J . Phys. Chem. 1992, 96, 1679-1683
Conclusions The 2c-3e S:.S bond strength in charged acyclic dithiols increases as the length of the methylene linkage increases. An exception is the 2c-3e bond in the five-membered ring with a trimethylene linkage which is more stable than the six-membered ring with a tetramethylene linkage due to reduced nonbonded repulsion. Except for the five-membered ring, all charged complexes prefer a C2-symmetrystructure. The theoretical calculations of 2c-3e bond strengths agree with experimental measurements of the absorbance maximum A, in the optical spectrum. For the series HS(CH,),,SH+ (n = 1-4), the 2c-3e bond strengths
1679
are predicted to be 13.1, 14.6, 24.8, and 24.3 kcal/mol, respectively. Acknowledgment. We thank the donors of the Petroleum Research Fund, administered by the American Chemical Society, for financial support. Computer time for this study was made available by the Alabama Supercomputer Network and the NSF-supported Pittsburgh Supercomputer Center. Dr. K.-D. Asmus is acknowledged for helpful conversations. Registry No. 1, 138407-13-3; 4, 95879-99-5; 8, 138407-14-4; 13, 138407-15-5,
Theoretical Study of Silicon Substitution in Borane and Carborane Cages Michael L. McKee Department of Chemistry, Auburn University, Auburn, Alabama 36849 (Received: September 5, 1991; In Final Form: October 21, 1991)
Silicon substitution into several borane and carborane cages has been studied with ab initio calculations. Examples of cages in which silicon contributes one, two, or three electrons to cage bonding have been considered. Silicon contributes one electron in the silaborane, SiH3-B5H8, and calculations correctly predict the order of stability: l-(SiH3)BsH8,2-(SiH3)BSHB,and p-(SiH3)B5H8. Closo octahedral cages are considered where silicon contributes either 2e- or 3e- to cage bonding. The silicon cage appears to be more stable when silicon contributes 2e- to cage bonding as opposed to 3e-. The most stable structure of the silacarborane, 1-(SiH2)-2,3-C2B4H6,is predicted to have two terminal Si-H bonds in the symmetry plane. Finally, heats of formation of several silaboranes and silacarboranes have been estimated from calculated heats of reaction.
Introduction While carbon substitution into a borane cage is common and gives rise to an entire class of compounds (carboranes), silicon substitution is rather rare.l There is only one published example2 (to the author’s knowledge) of a silaborane which is directly related to a carborane by substitution of silicon for carbon. Kinetic or electronic factors may prevent the formation of directly analogous compounds. More often silicon donates one or two electrons to cage b ~ n d i n grather ~ . ~ than three electrons as is the case for carbon. An example of one-electron donation is SiMe3-B5H8, where a trimethylsilyl group replaces a terminal, basal, or bridging hydrogen. In a series of elegant experiments, Gaines and cow o r k e r ~have ~ , ~ shown that p(SiMe3)B5H8rearranges in the presence of a Lewis base by a first-order reaction to give 2(SiMe3)BSH8. By labeling the apical position with deuterium, they were able to show that the rearrangement did not exchange basal and apical hydrogens. At higher temperature, a second pathway exists which gives 1-(SiMe3)BSH8as well as exchanging basal and apical hydrogens. Isotopic labeling experiments on BSH9 provide strong evidence that the process involves- cage rear(1) (a) Grimes, R. N. Reo. Silicon, Germanium, Tin Lead Compd. 