ge numbe o c i ical poin s, hei cha ac e is ics, a la ge se o bond pa hs, e c.
Alba Campo Cacha ón
74
x
1
)(
, (eq. 3.104)
whe e x is a i ed pa ame e , o iginally se o 0.5, hough o he alues ha e been
p oposed. The choice o his pa ame e has li le impac in sol en s wi h la ge dielec ic
cons an whe eas he esul s a e mo e a ec ed i he sol en shows low dielec ic
cons an .
Figu e 3.6. Ca i y cons uc ion o he PCM calcula ions as pe o med wi h Gaussian.
The e o e, he sol en is ea ed as a dielec ic, wi h appa en cha ges de ining he
eac ion ield ob ained applying conduc o bounda y condi ions, and p ope ly scaled as
o ep esen a speci ic alue o he dielec ic cons an . COSMO is especially obus wi h
espec o a i ac s ha esul om he small pe cen age o he solu e’s cha ge eaching
he ou e side o he ca i y, he so-called ou lying cha ge.
In any uncons ained elec onic s uc u e calcula ion o he solu e he e is a ail ha
ex ends beyond he ca i y su ace. The e o e, he e is a small pe cen age o he elec on
densi y in he dielec ic.[149] A p ope o mula ion o his p oblem should include no
only he su ace pola iza ion bu also a olume pola iza ion ou side he ca i y,
in oducing appa en olume cha ges a poin s ou side he ca i y. COSMO includes an
app oxima ion o olume pola iza ion making a inal calcula ion ex ending somewha
he limi s o he ca i y and compa ing he alues ob ained wi h he o iginal and he
ex ended su aces. I should be aken in o accoun ha ou lying cha ge e o s can easily
3. Me hodology
75
each 20% o neu al species, and be e en la ge o anions, so a p ope co ec ion o
hese e ec s should be conside ed. This has been a p oblem in D-PCM me hods which
led o inco po a e COSMO in o he PCM sui e (C-PCM), hough he la es de elopmen s
in PCM models such as he in eg al equa ion o malism a ian PCM (IEFPCM) include an
app oxima e co ec ion o his p oblem.[147]
3.8. Re e ences
[1] P. Hobza, R. Za adnik, In e molecula complexes : he ole o an de Waals
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[2] I. Kaplan, In e molecula In e ac ions : Physical Pic u e , Compu a ional Me hods,
John Wiley & Sons, Chiches e , 2006.
[3] A. J. S one, The heo y o in e molecula o ces, Ox o d Uni e si y P ess, Ox o d,
2013.
[4] M. . Hop ga en, G. F enking. WIREs Compu . Mol. Sci. 2012, 2, 43-62.
[5] G. Chalasinski, M. M. Szczesniak. Chem. Re . 1994, 94, 1723-1765.
[6] G. Cha asi ski, M. M. Szcz niak. Chem. Re . 2000, 100, 4227-4252.
[7] K. Szalewicz, B. Jezio ski. J. Chem. Phys. 1998, 109, 1198-1200.
[8] S. S. Xan heas. J. Chem. Phys. 1996, 104, 8821-8824.
[9] E. Cabalei o-Lago, J. Rod íguez-O e o, Á. Peña-Gallego. Theo . Chem. Acc. 2011,
128, 531-539.
[10] E. M. Cabalei o-Lago, M. A. R os. J. Chem. Phys. 2000, 112, 2155-2163.
[11] A. Campo-Cacha ón, E. M. Cabalei o-Lago, J. Rod íguez-O e o. ChemPhysChem
2012, 13, 570-577.
[12] E. M. Cabalei o-Lago, Á. Peña-Gallego, J. Rod íguez-O e o. J. Chem. Phys. 2008,
128, 194311/1-194311/8.
[13] C. D. She ill Compu a ions o Nonco alen π In e ac ions, in Re iews in
Compu a ional Chemis y Vol. 26, John Wiley & Sons, New Yo k, 2009.
[14] F. B. an Duijne eld , J. G. C. M. an Duijne eld - an de Rijd , J. H. an Len he.
Chem. Re . 1994, 94, 1873-1885.
[15] H. B. Jansen, P. Ros. Chem. Phys. Le . 1969, 3, 140-143.
[16] S. F. Boys, F. Be na di. Mol. Phys. 1970, 19, 553-566.
[17] J. Al a ez-Idaboy, A. Galano. Theo . Chem. Acc. 2010, 126, 75-85.
[18] A. J. C. Va andas. J. Phys. Chem. A 2009, 114, 8505-8516.
[19] Ł. M. Men el, E. J. Bae ends. J. Chem. Theo y Compu . 2013, 10, 252-267.
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4. E ec s o mic ohyd a ion on he
cha ac e is ics o ca ion-phenol
complexes
4. Phenol mic ohyd a ion
83
4.1. In oduc ion
In e molecula in e ac ions a e known o play a key ole in many aspec s o
chemis y and biology, being c ucial o phenomena as p o ein···ligand in e ac ion and
molecula ecogni ion.[1, 2] Among he di e en in e molecula o ces, hose in ol ing
a oma ic moie ies p esen especial cha ac e due o he p esence o conjuga ed
elec ons and a plana geome y.[3-5] Also, as ega ds biochemis y, in e ac ions in ol ing
a oma ic uni s a e c ucial in p o ein s uc u e. I is belie ed ha a oma ic g oups
in e ac in a di e en manne han alipha ic uni s in he side chains o amino acids, and
can p o ide speci ici y in p o ein olding.[4-8]
Ca ion··· in e ac ions a e s ong in e ac ions in he gas phase and ha e been
ecognized as one o he s uc u al mo i s condi ioning he s uc u e in p o eins.[5, 9]
Since he ini ial wo ks om Doughe y e al. he ca ion··· in e ac ion is now ega ded as
one key ac o in de e mining he cha ac e is ics o p o eins, oge he wi h hyd ogen
bonds, s acking in e ac ions and sal b idges.[5-7, 9, 10] The impo ance o hese ca ion···
in e ac ions in p o eins is easily unde s ood aking in o accoun ha some amino acids
as phenylalanine, y osine, yp ophan and his idine bea an a oma ic uni in hei side
chains, whe eas o he amino acids as a ginine, lysine and his idine possess ca ionic
g oups depending on he pH. Thus, in e ac ions be ween side chains o hese amino
acids a e o en obse ed in p o ein s uc u e sugges ing hei ele ance as a s abilizing
mo i .[5, 9, 11]
Though ca ion··· in e ac ions a e known o be s ong in e ac ions in he gas phase,
his has no o be ue in solu ion. Di e en s udies gi e con adic o y esul s anging
om an impo an con ibu ion o p o ein s abiliza ion o an almos negligible e ec .[11-
22] These disc epancies a e gene ally add essed o sol en e ec s, depending on he
deg ee o exposu e o he ca ion··· con ac o he sol en . Se e al s udies exis in
li e a u e dealing wi h he in e ac ion o alkali ca ions wi h benzene, showing he usual
end o s onge in e ac ion as he size o he ca ion dec eases.[23-26] Also, se e al
au ho s ha e s udied he e ec o wa e coo dina ed o he ca ion on he s eng h o
he ca ion···benzene in e ac ion.[27-32] Howe e , mos s udies ha e been ca ied ou wi h
benzene as a model o a oma ic in e ac ion, wi h ew wo ks de o ed o o he a oma ic
uni s.[33-36] In his wo k, a s udy o he in e ac ion be ween a K+, Na+, Li+ o Mg2+ ca ion
wi h phenol in he p esence o a small numbe o wa e molecules has been pe o med
by employing ab ini io and densi y unc ional heo y me hods. Phenol is no only a
common chemical bu also he ch omopho e o he a oma ic amino acid y osine.
Con a y o benzene, phenol possesses wo di e en egions whe e a ca ion can
es ablish a s abilizing in e ac ion: he a oma ic cloud and he lone pai s o he hyd oxyl
oxygen.[37, 38] Also, he hyd oxyl g oup can ac bo h as dono o accep o in hyd ogen
bonds wi h he wa e molecules included in he clus e . The e o e, e en when phenol is
Alba Campo Cacha ón
90
op imum ca ion···wa e in e ac ion, e en a he cos o loosing pa o he s abiliza ion
gained by he o ma ion o OH···O o O-H··· con ac s. Wi h he smalle ca ions, he e
a e la ge di e ences be ween s uc u es wi h wa e coo dina ed o he ca ion wi h
espec o o he s uc u es wi h wa e hyd ogen bonded o phenol. In ac , i can be
obse ed om Table 4.2 ha he ene gy di e ence be ween s uc u es Phe-X1-1H2O
and Phe-X2-1H2O dec eases as he size o he ca ion inc eases. Tha is, o K+ complexes
he hyd oxyl g oup o phenol can compe e wi h he ca ion o in e ac ing wi h wa e ,
whe eas o smalle ca ions he di ec coo dina ion o he ca ion is clea ly a o ed.
Table 4.2. Complexa ion ene gies (kcal/mol) o he mos s able monohyd a ed
ca ion···phenol complexes as ob ained a he MP2/6-31+G(2d,p)//MP2/6-31+G(d) le el.
Phe-X1-
1H2O
Phe-X2-
1H2O
Phe-X3-
1H2O
Phe-X4-
1H2O
Phe-X5-
1H2O
Phe-X6-
1H2O
K+
-31.87
-30.24
-33.30
-33.07
-29.94
-35.72
Na+
-41.80
-36.13
-42.41
-42.35
-35.56
-43.70
Li+
-61.01
-48.99
-
-62.23
-50.02
-
Mg+2
-171.40
-140.45
-
-174.91
-140.61
-
4.3.3. Dihyd a ed ca ion···phenol complexes
Wi h he inclusion o he second wa e molecule, a g ea e a ie y o s uc u es has
been loca ed, so only he mos s able among he minima loca ed will be discussed o
each ca ion. Gene ally speaking, he la ge he ca ion, he la ge he numbe o di e en
minima wi hin a gi en ene gy in e al, so he beha io is simple o Li+ and Mg2+
clus e s, whe eas o K+ he mos complex beha io a ises.
Figu e 4.3 shows he mos s able minima loca ed o complexes o med by phenol
wi h K+ and Na+ ca ions including wo wa e molecules. I can be obse ed ha he i s
ou s uc u es ha e simila cha ac e is ics o bo h ca ions, whe eas di e ences appea
o he o he wo p esen ed in Figu e 4.3. Conside ing K+ complexes and he alues o
complexa ion ene gies lis ed in Table 4.3, i can be obse ed ha s uc u es wi h he K+
ca ion o e he a oma ic ing o phenol a e mo e s able han he analogous s uc u e
wi h K+ in e ac ing wi h he oxygen a om.
The h ee s uc u es named as Phe-X2-2H2O, Phe-X4-2H2O and Phe-X6-2H2O p esen
simila complexa ion ene gies, showing ha in he case o K+ complexes he e is no
signi ican ene gy di e ence when wa e molecule coo dina es o K+ di ec ly o in e ac s
wi h he OH g oup o phenol, and he same can be obse ed in he es o s uc u es
wi h K+ in e ac ing wi h he hyd oxyl g oup.
4. Phenol mic ohyd a ion
91
Figu e 4.2. Mos s able minima o he monohyd a ed ca ion···phenol complexes. The
numbe s co espond o dis ances in Å as ob ained a he MP2/6-31+G(d) le el o
calcula ion.
Phe-X1-1H2O
2.685
2.298
1.870
2.002
K+2.676
Na+2.276
Li+1.882
Mg+2 1.987
Phe-X2-1H2O
2.625
2.252
1.842
1.955
1.761
1.743
1.697
1.468
Phe-X3-1H2O
2.709
2.300
2.645
2.273
2.460
2.274
2.669
2.277
1.876
1.986
2.913
2.503
1.967
2.004
Phe-X4-1H2O
2.848
2.392
1.911
1.944
1.794
1.780
1.760
1.609
Phe-X5-1H2O
Phe-X6-1H2O
2.936
2.513
2.626
2.276
1.963
2.036
Alba Campo Cacha ón
92
Figu e 4.3. Mos s able minima loca ed a he MP2/6-31+G(d) le el o he dihyd a ed
complexes o K+ and Na+ wi h phenol.
Phe-X1-2H2O Phe-X2-2H2O
Phe-X4-2H2OPhe-X3-2H2O
Phe-K5-2H2O Phe-K6-2H2O
Phe-Na5-2H2O Phe-Na6-2H2O
4. Phenol mic ohyd a ion
93
The mos s able minima co esponds o a igonal a angemen o he wo wa e
molecules and he phenyl ing a ound he K+ ca ion, hough Phe-X6-2H2O shows simila
s abili y, wi h bo h wa e molecules in e ac ing di ec ly wi h K+, simul aneously
es ablishing a hyd ogen bond be ween hem, keeping an O···K···O angle o only 65
deg ees. Howe e , as indica ed abo e, se e al o hese minima show s abili y
di e ences wi hin he e o o he me hods employed, so he beha io could sligh ly
change i mo e sophis ica ed (and cos ly) me hods a e employed.
Table 4.3. Complexa ion ene gies (kcal/mol) o he mos s able dihyd a ed complexes as
ob ained a he MP2/6-31+G(2d,p)//MP2/6-31+G(d) le el o calcula ion.
