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On the Bonding in Carbosilanes.

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acts as a mass marker. This avoids the problem of imprecise
mass assignment that occasionally arises when using the
"linked-scan'' method. For the neutralization of the Cki and
CsOHe'+ions (Fig. 2d) an experiment analogous to that described for the spectrum in Figure 2 c was performed as follows: To obtain the highest possible yield of neutral species
in the electron transfer processes, a neutralization gas was
used whose ionization energy (IE) lies close to the IE of C,,
(7.6 eV)r141(condition of near resonant electron transfer).
From a great many neutralization experiments on C;' clust e r ~ [ (CH,),N
'~~
(IE =7.8 eV)['61 proved to be of the best
reducing agents for C,:. Thus collision cell C 5 was charged
with (CH,),N at a pressure that reduced the beam transmission to approximately 10%. All unreacted ions were removed from the beam by maintaining the deflector electrode
at 1000 eV so that only the beam of neutral species entered
collision cell C 6. In this cell a fraction of the neutral species
was reionized by collision-induced ionization with (CH,),N
as a target gas. Since the energy required for the collision-induced reionization was taken from the translational energy
of the mjz 724 ion beam, the voltage applied to sector E 2 was
reduced slightly so that the C,oHe'+ signal was detected at
optimal transmission.
As shown in Figure 2d, the recovery.signa1 for C,,He
shows up very clearly. This demonstrates unequivocally the
existence of a species with the composition C,,He for which
the endohedral structure He@C,, is the only conceivable
physical arrangement. This result makes neutral He@C,,
the first identified noble gas -carbon compound." 1'
Considering the vertical nature of the electron transfer
we
processes in neutralization -reionization
conclude that the He@C',: ionic complex also has the endohedral structure. In addition, the noble gas-fullerene complexes MC;' (M = He, Ne; x = C52-C,o) exhibit the same
characteristics as He@C;: in gas phase experiments [see
Eqn. (a)] and must thus also have the endohedral struct~re.['~]
Received: December 6, 1991 [Z 5059 IE]
German version Angew Chem. 1992, 104, 242
a) L. M. Roth, Y. Huang, J. T. Schwedler, C. J. Cassaday, D. Ben-Amotz,
B. Kahn, B. S. Freiser, J. Am. Chem. SOC.
1991, 113, 6298; b) Y. Huang,
B. S. Freiser, ibid. 1991, 113, 9418.
a) T. Weiske, D. K. Bohme, J. HruSak, W. Kratschmer, Angew. Chem.
1991, 103, 898; Angew. Chem. Int. Ed. Engl. 1991, 30, 884; b) T. Weiske,
J. HruSak, D. K. Bohme, H. Schwarz, Helv. Chim. Acta, in press.
a) M. M. Ross, J. H. Callahan, J. Phys. Chem. 1991, 95, 5720; b) K. A.
Caldwell, D. E. Giblin, C. S. Hsu, D. Cox, M. L. Gross, J. Am. Chem. Soc.
1991,113,8519;c)Z. Wan, J. F. Christian, S. C. Anderson,J. Phys. Chem.,
submitted: d) K. A. Caldwell, D. E. Giblin, M. L. Gross, J. Am. Chem.
Soc., in press: e) E. E. B. Campbell, R. Ehrlich. A. Hielscher, J. M. A.
Frazav, 1. V. Hertel, Z . Phys. D., in press: f) R. C. Mowrey, M. M. Ross,
J. H. Callahan, J. Phys. Chem., submitted.
For experiments in which doubly and triply charged fullerene-noble gas
complexes are generated, see: a) T. Weiske, J. HruSik, D. K. Bohme,
H. Schwarz, Chem. Phys. Lett. 1991,186,459; b) T. Weiske, D. K. Bohme,
H. Schwarz, J. Phys. Chem. 1991, 95, 8451.
Reviews: a) C. Wesdemiotis, F. W. McLafferty, Chem. Rev. 1987, 87,485:
b) J. K. Terlouw, H. Schwarz. Angew. Chem. 1987.99.829; Angew. Chem.