1977, 2,223. (b) Grimes, R. N. In Carboranes;Academic Press: New York, 1970. (c) Grimes, R. N. In Comprehensive OrganometaNic Chemistry; Wilkinson, G., Stone, F. G. A., Abel, E. W., Us.Pergamon ; Press: Oxford, U.K., 1982; Vol. 1, and references therein. (d) Grimes, R. N., Ed.Metal Interactions with Boron Clusters; Plenum: New York, 1982. (e) Hosmane, N. S.; Maguire, J. A. In Advances in Boron and the Boranes; Liebman, J. F., Greenberg, A., Williams, R. E., Eds.; VCH: New York, 1988; pp 297-328. (f) Hosmane, N. S.; Maguire, J. A. Adv. Organomef. Chem. 1990, 30, 99. (2) The silaborane (SiMe)2B,oHIois isostructural to o-C2Bl0H,,: Seyferth, D.; Bilchncr, K.; Rees, W. S., Jr.; Davis, W. M. Angew. Chem., Itit. Ed. Engl. 1990, 29, 918. (3) Hosmane, N. S.; de Meester, P.; Siriwardane, U.; Islam, M. S.; Chu, S. C. J . Chem. SOC.,Chem. Commun. 1986, 1421. (4) Experimental work refers to the C-diethyl derivative: Siriwardane, U.; Islam, M. S.; West, T. A.; Hosmane, N. S.; Maguire, J. A.; Cowley, A. H. J . Am. Chem. SOC.1987, 109, 4600. (5) (a) Gaines, D. F.; Iorns, T.V. J . Am. Chem. Soc. 1968, 90, 6617. (b) Heppert, J. A.; Gaines, D. F. Inorg. Chem. 1983, 22, 3155. (6) Gaines, D. F.; Coons, D. E.; Heppert, J. A. In Advances in Boron and rhe Boranes: Liebman, J. F., Greenberg, A,, Williams, R. E., Eds.;VCH: New York, 1988; pp 91-104.
rangement rather than substituent migration.6 Several cages with silicon substituted at a vertex have been synthesized by Hosmane and co-~orkers’~-~ by reacting a derivative 2-, with various subof nido-2,3-C2B4H8, [2,3-(SiMe3)2C2B4H4] strates. Reaction with silicon tetrachloride gave a closo pentagonal bipyramid which was characterized by its N M R and mass ~ p e c t r a . ~The structure proposed was isostructural with 2,3C2BSH7,a known carborane? In order to maintain a cage electron count of 16e- as predicted by Wade’s rules8 for a closo cage, silicon must donate 2e- which would leave two electrons as an exocyclically directed lone pair. In the same reaction a second silicon-containing cage was isolated and the structure determined ~rystallographically.~~~ In this structure, the silicon atom of the pentagonal bipyramid is capped by a second nido-C2B4Hs2- derivative which allows the silicon atom to share 2e- with each moiety. A related silicon-containing pentagonal bipyramid is obtained when a derivative of [2,3-C2B4H6I2-reacts with SiH2C12.4 The structure, a derivative of 1-SiH2-2,3-CzB4H6,is consistent with one hydrogen strongly bound to silicon and one weakly bound, perhaps a bridging interaction. It was pointed out that if both hydrogens are terminal, then silicon would be in the +4 oxidation state, while one terminal hydrogen and one bridging hydrogen would leave silicon in a +2 state and give a cage electron count appropriate for a nido c o m p o ~ n d . I ~Unfortunately, *~ suitable crystals were not obtained for an X-ray structure determination. In a reaction of [2,3-(SiMe3)2C2B4H4]2-with a phosphine, 2,4,6-(t-Bu),C6H2pCl2, a closo-phosphacarborane complex is formed with a terminal phenyl group on phosphor~s.~For a seven-vertex closo cage, application of Wade’s rules would give a predicted cage count of 16 electrons. Donation of 2 cage (7) Experimental work refers to the C-methyl, C-trimethylsilyl derivative: (a) Beck, J. S.; Sneddon, L. G. Inorg. Chem. 1990,29,295. (b) Beck, J. S.; Kahn, A. P.; Sneddon, L. G. Organometallics 1986, 5, 2552. (8) (a) Wade, K. Ado. Inorg. Chem. Radiochem. 1976,18, 1. (b) Mingos, D. M. P.; Wales, D. J. Introducrion to Cluster Chemistry; Prentice Hall: Englewood Cliffs, NJ, 1990. (9) Hosmane, N. S.; Lu, K.-J.; Cowley, A. H.; Mardones, M . A. Inorg. Chem. 1991, 30, 1325.