Phe-X1-2H2O
Phe-X2-2H2O
Phe-X3-2H2O
Phe-X4-2H2O
Phe-X5-2H2O
Phe-X6-2H2O
K+
-46.77
-48.30
-45.30
-47.07
-46.42
-47.92
Na+
-59.46
-59.89
-55.15
-55.76
-54.36
-54.00
Li+
-83.52
-81.95
-74.81
-75.14
-75.15
-75.84
Mg+2
-218.63
-218.96
-196.73
-196.97
-198.46
-201.75
In he case o Na+ complexes, hough he minima a e simila , he ene gy o de ing
depends mo e on he a angemen o wa e molecules a ound he ca ion, so he wo
mos s able s uc u es co espond o a simila igonal a angemen , he di e ence
being he loca ion o he ca ion o e he ing o close o he hyd oxyl g oup. The es o
he s uc u es a e less s able wi h ela i e ene gies mo e han 4 kcal/mol abo e he
mos s able minimum. I is wo h no ing ha no s able minimum was ound simila o
hose obse ed o K+ ca ion, wi h wa e molecules bound o he ca ion and in e ac ing
be ween hemsel es. In he case o Na+, he in e ac ion wi h wa e is s onge , so he
dis o ed hyd ogen bond be ween wa e molecules canno o e come he ene gy loss
when depa ing om he igonal a angemen . Fo K+ complexes, minima simila o
hose ob ained o Na+ can be ound, wi h complexa ion ene gies amoun ing o -44.9
and -43.5 kcal/mol. Li+ and Mg2+ complexes shown in Figu e 4.4 p esen simila
cha ac e is ics o hose ound o Na+. Fo bo h ca ions he same minima a e ob ained,
wi h ene gies lis ed in Table 4.3. The mos s able s uc u es co espond o a igonal
a angemen a ound he ca ion, wi h no la ge di e ences ega ding whe he he ca ion
is on he ing o o e he hyd oxyl g oup. The e is a signi ican ene gy gap wi h he es
o s uc u es, eaching 6 kcal/mol and 17 kcal/mol o Li+ and Mg2+, espec i ely. I is also
wo h no ing ha in Mg2+ complexes, coo dina ion wi h a wa e molecule in he second
shell is ene ge ically a o ed o e coo dina ion o he hyd oxyl g oup o phenol, con a y
o he beha io obse ed wi h he o he ca ions, whe e he hyd oxyl g oup can be
compe i i e o coo dina ing wa e molecules compa ed wi h o he wa e uni s al eady
p esen in he complex.
Alba Campo Cacha ón
94
Figu e 4.4. Mos s able minima loca ed a he MP2/6-31+G(d) le el o he dihyd a ed
complexes o Li+ and Mg2+ wi h phenol.
Phe-X1-2H2O Phe-X2-2H2O
Phe-X5-2H2O Phe-X6-2H2O
Phe-X3-2H2O Phe-X4-2H2O
4. Phenol mic ohyd a ion
95
Figu e 4.5. Mos s able minima loca ed o he ihyd a ed complexes o K+ wi h phenol.
Numbe s co espond o complexa ion ene gies in kcal/mol a he MP2/6-
31+G(2d,p)//MP2/6-31+G(d) le el.
Phe-K2-3H2O
Phe-K1-3H2O
-59.22
-59.08
Phe-K4-3H2O
Phe-K3-3H2O
-59.75
-58.83
Phe-K6-3H2OPhe-K5-3H2O
-60.04
-60.28
Alba Campo Cacha ón
96
Figu e 4.6. Mos s able minima loca ed o he ihyd a ed complexes o Na+, Li+ and
Mg2+ wi h phenol. Numbe s co espond o complexa ion ene gies in kcal/mol a he
MP2/6-31+G(2d,p)//MP2/6-31+G(d) le el.
Phe-Li1-3H2OPhe-Na1-3H2O
-100.54-73.63
Phe-Mg1-3H2O
-257.98
Phe-Li2-3H2OPhe-Na2-3H2O
-99.28-73.76
Phe-Mg2-3H2O
-254.73
Phe-Li3-3H2OPhe-Na3-3H2O
-98.11-72.02
Phe-Mg3-3H2O
-245.94
Phe-Li4-3H2OPhe-Na4-3H2O
-97.64-72.17
Phe-Mg4-3H2O
-244.70
4. Phenol mic ohyd a ion
97
4.3.4. T ihyd a ed complexes
The inco po a ion o a hi d wa e molecule inc eases he complexi y o he po en ial
ene gy su ace o he complexes gi ing ise o a g ea a ie y o minima, usually wi h
simila s abili ies, especially o he la ge ca ions. The e o e, K+ complexes p esen he
mos complex beha io wi h he la ges numbe o minima wi hin a small ene gy
in e al. The mos s able minima ound a e shown in Figu e 4.5, di e ing in s abili y by
less han 1 kcal/mol. The e o e, as wa e molecules a e included in he complex, he e
a e smalle di e ences be ween di ec coo dina ion o he K+ ca ion, o ano he wa e
molecule o o he hyd oxyl g oup, hus allowing o a g ea e a ie y o s uc u es.
The mos s able complexes o med wi h Na+, Li+ and Mg2+ a e shown in Figu e 4.6. In
Na+ and Li+ clus e s, he wo mos s able s uc u es show e y di e en s uc u al
a angemen s. Whe eas Phe-X1-3H2O co esponds o he e ahed al a angemen o
wa e and phenol a ound he ca ion, in Phe-X2-3H2O he ca ion is su ounded by he
h ee wa e molecules and does no in e ac di ec ly wi h phenol, so he in e ac ion
akes place be ween a hyd a ed ca ion and he phenol moie y. Finally, in Mg2+
complexes he e ahed al a angemen s a e he mos s able, he es o he minima
ound being less s able by mo e han 10 kcal/mol.
4.3.5. Te ahyd a ed clus e s
The inclusion o a ou h wa e molecule complica es e en mo e he explo a ion o he
po en ial ene gy su ace o he clus e s. The e o e, a pa ial explo a ion s a ing om
he mos s able complexes ound o ihyd a ed clus e s was pe o med. The ou h
mos s able minima o each o he ca ions ound in his wo k a e shown in Figu e 4.7
oge he wi h hei complexa ion ene gies. These minima a e simila o hose al eady
ound by Vaden and Lisy [37] hough since he le els o calcula ion a e di e en ,
di e ences a ise. Fo example, he minima in Figu e 4.7 o K+ a e wi hin 1.5 kcal/mol,
whe eas hose epo ed by Vaden and Lisy span o e 5 kcal/mol.
Though complexa ion ene gies become mo e nega i e as he pola izing powe o he
ca ion inc eases as be o e, he ene gy di e ences among s uc u es o a gi en ca ion
a e almos negligible. No s able s uc u e wi h he i e oxygen a oms su ounding he
ca ion was loca ed, so mos complexes p esen a e ahed al a angemen o oxygen
a oms a ound he ca ion, whe eas he i h oxygen a om in e ac s in a second hyd a ion
shell.
The e o e, all e ahyd a ed complexes exhibi in e ac ions among wa e molecules o
be ween wa e and phenol. In summa y, i can be obse ed ha as mo e wa e
molecules a e included, he e a e ewe di e ences be ween he di e en kinds o
union: wa e ···wa e , wa e ···phenol o wa e ···ca ion. Fo he smalles ca ions his
implies ha only a couple o s uc u es p esen simila s abili y whe eas he es a e
signi ican ly less s able. Howe e , o Na+ complexes and, especially o K+ complexes,
Alba Campo Cacha ón
98
he e can be mo e s able s uc u es wi hin a small ene gy in e al so he e can be
con ibu ions o se e al con o me s o he p ope ies o he sys em, as al eady
sugges ed by he in a ed spec a o be discussed in he ollowing sec ion.
I he a ia ions on complexa ion ene gy upon inco po a ion o a wa e molecule a e
conside ed (Table 4.4), he ollowing beha io s can be obse ed. Fo K+ complexes, he
addi ion o he i s wa e molecule s abilizes he complex in a la ge quan i y han he
complexa ion o K+ o phenol. This is due o he s ong K+···H2O in e ac ion, bu also o
he o ma ion o he O-H···O hyd ogen bond. In Na+ complexes he s abili y gain
associa ed o his i s wa e molecule is sligh ly smalle han he ca ion··· in e ac ion.
Fo Li+ and Mg2+, e en hough he in e ac ion wi h wa e is s onge , he complex is
s abilized by a conside ably smalle quan i y han he o iginal ca ion··· in e ac ion. As
mo e wa e molecules a e included in he complex he s abili y gain dec eases s eadily,
hough o K+ complexes he ene gy changes upon inclusion o he second and hi d
wa e molecules a e equi alen , sugges ing he g ea e capaci y o po assium o
accommoda ing wa e molecules and also he ex a s abiliza ion due o he o ma ion o
hyd ogen bonds. Fo all ca ions, he inclusion o he ou h wa e molecule is
accompanied by a s abili y gain oughly hal o ha ob ained wi h he i s wa e uni .
Table 4.4. Complexa ion ene gy changes (kcal/mol) o he inco po a ion o one wa e
molecule o a complex as ob ained a he MP2/6-31+G(2d,p)//MP2/6-31+G(d) le el o
calcula ion.
Wa e molecules n
K+
Na+
Li+
Mg2+
0
-17.19
-22.61
-35.99
-116.4
1
-18.56
-21.09
-26.21
-58.51
2
-12.55
-16.19
-21.32
-43.72
3
-11.98
-13.87
-17.02
-39.35
4
-10.29
-12.24
-13.36
-23.97
4. Phenol mic ohyd a ion
99
Figu e 4.7. Mos s able minima loca ed o e ahyd a ed complexes. Numbe s
co espond o complexa ion ene gies in kcal/mol a he MP2/6-31+G(2d,p)//MP2/6-
31+G(d) le el.
Phe-Mg1-4H2O
Phe-Mg2-4H2O
Phe-Mg3-4H2O
Phe-Mg4-4H2O
Phe-K3-4H2O
Phe-K4-4H2O
Phe-Li1-4H2O
Phe-Li2-4H2O
Phe-Li3-4H2O
Phe-Li4-4H2O
Phe-Na1-4H2O
Phe-Na2-4H2O
Phe-Na3-4H2O
Phe-Na4-4H2O
-71.83
-71.18
-70.55
-86.00
-85.37
-85.79
-85.97
-112.55
-112.40
-113.53
-113.90
-278.95
-281.12
-281.48
-281.95
Phe-K2-4H2O
Phe-K1-4H2O
-71.54
Alba Campo Cacha ón
106
[58] M. J. F isch, G. W. T ucks, H. B. Schlegel, G. E. Scuse ia, M. A. Robb, J. R.
Cheeseman, G. Scalmani, V. Ba one, B. Mennucci, G. A. Pe e sson, H. Naka suji,
M. Ca ica o, X. Li, H. P. H a chian, A. F. Izmaylo , J. Bloino, G. Zheng, J. L.
Sonnenbe g, M. Hada, M. Eha a, K. Toyo a, R. Fukuda, J. Hasegawa, M. Ishida, T.
Nakajima, Y. Honda, O. Ki ao, H. Nakai, T. V e en, J. J. A. Mon gome y, J. E.
Pe al a, F. Oglia o, M. Bea pa k, J. J. Heyd, E. B o he s, K. N. Kudin, V. N.
S a o e o , R. Kobayashi, J. No mand, K. Ragha acha i, A. Rendell, J. C. Bu an , S.
S. Iyenga , J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B.
C oss, V. Bakken, C. Adamo, J. Ja amillo, R. Gompe s, R. E. S a mann, O. Yazye ,
A. J. Aus in, R. Cammi, C. Pomelli, J. W. Och e ski, R. L. Ma in, K. Mo okuma, V. G.
Zak zewski, G. A. Vo h, P. Sal ado , J. J. Dannenbe g, S. Dapp ich, A. D. Daniels, Ö.
Fa kas, J. B. Fo esman, J. V. O iz, J. Cioslowski, D. J. Fox, Gaussian 09, e ision
A.02, 2009.
[59] M. S. Ma shall, R. P. S eele, K. S. Than hi iwa e, C. D. She ill. J. Phys. Chem. A
2009, 113, 13628-13632.
5. In e ac ion o a oma ic uni s o
amino acids wi h guanidinium
ca ion. The in e play o π···π, X-
H···π and M+···π con ac s
5. Guanidinium a oma ic ime s
109
5.1. In oduc ion
Non-co alen in e ac ions play a key ole in many a eas o mode n chemis y,
especially in he ield o sup amolecula chemis y and molecula ecogni ion, as well as
in biochemis y.[1, 2] Among he di e en kinds o non-co alen con ac s ele an in
biological sys ems, a special place is occupied by in e ac ions wi h pa icipa ion o
a oma ic uni s.[3-6]
I is belie ed ha a oma ic g oups in e ac in a di e en manne han alipha ic uni s
in he side chains o amino acids, and can p o ide speci ici y in p o ein olding. Mo e
speci ically, h ee kinds o non-co alen in e ac ions in ol ing π sys ems a e usually
conside ed: ion···π, XH···π and π···π con ac s, which a e a ac i e in e ac ions ha can
a ec signi ican ly o he beha io o a gi en sys em.[3-5]
π···π in e ac ions, like in benzene dime , a e usually go e ned by dispe sion e ec s
and play an essen ial ole in he olding o p o eins and in he s uc u e o DNA as well as
in i s in e ac ions wi h small molecules.[3, 5] Hyd ogen bonding in e ac ions o he
a oma ic cloud (XH···π) a e also impo an as o de e mine he cha ac e is ics o many
sys ems.[4, 7, 8] These hyd ogen bonds a e usually weake han he ypical OH···O ones,
and usually exhibi a la ge dispe si e na u e. These wo kinds o π in e ac ions a e
no mally weak, hough he combined e ec o many o hem can ha e a deep impac on
he cha ac e is ics o he sys em. On he o he hand, ion···π in e ac ions a e s ong
in e ac ions in he gas phase,[4, 9-11] usually domina ed by elec os a ic and pola iza ion
e ms as a consequence o he p esence o he ion and a pola izable π cloud.[12, 13]
Ca ion···π in e ac ions a e ecognized o be an impo an ac o in ion selec i i y in
po assium channels, and hei impo ance has been demons a ed in neu o ansmi e
ecep o s.[4, 11, 14, 15]
The impo ance o he ca ion···π in e ac ion in p o eins is easily unde s ood aking
in o accoun ha some amino acids such as phenylalanine, y osine, yp ophan, and
his idine bea an a oma ic uni in hei side chains, whe eas o he amino acids as
a ginine, lysine, and his idine possess ca ionic g oups depending on he pH.[6, 16] Thus,
in e ac ions be ween side chains o hese amino acids a e o en obse ed in p o ein
s uc u e sugges ing hei ele ance as a s abilizing mo i . Though he ca ion···
in e ac ion is usually s onge han π···π o XH···π con ac s in he gas phase, as
co esponds o he in e ac ion o a ba e ca ion wi h a pola izable and elec on- ich
a oma ic cloud, he en i onmen can signi ican ly al e i s cha ac e is ics.[11, 17] Se e al
s udies ha e shown how he coo dina ion o elec on- ich sol en molecules o he
ca ion dec eases he in ensi y o he in e ac ion wi h he ca ion, as i would be expec ed
aking in o accoun he dec ease o he e ec i e cha ge ca ied by he ca ion due o he
sol en molecules.[18-22] In any case, he beha io and s abili y o a sys em, e en a simple
one, will be usually he esul o he in e play o di e en non-co alen in e ac ions. I
a oma ic molecules a e p esen i is p obable o all π···π, XH···π and ion···π o play a
ole.
