esea ch pape s
862 doi:10.1107/S0108768107045880 Ac a C ys . (2007). B63, 862–868
Ac a C ys allog aphica Sec ion B
S uc u al
Science
ISSN 0108-7681
Expe imen al and heo e ical cha ac e iza ion o
he Zn—Zn bond in [Zn
2
(g
5
-C
5
Me
5
)
2
]
Juan F. Van de Maelen,
a
*
En ique Gu ie
´ ez-Puebla,
b
A
´ngeles Monge,
b
San iago
Ga cı
´a-G anda,
a
I ene Resa,
c
E nes o Ca mona,
c
Ma ı
´a Te esa
Fe na
´ndez-Dı
´az,
d
Ga y J.
McIn y e,
d
Philip Pa ison
e
and
Hans-Pe e Webe
a
Depa amen o Quı
´mica Fı
´sica y Analı
´ ica,
Facul ad de Quı
´mica, A da. Julia
´n Cla e ı
´a8,
Uni e si y o O iedo, E-33006 O iedo, Spain,
b
Ins i u o de Ciencia de Ma e iales, Consejo
Supe io de In es igaciones Cien ı
´ icas, So
Juana Ine
´s de la C uz 3, E-28049 Mad id, Spain,
c
Ins i u o de In es igaciones Quı
´micas, Consejo
Supe io de In es igaciones Cien ı
´ icas, Ame
´ ico
Vespucio 49, E-41092 Se illa, Spain,
d
Ins i u
Laue–Lange in, A . des Ma y s BP 156, F-
38042 G enoble CEDEX, F ance,
e
Swiss-
No wegian Beam Lines, Eu opean Synch o on
Radia ion Facili y, Jules Ho owi z 6, BP 220,
F-38043 G enoble CEDEX, F ance, and
Labo a o y o C ys allog aphy, Swiss Fede al
Ins i u e o Technology, CH-1015 Lausanne,
Swi ze land
Co espondence e-mail: [email p o ec ed]
#2007 In e na ional Union o C ys allog aphy
P in ed in Singapo e – all igh s ese ed
The exis ence and cha ac e iza ion o a bond be ween he Zn
a oms in he ecen ly syn hesized complex [Zn
2
(
5
-C
5
Me
5
)
2
],
as well as be ween Zn and ligand C a oms is i mly based on
neu on di ac ion and low- empe a u e X- ay synch o on
di ac ion expe imen s. The mul ipola analysis o he
expe imen al elec on densi y and i s opological analysis by
means o he ‘A oms in Molecules’ (AIM) app oach e eals
de ails o he Zn—Zn bond, such as i s open-shell in e -
media e cha ac e ( he esul s a e consis en wi h a ypical
me al–me al single bond), as well as many o he opological
p ope ies o he compound. Expe imen al esul s a e also
compa ed wi h heo e ical ab ini io calcula ions o he DFT
(densi y unc ional heo y) and MP2 (Mølle -Plesse pe u -
ba ion heo y) elec on densi ies, gi ing a cohe en iew o he
bonding in he complex. Fo ins ance, cha ges calcula ed om
he AIM app oach applied o he a omic basin o each Zn
a om a e, on a e age, +0.72 e om bo h he expe imen al and
he heo e ical elec on densi y, showing a mode a e cha ge
ans e om he me al, con i med by he calcula ed
opological indexes.
Recei ed 23 May 2007
Accep ed 18 Sep embe 2007
1. In oduc ion
Recen ly, we epo ed (Resa e al., 2004) he i s s able
molecula compound o zinc wi h a me al–me al bond,
bis[1,2(
5
)-pen ame hylcyclopen adienyl]dizinc(II)(Zn—Zn),
[Zn
2
(
5
-C
5
Me
5
)
2
] (1), which a ac ed g ea in e es in he
scien i ic communi y, and consequen ly h ee new species ha e
been ecen ly s udied (Wang e al., 2005; Zhu e al., 2006;
G i ane e al., 2007). These compounds ha e been cha -
ac e ized by a numbe o echniques (including NMR, IR and
Raman spec oscopies, and con en ional X- ay single-c ys al
di ac ion) in o de o demons a e, among o he hings, he
absence o any b idging H a om be ween he Zn a oms. The
appea ance o such an elusi e me al–me al bond, in spi e o
he ac ha o ganozinc compounds ha e been well known
since he ea ly days o o ganome allic chemis y, mo ed us o
s udy synch o on X- ay di ac ion da a, and also he heo-
e ical opological p ope ies o he Zn—Zn bond.