Int. Ed. Engl. 1987, 26, 805; c) H. Schwarz, Pure Appl. Chem. 1989, 61,
685; d) J. L. Holmes, Adv. Mass Spectrom. 1989, 1 1 , 53; e) J. K. Terlouw,
Adv. Mass Spectrom. 1989, 11, 984; f) J. L. Holmes, Mass Spectrom. Rev.
1989,8, 513; g) F. W McLafferty, Science 1990,247,990: h) F. W. McLafferty, Adv. Mass Spectrom. 1992, 12. in press.
For speculations and "experiments" regarding carbon clusters of unspecified structure as containers for noble gas atoms and their presence in
interstellar space: a) R. S. Lewis, B. Srinivasan, E. Anders, Science 1975,
190, 1251; b) S. Niemeyer, K. Marti, Proc. Lunar Planer Sci. 1981, 12B,
1177; c) D. Heymann, J. Geophys. Res. 1986, B91, E135.
For a detailed description see: a) R. Srinivas, D. Siilzle. T. Weiske, H.
Schwarz, Inr. J. Mass Spectrom. Ion Processes 1991,107, 369; b) R. Srinivas, D. Siilzle, W. Koch, C. H. DePuy, H. Schwarz, J. Am. Chem. Soc.
1991, 113, 5970.
a) D. L. Lichtenberger, K. W. Nebesny, C. D. Ray, Chem. Phys. Letr.
1991, 176, 203; b) J. A. Zimmermann, J. R. Eyler, S. B. H. Bach,
S. W. McElvany, J. Chem. Phys. 1991,94, 3556.
T. Wong, T. Weiske, J. K. Terlouw and H. Schwarz, Int. J Mass Spectrom.
Ion Processes, in press.
S . G. Lias, J. E. Bartmess, J. F. Liebman, J. L. Holmes, R. D. Levin, W. G.
Mallard, J. Phys. Chem. Ref. Data 1988, Supplement 1.
G. Frenking, D. Cremer, Structure and Bonding 1990, 73, 17, and references cited therein.
a) P. Fournier, J. Appell, F. C. Fehsenfeld, J. Durup, J. Phys. B 1972, 5,
L58; b) F. C. Fehsenfeld, J. Appell, P. Fournier, J. Durup, J. Phys. B 1973,
6, L268: c) J. C. Lorquet, B. Ley-Nihant, F. W McLafferty, Inr. Mass
Spectrom. Ion Processes 1990. 100, 465.
Initial communication: H. Schwarz, Workshop on Fulkrene Clusters, Riso
National Laboratory, Roskilde (Denmark), December 6-7, 1991.
CAS Registry numbers:
C,,He*+, 138855-72-8: He@C,,, 138855-73-9
On the Bonding in Carbosilanes""
[l] Recent reviews: a) H. W. Kroto, Science 1988, 242, 1139; b) W. Weltner,
Jr., R. J. Van Zee. Chem. Rev. 1989. 89, 1713; c) R. E. Smalley, in Atomic
and Molecular Clusters, (Ed.: E. R. Bernstein), Elsevier, Amsterdam 1990,
Chapter 1 ; d) J. S. Miller, Adv. Mater. 1991, 3, 262; e) H. W. Kroto,
A. W. Allaf, S. P. Balm, Chem. Rev. 1991, 91, 1213; f) R. F. Curl,
R. E. Smalley, Scienrific American 1991, 32; g) R. E. Smalley, Large Carbon Clusters, (Eds.: C. Hammond, V. Kuck), (ACS Symp. Ser., in press);
h) H. W Kroto, Angew. Chem., in press.
[2] J. M. Hawkins, A. Meyer, T. A. Lewis, S. Loren, F. I. Hollander, Science
1991,252, 312.
[3] H. Hopf. Angew. Chem. 1991, 103, 1137; Angew. Chem. Int. Ed. Engl.
1991, 30, 1117.
[4] For theoretical work see: a) A. Rosen, B. Wastberg, J. Am. Chem. Soc.