Alba Campo Cacha ón
110
In he p esen wo k, he in e play among hese in e molecula con ac s is analysed in
e na y sys ems con aining one ca ionic uni and wo equal o di e en a oma ic uni s.
T ying o ep esen possible con ac s among amino acid side chains he a oma ic
molecules conside ed ha e been benzene, phenol and indole, as models o
phenylalanine, y osine and yp ophan, espec i ely. Guanidinium C(NH2)3+ has been
chosen as ca ion since i is pa o he side chain o a ginine. Guanidinium is widely used
as a dena u an since i is belie ed o in e ac wi h he side chains o p o eins, as well as
a basic uni o cons uc ing anion selec i e ecep o s o ionic liquids.[23, 24] Besides, due
o i s special plana s uc u e guanidinium ca ion is mo e p one han simple ca ions o
p esen pa allel-s acked s uc u es which can be o impo ance in hese sys ems.[20, 25] In
ac , s acking has been obse ed be ween sol a ed guanidinium ca ions in wa e
solu ion.[26, 27]
An in e es ing phenomenon when dealing wi h in e molecula in e ac ions is he
possibili y o coope a i e o an icoope a i e e ec s in sys ems wi h mo e han wo
species.[28, 29] These phenomena a e usually weak hough hey can be o impo ance as
o cha ac e ize he beha io o he sys em, as indica ed by se e al s udies ecen ly
de o ed o he ask o e alua ing hese e ec s.[12, 30-34] Usually, coope a i e e ec s a e
associa ed o pola iza ion, so he combina ion o a ca ion and a pola izable a oma ic
cloud, like in he ime s objec o his s udy, is indica i e ha coope a i i y, a p io i,
could be signi ican in de e mining he cha ac e is ics o hese sys ems.[12]
In summa y, he p esen wo k in ends o shed ligh on he cha ac e is ics on he
in e ac ion be ween guanidinium and a oma ic moie ies o amino acids. The esul s
ob ained would help o a ionalize he esul s obse ed in mul iple ca ion···π
in e ac ions in p o eins and hei mu ual in luence.
5.2. Me hods
As commen ed abo e, sys ems consis ing on a guanidinium ca ion and wo a oma ic
molecules among benzene, phenol and indole ha e been conside ed in his s udy. These
complexes ha e been ully op imized a he M06-2X/6-31+G* le el o calcula ion[35]
s a ing om a a ie y o di e en s uc u es. S a ing s uc u es we e cons uc ed om
p o o ypes obse ed in he guanidinium-a oma ic and a oma ic-a oma ic dime s.
The e o e, he pa allel, displaced-pa allel and T-shaped s uc u es o benzene dime
ha e been employed, and analogous s uc u es ha e also been used o phenol and
indole.[5, 36] T-shaped and pa allel o ien a ion o he guanidinium ca ion wi h espec o
he a oma ic clouds ha e been conside ed,[20, 37] wi h he ca ion loca ed be ween he
a oma ic molecules o bounded o only one o hem. O he possible s uc u es
co esponding o hyd ogen-bonded clus e s ha e also been es ed ollowing chemical
knowledge (i.e. O-H···O in phenol dime , N-H···π in indole-con aining clus e s, e c.). A e
5. Guanidinium a oma ic ime s
111
one s a iona y poin is loca ed a equency calcula ion has been ca ied ou in o de o
ensu e ha he s uc u e co esponds o a minimum.
Fo he minima he complexa ion ene gy has been ob ained by applying he
coun e poise p ocedu e wi h a a ie y o me hods.[38, 39] The e o e, he complexa ion
ene gy o he complexes has been ob ained as:
i
complex
i
complex
i
i
isola ed
i
complex
complex iEijkEiEijkEE )(...)()(...)(
(eq. 5.1)
whe e supe sc ip s e e o he geome y employed, subsc ip s o he agmen
conside ed and e ms in pa en heses o he basis se employed in he calcula ion.
Applying his p ocedu e, M06-2X/6-31+G* complexa ion ene gies ha e been ob ained.
Also, complexa ion ene gies ha e been ob ained wi h he MP2 me hod. Single poin
calcula ions ha e been ca ied ou a he M06-2X/6-31+G* op imized geome ies
employing MP2 wi h he aug-cc-pVDZ and aug-cc-pVTZ basis se s. Wi h hese esul s, a
wo-poin ex apola ion o he co ela ion ene gy o he basis se limi has been
pe o med applying[40]
3;
)1(
)1(
)1(
)1( 2,
33
3
2,
33
3
2,
XE
XX
X
E
XX
X
EZXpV MPco
pVXZ
MPco
CBS MPco
.
(eq. 5.2)
The MP2 complexa ion ene gy o basis limi is he es ima ed as
CBS MPco
pVTZ
HF
CBS
MP EEE 2,2
. (eq. 5.3)
Howe e , i is well know ha MP2 ends o o e es ima e he magni ude o he
in e ac ion when a oma ic molecules a e in ol ed, especially when o ien ed in
pa allel.[5, 41] A a ie y o empi ical p ocedu es ha e been p oposed o co ec o his
de iciency, mos ly based in a di e en scaling o he con ibu ions o pa allel and
an ipa allel elec ons o co ela ion. The i s p oposal o his kind is he Spin
Componen Scaled MP2 (SCS-MP2) p oposed by G imme, whe e opposi e-spin and
same-spin con ibu ions a e scaled by 1.20 and 0.33, espec i ely.[42] The e o e SCS-MP2
complexa ion ene gies ha e been ob ained wi h he aug-cc-pVDZ and aug-cc-pVTZ basis
se s, and we e also ex apola ed o basis se limi (SCS-MP2/CBS).
In o de o analyze he balance o he in e ac ions be ween agmen s in he ime ,
pai ene gy con ibu ions ha e also been calcula ed. The e o e, he in e ac ion ene gy is
exp essed as
ij bodyij EEE 3
(eq. 5.4)
whe e he ∆Eij a e he in e ac ion ene gies o each pai o med in he ime as
compu ed employing he whole basis se and he op imized geome y o he ime .[28,
Alba Campo Cacha ón
112
29] The di e ence be ween he summa ion o pai ene gies and he in e ac ion ene gy o
he ime is he con ibu ion om 3-body e ec s. This pa i ioning has been pe o med
wi h he me hods commen ed abo e.
Finally, in o de o ha e mo e insigh in o he na u e o he in e ac ion and he
balance o di e en con ibu ions, an ene gy pa i ioning scheme has been applied.
The e o e, he in e ac ion ene gies ha e been decomposed in elec os a ic, epulsion
(exchange + epulsion), pola iza ion and dispe sion componen s by applying he Local
Molecula O bi al-Ene gy Decomposi ion Analysis (LMO-EDA).[43] The pa i ioning has
been pe o med wi h bo h he M06-2X and MP2 me hods.
Op imiza ions and equency calcula ions ha e been pe o med wi h Gaussian09;[44]
LMO-EDA calcula ions we e pe o med wi h GAMESS,[45, 46] and Tu bomole has been
employed in he MP2 calcula ions.[47] In o de o sa e compu a ion ime, he esolu ion
o he iden i y has been applied in MP2 calcula ions, bo h o he co ela ion calcula ion
(RI-MP2) and o he HF one (RI-JK), employing sui able auxilia y basis se s as p o ided in
Tu bomole. The e o e he co esponding aug-cc-pVXZ i ing basis se s ha e been
employed in he co ela ion pa whe eas de 2-TZVPP has been used o RI-JK
calcula ions.[47-49]
5.3. Resul s
Minimum ene gy s uc u es and complexa ion ene gies will be p esen ed i s o
complexes o med by guanidinium and wo equal a oma ic uni s, ollowed by esul s
ob ained o complexes o med by guanidinium ca ion and wo di e en a oma ic
molecules (mixed complexes).
5.3.1. Complexes wi h he same a oma ic molecules
Figu e 5.1 shows he s uc u es o he mos s able minima loca ed o he complexes
o med by guanidinium ca ion and wo benzene molecules, whe eas Table 5.1 lis s he
alues ob ained o hei complexa ion ene gies wi h di e en le els o calcula ion.
Fou di e en minima ha e been ound o hese complexes. Bz-Bz-1 co esponds o
a s uc u e wi h s acked a oma ic ings and he guanidinium ca ion in e ac ing wi h one
o hem, adop ing a pe pendicula a angemen which has been shown o be he mos
s able minimum in guanidinium···Bz complexes.[20, 37] Two N-H···π con ac s a e obse ed:
one a 2.3 Å and a longe one a 2.9 Å. Bz-Bz-2 and Bz-Bz-3 co espond o s uc u es
whe e benzene ings display a pe pendicula a angemen (T-shaped) wi h C-H···π
con ac s a a ound 2.5-2.6 Å o he cen e o he o he a oma ic ing. These
a angemen s oughly co espond o he ypical s uc u es ound o benzene dime
(pa allel displaced and C-H···).[5] Finally, Bz-Bz-4 co esponds o a doubly T-shaped
s uc u e, whe e he a oma ic ings a e a apa , bo h o hem coo dina ing he
5. Guanidinium a oma ic ime s
113
guanidinium ca ion in pe pendicula a angemen s, o ming hyd ogen bonds a 2.3 Å o
he cen e o he ing.
Table 5.1 shows he complexa ion ene gies o Bz-Bz complexes as ob ained wi h a
a ie y o me hods. Taking in o accoun he alues in Table 5.1 he esul s ob ained a
he M06-2X/6-31+G* and a he SCS-MP2/CBS le els o calcula ion a e p e y simila ,
whe eas MP2 gi es in all cases o e es ima ed complexa ion ene gies, especially wi h he
la ge basis se . The e o e, in he ollowing we will mainly discuss alues ob ained wi h
hese wo le els o calcula ion.
Table 5.1. Complexa ion ene gies (kcal/mol) ob ained o complexes o med by
guanidinium and wo equal a oma ic molecules as ob ained wi h di e en me hods, all
employing he op imized M06-2X/6-31+G* geome y.
631+G*
aug-cc-pVDZ
CBS
M062X
MP2
SCS-MP2
MP2
SCS-MP2
Bz-Bz-1
-18.55
-21.03
-16.97
-22.79
-18.54
Bz-Bz-2
-21.03
-22.44
-18.58
-24.30
-20.27
Bz-Bz-3
-20.58
-21.41
-17.20
-23.25
-18.85
Bz-Bz-4
-25.62
-27.12
-23.52
-29.25
-25.48
Ph-Ph-1
-33.19
-31.93
-27.83
-34.05
-29.71
Ph-Ph-2
-31.21
-30.47
-25.76
-32.80
-27.85
Ph-Ph-3
-29.47
-29.93
-26.34
-31.88
-28.10
Ph-Ph-4
-28.73
-27.31
-22.36
-29.58
-24.36
Ph-Ph-5
-32.20
-31.05
-26.76
-33.20
-28.67
Ph-Ph-6
-32.21
-32.71
-29.05
-34.67
-30.81
Ph-Ph-7
-32.81
-30.63
-27.90
-32.17
-29.35
In-In-1
-29.61
-34.47
-27.43
-36.87
-29.53
In-In-2
-32.72
-36.01
-30.25
-38.37
-32.36
In-In-3
-31.54
-34.70
-28.94
-37.04
-31.04
In-In-4
-33.14
-36.39
-30.55
-38.79
-32.70
In-In-5
-38.16
-40.04
-34.70
-42.69
-37.09
Alba Campo Cacha ón
114
Figu e 5.1. Mos s able minima ound o complexes o guanidinium wi h wo benzene
molecules as ob ained a he M06-2X/6-31+G* le el. Selec ed dis ances in Å.
Bz-Bz-2Bz-Bz-1
Bz-Bz-3 Bz-Bz-4
2.262
2.911 2.172
3.107
2.331
2.632
3.652 2.293
2.292
2.930
2.962
5. Guanidinium a oma ic ime s
115
As expec ed, Bz-Bz-4, wi h a doubly T-shaped s uc u e is he mos s able complex
wi h a complexa ion ene gy o -25.5 kcal/mol because guanidinium can coo dina e a
he same ime he wo benzene ings, es ablishing wo simul aneous ca ion···
in e ac ions. Bz-Bz-2, wi h one T-shaped con ac , is abou 5 kcal/mol less s able (-20.3
kcal/mol). He e, one o he benzene ings coo dina es o he guanidinium ca ion h ough
a ca ion··· in e ac ion and by means o a CH··· con ac o he o he benzene ing. Bz-
Bz-1 co esponds o a pa allel-displaced benzene dime coo dina ed o guanidinium by
one o he phenyl ings. The lack o di ec con ac be ween guanidinium and one o he
benzene moie ies makes his s uc u e less s able, eaching only -18.5 kcal/mol. Finally,
in Bz-Bz-3 he benzene ing ha does no in e ac di ec ly wi h he guanidinium ca ion
mo es away om he pe pendicula a angemen . This s uc u e could be conside ed as
a combina ion o wo o he minima o guanidinium···benzene complexes; one T-shaped
and one pa allel displaced wi h guanidinium pa allel o he ing.[20, 37] This is he only
s uc u e which shows signi ican di e ences be ween M06-2X (-20.6 kcal/mol) and SCS-
MP2/CBS (-18.9 kcal/mol) esul s.