0022-3654/92/ 2096- 1679$03.OO/O 0 1992 American Chemical Society
McKee
1680 The Journal of Physical Chemistry, Vol. 96, No. 4, I992 TABLE I: Absolute Energies (Hartrees) and Zero-Point Energies of Several Silaboranes and Silacarboranes
symmetry D- h
HZ BH3 CH4
D3h Td
SiH; SiH,
c 2 0
B5H9 1,6-C2B4H6 1,2-C2B4H6 2,3-C2BSH? SiH,-B4H8
C4"
Td
1 2
D4h
C2"
c2, c, c 5
3
CS
4
C,
Si2B4H6 5 6
HF/3-21G* -1.1 22 96 -26.237 30 -39.976 88 -288.560 27 -289.784 26 -127.821 96 -176.917 62 -176.909 65 -202.05 1 IO
HF/6-31G* -1.12681 -26.390 01 -40.195 17 -289.999 77 -291.225 13 -128.578 07 -177.943 16 -177.932 70 -203.21 129
MP2/6-31G* -1.144 14 -26.464 22 -40.332 42 -290.067 02 -29 1.307 01 -129.048 58 -178.558 96 -178.54298 -203.91 190
MP4/6-31G* -1.15089
-4 16.472 74 -416.467 50 -4 1 6.45 7 08 -416.45865
-41 8.660 06 -418.655 10 -418.64251 -418.642 11
-419.21 144 -41 9.206 41 -419.199 62 -419.196 69
-419.298 81 -419.29458 -419.28683 -41 9.284 5 1
-676.542 76 -676.531 12
-679.98291 -679.965 31
-680.518 36 -680.50096
47.21 (0) 46.58 (2)
-701.621 70 -701.58367
-705.196 12 -705.15660
-705.81 199 -705.761 35
40.73 (0) 40.48 (0)
-465.556 99 -465.52901 -465.481 97 -465.491 38 -465.53441
-467.997 -467.967 -467.923 -467.940 -467.975
-468.702 -468.675 -468.625 -468.646 -468.693
70.00 69.66 67.95 70.19 65.72
-291.331 26 -1 29.118 56
ZPE (NIF)" 6.66 (0) 17.29 (0) 30.12 (0) 8.02 (0) 21.12 (0) 69.50 (0) 56.88 (0) 57.08 (0) 66.87 (0) 80.77 80.53 80.57 80.52
(1) (0) (1) (0)
Si2C2B2H4
1 8 SiC2B4H8 9 10 11 12 13
+ H2
59 93 35 11 63
28 74 74 75 96
(0) (1) (1) (0) (0)
"Zero-pint correction in kilocalories per mole. The number of imaginary frequencies is given in parentheses. bThe 'Al state is calculated. electrons from phosphorous would bring the total to 16, leaving phosphorous with 3 "extra" valence electrons. One electron is used to form a 2c-2e bond to the phenyl group, leaving two electrons as an exocyclic lone pair. In contrast, the NH unit in closoazaborane, B9H9NH,Iocontributes four electrons to cage bonding (and one electron to form a 2c-2e N H bond) to maintain the 22ecount predicted by Wade's rules. Thus, the phosphorus atom in the phosphacarborane donates two of the four available valence electrons while the nitrogen atom in azaborane donates all four. It appears that third period elements (phosphorus and silicon) contribute a smaller number of valence electrons to cage bonding compared to the second period elements (nitrogen and carbon). The different utilization of available electrons is probably due to differences in hybridization and/or the overlap of the p-orbital of the heteroatom with the fragment orbitals of the borane cage. However, in the icosahedral closo cages, H N B l l H l l and MePBllHl1, nitrogen and phosphorus both donate four electrons to cage bonding."