Se e al heo e ical calcula ions dedica ed o (1) and ela ed
compounds ha e been published o da e (Del Rı
´oe al., 2005;
Xie, Schae e III & Jemmis, 2005; Xie, Schae e III & King,
2005; Timoshkin & Schae e III, 2005; Xie & Fang, 2005; K ess,
2005; Kang, 2005; Philpo & Kawazoe, 2006a,b; Pa hak e al.,
2006). These s udies, based on he molecula o bi al (MO)
app oach, ha e ound he minima in he po en ial ene gy
su ace o (1), wi h geome ies ha closely esemble he
p e iously published expe imen al geome y. They ha e also
shown ha he Zn—Zn bond is compa able in s abili y o
o he me al–me al bonds, wi h dissocia ion ene gies calcula ed
be ween 259.58 and 309.82 kJ mol
1
depending on he heo-
e ical model used (Xie & Fang, 2005; G i ane e al., 2007). As
a as we know, no s udies ela ed o he opological p ope ies
o he Zn—Zn bond, ei he om a heo e ical o an expe i-
men al poin o iew, ha e been published so a , al hough
some au ho s ha e men ioned he u gen need o such s udies
(Philpo & Kawazoe, 2006a). Ou heo e ical app oach o his
p oblem is based on he Quan um Theo y o A oms in
Molecules (QTAM o AIM; Bade , 1990) and cen ed no only
on he Zn—Zn bond, bu also co e ing he Zn–ligand bonds.
This ea men is complemen a y o he abo e-men ioned
s udies gi ing a ully cohe en and mo e comple e iew o he
bonding in (1) when combined wi h he MO calcula ions
while, on he o he hand, ha ing he addi ional ad an age o
being equally applicable o bo h expe imen al and heo e ical
elec on densi ies.
2. Expe imen al and
compu a ional de ails
2.1. Neu on di ac ion expe imen
A pla e-like single c ys al wi h
maximum dimensions 2 1
0.3 mm
3
was plucked om a pool o
poly lo ine he oil using a s anda d
1 mm diame e anadium pin, and
placed quickly in he p e-cooled
helium- low c yos a o he new Ve y-
In ense Ve ical-Axis Laue Di ac -
ome e (VIVALDI) a he Ins i u
Laue Lange in (ILL) in G enoble
(F ance) o he neu on di ac ion
expe imen . VIVALDI uses he Laue
di ac ion echnique on an unmono-
ch oma ed he mal-neu on beam
and wi h a la ge solid-angle (8 s e ad)
cylind ical image-pla e de ec o
(Wilkinson e al., 2002) o inc ease he
de ec ed di ac ed in ensi y by one-
o- wo o de s o magni ude compa ed
wi h a con en ional monoch oma ic
expe imen . The e we e 17 Laue
di ac ion pa e ns, each accumu-
la ed o e 2.5 h, collec ed a 170 K
ypically in 10in e als du ing he
o a ion o he c ys al pe pendicula
o he inciden neu on beam. The
pa e ns we e indexed using he
p og am LAUEGEN o he Da es-
bu y Labo a o y Laue Sui e (Camp-
bell, 1995; Campbell e al., 1998) and
he e lec ions in eg a ed using he
local p og am ARGONNE_BOXES,
which uses a wo-dimensional e sion
o he (I)/Ialgo i hm (Wilkinson e
al., 1988). No co ec ion o abso p-
ion was deemed necessa y in iew o
he small c ys al dimensions. The in eg a ed e lec ions we e
no malized o a common inciden wa eleng h, using a cu e
de i ed by compa ing equi alen e lec ions and mul iple
obse a ions, ia he p og am LAUENORM (Campbell e al.,
1986). Re lec ions we e obse ed wi h wa eleng hs be ween
0.85 and 3.56 A
˚, bu only e lec ions wi h wa eleng hs less
han 3.0 A
˚we e accep ed o scaling, as e lec ions a longe
wa eleng h had oo ew equi alen s o be able o de e mine
he no maliza ion cu e wi h con idence. In all, 12 265
e lec ions we e obse ed, o which 8553 we e single well-
esol ed e lec ions wi h wa eleng hs be ween 0.85 and 3.0 A
˚,
which yielded 1665 unique e lec ions, co esponding o 73.7%
o he possible unique e lec ions o dspacings > 0.96 A
˚, he
minimum dspacing obse ed. The con en ional X- ay single-
c ys al pa ame e s o non-H a oms (Resa e al., 2004) we e
used as he ini ial model. The H a oms we e all loca ed om
di e ence-Fou ie maps. Re inemen s we e ca ied ou using
esea ch pape s
Ac a C ys . (2007). B63, 862–868 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond 863
Table 1
Expe imen al de ails.