1988, 110, 8701; b) J. Cioslowski, ibid. 1991, 113, 4139; c) J. Cioslowski,
E. D. Fleischmann, J. Chem. Phys. 1991, 94, 3730: d) A. H. H. Chang,
W. C. Ermler, R. M. Pitzer, J. Chem. Phys. 1991, 94,5004; e) D. Bakewies,
W. Thiel, J. Am. Chem. Soc. 1991, 113, 3704: f) B. Wlstberg, A. Rosen,
Phys. Scr. 1991, 44, 276; g) P. P. Schmidt, B. I. Dunlap, C. I. White, J.
Ph.w Chem., submitted.
[5] a) J. R. Heath, S. C. O'Brien, Q. Zhang, Y Lin, R. F. Curl, H. W Kroto,
F. K. Tittel, R. E. Smalley, J. Am. Chem. Soc. 1985, 107, 7779: b)
F. D. Weiss, J. L. Elkind, S. C. O'Brien, R. F. Curl, R. E. Smalley, ibid.
1988, 110, 4464; c) Y. Chai, T. Guo, C. Jin, R. E. Haufler, L. P. F.
Chibante, J. Fure. L. Wang, J. M. Alford, R. E. Smalley, J. Phys. Chem.
1991, 95, 7564: d) J. H. Weaver, Y. Chai, G. H. Kroll, C. Jin, T. R. Ohno,
R. E. Haufler, T. Guo, J. M. Alford, J. Conceicao, L. P. F. Chibante,
A. Jain. G. Palmer, R. E. Smalley, Chem. Phys. Lett., submitted.
[6] D. M. Cox, D. J. Trevor, K. C. Reckmann, A. Kaldor, J Am. Chem. Soc.
1986. 108. 2457.
Angew. Chem. Int. Ed. Engl. 31 (1992) N o . 2
0 VCH
By Andreas Savin,* Heinz-Jurgen Flad, Jiirgen Flad,
Heinzwerner Preuss, and Hans Georg von Schnering
Two problems among the variety of studies on the structural chemistry of the carbosilanes have attracted particular
attention:
1. Does a through-space Si-Si bond exist in 1,3-disilacyclobutane? For example, in octachlorohexasilaasterane
Si,C,H,Cl,
the bond lengths d(Si-C) = 189, d(SiSi) = 261 pm and bond angles Si-C-Si = 87.2, C-SiC = 92.7 are observed, in a hexadecamethyloctasiladispiro[5.1.5. Iltetradecane Si,C,,H,, , d(Si-C) = 192,
d(Si-Si) = 262 pm and Si-C-Si = 85.9 '.['I The Si-Si distances in these compounds are respectively 26 and 27 pm
larger (11 X)than a single bond (235pm in silicon).
[*] Priv.-Dor. Dr. A. Savin, DipLChem. H.-J. Flad, Dr. J. Flad,
Prof. Dr. H. Preuss
Institut fur Theoretische Chemie der Universitat
Pfaffenwaldring 55, D-W-7000 Stuttgart 80 (FRG)
Prof. Dr. H. G. von Schnering
Max-Planck-Institut fur Festkorperforschung
Heisenbergstrasse 1, D-W-7000 Stuttgart 80 (FRG)
[*'I This work was supported by the Fonds der Chemischen Industrie
Verlagsgesellschafr mbH, W-6940 Weinheim, 1992
0570-0833/92/0202-018S$3.50+ ,2510
185
2. Does the very large C-C distance of 178 pm in 1,1,3,3-tetramethy1-2,4-bis(trimethylsilyl)-l,3-disilabicyclo[l.l .O]butane represent a C-C bond?['] Here d(C-C) is 24 pm
(1 6 O h ) longer than a single bond.
To answer these questions we applied the electron localization function (ELF)13] to pure carbosilanes 1 and 2.