Method All calculations have been made by using the GAUSSIAN 88 program system.I2 Geometries of silicon-containing compounds have been optimized with a 3-21G* basis set,13 which includes a set of d-functions on third period elements. Single-point calculations are made at the MP2 or MP4 levels of electron correlation (frozen-core approximation) with the 6-31G* basis set. Vibrational frequencies have been calculated to characterize the nature of the stationary points and to make zero-point corrections (scaled by 0.9). Absolute energies and zero-point energies are given in Table I while geometries are given in Figure 1. Relative energies in kilocalories per mole are given in Table I1 with respect to each silaborane or silacarborane. Unless otherwise indicated, (10) Todd, L. J.; Arafat, A.; Baer, J.; Huffman, J. C. In Advances in Boron and the Boranes; Liebman, J. F., Greenberg, A., Williams, R. E., Eds.; VCH: New York, 1988; pp 287-295. (11) Mailer, J.; Runsink, J.; Paetzold, P. Angew. Chem., Inr. Ed. Engl. 1991, 30, 175. (12) Frisch, M.J.; Head-Gordon, M.;Schlegel, H.B.;Raghavachari, K.; Binkley, J. S.;Gonzales, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Secgcr, R.; Melius, C. F.; Baker, J.; Martin, R. L.; Kahn, L. R.; Stewart, J. J. P.;Fluder, E. M.;Topiol, S.; Pople, J. A. GAuSSlAN 88; Gaussian, Inc.: Pittsburgh, PA, 1988. (13) For a description of basis sets, see: Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986.
TABLE II: Relative Energies (kcal/mol) and Silaboranes and Silacarboranes
HF/ 3-21G*
HF/ 6-31G*
MP2/ 6-31G*
1 2 3 4
0.0
0.0
0.0
3.3 9.8 8.8
3.1 11.0 11.3
5 6
0.0
0.0
7.3 0.0 23.9
11.0 0.0 24.8
3.2 7.4 9.3 0.0 10.9 0.0 31.8 0.0 16.6 48.0 34.8 5.2
7 8 9 10 11 12 1 3 + H2
0.0
0.0
17.6 47.1 41.2 14.2
18.6 46.6 36.1 13.8
MP4/ 6-31G* 0.0 2.6 7.5 9.0
+ZPC" 0.0 2.4 7.3 8.8 0.0 10.3 0.0 31.6 0.0 16.3 46.2 35.0 1.4
Zero-pint correction is added to the MP4 relative energies for 1-4 and to the MP2/6-31G* relative energies for the other entries. the energy differences used in the discussion below are at the MP2/6-31GS//3-21G*+ZPC level of theory.
Results and Discussion The geometry of four silaboranes (1-4) were determined where a silyl group is substituted in the 1-position (1),the 2-position (2), and a position bridging two basal borons (3, 4). The silyl group causes very minor variations in the cage distances of the BsHs cage (Figure 1). In addition to 1, a second conformation of 1-(SiH,)BSH8 was calculated (not shown) where the hydrogen of the silyl group eclipses a boron-boron bond. At all levels, the energies of the two conformations are nearly identical. While both conformations of the silyl group had one imaginary frequency, the small magnitude of the imaginary frequency of 1 (2i cm-I) suggests that the rotational barrier is very small. The distortion caused by the silyl group in the second isomer considered (2) is somewhat greater than that in 1 but still small (Figure 1). At the MP4/6-31G*//3-21G1+ZPC level, 1 is 2.4 kcal/mol more stable than 2. The greater stability of 1 is likely due to (1) the greater negative charge on the apical boron, which should stabilize the electropositive silyl substituent, and (2) less steric hinderance of the apical position, which should favor the larger bulk of the silyl group.
Silicon Substitution in Borane and Carborane Cages
The Journal of Physical Chemistry, Vol. 96, No. 4, 1992 1681
A H
H.