X- ay Neu on
C ys al da a
Chemical o mula C
20
H
30
Zn
2
C
20
H
30
Zn
2
M
401.18 401.18
Cell se ing, space g oup T iclinic, P
11 T iclinic, P
11
Tempe a u e (K) 100 (1) 170 (2)
a,b,c(A
˚) 6.9115 (6), 10.889 (1), 13.893 (1) 6.9329 (3), 10.8831 (5), 13.8384 (7)
,,() 109.91 (1), 101.551 (8), 93.905 (9) 109.777 (1), 101.603 (1), 94.201 (1)
V(A
˚
3
) 952.6 (2) 951.09 (8)
Z22
D
x
(Mg m
3
) 1.399 1.452
Radia ion ype Synch o on Whi e beam
(mm
1
)2.51 –
C ys al o m, colo Pla e, colo less P isma ic, colo less
C ys al size (mm) 0.70 0.70 0.05 2.0 1.0 0.3
Da a collec ion
Di ac ome e CCD a ea de ec o VIVALDI
Da a collec ion me hod ’and !scans Laue
Abso p ion co ec ion Mul i-scan (based on symme y-
ela ed measu emen s)
None
T
min
0.272 –
T
max
0.881 –
No. o measu ed, independen
and obse ed e lec ions
57 003, 13 873, 12 354 8553, 1665, 985
C i e ion o obse ed
e lec ions
I>2(I)I>2(I)
R
in
0.054 0.364

max
() 43.5 21.8
Re inemen
Re inemen on FF
2
R[F
2
>2(F
2
)], wR(F
2
), S0.036, 0.040, 1.09 0.105, 0.264, 1.08
No. o e lec ions 11 249 1665
No. o pa ame e s 782 469
H-a om ea men Mix u e o independen and
cons ained e inemen
Mix u e o independen and
cons ained e inemen
Weigh ing scheme w= 1/[
2
(F
o
)] w= 1/[
2
(F2
o) + (0.1322P)
2
], whe e
P=(F2
o+2F2
c)/3
(/)
max
0.047 0.032

max
,
min
(e A
˚
–3
) 0.59, 0.48 0.67, 0.60
Compu e p og ams used: C ysAlis CCD and C ysAlis RED (Ox o d Di ac ion, 2004), SORTAV (Blessing, 1989),
SHELXL97 (Sheld ick, 1997), XD2006 (Volko e al., 2006).
SHELXL97 (Sheld ick, 1997) by ull-ma ix leas -squa es
analysis wi h aniso opic displacemen pa ame e s o all
a oms, including H a oms, wi h he la e conside ed as iding
on hei me hyl g oups. No diso de ea men was applied
he e o he me hyl g oups. Fu he de ails a e gi en in Table 1
and he molecula geome y ob ained is shown in Fig. 1. As
may be clea ly seen in Fig. 1, no b idging H a oms we e ound
be ween he Zn a oms. This esul was he main pu pose o he
neu on di ac ion expe imen , i.e. o elimina e he emo e
possibili y o ha ing missed b idging hyd ide ligands in he
p io expe imen al s udies, as ce ainly happened in he well
known p oposed cobal compound [Co
2
(
5
-
C
5
Me
5
)
2
], i s ly epo ed as ha ing a Co—Co
bond bu which, in ac , is a hyd ide (Ke s en
e al., 1992). Fo he expe imen al cha ge-
densi y s udy he esul s we e ob ained om
he synch o on X- ay expe imen wi hou he
use o neu on da a.
2.2. Synch o on X- ay di ac ion expe imen
In o de o ob ain be e da a o he
mul ipola e inemen han he da a collec ed p e iously om
con en ional X- ay di ac ion, a synch o on di ac ion
expe imen was pe o med. A lamina colo less single c ys al
o 0.70 0.70 0.05 mm
3
was selec ed. Measu emen s we e
ca ied ou a he BM01A (Swiss–No wegian Beam Line) o
he Eu opean Synch o on Radia ion Facili y (ESRF) in
G enoble (F ance). Da a collec ion was ia a KUMA KM6-
CH (equipped wi h a CCD de ec o ) six-ci cle single-c ys al
di ac ome e , u ilized as a s anda d ou -ci cle ins umen .
The da a collec ion empe a u e, con olled by an Ox o d
c yos eam cooling sys em, was 100 (1) K, and he wa eleng h
o he adia ion used was 0.71 A
˚.
1
The expe imen al s a egy
was as ollows:
(i) a good di ac ing c ys al was selec ed ( he c ys al was
moun ed on he di ac ome e and a couple o ames we e
obse ed p io o s a ing he comple e da a collec ion);
(ii) a ound 20 ames we e hen collec ed o indexing
pu poses;
(iii) a un o ca 2 h o da a collec ion was hen used o y
and sol e he s uc u e;
(i ) inally he ull da ase was collec ed.