Con a y o benzene, phenol possesses wo di e en egions whe e a ca ion can
es ablish a s abilizing in e ac ion: he a oma ic cloud and he lone pai s o he hyd oxyl
oxygen. The e o e, e en when phenol is e y simila o benzene, he p esence o he
hyd oxyl g oup in oduces a g ea e complexi y on he po en ial ene gy su ace o he
clus e s, allowing o a g ea e a ie y o s able s uc u es. Figu e 5.2 shows he
s uc u es o he mos s able minima loca ed o he complexes o med by guanidinium
ca ion and wo phenol molecules. I can be obse ed ha phenol complexes canno be
classi ied in o p o o ypical s uc u es as easily as benzene ones, since due o he
p esence o he hyd oxyl g oup he e is a endency o o m O-H···O hyd ogen bond
con ac s. Ph-Ph-6 and Ph-Ph-7 co espond o doubly T-shaped s uc u es. In Ph-Ph-6
guanidinium ca ion coo dina es he phenyl ing and he hyd oxyl g oup whe eas in Ph-
Ph-7 i is coo dina ed only o he hyd oxyl g oups. I is wo h no ing ha simila
s uc u es bu wi h di e en disposi ion o he ings ha e been loca ed, hough only he
mos s able ones a e included in Figu e 5.2. In mos cases he s uc u es show O-H···O
sho hyd ogen bonds a 1.7-1.9 Å, whe eas guanidinium is also hyd ogen-bonded o he
hyd oxyl g oup by means o N-H···O hyd ogen bonds a a ound 1.8-1.9 Å. The con ac s
be ween guanidinium and he phenyl ing show simila beha io as ha obse ed in
benzene complexes.
No ypical s acked s uc u e has been ound in complexes wi h phenol because he
hyd oxyl g oup ends o in e ac es ablishing OH···π o OH···O hyd ogen bonds as i can
be obse ed in all minima in Figu e 5.2 excep he doubly T-shaped ones. As ega ds T-
shaped s uc u es, only Ph-Ph-3 could be conside ed wi hin his a angemen because i
is he only one ha p esen s bo h a oma ic ings in e ac ing in a pe pendicula
disposi ion, e en hough he in e ac ion akes place by means o a O-H···O con ac .
Alba Campo Cacha ón
122
Figu e 5.4. Selec ed minima o complexes o med by guanidinium, benzene and phenol
as ob ained a he M06-2X/6-31+G* le el. Selec ed Dis ances in Å.
Bz-Ph-DT
2.243 2.950
1.982
1.964
2.191
2.067
2.321 1.912
1.918
2.334
2.270
Ph-Bz-PBz-Ph-P
Bz-Ph-T Ph-Bz-T
5. Guanidinium a oma ic ime s
123
Figu e 5.5. Selec ed minima o complexes o med by guanidinium, benzene and indole
as ob ained a he M06-2X/6-31+G* le el. Selec ed Dis ances in Å.
Bz-In-DT
2.264 2.894 2.253 2.203
2.173 2.518
2.241 2.192
2.241
2.965
3.056
2.249
2.241
In-Bz-PBz-In-P
Bz-In-T In-Bz-T
Alba Campo Cacha ón
124
Figu e 5.6. Selec ed minima o complexes o med by guanidinium, phenol and indole as
ob ained a he M06-2X/6-31+G* le el. Selec ed Dis ances in Å.
1.962
2.698
2.408
1.956
2.207 2.205
2.252 1.849
2.239
2.436
2.285
2.230
2.306
2.405
2.314
2.292
Ph-In-PPh-In-P
Ph-In-T Ph-In-T
Ph-In-DT
5. Guanidinium a oma ic ime s
125
Finally, o complexes con aining he ca ion plus indole and phenol (Figu e 5.6) he
beha io is simila o e all. Fo he doubly T-shaped minimum he complexa ion ene gy is
hal way be ween hose o complexes wi h only one kind o a oma ic molecule.
Howe e , i can be obse ed ha phenol coo dina ion is p e e ed o e indole o
s acked and T-shaped s uc u es. This is because in he p esence o phenol, In-Ph
s uc u es co espond o ou p o o ypes, bu o Ph-In complexes he e a e clea
de ia ions. The e o e whe eas In-Ph-P is a ypical s acked s uc u e wi h a complexa ion
ene gy o -27 kcal/mol, Ph-In-P minimum is no s acked, and guanidinium in e ac s wi h
bo h a oma ic uni s leading o a complexa ion ene gy o -31.7 kcal/mol. In ac his
minimum co esponds mo e closely o a guanidinium coo dina ed o he hyd oxyl g oup
which es ablishes a O-H···π hyd ogen bond o he py ol ing o indole. T-shaped minima
bo h p esen hyd ogen bonds. Ph-In-T o ms a O-H···π hyd ogen bond o he py ol ing
o indole, whe eas a N-H···π hyd ogen bond is obse ed in In-Ph-T, his la e s uc u e
being dis a o ed by abou 2 kcal/mol.
So, hese mixed complexes beha e hal way he complexes o med wi h only one kind
o a oma ic molecule. This is especially e iden in he case o doubly T-shaped
s uc u es, which always show complexa ion ene gies almos midway he complexes
wi h only one kind o a oma ic molecule. These doubly T-shaped s uc u es a e always
he mos s able ound among he clus e s s udied. A simila beha io is obse ed in
s acked clus e s o benzene and indole, bu he p esence o phenol and he endency o
i s hyd oxyl g oup o o m hyd ogen bonds in oduce o he possibili ies o he
in e ac ion. In he absence o ex a in e ac ions wi h he guanidinium ca ion o
hyd ogen bonds, s acked s uc u es a e he leas s able. T-shaped minima a e usually
he second mos s able, bu again in phenol complexes he o ma ion o hyd ogen bonds
can al e he o de o s abili y, a o ing coo dina ion o phenol by he guanidinium
ca ion. In he absence o hese e ec s guanidinium coo dina es p e e en ially o indole
o e phenol and o e benzene.
A ques ion a ises abou whe he he kind o s uc u es al eady discussed is p esen in
p o eins. I is known ha s acking in e ac ions be ween a oma ic side chains a e
equen , as i is he case wi h he ca ion···a oma ic in e ac ions.[4, 11] I is expec ed,
howe e ha he mo i s conside ed in his wo k, simul aneously in ol ing h ee
di e en side chains will be less equen . Howe e , sea ching in o he P o ein Da a
Bank Eu ope i is possible o ind he kind o s uc u es conside ed in his wo k.[52] As
example, sea ching o a pa e n o med by a ni ogen a om o guanidinium in a ginine
con ac ing wi h indole ing in yp ophan, which in u n is s acked o phenyl g oup o
phenylalanine (like in In-Bz-P) esul s in mo e han o y coincidences. Among hese
s uc u es he e a e se e al o hem ha esemble he pa e ns shown in he
manusc ip . O cou se he e a e geome ical di e ences ha a e mainly associa ed o
he mo e complex en i onmen in he p o ein, and o he es o he side chains
hinde ing he ee o ien a ion o he a oma ic ings and he ca ionic agmen o in e ac
Alba Campo Cacha ón
126
in an op imal way. In any case, many o he s uc u es ound esemble he minima
conside ed in his wo k, so i can be expec ed ha hei cha ac e is ics would be help ul
in o de o unde s and hese kind o con ac in p o eins. Also, gas phase esul s would
help o isola e o he ac o s like sol en e ec s o o he g oups nea by which can al e
he mu ual a angemen o a oma ic and ca ionic side chains.
5.3.3. Pai ene gies
In o de o unde s and mo e closely he beha io o hese e na y sys ems, a
decomposi ion on pai con ibu ions has been pe o med o he clus e s discussed
abo e. Table 5.3 shows he esul s ob ained o he pai ene gies o complexes as
ob ained a he M06-2X/6-31+G* le el o calcula ion, oge he wi h he con ibu ions
om h ee-body e ec s. I can be obse ed ha in all complexes he in e ac ion o
guanidinium wi h benzene, phenol and indole amoun s o -14 kcal/mol, -18 kcal/mol
and -21 kcal/mol, espec i ely. The s eng h o hese in e ac ions is almos he same in
all minima conside ed, hus indica ing ha he p esence o a second a oma ic uni
ha dly a ec s he guanidinium···π in e ac ion. Fo example guanidinium···benzene
in e ac ion a ies be ween -12.8 and -13.9 kcal/mol, and simila a ia ions a e obse ed
o he o he a oma ic species. Pa o hese changes can be a ibu ed o changes in he
geome y o he ca ion···π in e ac ion depending on he complex conside ed. In any
case, he e ec o he second a oma ic uni on he guanidinium···π in e ac ion is
desc ibed by he 3-body con ibu ion o he in e ac ion ene gy, which in mos cases is
no la ge.
In doubly T-shaped s uc u es he e is a simila pa e n o he pai in e ac ions in all
cases. As expec ed, he e a e wo s ong in e ac ions due o guanidinium···π
in e ac ions, plus one weak epulsi e in e ac ion due o he in e ac ion o he wo
a oma ic molecules loca ed a apa . Fo he doubly T-shaped minima he con ibu ion
o he 3-body e m is des abilizing, amoun ing o be ween 1.3 kcal/mol o Bz-Bz
complex o 2.7 kcal/mol in In-In complex. This is a consequence o he cha ge o he
ca ion being sha ed by he wo a oma ic molecules. Mixed complexes show a simila
beha io , bu he wo ca ion···π con ac s a e no equi alen showing a pai o alues
ypical o he wo a oma ic uni s conside ed.
T-shaped minima ypically show one s ong in e ac ion due o he ca ion in e ac ing
wi h he close a oma ic molecule, plus wo simila weak a ac i e in e ac ions
be ween he ca ion and he o he a oma ic molecule, and be ween bo h a oma ic
molecules. The e o e, in Bz-Bz-2 he e is a guanidinium···benzene con ac amoun ing o
a ound -13 kcal/mol, plus an in e ac ion o -6 kcal/mol be ween guanidinium and he
o he benzene molecule a apa . Finally, bo h benzene molecules con ibu e wi h -2
kcal/mol o he in e ac ion due o a C-H···π con ac . As in he case o doubly T-shaped
minima, 3-body e ec s a e epulsi e and small.
5. Guanidinium a oma ic ime s
127
Alba Campo Cacha ón
128
Figu e 5.7. Pai ene gy con ibu ions in complexes wi h benzene and indole as ob ained
a he M06-2X/6-31+G* le el. C is always guanidinium ca ion. In he X-Y pai , A
co esponds o X and B o Y.
A simila beha io is obse ed in mixed complexes whe e benzene is coo dina ed o
he ca ion. In he case o indole and phenol complexes he e is also a s ong ca ion···π
in e ac ion oge he wi h wo weake con ibu ions om he o he molecule pai s.
Howe e , in hese complexes he in e ac ion be ween he wo a oma ic molecules
occu s by means o a hyd ogen bond, so he s abiliza ion inc eases wi h espec o
benzene complexes. Thus, in he T-shaped minima con aining wo indole molecules, he
N-H···π hyd ogen bond con ibu es wi h a ound -8 kcal/mol o he s abili y o he
complex. Mos complexes wi h phenol o indole coo dina ed o guanidinium show
simila alues ( hough somewha weake , a ound -4 o -5 kcal/mol). Compa ing he
alues ob ained o he mixed Ph-In complexes, i can be app ecia ed how he O-H···π
con ac (-7.3 kcal/mol) is s onge han he N-H···π one (-5.7 kcal/mol). Also, in hese
s uc u es, con a y o benzene ones, 3-body e ec s a e a ac i e, amoun ing be ween
-1.5 o -2.7 kcal/mol, hese alues being a consequence o he p esence o he hyd ogen
bonds. Pa allel minima show simila ene gy decomposi ion as T-shaped s uc u es, wi h
a s ong ca ion···π con ac plus wo weak con ac s om he o he pai s. When phenol
and indole a e in ol ed, he in e ac ion be ween a oma ic molecules can each a ound -
5 kcal/mol, being only sligh ly weake han he in e ac ion in hyd ogen-bonded
s uc u es p esen in T-shaped minima. Th ee body e ec s a e mos ly a ac i e bu
weake han hose obse ed in he o he s uc u al a angemen s. The di e en pai
con ibu ions can be easily seen in Figu e 5.7, whe e esul s a e shown o benzene and
indole-con aining complexes, showing he pa e ns discussed abo e.
-45
-35
-25
-15
-5
5
Bz-Bz
Bz-In
In-Bz
In-In
Bz-Bz
Bz-In
In-Bz
In-In
Bz-Bz
Bz-In
In-In
Ene gy (kcal mol-1)
AB
AC
BC
3-body
Pa allel T-Shaped DoublyT-Shaped
Ene gy (kcal/mol)
5. Guanidinium a oma ic ime s
129
5.3.4. LMO-EDA analysis
LMO-EDA decomposi ion has been pe o med wi h bo h M06-2X and MP2 me hods.
I has o be aken in o accoun ha in he case o pos -HF me hods, he so-called
dispe sion con ibu ion co esponds o he con ibu ion o he co ela ion o he
in e ac ion ene gy. Wi h DFT me hods, on he o he hand, dispe sion (ob ained as a
di e ence be ween a sum o e ms and he in e ac ion ene gy om a supe molecule
calcula ion) also eco e s de ia ions om o he con ibu ions. Along his sec ion only
esul s ob ained wi h he MP2/aug-cc-pVDZ pa i ioning will be conside ed, he M06-2X
ones p esen ed in Appendix B. The la ges di e ences be ween bo h me hods ha e
been obse ed in he epulsion e m, which is la ge wi h M06-2X, hus leading as
compensa ion o oo la ge dispe sion con ibu ions. Figu es 5.8 and 5.9 show he esul s
ob ained o his decomposi ion o he s uc u es p esen ed in Figu es 5.1 o 5.6.