Sic2 2.692 SiB, 2.208 SIB6 1.998 CzCs 1.423 C2Bs 1.651 C2B7 1.807 B4B5 1.768 B4B7 1.872 B5B7 1.684 SiH'B5 1.474, 2.806
H
SiBl BIB2 BIB. B;B;
1.982 1.714 1.714 1.826 BSB; 1.826 B4B5 1.828 BzHbB3 1.348 BsHbB4 1.350,1.347 B4HbB6 1.348
I
Sic2 2.156 SiB4 2.231 SiB5 2.097 CzCs 1.513 C2B6 1.548 C2B7 1.757 B4B5 1.715 B4B7 1.804 B5B7 1.833
1 SiB2 2.006 BIB2 1.720 BIB3 1.706 BlB4 1.714 BpBj 1.841 B3B4 1.823 BpHbBj 1.341,1.360 BsHbB4 1.343,1.352
\
i
H
B2SibB3 2.103,2.626 BIB2, BIBS 1.770, 1.650 BlB4, BIB5 1.719, 1.711 B2B3 1.836 BjB4, BsB6 1.804, 1.885 B4B5 1.832
H
I
"\
Sic2 SiB4 SiBb C2C3 C2Bs C2B7
2.081 2.852 3.376 1.594 1.669 1.711 B4B5 1.747 B4B7 1.830 BsB, 1.769 BSHb 1.240 BsHb 1.900 SiHb 2.641
Sic2, Sics 3.034, 2.446 SiB,, SiBa 2.142, 3.222 2.534 1.435 1.621, 1.577 1.812, 1.819 1.722, 1.849 1.785, 1.797 1.778 1.317 1.329 2.417
Sic2 2.167 12.23, 2.251 SiB4 2.184 [2.10, 2.101 SiBK 2.140 [2.10] CsCs 1.467 C S B ~1.562 CzB, 1.810 BdB5 1.707 B4B7 1.835 B5B7 1.562
5
7
Figure 1. Selected geometric parameters are given at the HF/3-21G* levels. The boldface numbers correspond to the entries in the tables and text. The geometry of B5H9 is provided at the same level of theory (without boldface number) to allow comparisons with the silyl-substituted derivatives (1-4). Values in brackets are experimental X-ray values for a related structure.
1682 The Journal of Physical Chemistry, Vol. 96, No. 4, 1992
McKee
TABLE 111: Heats of Reaction Involving Silaboranes and Sdacarboranes and Estimated Heats of Formation"
--
+
1 + H2 B5H9 SiH4 5 2CH4 1,2-C2B4H6 + 2SiH4 6 + 2CH4 1,6-C2B4H6+ 2SiH4
+
----
lr6-C2B4H6+ 2SiH2 1,2-C2B4H6+ 2SiH2 2,3-C2B5H, 2CH4 + 5BH3- 8H2 9 + 2BH3 2,3-C2B5H7 + 2SiH4 7 + 2BH3 8 + 2BH3
HF/3-21G*
HF/6-31G*
-6.6 11.5 -0.8 36.5 17.6 -66.2 -25.8
-10.2 -6.1 -23.7 21.0 2.1 -7 1.9 -30.6
MP2/6-31G* MP4/6-31G* 0.0 16.4 -4.5 29.8 8.0 49.6 -32.9
-0.1
+ZPC
AHf (estd)bd
2.8 9.1 -11.1 27.8 6.3 25.7 -32.3
25.2 7 1.6'
83.4' 64.0' 94.2' 64.3' 80.7
'The heat of formation of the reactant nonclassical cage is estimated from the calculated exothermicity of the given reaction and experimental or estimated heats of formation. *The experimental heats of formation of BH, (26.4 kcal/mol), B5H9(17.5 kcal/mol), NH, (-9.3 kcal/mol), CHI (-16.0 kcal/mol), and SiH4 (10.5 kcal/mol) at 0 K are taken from: Chase, M. W., Jr.; Davies, C. A.; Downey, J. R., Jr.; Frurip, D. J.; McDonald, R. A.; Syverud, A. N. JANAF Thermochemical Tables, 3rd ed. J . Phys. Chem. Re5 Data, Suppl. 1 1985, 14. CTheheats of formation of 1,2C2B4H6(27.7 kcal/mol) and lr6-C2B4H6(19.0 kcal/mol) are estimated from ab initio calculations. See ref 15. dThe heat of formation of SiH, is taken as 62.8 kcal/mol, which is derived from the G2 atomization energy and experimental heats of formation of atoms: Curtis, L. A.; Ragavachari, K.; Trucks, G. W.; Pople, J. A. J . Chem. Phys. 1991, 94, 7221. 