H
H
1
2a
2b
The distribution of the electron pairs is influenced by the
antisymmetry of the wave-function : the presence of one electron at position r lowers the probability of finding another
electron with parallel spin in its vicinity (Pauli repulsion). A
measure of this probability is the electron localization function. The value of the function approaches 1 when the wavefunction allows the electrons to avoid each other and tends
toward 0 when the electrons are forced to remain there in the
same neighborhood around r. The regions of space in which
the ELF values are high can be associated with the concepts
bond, lone pair, or inner electronic hell.^^,^]
Technical details: The ELF was calculated at the HartreeFock level. The Hartree-Fock calculations themselves were
performed with the program MOLPR0[5J using pseudopotentials.[61The structural optimization did not yield a planar structure for 1; instead the molecule was shown to be
slightly folded. Nevertheless, since the energy difference between the planar and folded structure is small, the planar
structure will be discussed. The calculated structural
parameters of disilacyclobutane 1 (d(Si-C) = 189, d(SiSi) = 264 pm, Si-C-Si = 88.7, C-Si-C = 91.3') agree well
with experimental parameters."]
The structural optimization of 2 shows that the HartreeFock calculation yields too small a C-C distance (166 pm).
If the configurational space is extended to include another
orbital, the bond energy sinks to 49 kJmol-' and d(C-C)
lengthens to 179 pm. The structure is virtually identical from
a CASSCF or a MCSCF calculation, which takes into account only promotion from the localized C-C bonding orbital into the C-C antibonding orbital. This arises from the
C-C antibonding character of the included orbital. We wish
to emphasize that this orbital was determined by energy
optimization. Furthermore, in the improved calculation the
following parameters are obtained: d(Si-C) = 181 pm, C-SiC = 59.1, Si-C-C 60.5", and 51.0" for the angle between the
silacyclopropane planes (for comparison the experimental
values:['] 184 pm, 58, 61, 58").
For the graphical representationr7] of the ELF in selected
planes a published convention['] was used. The electron density appears as "cloud" against a black background. The
color of the points corresponds to the ELF value: analogous
to the representation of altitudes in maps, high values are
white, low values blue, and intermediate values are brown
and green. The pictures do not show the inner shells; only the
valence electron density is depicted.
In disilacyclobutane C,Si,H, (1) the angle Si-C-Si (88.7 ")
is smaller than C-Si-C (91.3'). According to the ELF, however, this effect is not attributable to a directly bonding Si-Si
interaction, since a blue-green region of low ELF values lies
between the Si atoms (Fig. 1 a). But ELF provides an alternative explanation for the small Si-C-Si angle. The ELF
186
VCH Verlagsgesellschafi mhH, W-6940 Weinheim. 1992
Fig. 1. Electron density p (as "cloud") and ELF (shown by color; scale at the
left of the frames) in selected planes of the molecules 1 and 2. a) and b) The
plane containing the four-membered ring in 1; to emphasize the structure of
ELF the adjacent value-ranges in b) are depicted alternately bright and dark.
The positions of the C and Si stoms are marked by white crosses: C left and
right, Si top and bottom. The region between the Si atoms is characterized by
a blue-green "valley". This implies that there is no direct Si-Si bond. The ELF
maximum lies distinctly off the topological connecting lines of the C,Si, ring
(see Fig. 2). c) and d) The two mirror planes of 2 (the views correspond to 2a
and 2b,respectively). The plane in c) contains the two C atoms and the H atoms
bound to them; the SiH, wings lie above and below the illustrated plane. The
small white region in the middle corresponds to the weak (bent) C-C bond, the
large white regions at lower left and right to the C-H bonds, and the smaller
white regions above the (blue) C atoms to fragments of the C-Si bonds. The
plane in d) contains both Si atoms and the H atoms bound to them. No white
region lies between the Si atoms. In the middle below the Si atoms, the plane
intersects the C-C bond (small white region below the linejoining the C atoms,
which is perpendicular to the plane illustrated).
maxima (M and M') lie outside the C,Si, ring (Fig. 1b). As
the calculation shows (Fig. 2), the Si-M and C-M distances
differ and the M-C-M' and M-Si-M' angles are approximately 109.5'. These different lengths correspond to the different
sizes of Si and C. The topological angles formed by the lines
joining the Si and C nucleii (C-Si-C = 91.3" > 90" and
Si-C-Si = 88.7 O < 90 ") arise naturally from combining atoms
of varying size and local bond angles of about 109.5" to form
an "eight-membered ring" C-M-Si-M-C-M-Si-MI.One can
Si
Fig. 2. ELF of 1 as contour diagram. Only the values 0.80,0.84,0.88,0.92,
and
0.96 are depicted. The dotted lines of the topological connections between the
atoms represent the classical bonds with bond angles close to 90". The solid lines
join the C and Si nuclei with the ELF maxima M and M'. The resulting angles
are indicated (see text).