I can be obse ed ha in Bz-Bz complexes he epulsion is almos cons an and
p o ides a kind o backg ound agains which he a ac i e con ibu ions o
elec os a ics, pola iza ion and dispe sion b ing close oge he he agmen s in he
complex. In he doubly T-shaped minimum Bz-Bz-4 he main con ibu ion o he s abili y
o he complex is elec os a ic, amoun ing o -21 kcal/mol, as a consequence o he
in e ac ion o he ca ion wi h bo h a oma ic clouds o he benzene molecules. On he
o he hand, dispe sion con ibu es wi h almos -13 kcal/mol o he s abili y o he
complex. The pola iza ion due o he ca ion also con ibu es signi ican ly o he s abili y,
eaching -15 kcal/mol. In he pa allel s uc u e Bz-Bz-1 he elec os a ic con ibu ion
d ops o -17 kcal/mol, and consequen ly, he con ibu ion o pola iza ion also dec eases
o -11 kcal/mol. These joined con ibu ions in oduce a di e ence o abou 8-9 kcal/mol
wi h espec o he doubly T-shaped one. This is pa ly eco e ed by an inc ease o
dispe sion con ibu ion due o he s acking o he ings. As ega ds T-shaped s uc u es
he dis ibu ion o con ibu ions is p e y simila o he pa allel ones. The e o e, he
p e e ence o doubly T-shaped minima is a consequence o la ge elec os a ic and
pola iza ion con ibu ions, whe eas o he s uc u es a e mo e a o ed by dispe sion.
In Ph-Ph clus e s, he elec os a ic con ibu ion is la ge in all minima, e en in pa allel
o T-shaped ones. This is ela ed o he o ma ion o hyd ogen bonds in mos o he
minima. In Ph-Ph-1 and Ph-Ph-5 he elec os a ic con ibu ion is he la ges , because in
hese minima guanidinium is coo dina ed o he hyd oxyl g oup, which simul aneously
o ms a O-H···O (Ph-Ph-1) o O-H···π (Ph-Ph-5) hyd ogen bond. The chain-like
a angemen o he con ac s p oduces la ge elec os a ic and pola iza ion con ibu ions.
In-In complexes esemble he beha io o benzene agg ega es. The doubly T-shaped
minimum p esen s la ge elec os a ic, pola iza ion and dispe sion con ibu ions,
combined wi h he smalles epulsion e m. On he o he hand he pa allel s uc u e In-
In-1 shows much smalle elec os a ic and pola iza ion e ms, while dispe sion is la ge ,
pa ly cancelled ou wi h he inc ease in epulsion.
Alba Campo Cacha ón
130
Figu e 5.8. LMO-EDA decomposi ion o complexes wi h he same a oma ic molecules a
he MP2/aug-cc-pVDZ le el.
-16.6
-17.0
-17.5
-21.2
22.7
21.4
23.3
22.2
-11.0
-12.1
-10.8
-15.4
-16.1
-14.5
-16.6
-12.6
-80
-60
-40
-20
0
20
40
Bz-Bz-1
Bz-Bz-2
Bz-Bz-3
Bz-Bz-4
Ene gy (kcal mol-1)
Elec os a ic
Repulsion
Pola iza ion
Dispe sion
-37.4
-35.5
-34.0
-30.7
-35.8
-31.7
-34.1
35.9
37.5
34.6
32.9
34.6
28.3
38.9
-17.3
-17.4
-20.4
-14.0
-15.8
-17.8
-16.2
-14.1
-16.6
-11.5
-18.1
-15.6
-12.2
-21.1
-80
-60
-40
-20
0
20
40
Ph-Ph-1
Ph-Ph-2
Ph-Ph-3
Ph-Ph-4
Ph-Ph-5
Ph-Ph-6
Ph-Ph-7
Ene gy (kcal mol-1)
Elec os a ic
Repulsion
Pola iza ion
Dispe sion
-25.8
-27.4
-27.8
-28.0
-30.9
35.4
31.2
31.4
31.3
30.1
-15.3
-17.1
-18.5
-18.3
-19.6
-28.9
-21.9
-21.0
-21.4
-19.4
-80
-60
-40
-20
0
20
40
In-In-1
In-In-2
In-In-3
In-In-4
In-In-5
Ene gy (kcal mol-1)
Elec os a ic
Repulsion
Pola iza ion
Dispe sion
Ene gy(kcal/mol) Ene gy(kcal/mol)Ene gy(kcal/mol)
5. Guanidinium a oma ic ime s
131
Figu e 5.9. LMO-EDA decomposi ion o complexes wi h di e en a oma ic molecules a
he MP2/aug-cc-pVDZ le el.
-19.0
-22.2
-20.3
-23.0
-38.8
-24.2
26.3
25.7
29.3
29.6
38.6
30.7
-11.7
-11.3
-12.6
-13.9
-17.2
-14.5
-18.5
-14.5
-22.1
-23.0
-19.4
-23.0
-80
-60
-40
-20
0
20
40
Bz-Ph-P
Ph-Bz-P
Bz-In-P
In-Bz-P
Ph-In-P
In-Ph-P
Ene gy (kcal mol-1)
Elec os a ic
Repulsion
Pola iza ion
Dispe sion
-29.3
-25.7
-20.5
-23.8
-30.1
-25.8
29.1
28.0
24.8
26.6
33.6
29.4
-14.3
-16.5
-13.3
-16.8
-18.9
-15.8
-16.2
-13.9
-18.5
-17.3
-18.4
-19.6
-80
-60
-40
-20
0
20
40
Bz-Ph-T
Ph-Bz-T
Bz-In-T
In-Bz-T
Ph-In-T
In-Ph-T
Ene gy (kcal mol-1)
Elec os a ic
Repulsion
Pola iza ion
Dispe sion
-26.5
-25.4
-30.6
25.3
26.9
28.0
-16.7
-16.5
-18.5
-12.5
-17.7
-15.3
-80
-60
-40
-20
0
20
40
Bz-Ph-DT
Bz-In-DT
Ph-In-DT
Ene gy (kcal mol-1)
Elec os a ic
Repulsion
Pola iza ion
Dispe sion
Ene gy(kcal/mol) Ene gy(kcal/mol)
Ene gy(kcal/mol)
Alba Campo Cacha ón
234
Figu e 9.6. NCI plo s o he complexes o med by SumaCN and he anions s udied. Only
complexes by he I line and he mos s able o ien a ion a e shown. The p oduc o he
densi y imes he sign o he second eigen alue o i s hessian is mapped on o an
isosu ace o educed densi y g adien wi h alue 0.5 a.u. The colo scale goes om -
0.015 a.u. (blue) o 0.015 a.u. ( ed).
Cl-
BF4-
NO3-
B -
ClO4-
CO2H-
9. Anion’s Na u e and sol en e ec s
235
9.3.4. NCI Analysis
Figu e 9.6 shows he non-co alen in e ac ion NCI plo s o complexes o med wi h
SumaCN. NCI maps he p oduc o he sign o he second eigen alue o he hessian o
he densi y imes he densi y on o an isosu ace o educed densi y g adien , allowing a
g aphical display o he mos ele an s abilizing (blue) and des abilizing ( ed)
in e ac ion in a sys em.[49, 50] Conside ing he plo s in Figu e 9.6, a egion o s abilizing
in e ac ions can be obse ed o Cl- complexes, co esponding o he six in e ac ions o
he anion wi h he cen al ca bons o he sumanene de i a i e. This a ac i e egion
ex ends o e he six Ca a oms (see Figu e 9.1), co esponding o six equi alen bond
c i ical poin s wi h densi y o 0.0106 a.u. acco ding o A oms in Molecules heo y.[59]
B omide complex shows a simila plo , hough i can be al eady app ecia ed in Figu e 9.6
ha he in e ac ion is sligh ly weake (ligh e blue), in acco dance wi h he smalle
alues o he c i ical poin s (0.0098 a.u.). The plo is mo e complex o igonal anions
which, in addi ion, show wo di e en o ien a ions. NO3- complex shows h ee a ac i e
egions oughly co esponding o con ac s wi h he h ee phenyl ings in SumaCN. These
h ee egions a e associa ed o a se o six bond c i ical poin s wi h densi y o 0.0111
a.u. The di e en o ien a ion o he mos s able complex wi h CO2H- anion (B) gi es ise
o a di e en pa e n, wi h wo pai s o bond c i ical poin s connec ing he anion wi h
he Cb a oms o he pen agonal (0.0124 a.u.) and hexagonal (0.0125 a.u.) ings. An
a ac i e in e ac ion be ween he anion and he hyd ogen a om o he CH2 g oup can
also be obse ed in he NCI plo . Finally, o BF4- and ClO4- complexes he beha io is
simila . In he mos s able o ien a ion h ee oxygen a oms poin o h ee di e en
phenyl ings, so h ee a ac i e egions a e displayed in he NCI plo . These a ac i e
egions a e ela ed o a se o six bond c i ical poin s connec ed o he Cc a oms, wi h
densi ies o 0.0114 a.u. o BF4- and 0.0113 a.u. o ClO4-.
Co aCN and SumaCN2 complexes show simila NCI plo s (Appendix D). The la ges
quali a i e di e ence is obse ed o SumaCN2 complexes which also display a eas o
weak in e ac ion which ex end owa ds he CN g oups. These egions a e al eady
obse ed in Cl- complex, becoming la ge as he size o he anion inc eases, and hey a e
p obably associa ed o he s e ic hind ance expe ienced by he anions due o he
disposi ion o he CN g oups, as commen ed abo e. The e o e, hese plo s allow
iden i ying he main a ac i e in e ac ions es ablished and quali a i ely ob aining
in o ma ion abou he in ensi y o he in e ac ion.
9.3.5. SAPT(DFT) Ene gy Analysis
Figu e 9.7 summa izes he esul s o he Symme y Adap ed Pe u ba ion Theo y
calcula ions o he mos s able complexes o med by each bowl wi h he anions
conside ed in his s udy. In ag eemen wi h p e ious wo k,[23] in he complex o med by
Cl- anion and Co aCN he la ges con ibu ion o he in e ac ion ene gy is he
elec os a ic one, eaching -41 kcal/mol, wi h con ibu ions om induc ion and
Alba Campo Cacha ón
236
dispe sion eaching -14 and -13 kcal/mol, espec i ely. Due o he la ge cancella ion o
elec os a ic and epulsion con ibu ion, he s abili y o he complex mainly comes om
he combined e ec o dispe sion and induc ion. When b omide is coo dina ed o
Co aCN, he e is an inc ease in epulsion ela i e o Cl- complex as a consequence o he
la ge size o he anion. Dispe sion sligh ly inc eases due o he same eason, whe eas
induc ion dec eases by a simila amoun ( his could be ela ed wi h he sligh ly la ge
equilib ium dis ance in B - complex). On he o he hand, he elec os a ic con ibu ion
inc eases wi h espec o ha obse ed in chlo ide complex. A p io i, he opposi e e ec
would be expec ed, due o he longe equilib ium dis ance bu , as indica ed in p e ious
wo k,[23] he elec os a ic con ibu ion comes o a signi ican ex en om pene a ion
e ec s and his could be he eason o he la ge elec os a ic con ibu ion in b omide
complex. Chlo ide and b omide complexes wi h SumaCN and SumaCN2 show he same
beha io al eady desc ibed o Co aCN. The e o e, in all cases he e a e inc emen s in
he elec os a ic, induc ion and dispe sion con ibu ions, hough pa ially cancelled ou
by he inc emen in epulsion.
Ni a e complexes wi h Co aCN and SumaCN show a la ge elec os a ic con ibu ion
oge he wi h signi ican epulsion, hough i mus be aken in o accoun ha he
balance o hese wo con ibu ions is less a o able han o bo h Cl- and B - complexes.
Induc ion is o simila magni ude as in complexes wi h mona omic anions, whe eas
dispe sion exhibi s a signi ican inc ease as a consequence o he la ge size o ni a e
anion and he close p oximi y o he walls o he bowl in o ien a ion A. In he complex
wi h SumaCN2 he epulsion con ibu ion unde goes a la ge inc ease oge he wi h a
small dec ease in elec os a ic con ibu ion, so he combina ion o hese i s -o de
e ms gi es an o e all balance o +7 kcal/mol (-6 kcal/mol in SumaCN). Dispe sion and
induc ion con ibu ions pa ially cancel his e ec showing inc emen s o a ound 1-2
kcal/mol each wi h espec o SumaCN complex. The la ge epulsion con ibu ion has i s
o igins in he un a o able in e ac ion wi h he CN g oups close o he oxygen a oms o
he ni a e anion in o ien a ion A. CO2H- anion o ms he mos s able complexes among
all anions s udied as a consequence o he la ge elec os a ic con ibu ion obse ed, jus
a bi smalle han in B - complexes. This, oge he wi h a signi ican inc ease in he
induc ion con ibu ion and also la ge dispe sion, o e comes he la ge epulsion
consequence o he sho dis ances be ween he oxygen a oms o he anion in
o ien a ion B and he ca bon a oms o he bowl.
Te ahed al anion complexes exhibi almos he same cha ac e is ics o a gi en
buckybowl. Thus, he ene gy con ibu ions a e almos he same o bo h anions, hough
dispe sion is always la ge o ClO4-, being he eason o he la ge s abili y o i s
complexes as compa ed wi h BF4- ones. Elec os a ic con ibu ions a e he smalles ones
obse ed among he di e en complexes, as also happens o induc ion.
9. Anion’s Na u e and sol en e ec s
237
Figu e 9.7. SAPT(DFT) decomposi ion o complexes o med employing he I app oaching
line and he mos s able o ien a ion.