'The silacarborane 5 is 11.8 kcal/mol more stable than 6 from a comparison of estimated heats of formation. The directly calculated value (Table 11) is 10.3 kcal/mol. Likewise, 7 is 30.2 kcal/mol more stable than 8 from a comparison of estimated heats of formation, while the directly calculated value is 31.6 kcal/mol. ,The estimated heat of formation of 2,3-C2B5H,is decreased by 2 kcal/mol per boron to compensate for underestimation of the stability of the nonclassical cage relative to CH4, BH,, and H, (see ,~ footnote c). Two structures were optimized for the bridging isomer because the symmetrical one (3) had one imaginary frequency. Following this mode gave 4 with an unsymmetrical silyl bridge, only 1.0 kcal/mol more stable at the HF/3-21G* level. At all other levels of theory (Table II), 3 is more stable than 4; this indicates that the symmetrical bridge is the true minimum. However, distortion of the bridge should not be costly, and crystal packing forces or asymmetrical substitution could result in a substantially unsymmetrical bridge. At the MP4/6-31G*//3-21G*+ZPC level, 3 is 7.3 kcal/mol less stable than 1 and 4.9 kcal/mol less stable than 2. The predicted energy ordering of 1-3 is in agreement with the known reactions of SiMe3-BsHs which indicate that CL(SiMe3)BSH8rearranges to 2-(SiMe3)BSHsunder mild conditions and to l-(SiMe,)BSHs under more extreme conditiom6 In each reaction, the more thermodynamically stable product is expected. Two examples of silicon contributing three valence electrons to cage bonding were considered in a closo octahedral cage. In 5, silicon replaces carbon in 1,2-C2B4H6,and in 6, silicon replaces carbon in 1,6-C2B4H6. In contrast to the carborane where the 1,6-isomer is known to be more stable,I4 the 1,2-SizB4H6isomer 5 is predicted to be 10.3 kcal/mol more stable than the 1,6-SizB4H6 isomer 6 (Table 11). An earlier study15 of P2B4H4,which is isoelectronic with Si2B4H6,also found that the 1,2-isomer was more stable than the 1,6-isomer. The high symmetry of the lI6-isomer (D4,,)and long P-B bonds force the B-B bonds in the equatorial plane to be longer than optimal, which causes the cage to be de~tabi1ized.l~ A similar argument would rationalize the stability order in Si2B4H6. The icosahedral cage, 1,2-(SiMe)2BloH,o,is known2 to be isostructural to o-C2BloH12 with a Si-Si distance of 2.308 A. This is the only silaborane known in which silicon donates 3 2 to cage bonding. In 1,2-Si2B4H6(5), the Si-Si distance is predicted to be similar, 2.226 A (Figure 1). Two silacarboranes were also calculated where two silicon atoms replace two BH groups (7, 8). In these two cages, each silicon contributes two valence electrons to cage bonding and each has an exocyclic lone pair. In an attempt to discern a preference of silicon for the number of electrons donated to cage bonding, several reactions have been investigated (eqs 1-4). In the first two 5 + 2CH4 1,2-C2B4H6+ 2SiH4 (1)
6 + 2CH4
7 + 2BH3
--
-
+ 1,6-C2B4H6+ 2SiH2 1,2-C2B4H6+ 2SiH2
1,6-C2B4H6 2SiH4
(2) (3)
2BH3 (4) reactions, silicon is in the +4 oxidation state, while, in the second two, it is in the +2 oxidation state. Equations 1 and 2 evaluate the relative ability of silicon to donate 3e- to cage bonding com8
(14) Onak, T.; Drake, R. P.; Dunks, G. B. Inorg. Chem. 1964, 3, 1686. (15) McKee, M. L. J . Phys. Chem. 1991, 95, 9273.