In ac , h ee di e en da ase s we e collec ed a his s age: a
high-angle da ase , using no il e , was collec ed i s ; hen a
low-angle da ase was collec ed using a 50 mm Cu il e ; inally
a e y low-angle da a collec ion was pe o med wi h a 100 mm
Cu il e . A o al o 57 003 e lec ions we e measu ed
[(sin /)
max
=1.08A
˚
1
], co e ing 90.3% o all possible
e lec ions om = 2.01 o 
max
. Da a educ ion was hen
applied using he SORTAV p og am (Blessing, 1989), gi ing a
o al o 13 873 unique e lec ions (R
in
= 0.054), and an
abso p ion co ec ion was also applied using SADABS
(Sheld ick, 2003; Blessing, 1995). Solu ion and s anda d
(sphe ical a oms) e inemen we e made using he WinGX
p og am package (Fa ugia, 2005). Some diso de in he
me hyl g oups was obse ed du ing he e inemen and
he e o e some we e spli in o wo componen s in o de o
p e en hem om being non-posi i e de ini e using he usual
cons ain s (Van de Maelen U ı
´a & Sheld ick, 1996; Van de
Maelen U ı
´a, 1999). Fu he de ails o his expe imen a e
gi en in Table 1.
2
A selec ion o he molecula geome y da a,
compa ed wi h he esul s om neu on di ac ion, is shown
esea ch pape s
864 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond Ac a C ys . (2007). B63, 862–868
Table 2
Selec ed molecula geome y da a (A
˚,) o (1).
Bond dis ance o angle Con en ional X- ay† Neu on di ac ion‡ Mul ipole X- ay‡
Zn—Zn 2.305 (3) 2.292 (1) 2.3186 (3)
Zn—C§ 2.268 (2)–2.306 (2) 2.272 (4)–2.326 (3) 2.2756 (12)–2.3132 (9)
Zn—Zn—C§ 145.72 (6)–150.52 (6) 145.2 (4)–150.2 (4) 145.12 (6)–150.65 (4)
† Da a om Resa e al. (2004). ‡ This wo k. § Lowes and highes alues; indi idual alues may be ound
in he supplemen a y ma e ial (Tables S1 and S2).
Figu e 1
Displacemen ellipsoid plo o (1) om he neu on di ac ion
expe imen , d awn a he 80% p obabili y le el, showing he a omic
labelling scheme (labels o H a oms a e omi ed o cla i y).
1
In ou p oposal o he expe imen , di e en expe imen al condi ions we e
asked o : a wa eleng h o 0.5 A
˚and a empe a u e o 10 K, bu only a mo e
s anda d se -up was made a ailable.
2
Supplemen a y da a o his pape a e a ailable om he IUC elec onic
a chi es (Re e ence: BS5050). Se ices o accessing hese da a a e desc ibed
a he back o he jou nal.
in Table 2. All in all, due mainly o a g ea e edundancy o he
da a collec ed, a be e p ecision han in he con en ional X-
ay di ac ion expe imen was achie ed, as e lec ed in he
lowe s anda d de ia ions (see x3 o mo e de ailed
commen s).