Cl B NO3 CO2H BF4 ClO4
-50
-40
-30
-20
-10
0
10
20
30
40
50
-40.8
-42.7
-34.8
-41.3
-31.1
-31.0
31.9
35.3
31.9
36.4
29.1
30.0
-14.4
-13.0
-13.1
-17.0
-12.0
-11.3
-13.0
-14.1
-18.0
-15.9
-14.7
-17.9
-36.3
-34.5
-34.0
-37.6
-28.7
-30.1
Co aCN
Elec Rep Ind Disp To al
E (kcal mol
-1
)
Cl B NO3 CO2H BF4 ClO4
-50
-40
-30
-20
-10
0
10
20
30
40
50
-50.0
-51.7
-42.1
-49.4
-36.1
-35.7
37.0
40.6
36.2
40.4
31.5
32.6
-16.1
-14.8
-14.5
-18.7
-12.9
-12.4
-14.8
-16.0
-19.7
-17.6
-15.8
-19.4
-43.9
-42.0
-40.1
-45.4
-33.3
-34.8
SumaCN
Elec Rep Ind Disp To al
E (kcal mol
-1
)
Cl B NO3 CO2H BF4 ClO4
-50
-40
-30
-20
-10
0
10
20
30
40
50
-43.0
-45.5
-33.5
-43.0
-26.9
-27.2
40.6
45.9
40.7
47.4
32.7
35.1
-16.9
-15.8
-15.6
-19.8
-13.4
-12.8
-16.4
-17.9
-21.2
-19.8
-16.5
-20.5
-35.6
-33.4
-29.6
-35.2
-24.0
-25.4
SumaCN2
Elec Rep Ind Disp To al
E (kcal mol
-1
)
Co aCN
SumaCN
SumaCN2
Cl-B -CO2H-ClO4-
BF4-
NO3-
Cl-B -CO2H-ClO4-
BF4-
NO3-
Cl-B -CO2H-ClO4-
BF4-
NO3-
Ene gy(kcal/mol) Ene gy(kcal/mol)
Ene gy(kcal/mol)
Alba Campo Cacha ón
238
Figu e 9.8. SAPT(DFT) decomposi ion o complexes o med wi h B -, NO3-, ClO4- and
SumaCN along di e en app oaching lines employing he mos s able o ien a ion.
I O H R
-50
-40
-30
-20
-10
0
10
20
30
40
50
-51.7
-37.0
-28.8
-20.9
40.6
29.4
21.4
27.4
-14.8
-14.4
-10.9
-15.4
-16.0
-9.9
-8.2
-8.5
-42.0
-31.9
-26.5
-17.4
B
Elec Rep Ind Disp To al
E (kcal mol -1)
I O H R
-50
-40
-30
-20
-10
0
10
20
30
40
50
-42.1
-31.7
-26.1
-18.3
36.2
25.6
20.5
19.8
-14.5
-14.4
-11.6
-11.8
-19.7
-10.1
-11.1
-7.8
-40.1
-30.7
-28.3
-18.2
NO3
Elec Rep Ind Disp To al
E (kcal mol -1)
I O H R
-50
-40
-30
-20
-10
0
10
20
30
40
50
-35.7
-26.2
-22.9
-12.3
32.6
19.0
17.5
16.0
-12.4
-10.9
-9.7
-10.2
-19.4
-10.5
-10.1
-8.3
-34.8
-28.6
-25.2
-14.8
ClO4
Elec Rep Ind Disp To al
E (kcal mol -1)
B -
NO3-
ClO4-
I O RH
I O RH
I O RH
Ene gy(kcal/mol) Ene gy(kcal/mol)Ene gy(kcal/mol)
9. Anion’s Na u e and sol en e ec s
239
On he o he hand, o hese bulky anions dispe sion is la ge, only ni a e complexes
showing la ge dispe sion con ibu ions. E en hough la ge epulsion con ibu ions could
be expec ed, hese anions a e loca ed u he away han smalle ones so epulsion is no
as la ge as o o he anions. Thus, epulsion con ibu ion is he smalles among
complexes s udied, bu i s ela i e weigh is he la ges .
Figu e 9.8 explains he p e e ence o I o ien a ion o e o he possibili ies. When he
anion app oaches he bowl by he cen al ing o he con ex ace o he bowl (O), he e
is a sha p dec ease on elec os a ic con ibu ion ela i e o I, since he MEP by he
con ex ace o he bowls is less posi i e. Repulsion also dec eases since he e a e ew
a oms close by, bu he combina ion o bo h con ibu ions al eady a o s by 3 kcal/mol
he o ma ion o he B - complex by he conca e side. Howe e , as he size o he anion
g ows, he combina ion o elec os a ic plus epulsion becomes mo e a o able o he O
complex (see esul s o ClO4-). Induc ion shows simila con ibu ions by bo h aces o
he bowl (I and O), while dispe sion dec eases by 6-10 kcal/mol o he O s uc u es.
Complexes by he H line a e e en less s able since all con ibu ions diminish, especially
he elec os a ic (and induc ion) one. When he anion in e ac s di ec ly wi h a C-H g oup
(R) o ming a hyd ogen bond o he im o he bowl, he elec os a ic con ibu ion is he
smalles one obse ed o he di e en a acking lines. Dispe sion also dec eases, as
expec ed aking in o accoun he la ge dis ances o o he a oms. This, combined wi h a
epulsion la ge han he elec os a ic con ibu ion makes hese complexes he leas
s able ones among hose conside ed in his wo k.
Figu e 9.9. SAPT(DFT) decomposi ion o complexes o med wi h NO3-, ClO4- and SumaCN
employing di e en anion o ien a ion and he I app oaching line.
NO3 – A NO3 – B ClO4 – A ClO4 – B ClO4 – C
-50
-40
-30
-20
-10
0
10
20
30
40
50
-42.1
-38.4
-28.8
-35.7
-33.5
36.2
30.8
21.7
32.6
28.8
-14.5
-14.2
-10.4
-12.4
-11.7
-19.7
-16.1
-14.6
-19.4
-17.4
-40.1
-37.9
-32.1
-34.8
-33.9
SAPT - SumaCN
Elec Rep Ind Disp To al
E (kcal mol -1)
NO3--A NO3--A ClO4--A ClO4--CClO4--B
Ene gy(kcal/mol)
Alba Campo Cacha ón
240
The sou ce o he o ien a ion dependence o he in e ac ion ene gy can be analyzed in
Figu e 9.9, which shows he e ec o he o ien a ion o he anion on he in e ac ion
when app oaching SumaCN by he I line. In he case o ni a e complexes, o ien a ion A
in oduces mo e epulsion since he h ee oxygen a oms a e close o he bowl (only
wo in B). The la ge epulsion in A is compensa ed by la ge dispe sion and elec os a ic
con ibu ions, he esul being ha minimum A is a o ed. In ac , i is he la ge
con ibu ion om dispe sion which makes he o ma ion o he A complex mo e
a o able (in he case o CO2H- induc ion is wha makes B mo e s able). In ClO4-
complexes o ien a ion B is he mos s able one because, despi e he la ge epulsion
con ibu ion, i maximizes he s abilizing con ibu ions, eaching he la ges alues o
elec os a ic, dispe sion and induc ion.
9.3.6. Sol en E ec
The in e ac ion ene gies o he complexes s udied ha e been ob ained in di e en
sol en s by applying he C-PCM me hod a he M062X/6-31+G* le el. The p esence o a
dielec ic medium has a deep impac on o he ene ge ics o he complexes, bu in all
cases he mos s able s uc u es s ill co espond o complexes o med by he I line and,
o e all, he s abili y o de ob ained o he di e en a acking lines is he same as
obse ed in he gas phase. Sol en e ec is la ge in complexes o med wi h he conca e
ace o he bowl, whe e he anion has o desol a e o a la ge ex en since pa o i s
su ace is con ac ing wi h he bowl. On he o he hand, R complexes a e he leas
penalized since almos he whole anion su ace is s ill exposed o he sol en . Despi e
his, he s abili y di e ences obse ed in he gas phase a e so la ge ha no changes in
he s abili y o de due o he sol en depending on he a acking line ha e been
obse ed. The e o e, Table 9.4 only shows I complexes in a se ies o sol en s wi h
a ying dielec ic cons an o he mos s able o ien a ion o he anion.
Complexes o med wi h Co aCN in oluene al eady exhibi signi ican changes wi h
espec o he alues ob ained in he gas phase despi e he low dielec ic cons an o he
sol en . Thus, complexa ion ene gies dec ease by a ound one hal in all cases wi h
espec o he gas phase, so he mos s able complexes ba ely each -19 kcal/mol.
Fu he dec eases a e obse ed as he dielec ic cons an o he sol en inc eases, and
al eady in chlo o o m he in e ac ion ene gies a e a ound one hi d o he gas phase
alues. In dime hylchlo ide and sol en s wi h la ge dielec ic cons an s he in e ac ion
ene gies s abilize in alues a ound 20-15 % o he o iginal gas phase alues.
Thus, in wa e , complexa ion ene gies ha dly each -7 kcal/mol o any o he
complexes wi h Co aCN. SumaCN complexes also show simila changes as he sol en
becomes mo e pola . Howe e , as in he gas phase, complexes o med wi h SumaCN a e
mo e s able han hose o med wi h Co aCN. In chlo o o m, he mos a o able
complexes exhibi complexa ion ene gies a ound -15 o -16 kcal/mol, which educe e en
mo e and ha dly each -9 kcal/mol a mos in wa e . Complexes o B - and Cl- wi h
9. Anion’s Na u e and sol en e ec s
241
SumaCN2 show simila alues o hose ob ained in SumaCN as he dielec ic cons an o
he sol en inc eases. Polya omic anions exhibi smalle s abili ies as a consequence o
he educed size o he ca i y due o he p esence o he CN g oups in he conca e side
o he bowl.
Table 9.4. M06-2X/6-31+G* in e ac ion ene gies, in kcal/mol, o complexes o med
employing I app oaching line, he mos s able o ien a ions and di e en sol en s
modeled wi h C-PCM, as ob ained a he minima o he M06-2X/6-31+G* gas-phase
cu es.
Gas-
phase
Toluene
CHCl3
THF
Cl2C2H4
E hanol
DMSO
H2O
1.00
2.37
4.71
7.43
10.13
24.85
46.82
78.36
Co aCN
Cl-
-36.97
-18.16
-11.46
-9.00
-7.87
-6.03
-5.44
-5.17
B -
-35.39
-18.42
-12.37
-10.15
-9.13
-7.47
-6.93
-6.69
NO3-
-35.15
-17.90
-11.68
-9.38
-8.32
-6.58
-6.03
-5.77
CO2H-
-39.47
-18.62
-10.88
-7.98
-6.62
-4.41
-3.70
-3.37
BF4-
-30.77
-15.18
-9.55
-7.45
-6.49
-4.90
-4.39
-4.16
ClO4-
-30.86
-16.22
-10.99
-9.06
-8.16
-6.71
-6.24
-6.03
SumaCN
Cl-
-45.29
-22.96
-14.91
-11.93
-10.55
-8.31
-7.59
-7.26
B -
-43.46
-23.21
-15.92
-13.21
-11.97
-9.94
-9.28
-8.99
NO3-
-41.66
-21.62
-14.34
-11.63
-10.38
-8.34
-7.68
-7.38
CO2H-
-48.02
-24.16
-15.24
-11.88
-10.31
-7.74
-6.91
-6.53
BF4-
-35.59
-17.92
-11.51
-9.12
-8.02
-6.21
-5.63
-5.37
ClO4-
-35.57
-18.90
-12.96
-10.75
-9.74
-8.08
-7.55
-7.30
SumaCN2
Cl-
-37.33
-18.83
-12.60
-10.36
-9.35
-7.72
-7.20
-6.96
B -
-35.40
-19.06
-13.57
-11.61
-10.72
-9.30
-8.85
-8.64
NO3-
-31.38
-14.94
-9.24
-7.17
-6.22
-4.69
-4.20
-3.98
CO2H-
-38.40
-17.92
-10.53
-7.78
-6.52
-4.45
-3.79
-3.48
BF4-
-25.85
-11.77
-6.96
-5.21
-4.41
-3.12
-2.71
-2.52
ClO4-
-26.18
-13.02
-8.59
-7.00
-6.27
-5.11
-4.74
-4.57
Alba Campo Cacha ón
242
Figu e 9.10. Va ia ions in in e ac ion ene gies ela i e o Cl- complexes as he dielec ic
cons an o he sol en is changed. C-PCM esul s ob ained a he M06-2X/6-31+G*
le el.
dielec ic cons an
010 20 30 40 50 60 70 80
Ein (kcal mol-1)
-2
0
2
4
6
dielec ic cons an
010 20 30 40 50 60 70 80
Ein (kcal mol-1)
-2
0
2
4
6
dielec ic cons an
010 20 30 40 50 60 70 80
Ein (kcal mol-1)
-2
0
2
4
6
Col 1 s Col 2
Col 1 s Col 3
Col 1 s Col 4
Col 1 s Col 5
Col 1 s Col 6
Col 7 s Col 8
Co aCN
Col 1 s Col 2
Col 1 s Col 3
Col 1 s Col 4
Col 1 s Col 5
Col 1 s Col 6
Col 7 s Col 8
Col 1 s Col 2
Col 1 s Col 3
Col 1 s Col 4
Col 1 s Col 5
Col 1 s Col 6
Col 7 s Col 8
Cl-
B -
NO3-
CO2H-
BF4-
ClO4-
Col 1 s Col 2
Col 1 s Col 3
Col 1 s Col 4
Col 1 s Col 5
Col 1 s Col 6
Col 7 s Col 8
Col 1 s Col 2
Col 1 s Col 3
Col 1 s Col 4
Col 1 s Col 5
Col 1 s Col 6
Col 7 s Col 8
Cl-
B -
NO3-
CO2H-
BF4-
ClO4-
Col 1 s Col 2
Col 1 s Col 3
Col 1 s Col 4
Col 1 s Col 5
Col 1 s Col 6
Col 7 s Col 8
Col 1 s Col 2
Col 1 s Col 3
Col 1 s Col 4
Col 1 s Col 5
Col 1 s Col 6
Col 7 s Col 8
Cl-
B -
NO3-
CO2H-
BF4-
ClO4-
Col 1 s Col 2
Col 1 s Col 3
Col 1 s Col 4
Col 1 s Col 5
Col 1 s Col 6
Col 7 s Col 8
Col 1 s Col 2
Col 1 s Col 3
Col 1 s Col 4
Col 1 s Col 5
Col 1 s Col 6
Col 7 s Col 8
Cl-
B -
NO3-
CO2H-
BF4-
ClO4-
SumaCN2
SumaCN
Ene gy(kcal/mol) Ene gy(kcal/mol)Ene gy(kcal/mol)
9. Anion’s Na u e and sol en e ec s
243
Howe e , he e ec o he sol en upon he s abili y o a gi en complex is ema kably
di e en o each anion. While b omide complex becomes he mos s able complex wi h
Co aCN as he dielec ic cons an g ows, CO2H- complex is penalized o a la ge ex en ,
becoming one o he leas s able complexes ob ained.