pared to forming three 2c-2e bonds to hydrogen. On the other hand, eqs 3 and 4 evaluate the relative ability to donate 2e- to cage bonding compared to forming two 2c-2e bonds to hydrogen. While the reaction energies cannot be directly compared because eqs 1 and 2 are with respect to carbon and eqs 3 and 4 are with respect to boron, an indication of stability can be obtained by comparing eq 1 with 3 and eq 2 with 4. The silicon in the cages of eqs 1 and 3 are in adjacent positions, while they are nonadjacent in the cages of eqs 2 and 4. Equation 3 is 18.7 kcal/mol more endothermic than eq 1, while eq 4 is 17.4 kcal/mol more endothermic than eq 2 (Table 111). Both comparisons point to a more stable cage when silicon donates 2e- compared to donating 3ein the octahedral closo cage. Silicon substitution was also considered in the seven-vertex cage, (!3-12), a derivative of which has been I-(SiH2)-2,3-c$& studied by N M R and mass ~ p e c t r a .In ~ contrast to the experimental results which suggest that silicon has one strong attachment to hydrogen (terminal bond) and one weak attachment (hydrogen bridge), the present work finds the most stable structure to have two terminal hydrogens on silicon (9) with the preferred orientation of the SiH2 group in a plane which bisects the C-C bond. The SiH2 group in 9 is slipped away from the carbon atoms ( S i x ; 2.692 A) and toward the boron atoms (Si-B; 2.208, 1.998 A). A transition state for rotation of the SiH, group was located (10) and found to be 16.3 kcal/mol higher in energy than 9. An alternate structure considered was 11 with a triply bridging hydrogen between B4, BS, and B6 (Figure l), which was 46.2 kcal/mol above 9. The calculated vibrational frequencies revealed one imaginary frequency for 11, a motion of the triply bridging hydrogen toward one of the silicon atoms. A doubly bridging structure was then located (12). It was found to be 11.2 kcal/mol more stable than the triply bridging structure but still 35.0 kcal/mol above 9. In both 11 and 12, the SiH group has moved over to one side of the five-membered ring, forming an open four-membered face (Figure 1). Apparently, theory and experiment are in disagreement as to the types of hydrogens attached to silicon. The experimental interpretation is based on the proton-coupled 29Si-NMR spect r u m " ~which ~ is split into a broad doublet with a large coupling constant ('J = 362 Hz), each line of which is further split into doublets with a smaller coupling constant ('J = 42 Hz). The logical interpretation is that the silicon resonance is split by one strong interaction with hydrogen (terminal) and further split by a weaker interaction with another hydrogen (bridging). Theory, on the other hand, predicts two terminal hydrogens which should interact similarly with silicon, A possible resolution to the disagreement might come from a consideration of the c-C bond length which is considerably shorter in 9 (1.423 A) as compared to that in 11 (1.594 A). The system studied experimentally had bulky substituents on carbon (SiMe, and CH,). The resulting steric strain might stabilize a structure with a longer C-C bond length such as 11 relative to 9 to the extent that 11 could be a
J . Phys. Chem. 1992,96, 1683-1690 stable species (i-e., no imaginary frequencies) in equilibrium with 9. It is also possible that the repulsion could alter the equilibrium structure of 9 in the direction of 11. The SiH’ bond closest to B5 (BsH’; 2.806 A) in 9 is 0.015 A longer than the other SiH bond, which may be indicative of incipient bridging character. A known silacarborane related to 9 was also calculated where a silicon atom is substituted for SiH2in the 1-position (13). The structure is compared to an X-ray structure3 of a silacarborane in which two 2,3-C2B4H6groups cap opposite sides of a silicon atom. The silicon atom is calculated to be very slightly shifted away from the carbon atoms, which agrees with experimenL3 The formation of 13 plus H2 is predicted to be nearly thermoneutral with respect to 9 (1.4 kcal/mol endothermic, Table 11).