2.3. Mul ipole e inemen
The mul ipole e inemen was ca ied ou by means o he
p og am XD2006 (Volko e al., 2006), which uses he
Hansen–Coppens o malism o he asphe ical a omic densi y
expansion (Hansen & Coppens, 1978). Se e al models we e
ied, bu he bes esul s we e ob ained wi h a ea men ha
p oceeded as ollows. Hexadecapole ep esen a ion was used
o he Zn and C a oms, while he H a oms we e ea ed as
o ien ed dipoles, wi h hei coo dina es ixed, du ing he ea ly
s ages o he mul ipole e inemen p ocess, a he posi ions
ound in he sphe ical-a om e inemen . An a e age dis ance
o 1.0495 A
˚, ob ained om he neu on di ac ion expe i-
men , was used la e as a cons ain o all he C—H bond
dis ances. Radial pa s o co e, sphe ical- alence and de o -
ma ion- alence densi ies we e all cons uc ed using ela i is ic
Di ac–Fock a omic wa e unc ions expanded o e Sla e - ype
basis se s o he Zn a oms (Su & Coppens, 1998), while o C
and H a oms he adial pa s o he de o ma ion alence
densi ies we e single-Sla e - ype unc ions. Fu he
cons ain s we e used o keep he e ined pa ame e s o all he
H a oms wi hin each me hyl g oup equal. Radial scaling
pa ame e s o he sphe ical and de o ma ion pa s o he
alence densi y (and 0
l;l= 0–4) we e independen ly e ined
o bo h Zn a oms, while o he C a oms only and 0
0we e
independen ly e ined, using he cons ain 0
l=0
0(l= 1–4) o
he o he scaling pa ame e s. Fo he H a oms all hese
pa ame e s we e le ixed o hei de aul alues. In addi ion,
occupa ion ac o s o he wo componen s o he diso de ed
me hyl g oups ha we e spli du ing he sphe ical a om
e inemen we e le ixed a hei ea lie alues (P
al
pa a-
me e s). A o al o 782 pa ame e s we e e ined agains he
11 249 ‘obse ed’ e lec ions [F>3(F)] included in he
e inemen (N
e
/N
pa
= 14.4). The inal con en ional R ac o
o e Fwas 0.036 o he ‘obse ed’ e lec ions and 0.043 o
he whole se o unique e lec ions. Re inemen alues gi en in
Table 1 a e o wha we conside o be he ‘bes ’ expe imen al
model (BE model), in he sense ha i has he bes inal
s a is ical indexes (R,S,
max,min
, di e ence Fou ie map,
con e gence c i e ia e c.), bu we also used o he mul ipole
models in he opological calcula ions in o de o u he
check hei accu acy agains opological indexes (see below).
2.4. Expe imen al and heo e ical opological calcula ions
The XDPROP module o he p og am XD2006 (Volko e
al., 2006) was used o s udy he opological p ope ies o he
expe imen al elec on densi y by means o he AIM app oach
(Bade , 1990; Coppens, 1997). Bo h local (loca ion o c i ical
poin s and bond-pa h analyses, among o he s) and in eg al
p ope ies (a omic cha ges, olumes, dipole momen s e c.)
we e calcula ed. Usually he calcula ions we e ca ied ou
using he de aul alues gi en by he p og am o he di e en
con ol pa ame e s; howe e , o he in eg al p ope ies
se e al in eg a ion pa ame e s had o be es ed and modi ied
in o de o inc ease he accu acy o he esul s. The be a-
sphe e adii o he a oms we e aken, o he in eg a ions, as
he dis ance be ween he a om nucleus and i s closes bond-
c i ical poin (b.c.p.). S a ing om he ‘bes ’ expe imen al
model ob ained in he mul ipola e inemen , as de ined
abo e, he p ocedu e ollowed was able o ind all he b.c.p.s in
he molecule, whe eas o he o he models se e al b.c.p.s
we e ei he missing o loca ed a odd posi ions (e.g. be ween
he H a oms o di e en me hyl g oups). Acco dingly, only he
BE model was used o ob ain he compu a ionally leng hy
in eg al p ope ies.
On he o he hand, bo h molecula geome ies ob ained
om neu on and X- ay di ac ion expe imen s we e used o
he heo e ical elec onic s uc u e calcula ions pe o med
using he GAUSSIAN03 p og am package (F isch e al., 2004).
The elec onic s uc u e calcula ions we e pe o med on he
expe imen al geome ies using bo h DFT and ab ini io
pe u ba ion heo y me hods. The ollowing me hods we e
used: he hyb ids B3LYP, B3P86 and B3PW91 Becke’s h ee-
pa ame e exchange unc ional (Becke, 1993) wi h he non-
local Lee-Yang-Pa (Lee e al., 1988), Pe dew (Pe dew, 1986)
and Pe dew-Wang (Pe dew e al., 1996) co ela ion unc-
ionals, espec i ely, and he Vosko–Wilk–Nusai local co e-
la ion unc ional (Vosko e al., 1980), oge he wi h he
Mølle –Plesse MP2 and MP3 me hods we e ied. All-elec-
on s anda d basis se s 6-31G(d), 6-31G(d,p) and 6-311G(d,p)
ha e been used o all a oms as is usual o o he calcula ions
o o ganome allic compounds (Van de Maelen U ı
´ae al.,
2003, 2005). The g ound-s a e elec onic wa e unc ions
ob ained we e hen used o u he calcula ions on he
opology o he heo e ical elec on densi y, including bo h
local and in eg al p ope ies, pe o med wi h he aid o he
p og am AIM2000 (Biegle -Ko
¨nig & Scho
¨nbohm, 2002). The
accu acy o he in eg a ed p ope ies was inally se a 1.0 
10
4
om he Laplacian o he in eg a ed elec on densi y,
whe eas o he local p ope ies he accu acy was much
g ea e (1.0 10
10
om he g adien o he elec on densi y
a he b.c.p.s). Some heo e ical models (a combina ion o
molecula geome y, me hod and basis se ) we e able o ind
all he b.c.p.s ound om he ‘bes ’ expe imen al (BE) model,
bu he bes esul s, in he sense ha heo e ical local p op-
e ies we e close o he expe imen al ones, we e ob ained
using he MP2/6-311G(d,p) model wi h he neu on di ac ion
geome y (BT model). In ac , some calcula ions made on he
X- ay di ac ion geome y we e e en unable o ind he Zn—
Zn b.c.p. Consequen ly, in eg al p ope ies we e hen calcu-
la ed using only he BT model, which we call he ‘bes ’ heo-
e ical model.