0870-0833f92/0202-01863 3.50f .2SfO
Angew. Chem. Inr. Ed. Engl. 31 (1992) No.2
easily verify this result half quantitatively using a model kit
as analog computer. The different sizes of C and Si are simulated with tetrahedral joints whose arm lengths differ[*]and
the atoms are joined by flexible bonds (bent bonds).
In disilabicyclo[l .1.O]butane C,Si,H, (2) the region between the two C atoms does have a high ELF value (Fig. 1 c
and 1 d). This confirms the previously described bond.['] The
relatively small region of high ELF values implies a weak
bond, in agreement with the long bond length. The white
ELF maximum is also clearly off the straight topological
C-C connecting line. Its position is remarkably close to that
of the bent bond derived from the simple structural model.IZ1
As expected, there is no bond between the Si atoms (Fig. 1 d).
Received: August 12, 1991 (24863 IEJ
German version: Angew. Chem. 1992,104, 185
CAS Registry numbers:
1, 287-55-8; 2, 79647-93-1.
[l] G. Sawitzki, H. G. von Schnering, Z . Anorg. Allg. Chem. 1973, 399, 257262; K. Peters, E.-M. Peters, H. G. von Schnering, ibisd. 1983,502,61-65;
C,Si,H, was studied theoretically by, for example, M. OKeeffe, G. V.
Gibbs, L Phys. Chem. 1985,89,4574-4577; the Si-Si bond was discussed
by. for example R. S. Grey, H. F. Schaeffer 111,L Am. Chem. SOC.1987,109.
6577 -6585.
121 G. Fritz, S. Wartanessian, E. Matern, W. Honle, H. G. von Schnering, Z .
Anorg. Allg. Chem. 1981, 475, 87-108; P. von R. Schleyer, A. F. Sax, J.
Kalcher. R. Janoschek, Angew. Chem. 1987, 99, 374-377; Angew. Chem.
i n t . Ed. Engl. 1987, 26, 364.
[3] A. D. Becke, K. E. Edgecombe, J. Chem. Phys. 1990, 92. 5397-5403.
(41 A. Savin, A. D. Becke, J. Flad, R. Nesper, H. Preuss, H. G. von Schnering,
Angew. Chem. 1991, 103,421-424; Angew. Chem. Inr. Ed. Engl. 1991, 30,
409 -4 12.
(51 Program MOLPRO: SCF part by W Meyer, H. J. Werner; MC-SCF part
by H. J. Werner, P. J. Knowles, ( J Chem. Phys. 1985,82,5053-5063; Chem.
Phys. Len. 1985, 115, 259-267); kindly made available by Prof. Dr. H. J.
Werner and installed by Prof. H. Stoll on the Cray-2 in Stuttgart. Mr. M.
Kohout (Universitat Stuttgart) contributed to the development of the program MEROP (for the calculation of the electron density and of ELF) and
wrote the program MPLOT (for drawing the contour lines of Fig. 2).
(61 G. Igel-Mann, H. Stoll, H. Preuss, Mot. Phys. 1988, 65, 1321-1328; basis
sets: [4s, 4p] to (2s,2p) stipulated according to H.-J. Poppe (personal communication, 1988). Polarization functions: see P. L. Harihan, J. A. Pople,
Theor. Chim. Acta 1973, 28, 213-222; M. M. Franc], W. J. Pietro. W J.
Hehre, J. S . Binkley, M. S. Gordon, D. J. De Frees, J. A. Pople, J Chem.