Chlo ide and NO3- complexes exhibi simila in e ac ion ene gies, whe eas ClO4-
complexes a e ela i ely a o ed, eaching in e ac ion ene gies simila o hose o NO3-
complexes. These ends a e mo e easily seen in Figu e 9.10, which shows he changes
in in e ac ion ene gy o he complexes as he dielec ic cons an changes ela i e o
chlo ide complexes. As commen ed abo e, s abili y di e ences in he gas phase a e
qui e la ge, spanning an ene gy ange o a ound 8-12 kcal/mol. Howe e , he
inco po a ion o he sol en quickly dec eases his ange and al eady in chlo o o m i
only amoun s o a ound 4 kcal/mol. I can be obse ed ha all anion complexes wi h
Co aCN gain s abili y ela i e o chlo ide ones, excep in he case o CO2H-, which is he
mos des abilized by he sol en as commen ed abo e. Fo dielec ic cons an s a ound
10 o la ge , only BF4- and CO2H- complexes a e less s able han Cl- ones; NO3- and ClO4-
exhibi simila s abili ies, whe eas B - complexes a e clea ly he mos s able ones. The
same beha io is obse ed o SumaCN complexes, e en hough in his case Cl-
complexes a e equally s able as NO3- and ClO4-. SumaCN2 complexes show a di e en
beha io , and in his case only B - complexes a e mo e s able han Cl- ones,
independen ly o he dielec ic cons an o he sol en .
Conside ing he dec eases in in e ac ion ene gies ela i e o gas phase, i becomes
clea ha he mos des abilized complexes a e CO2H- ones, ollowed by Cl- and BF4- ones.
On he o he hand, B - and ClO4- complexes a e he leas a ec ed by he p esence o he
sol en , while NO3- occupies an in e media e posi ion. These ends a e he
consequence o wo main ac o s. Fi s , he la ge he in ensi y o he in e ac ion
be ween bowl and anion in he gas phase, he la ge would be he s abili y in sol en , as
al eady indica ed by he ac ha he s abili y o de depending on he a acking line is
p ese ed om he gas phase. Second, he desol a ion cos o he anion has he la ge
impac on he inal ene gy di e ences. In his case, he la ge he in e ac ion in he gas
phase he la ge he in e ac ion wi h he sol en molecules and he la ge he
desol a ion cos . Thus, pola izing anions such as Cl- and CO2H- a e clea ly dis a o ed by
desol a ion, whe eas bulkie anions as B - and ClO4- a e he ones aking he la ge
bene i . O e all, i can be obse ed ha complexes o med wi h B - anion a e he mos
s able ones, whe eas he leas s able a e he BF4- ones. As ega ds he es o he anions,
he e a e changes in he o de o s abili y depending on he sol en and he bowl
conside ed. O e all, he p esence o he sol en clea ly a o s complexes wi h B -, while
CO2H- unde goes he la ges des abiliza ion becoming one o he leas s able complexes
Alba Campo Cacha ón
251
Complexes in ol ing ion···π in e ac ions ha e been compu a ionally s udied in o de o
gain insigh abou he cha ac e is ics and ac o s con olling he in e ac ions. A a ie y
o sys ems ha e been conside ed anging om ca ion···π con ac s in simple a oma ic
moie ies o ion···π in e ac ions in mo e complex s uc u es as buckybowls. Below, he
main conclusions eached in hese s udies a e lis ed.
The inco po a ion o wa e molecules o phenol···ca ion complexes leads o a g ea
a ie y o simila ly s able s uc u es di e ing on he opology o he hyd ogen bond
ne wo k. The beha io is mo e complex han in benzene analogues because he
hyd oxyl g oup o phenol s a s pa icipa ing in hyd ogen bonds when h ee and ou
wa e molecules a e included.
Li+ and Mg2+ complexes show s uc u es wi h wa e and phenol su ounding he ions
wi hou o ming hyd ogen bonds among hemsel es. O he wise Na+ and K+ in e ac
mo e weakly wi h wa e and phenol so hyd ogen bonds s a being compe i i e, leading
o minima wi h hyd ogen bonds be ween wa e molecules o be ween wa e and
phenol.
Vib a ional spec a in he egion o he O-H s e ching mode a e qui e simple in Li+
and Mg2+ complexes, wi h shi s associa ed o hyd ogen bonds being only obse ed
when he ou h wa e molecule is loca ed in he second sol a ion shell. Na+ and K+
complexes show mo e complex spec a, wi h impo an ed shi s associa ed o O-H···O
hyd ogen bonds be ween wa e molecules bu also wi h pa icipa ion o phenol in
φ-OH···O hyd ogen bonds.
Te na y complexes o med be ween guanidinium ca ion and a oma ic uni s om
amino acids show a a ie y o minima which can be oughly g ouped as pa allel s acked
( wo pa allel ings), T-shaped (pe pendicula ings) and doubly T-shaped (ca ion
be ween bo h ings). Mos s able s uc u es a e doubly T-shaped ones, ollowed by T-
shaped and pa allel s acked minima
The in e ac ion is mos ly con olled by he in ensi y o he ca ion···a oma ic con ac s
in he clus e . Guanidinium p e e s in e ac ing wi h indole han wi h phenol and
benzene. The o ma ion o hyd ogen bonds in complexes con aining phenol o indole
in oduces ex a s abili y in T-shaped s uc u es.
Th ee-body e ec s a e only coope a i e in T-shaped minima con aining indole o
phenol when hyd ogen bonds a e o med. Though he in e ac ion is domina ed by
elec os a ics, con ibu ions om dispe sion and induc ion a e also ele an .
10. Conclusions
252
The s udy o he in e ac ion o anions in simpli ied models o a syn he ic anion
channel based in naph halendiimide (NDI) uni s shows ha anion···π in e ac ions a e
highly a o able in he gas phase, wi h minima connec ing a pa h ha allows he anions
o mo e along he a oma ic su ace.
The p esence o wa e molecules s ongly a ec s he in e ac ion o luo ide and
hyd oxide anions wi h NDI, whe eas he e ec is less ema kable in he case o b omide
and chlo ide complexes. As a consequence, he in ensi y o he in e ac ion becomes
simila among he di e en anions, wi h di e ences below 4 kcal/mol (in gas phase
hese di e ences each mo e han 20 kcal/mol).
The esul s sugges ha a limi ed numbe o wa e molecules a ached o he anion
could be c ucial o o e come dehyd a ion cos s, also con ibu ing o he s abiliza ion o
he complex by means o a o able wa e ···NDI con ac s.
Subs i u ion o co annulene and sumanene is an e ec i e me hod o p omo e g ea
changes in he elec ic p ope ies o he bowls, ha dly changing hei geome y and
keeping hei cha ac e is ic bowl shape.
Subs i u ion allows modula ing he molecula elec os a ic po en ial (MEP) o he
bowls so hey can be uned o a o able in e ac ion wi h anions o ca ions. Elec on-
wi hd awing g oups as ni ile c ea e posi i e MEP egions on bo h aces o he bowl;
elec on-dona ing g oups as me hyl and unsubs i u ed bowls exhibi nega i e MEP
egions on bo h aces; o he g oups as luo ide p oduce almos ze o MEP allowing
a o able in e ac ion wi h bo h anions and ca ions.
The in e ac ion in hese sys ems is ha d o desc ibe wi h accu acy. Tes ing a a ie y
o me hods i has been ound ha he bes pe o mance is gi en by he SCS-MP2
me hod ex apola ed o basis limi , which ma ches almos pe ec ly he e e ence alues
ob ained a he MP2.X/6-31G(0.25) le el o calcula ion. M06-2X/6-31+G* also seems o
be able o p o ide a qui e balanced desc ip ion o he conca e/con ex ene gy
di e ences despi e he e o s in oduced in he in e ac ion ene gies.
Sumanene and i s de i a i es in e ac mo e a o ably han co annulene wi h anions
and ca ions. Subs i u ion e ec s in sumanene a e s onge i applied in he CH a oma ic
g oups han in he CH2 g oups o pen agonal ings. Ca ion complexes a e domina ed by a
la ge induc ion componen ha can be e en la ge han he elec os a ic con ibu ion,
whe eas in anion complexes elec os a ics and dispe sion a e he main s abilizing
componen s.
Alba Campo Cacha ón
253
Complexa ion ene gies oughly ollow he se ies o MEPs, being he mos s able
complexes hose o med wi h co annulene subs i u ed wi h CN g oups. Howe e , he e
a e also changes a ec ing o he induc ion and dispe sion con ibu ions which may
in oduce de ia ions o e he beha io expec ed om a pu ely elec os a ics poin o
iew.
Anions a e o ien ed so he la ges nega i e egions poin owa ds he posi i ely
cha ged su aces o he bowl. Te ahed al anions o ien hemsel es wi h h ee bonds
owa ds he bo om o he bowl. Ni a e complexes a e mo e s able wi h he anion
pa allel o he bo om o he bowl, he oxygen a oms o ien ed owa ds he posi i ely
cha ged six-ca bon ings. Fo ma e complexes a e mo e s able wi h he anion
pe pendicula o he bo om o he bowl, a oiding he in e ac ion o he hyd ogen a om
wi h he walls o he bowl.
The mos s able complexes co espond o he anion loca ed on he symme y axis o
he bowl by he conca e ace. The in e ac ion o he anions wi h he con ex ace o he
bowl o wi h he hyd ogen a oms on he im o he bowl is signi ican ly less a o able.
The o de o s abili y o he complexes o med wi h CN-subs i u ed bowls in he gas
phase as ob ained o he di e en anions is he ollowing: CO2H- > Cl- > B - > NO3- >>
ClO4- > BF4-.
The p esence o sol en has a deep impac on he p ope ies o he complexes, and
al eady in sol en s wi h low dielec ic cons an he in e ac ion s eng h dec eases
d ama ically. Sol en a ec s he di e en anions o dis inc ex en s, so he mo e
pola izing ones a e he mos a ec ed whe eas he bulkie ones egis e smalle
dec eases. The e o e, in sol en s o mode a e o la ge dielec ic cons an , he mos
s able complexes a e hose o med wi h B - whe eas CO2H- is among he leas a o able
complexes o med.
O e all, he esul s ob ained o ion complexes o med wi h p ope ly subs i u ed
buckybowls encou age o ollow his opic, since his s a egy p omises o be sui able o
designing selec i e anion ecep o s.
Appendices
Appendix A
257
Appendix A
Table A.1. Complexa ion ene gies (kcal/mol) o monohyd a ed ca ion···phenol clus e s
as ob ained wi h di e en le els o calcula ion.
Phe-X1-
1H2O
Phe-X2-
1H2O
Phe-X3-
1H2O
Phe-X4-
1H2O
Phe-X5-
1H2O
Phe-X6-
1H2O
B3LYP(a)
K+
-31.03
-28.16
-30.90
-30.77
-27.61
-32.35
MP2-A(b)
-31.12
-29.39
-33.18
-32.38
-29.14
-34.98
MP2-B(c)
-31.87
-30.24
-33.30
-33.07
-29.94
-35.72
MP2-C(d)
-31.91
-29.29
-33.19
-32.18
-29.10
-34.87
MP2-D(e)
-32.33
-30.01
-33.94
-32.99
-30.20
-36.13
MP2-E( )
-32.28
-30.26
-34.08
-33.30
-30.78
-36.62
B3LYP(a)
Na+
-44.89
-37.57
-44.89
-45.01
-37.40
-44.72
MP2-A(b)
-41.45
-35.23
-41.46
-41.52
-34.80
-42.94
MP2-B(c)
-41.80
-36.13
-42.41
-42.35
-35.56
-43.70
MP2-C(d)
-41.94
-35.65
-42.55
-41.88
-35.09
-43.23
MP2-D(e)
-41.25
-35.32
-42.10
-40.95
-34.48
-42.45
MP2-E( )
-41.05
-35.35
-41.99
-40.95
-34.73
-42.63
B3LYP(a)
Li+
-64.60
-51.59
-65.71
-53.44
MP2-A(b)
-61.00
-48.67
-62.14
-49.74
MP2-B(c)
-61.01
-48.99
-62.23
-50.02
MP2-C(d)
-61.17
-48.98
-62.27
-50.02
MP2-D(e)
-60.73
-49.10
-61.82
-49.93
MP2-E( )
-60.63
-49.04
-61.77
-49.99
B3LYP(a)
Mg+2
-183.04
-153.00
-185.71
-151.48
MP2-A(b)
-171.18
-139.90
-174.86
-140.31
MP2-B(c)
-171.40
-140.45
-174.91
-140.61
MP2-C(d)
-171.55
-140.50
-175.00
-140.62
MP2-D(e)
-170.32
-139.71
-173.15
-139.05
MP2-E( )
-170.98
-140.37
-174.03
-139.85
a) B3LYP/6-31+G(2d,p); b) MP2/6-31+G(2d,p)//B3LYP/6-31+G(2d,p);
c) MP2/6-31+G(2d,p)//MP2/6-31+G(d); d) MP2/631+G(2d,p);
e) MP2/6-311++G(2d,2p)//MP2/6-31+G(d); ) MP2/6-311++G(3d,2p) //MP2/6-31+G(d).
Alba Campo Cacha ón
258
Table A.2. OH s e ching equencies o selec ed complexes wi h sodium as ob ained a
he MP2/6-31+G(2d,p) le el. Values ob ained wi h he ha monic app oxima ion and
co ec ed om anha monici y a e p esen ed.