3. Resul s and discussion
Neu on di ac ion expe imen s ca ied ou a he ILL (see
x2) p o ided us bo h wi h expe imen al e idence o he
absence o b idging H a oms be ween he Zn a oms in (1), and
esea ch pape s
Ac a C ys . (2007). B63, 862–868 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond 865
wi h he nuclea coo dina es o be used in he heo e ical
elec onic s uc u e calcula ions, as explained ea lie . The
molecula geome y, shown in Fig. 1, does no di e much
om he p e ious esul s (Resa e al., 2004), gi ing he ypical
sandwich s uc u e al eady p oposed. In Table 2 some ele an
bond dis ances and angles ob ained om he neu on
di ac ion da a and om he X- ay synch o on di ac ion
da a a e compa ed wi h p e iously a ailable alues om
con en ional X- ay di ac ion. As may be seen om he able,
he Zn—Zn dis ance ob ained om he neu on di ac ion
expe imen is sho e han he dis ances ound om bo h X-
ay da a, whe eas he Zn—C dis ances a e only sligh ly longe
and he main bond angles a e almos he same. The neu on
Zn—Zn dis ance in (1) is e en sho e han he same dis ance
in he bulk me al, so he e could be an ex a epulsion om
he co e elec ons o he wo me al a oms ha would push
hem away om he in e me allic egion, he e o e gi ing an
X- ay dis ance la ge han he neu on alue. Published
heo e ical calcula ions o he op imized geome y o (1)
show Zn—Zn dis ances o e a wide ange, a ying om 2.287
o 2.339 A
˚, depending on he heo e ical model used (G i ane
e al., 2007; K ess, 2005; Xie & Fang, 2005). On he o he hand,
con en ional X- ay expe imen al da a ob ained o wo
ecen ly syn hesized compounds, Zn
2
[{(2,6-
i
P
2
C
6
H
3
)-
N(Me)C}
2
CH]
2
(Wang e al., 2005) and Zn
2
{C
6
H
3
-2,6-(C
6
H
3
-
2,6-
i
P
2
)
2
}
2
(Zhu e al., 2006), ga e Zn—Zn dis ances o
2.3586 (7) and 2.3591 (9) A
˚, espec i ely.
In o de o ob ain good quali y elec on densi ies sui able
o an expe imen al opological analysis (Coppens, 1997;
Ko i sanszky & Coppens, 2001; Coppens e al., 2005) we
ca ied ou a mul ipola analysis o he expe imen al elec on
densi y ob ained om he synch o on X- ay da a desc ibed in
x2, ollowed by he applica ion o he AIM app oach (Bade ,
1990). This analysis ga e a consis en iew o a ully connec ed
molecule, including he comple e se o one b.c.p. be ween he
Zn a oms, 10 b.c.p.s be ween Zn and C a oms, 20 b.c.p.s o he
C—C bonds and 30 b.c.p.s o he C—H bonds, oge he wi h
he 12 ing c i ical poin s ( .c.p.) and wo cage c i ical poin s
(c.c.p.). In Fig. 2 a g adien ajec o y map o (1) is shown,
whe e he c i ical poin and he bond pa h (b.p.) be ween he
Zn a oms a e clea ly seen. Also shown a e he b.c.p.s and b.p.s
ound be ween each o he Zn a oms, and he C-Me g oup in
he ligand ing loca ed in he plane o he plo . Owing o he
(nea ly) cylind ical symme y o he molecule, he image in
Fig. 2 may be o a ed a ound he Zn—Zn axis o ob ain a
comple e pic u e o he elec on-densi y g adien ield. In ac ,
e y simila plo s a e ound i di e en planes a e selec ed.
Fu he mo e, ou heo e ical calcula ions made a he ab ini io
le el show esul s ha closely esemble expe imen al calcu-
la ions. Fo ins ance, cha ges calcula ed om he AIM
app oach applied o he a omic basin o each Zn a om a e, on
a e age, +0.720 e om he expe imen al elec on densi y and
esea ch pape s
866 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond Ac a C ys . (2007). B63, 862–868
Figu e 2
G adien ajec o ies mapped on a o al densi y plo (con ou le els a
0.1 e A
˚
3
) o he Zn2—Zn1—C1 plane o (1). B.c.p.s ( ed ci cles) and
b.p.s (dashed lines) a e also shown.