Phys. 1982.77.3654-3665. The exponents of the Gauss functions are for C :
s: 2.581190,1.596882,0.408595,0.138945; p: 8.257547,1.960285,0.551454,
0.155007; d : 0.8. for Si: s: 3.513432, 1.503285, 0.408595, 0.089488; p:
1.462293, 0.939390, 0.152439, 0.058065; d: 0.45. H basis of R. Ditchfield,
W. J. Hehre, J. A. Pople, L Chem. Phys. 1971,54, 724-728 (with polarization function p: 1.1).
[7] J. Flad, F. X. Fraschio, 9 . Miehlich, Program GRAPA, Institut fur Theoretische Chemie der Universitat Stuttgart, 1989.
[8] C atom from the Prentice Hall Model Kit; Si atom as Dreiding model.
used in principle for solids as well (in methane and in diamond, for example). They can lead, however, to several
equivalent sets of orbitals for a given structure and are nonunique in this case. This ambiguity occurs, for example, in
monomeric monocycles such as benzene, or in an infinite
polyene chain."] In solids ambiguity often arises on account
of the higher coordination, and localized orbitals are therefore used only rarely. An analysis in positional space can
nevertheless be performed when instead of the equivocal
localized orbitals, the electron localization function (ELF) is
used. In this work we have calculated ELF for crystalline
solids for the first time.
The electron localization function was introduced by
Becke and Edgecombe as a measure of the probability of
finding an electron in the neighborhood of another electron
with the same spin."] ELF is thus a measure of the Pauli
repulsion. The explicit formulation is given in Equation (a)
The parameter K is the curvature of the electron pair density
for electrons of identical spin, e(r) the density at (Y), and Kh
the value of K in a homogeneous electron gas with density e.
The ELF values lie by definition between zero and one. Values are close to 1 when in the vicinity of one electron, no
other with the same spin may be found, for instance as occurs in bonding pairs or lone pairs. Small values are typical
for the region between two electron shells (Pauli principle).
In a homogeneous electron gas, ELF = 0.5.
The method of local density functionals (LDF)t374]has
proved exceptionally reliable for studies on solids. But in
LDF the pair density and its curvature K are not explicitly
defined. ELF may, however, be interpreted differently from
(a), in order that the determination of its value is compatible
with the LDF method. In this method (Kohn and Shamc6])
the single particle density matrix y [Eq. (b)] is determined by
energy minimization for a given electron density e(r) [cp are
N
orbitals, Nis the number of electrons; y(r,r') = ~ ( r ) Because
].
y(r,r') occurs only in the expression for the kinetic energy T
[Eq. (c), V is the Nabla operator], the pertinent information
T=
Electron Localization in Solid-state Structures
of the Elements: the Diamond Structure**
By Andreas Savin,* Ove Jepsen, Jiirgen Flad,
Ole Krogh Andersen, Heinzwerner Preuss,
and Hans Georg von Schnering
The methods for obtaining localized orbitals-often used
in the chemistry of molecules to describe bonding-can be
["I
['"I
Priv.-Doz. Dr. A. Savin, Dr. J. Flad, Prof. Dr. H. Preuss
Institut fur Theoretische Chemie der Universitat
Pfaffenwaldring 55. D-W-7000 Stuttgart 80 (FRG)
Dr. 0. Jepsen, Prof. Dr. 0. Krogh Andersen,
Prof. Dr. H. G. von Schnering
Max-Planck-Institut fur Festkorperforschung
Heisenbergstrasse 1, D-W-7000 Stuttgart 80 (FRG)
This work was supported by the Fonds der Chemischen Industrie. We
thank Dr. 0. Gunnarsson, Stuttgart, for valuable suggestions.
Angew. Chem. I n t . Ed. Engl. 31 (1992) N o . 2
0 VCH
1V, Vrry(r,r')lr=r,d3r
is contained in the three-dimensional kinetic energy density
t(r,r') [Eq. (d)] and the six-dimensional function y(r,r') is not
required.
The function t(r) cannot exceed a certain thre~hhold,"~
which is defined by Equation (e). This minimum value occurs
&.
when the orbitals are proportional to
According to the
Pauli principle this is possible for at most two orbitals, one
Verlagsgesellsrhafi mbH. W-6940 Weinheim, 1992
0570-0833/92j0202-0187$3.50+.25/0
187
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