Ha monic
Anha monic
Fac o (*)
0.9797
1.0321
Phenol
3657.0
3657.0
Wa e
3672.9
3688.3
Phe-Na-O
3646.9
3649.2
Phe-Na-
3631.2
3631.8
Phe-Na1-1H2O
3758.3
3816.0
Phe-Na1-1H2O
3653.9
3685.2
Phe-Na1-1H2O
3648.9
3650.5
Phe-Na2-1H2O
3772.6
3778.8
Phe-Na2-1H2O
3650.7
3661.7
Phe-Na2-1H2O
3326.5
3251.6
Phe-Na3-1H2O
3750.0
3744.0
Phe-Na3-1H2O
3646.7
3647.0
Phe-Na3-1H2O
3629.3
3635.7
Phe-Na4-1H2O
3758.3
3829.1
Phe-Na4-1H2O
3654.0
3688.4
Phe-Na4-1H2O
3634.5
3635.7
Phe-Na5-1H2O
3766.0
3763.4
Phe-Na5-1H2O
3644.8
3654.3
Phe-Na5-1H2O
3372.9
3327.6
Phe-Na6-1H2O
3739.4
3736.8
Phe-Na6-1H2O
3626.3
3627.1
Phe-Na6-1H2O
3571.4
3570.7
(*) As commen ed in he ex , a co ec ion ac o is applied in o de o ep oduce he expe imen al
OH s e ching equency o phenol.
Appendix B
259
Appendix B
Table B.1. LMO-EDA pa i ion (kcal/mol) o he in e ac ion ene gy o complexes in he
manusc ip wi h equal a oma ic uni s, as ob ained a he M06-2X/aug-cc-pVDZ le el.
Elec os a ic
Exchange
Repulsion
Pola iza ion
Dispe sion
Bz-Bz-1
-15.05
-12.19
41.04
-9.69
-23.66
Bz-Bz-2
-15.89
-10.85
39.41
-10.19
-24.52
Bz-Bz-3
-16.09
-11.76
42.76
-9.13
-27.31
Bz-Bz-4
-19.61
-10.63
38.75
-12.78
-22.71
Ph-Ph-1
-35.71
-20.37
68.35
-16.88
-28.96
Ph-Ph-2
-33.56
-19.94
69.29
-16.11
-32.16
Ph-Ph-3
-32.52
-20.05
64.61
-19.78
-23.11
Ph-Ph-4
-29.29
-17.47
62.49
-12.44
-34.64
Ph-Ph-5
-34.16
-19.41
65.84
-15.35
-29.98
Ph-Ph-6
-30.16
-14.78
51.85
-15.85
-24.49
Ph-Ph-7
-34.13
-16.37
55.26
-16.20
-21.12
In-In-1
-24.12
-20.04
66.30
-14.00
-38.78
In-In-2
-26.13
-17.82
59.87
-14.72
-33.97
In-In-3
-26.70
-17.60
58.99
-15.93
-32.34
In-In-4
-26.89
-17.48
58.98
-15.72
-32.99
In-In-5
-29.66
-15.16
54.88
-16.34
-32.72
Alba Campo Cacha ón
266
.
Figu e C.2. In e ac ion ene gies ob ained o complexes o med by unsubs i u ed, CH3-
subs i u ed and CN-subs i u ed co annulene and sumanene wi h sodium ca ion by he
conca e (le ) and con ex ( igh ) aces o he bowls.
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-34
-32
-30
-28
-26
-24
-22
-20
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-34
-32
-30
-28
-26
-24
-22
-20
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-34
-32
-30
-28
-26
-24
-22
-20
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-34
-32
-30
-28
-26
-24
-22
-20
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a-in Co a-ou
Suma-in Suma-ou
Ene gy (kcal/mol)
Ene gy (kcal/mol)Ene gy (kcal/mol)
Ene gy (kcal/mol)
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-18
-16
-14
-12
-10
-8
-6
-4
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-20
-18
-16
-14
-12
-10
-8
-6
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-18
-16
-14
-12
-10
-8
-6
-4
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-18
-16
-14
-12
-10
-8
-6
-4
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-18
-16
-14
-12
-10
-8
-6
-4
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-18
-16
-14
-12
-10
-8
-6
-4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co aMe -in Co aMe -ou
SumaMe -in SumaMe -ou
SumaMe 2-in SumaMe 2-ou
Ene gy (kcal/mol)
Ene gy (kcal/mol)Ene gy (kcal/mol)
Ene gy (kcal/mol)Ene gy (kcal/mol)
Ene gy (kcal/mol)
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
2
4
6
8
10
12
14
16
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
2
4
6
8
10
12
14
16
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-6
-4
-2
0
2
4
6
8
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-6
-4
-2
0
2
4
6
8
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co aCN-in Co aCN-ou
SumaCN-in SumaCN-ou
SumaCN2-in SumaCN2-ou
Ene gy (kcal/mol)
Ene gy (kcal/mol)
Ene gy (kcal/mol)
Ene gy (kcal/mol)
Ene gy (kcal/mol)
Ene gy (kcal/mol)
Appendix C
267
Figu e C.3. Rela i e ene gy (in-ou ) o complexes o med by chlo ide anion wi h he
di e en bowls.
Figu e C.4. Rela i e ene gy (in-ou ) o complexes o med by sodium ca ion wi h he
di e en bowls.
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-12
-10
-8
-6
-4
-2
0
2
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co aF
SumaF
SumaF2
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
Ene gy (kcal/mol) Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-12
-10
-8
-6
-4
-2
0
2
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-12
-10
-8
-6
-4
-2
0
2
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co aMe
SumaMe
SumaMe 2
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-12
-10
-8
-6
-4
-2
0
2
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-12
-10
-8
-6
-4
-2
0
2
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-14
-12
-10
-8
-6
-4
-2
0
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co aCN
SumaCN
SumaCN2
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP
M062X
SAPT/scaledMP2.X/6-31G(0.25)
R (Å)
1,8 2,0 2,2 2,4 2,6 2,8 3,0 3,2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
1,8 2,0 2,2 2,4 2,6 2,8 3,0 3,2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
1,8 2,0 2,2 2,4 2,6 2,8 3,0 3,2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP
M062X
SAPT/scaledMP2.X/6-31G(0.25)
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
Co aF
SumaF
Co a
Suma
SumaF2
Ene gy (kcal/mol) Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-6
-4
-2
0
2
4
6
8
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP-D3BJ
M062X
SAPT/scaledMP2.X/6-31G(0.25)
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-4
-2
0
2
4
6
8
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-6
-4
-2
0
2
4
6
8
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP-D3BJ
M062X
SAPT/scaledMP2.X/6-31G(0.25)
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
R (Å)
2,4 2,6 2,8 3,0 3,2 3,4 3,6 3,8
E (kcal mol-1)
-10
-8
-6
-4
-2
0
2
4
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
BLYP-D3
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Co a
Suma
Co aCN
SumaCN
SumaCN2
Co aMe
SumaMe
SumaMe 2
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
Alba Campo Cacha ón
268
Figu e C.5. SAPT(DFT) ene gy decomposi ion o complexes o med by chlo ide anion
and unsubs i u ed, CH3-subs i u ed and CN-subs i u ed bowls. The e ical line indica es
he posi ion o he minimum ob ained a he MP2.X le el o calcula ion.
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
Eele -E ep
Eind Edis
E o
Eele -E ep
Eind Edis
E o
Co a-in Co a-ou
Suma-in Suma-ou
Ene gy (kcal/mol) Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
Eele -E ep
Eind Edis
E o
Co aMe -in Co aMe -ou
SumaMe -in SumaMe -ou
SumaMe 2-in SumaMe 2-ou
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
Eele -E ep
Eind Edis
E o
Co aCN-in Co aCN-ou
SumaCN-in SumaCN-ou
SumaCN2-in SumaCN2-ou
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
Appendix C
269
Figu e C.6. SAPT(DFT) ene gy decomposi ion o complexes o med by sodium ca ion
and unsubs i u ed, CH3-subs i u ed and CN-subs i u ed bowls. The e ical line indica es
he posi ion o he minimum ob ained a he MP2.X le el o calcula ion.
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP-D3BJ
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Eele -E ep
Eind Edis
E o
Co a-in Co a-ou
Suma-in Suma-ou
Ene gy (kcal/mol) Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Eele -E ep
Eind Edis
E o
Co aMe -in Co aMe -ou
SumaMe -in SumaMe -ou
SumaMe 2-in SumaMe 2-ou
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)
Ene gy (kcal/mol)
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
R (Å)
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
E (kcal mol-1)
-50
-40
-30
-20
-10
0
10
MP2/CBS
SCS-MP2/CBS
SCSN-MP2/CBS
MP2.X/6-31G*
MP2.X/6-31+G*
BLYP-D3BJ
M062X
SAPT/scaledMP2.X/6-31G(0.25)
Eele -E ep
Eind Edis
E o
Co aCN-in Co aCN-ou
SumaCN-in SumaCN-ou
SumaCN2-in SumaCN2-ou
Ene gy (kcal/mol) Ene gy (kcal/mol)Ene gy (kcal/mol)
Ene gy (kcal/mol) Ene gy (kcal/mol)
Ene gy (kcal/mol)
Alba Campo Cacha ón
270
Table C.1. SAPT(DFT) alues (kcal/mol) o complexes o med by he bowls and chlo ide
anion. The alues a e ob ained by in e pola ion o he SAPT(DFT) cu es a he
equilib ium geome y ob ained a he MP2.X/6-31G(0.25) le el (Table 8.1). Dispe sion
and dispe sion-exchange con ibu ions a e scaled by 1.193 as indica ed in he ex .
Eele
E ep
Eind
Edis
E o
CONCAVE/IN
co a
-6.01
21.32
-10.24
-12.76
-7.68
co aMe
-2.87
19.49
-11.17
-12.75
-7.31
Co aF
-20.62
27.80
-11.40
-14.37
-18.60
co aCN
-40.95
33.26
-14.66
-15.81
-38.16
suma
-8.33
22.41
-10.84
-13.71
-10.47
sumaMe
-5.46
20.21
-11.98
-13.82
-11.05
sumaF
-25.63
30.12
-12.17
-15.68
-23.38
sumaCN
-49.61
37.59
-16.23
-17.66
-45.91
suma
-8.33
22.41
-10.84
-13.71
-10.47
sumaMe 2
-10.55
24.96
-14.25
-16.29
-16.14
sumaF2
-25.46
34.77
-13.04
-16.94
-20.68
sumaCN2
-42.29
40.98
-16.86
-19.44
-37.61
CONVEX/OUT
co a
0.38
16.16
-10.48
-8.26
-2.20
co aMe
3.50
15.06
-11.00
-8.14
-0.57
Co aF
-11.34
21.72
-12.11
-9.54
-11.27
co aCN
-34.04
33.83
-17.61
-12.08
-29.90
suma
-0.64
16.52
-10.77
-8.59
-3.47
sumaMe
3.86
14.86
-11.28
-8.29
-0.85
sumaF
-12.76
21.13
-11.99
-9.66
-13.28
sumaCN
-39.72
33.96
-17.79
-12.43
-35.98
suma
-0.64
16.52
-10.77
-8.59
-3.47
sumaMe 2
-0.92
16.64
-11.72
-9.08
-5.07
sumaF2
-16.73
26.37
-13.73
-10.83
-14.92
sumaCN2
-30.67
33.23
-16.77
-12.46
-26.67
Appendix C
271
Table C.2. SAPT(DFT) alues (kcal/mol) o complexes o med by he bowls and sodium
ca ion. The alues a e ob ained by in e pola ion o he SAPT(DFT) cu es a he
equilib ium geome y ob ained a he MP2.X/6-31G(0.25) le el (Table 8.2). Dispe sion
and dispe sion-exchange con ibu ions a e scaled by 1.193 as indica ed in he ex .
Eele
E ep
Eind
Edis
E o
CONCAVE/IN
co a
-8.90
8.13
-24.56
-2.66
-27.99
co aMe
-12.89
9.02
-27.03
-2.83
-33.72
Co aF
4.62
6.59
-23.36
-2.41
-14.56
co aCN
24.26
4.40
-23.53
-1.99
3.15
suma
-8.06
8.24
-25.62
-2.80
-28.24
sumaMe
-12.36
9.33
-28.67
-3.01
-34.71
sumaF
7.53
7.04
-24.72
-2.62
-12.77
sumaCN
30.65
4.65
-25.08
-2.15
8.05
suma
-8.06
8.24
-25.62
-2.80
-28.24
sumaMe 2
-7.74
8.71
-29.05
-3.02
-31.10
sumaF2
7.32
5.08
-23.20
-2.31
-13.12
sumaCN2
20.53
2.69
-22.36
-1.78
-0.92
CONVEX/OUT
co a
-12.55
8.81
-23.66
-2.05
-29.46
co aMe
-16.52
9.51
-25.52
-2.15
-34.67
Co aF
-1.44
7.37
-22.65
-1.86
-18.58
co aCN
17.29
5.13
-22.61
-1.54
-1.73
suma
-10.54
7.73
-23.92
-2.06
-28.78
sumaMe
-15.88
8.56
-26.16
-2.18
-35.67
sumaF
1.31
6.39
-22.79
-1.85
-16.93
sumaCN
23.89
4.00
-22.70
-1.45
3.74
suma
-10.54
7.73
-23.92
-2.06
-28.78
sumaMe 2
-10.81
8.01
-25.42
-2.13
-30.35
sumaF2
4.16
5.21
-21.60
-1.67
-13.89
sumaCN2
15.16
3.37
-20.56
-1.34
-3.36
Appendix D
273
Appendix D
Figu e D.1. NCI plo s o he complexes o med by Co aCN (le ) and SumaCN2 ( igh )
and he anions s udied. Only complexes by he I line and he mos s able o ien a ion a e
shown. The p oduc o he densi y imes he sign o he second eigen alue o i s hessian
is mapped on o an isosu ace o educed densi y g adien wi h alue 0.5 a.u. The colo
scale goes om -0.015 a.u. (blue) o 0.015 a.u. ( ed).
Cl-
BF4-
NO3-
B -
ClO4-
CO2H-
Cl-
BF4-
NO3-
B -
ClO4-
CO2H-