Figu e 3
Th ee-dimensional ep esen a ion o he molecula elec os a ic po en ial
mapped on an elec on densi y isosu ace. Colo codes om +0.567 (da k
blue) o 0.002 e A
˚
1
(da k ed). Densi y con ou alue: 0.27 e A
˚
3
.

+0.725 e om he heo e ical elec on densi y. These alues
a e sligh ly lowe han he o mal cha ge o +1 e empi ically
pos ula ed o he Zn a oms in (1) and, compa ed wi h o he
heo e ical alues ob ained om MO app oaches (Resa e al.,
2004; Kang, 2005; K ess, 2005; G i ane e al., 2007), sugges
he exis ence o a ce ain amoun o cha ge ans e om he
ligands (see below). Acco dingly, a e age expe imen al and
heo e ical cha ges o he en C a oms o he wo Cp
*
ings
a e 0.39 and 0.27 e, espec i ely. Fig. 3 shows he expe i-
men al elec os a ic po en ial mapped on an elec on densi y
isosu ace.
In Table 3 a summa y o he opological p ope ies calcu-
la ed om bo h expe imen al and heo e ical elec on densi-
ies is shown. As clea ly seen in he able, he expe imen al
alue o he Zn—Zn bond leng h calcula ed om he bond
pa h (see Fig. 2) ma ches almos pe ec ly he X- ay
synch o on in e a omic dis ance (Table 2), hence showing no
bending in he bond pa h. Al hough he heo e ical alue
e lec s a sligh bending, gi ing a di e ence o only 0.15 A
˚
be ween he heo e ical bond-pa h leng h and he expe i-
men al in e a omic dis ance, i is ai o conclude ha his is a
nea ly pe ec bond, a esul which is con i med by he
ex emely low ellip ici y calcula ed o his bond (0.001). This
esul is in line wi h p e ious esul s, based on NBO and
simila MO analyses (K ess, 2005; G i ane e al., 2007), which
show ha he Zn—Zn bond is mainly o med by in e ac ion o
he 4sme al o bi als, al hough wi h small con ibu ions om
p

and d

o bi als (Philpo & Kawazoe, 2006a). Cu en bond
classi ica ions based on he a omic alence shell o molecules
in ol ing hea y a oms make use o bo h local (a he b.c.p.)
and in eg al (o e he a omic basin) p ope ies (Macchi e al.,
2002; Macchi & Si oni, 2003; Ge asio e al., 2004, 2005; Ga i,
2005). Among he o me , he elec on densi y (
b
), he
Laplacian o he elec on densi y (
2

b
), he o al ene gy
densi y a io (H
b
/
b
) and he kine ic-ene gy densi y a io (G
b
/

b
), wi h H( )=G( )+V( )and1
4
2
( )=2G( )+V( )[V( )is
he po en ial ene gy densi y], a e by a he mos common.
F om he alues in Table 3 i is clea ha he Zn—Zn bond in
(1) is a ypical open-shell me al–me al bond (e.g. Co—Co,
Macchi e al., 2002; Macchi & Si oni, 2003; o Ru—Ru, S ash e
al., 2005), which di e s om a pu e co alen bond (such as
C—C in e hane). This esul is con i med by he in eg al
p ope ies lis ed in Table 3, i.e. he delocaliza ion index, 
(Zn—Zn), and he elec on densi y in eg a ed o e he whole
Zn—Zn in e a omic su ace, HZn Zn ð Þ. The o me is indeed
nea ly equal o he o mal bond o de o 1.0, showing ha
he e is jus one elec on pai sha ed by he wo a oms, while
he la e has a alue compa able in magni ude o ha o pu e
co alen bonds (2.16 o he C—C bond in e hane; Ga i, 2005,
and e e ences he ein), despi e he ac ha 
b
is one o de o
magni ude lowe o (1).
Some opological p ope ies o he Zn—Cp
*
in e ac ions
a e also lis ed in Table 3. The e is mo e li e a u e on he
opological p ope ies o me al–ligand bonds han o me al–
me al bonds, bu hey a e mainly cen ed on me al–CO
in e ac ions (Pille e al., 2003; S ash e al., 2005; Fa ugia e al.,
2006). I is no unusual o ind jus one bond pa h be ween a
me al and a -bound ligand simila o Cp
*
(e.g. he Z –indenyl
in e ac ions; S ash e al., 2005). As men ioned abo e, a mos
ema kable ea u e o he opological analysis o he Zn—C
in e ac ions in (1) is ha some, al hough no all, o he models
ied, bo h expe imen al and heo e ical, p o ided he en
b.c.p.s and bond pa hs be ween he Zn and C a oms, a pai o
which is shown in Fig. 2. The e o e, in his case i is ai o
conclude ha we a e conce ned he e wi h eal bonds, no jus
‘in e ac ions’, in he sense ha eal bond pa hs ha e been
ound be ween Zn and C a oms. The opological pa ame e s
also e lec his ac ; o ins ance, he alue o he delocaliza-
ion index lis ed in Table 3 o each o he i e Zn—C bonds is
la ge enough o con i m he abo e asse ion and, in addi ion,
sugges s han jus one elec on pai is sha ed be ween a Zn
a om and i s bonded Cp
*
ing. The alues o he o he
opological magni udes shown in he able a e e y simila o
hose ound in o he me al—C bonds, no ably some Z —
C(indenyl) (S ash e al., 2005) and Z —C(imine) (Pille e al.,
2003) bonds. Acco ding o he classi ica ion o Macchi and
Si oni (Macchi & Si oni, 2003), hey a e no pu ely ionic bonds
bu hey may be labelled as dono –accep o bonds, wi h a
mode a e cha ge ans e e ealed by he ela i ely modes
alue o HZn Cð Þ. Mo eo e , since he a e age expe imen al
bond pa h leng h o he Zn—C bond in (1) di e s only
sligh ly om he a e age expe imen al in e a omic dis ance
(0.03 A
˚), i can be said ha hese a e nea ly s aigh bonds and
he e o e he e is a nea ly pu e ans e o app oxima ely one
elec on om each me al a om o i s ligand. Finally, om he
clea ly la ge alues ound o he expe imen al (3.21) and
heo e ical (4.20) ellip ici ies, i mus be concluded ha he
Zn—C bonds in (1) ha e a de ini e cha ac e , in ag eemen
wi h p e ious heo e ical s udies based on MO heo y (Xie &
Fang, 2005; Philpo & Kawazoe, 2006a,b).
esea ch pape s
Ac a C ys . (2007). B63, 862–868 Juan F. Van de Maelen e al. Cha ac e iza ion o he Zn—Zn bond 867
Table 3
Selec ed expe imen al ( i s ow) and heo e ical [second ow, MP2/6-3111G(d,p) le el] opological pa ame e s o (1).
d
A–B
: bond pa h leng h; 
b
: elec on densi y a he b.c.p.;
2

b
: Laplacian o he elec on densi y a he b.c.p.; H
b
/
b
: o al ene gy densi y a io a he b.c.p. (see ex );
G
b
/
b
: kine ic ene gy densi y a io a he b.c.p.; (A–B): delocaliza ion index (see ex ); HA B: in eg a ed elec on densi y (see ex ).
Bond dis ance d
A–B
(A
˚)
b
(e A
˚
3
)
2

b
(e A
˚
5
)H
b
/
b
(h e
1
)G
b
/
b
(h e
1
)(A–B)HA B(e A
˚
1
)
Zn—Zn 2.3206 (3) 0.348 (3) 1.824 (17)
2.1657 0.426 1.622 0.361 0.627 0.919 1.252
Zn—C† 2.2642 (12) 0.398 (8) 1.952 (20)
2.1699 0.332 3.922 0.160 1.118 0.225 0.254
† A e age alues.
4. Conclusions
In summa y, he exis ence and cha ac e iza ion o a bond
be ween he Zn a oms in he complex [Zn
2
(
5
-C
5
Me
5
)
2
], as
well as be ween he Zn and he Cp
*
C a oms, ha e been i mly
based on neu on di ac ion and low- empe a u e X- ay
synch o on di ac ion expe imen s, oge he wi h he mul i-
pola analysis o he expe imen al elec on densi y and he
opological analysis ia he AIM app oach o bo h he
expe imen al and he heo e ical elec on densi y. Fu he
s udies on his complex based on maps o he Laplacian o he
elec on densi y, as well as o he p ope ies, including he
opological analysis o he ligands hemsel es, a e in p og ess
in ou labo a o y.
Financial suppo om he Spanish Minis e io de Educa-
cio
´n y Ciencia (MAT2006-01997 and ‘Fac o ı
´a de C is aliza-
cio
´n’ Consolide -Ingenio 2010) is g a e ully acknowledged.
We also like o hank he Co-edi o and he e e ees, whose
help ul commen s and sugges ions much imp o ed he o iginal
manusc ip .
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