F’redicted Heats of Formation Heats of formation of 1-13 can be estimated by calculating heats of reactions involving known compounds. The reactions are chosen such that the reactants and products are as similar as possible (Table 111). The heats of formation of 1,6-C2B4H6and 1,2-C2B4H6have been estimated previously from ab initio calculation~,]~ and a similar method can be used to estimate the heat of formation of 2,3-C2BsH7. Basically, the calculated heat of reaction of eq 5 is used with experiment heats of formation to determine the heat of formation of 2,3-C2BsH7. In an earlier study, it was found necessary to 2,3-C2BsH7 2CH4 + 5BH3 - 8H2 (5) decrease the heat of formation of the nonclassical cage by 2 kcal/mol per boron to compensate for deficiencies in the calculation.16 The same correction was applied to the calculated heat of formation of 2,3-C2BsH7. +
(16) McKee, M. L. J . Phys. Chem. 1990, 94, 435.
1683
Relative energies in Table I1 can be combined with the heats of formation in Table I11 to predict heats of formation of the other structures. These values can be used with traditional additivity rules to predict heats of formation of various derivatives which may aid in devising synthetic strategies.
Conclusions Several silicon-containing cages have been studied. In agreement with the known chemistry of SiMe3-BsH8, a silyl group is most stable in the apical position followed by the basal position and bridging position. In a closo octahedral cage, silicon prefers to donate 2e- to cage bonding rather than 3e-. In the 1(SiH2)-2,3-C2B4H6system, the most stable conformation of the parent is with two terminal Si-H bonds in a plane bisecting the two carbon atoms. Heats of formation can be estimated by choosing appropriate reactions and calculating reaction energies. Note Added in Proof. MNDO calculations have been reported17 for the sandwich compound, commo-1,l’-Si( 1,2,3SiC2B4H6)2,a compound related to 9 in the present study. Acknowledgment. We thank the donors of the Petroleum Research Fund, administered by the America1 Chemical Society, for financial support. Computer time for this study was made available by the Alabama Supercomputer Network and the NSF-supported Pittsburgh Supercomputer Center. Registry No. 1, 28556-29-8; 2, 22142-52-5; 3, 22044-27-5; 5, 138407-46-2; 6, 138407-45-1; 7, 138433-43-9; 8, 138433-44-0; 9, 110152-54-0; 13, 110175-42-3; HZ, 1333-74-0; BHB, 13283-31-3; CH4, 74-82-8; SiH2, 13825-90-6; SiH4, 7803-62-5; BsH9, 19624-22-7; 1,6C2B4H6, 20693-67-8; lr2-C2B4H6,20693-68-9; 2,3-C2BSH,, 30347-95-6. (17) Maguire, J. A. Organometallics 1991, 10, 3150.
Theoretical Study of Iron-Ligand Binding. Mechanism of Ferrocene Formation from Iron plus Cyclopentadiene Michael L. McKee Department of Chemistry, Auburn University, Auburn, Alabama 36849-531 2 (Received: September 20, 1991)
The mechanism of ferrocene formation from atomic iron and cyclopentadiene has been studied by ab initio methods. A reasonable qualitative interpretation can be obtained after empirical corrections are made for deficiencies in the calculation. The first correction compensates for the energy difference between ground-state iron (4s23d6)and a configuration appropriate for binding the cyclopentadienyl (Cp) groups. The second correction compensates for the underestimation of the Cp binding energy to iron. The initial step of the mechanism is the insertion of Fe into a CH bond of cyclopentadiene. The resulting high-spin complex binds another molecule of cyclopentadiene and undergoes conversion to a low-spin complex. Elimination of H2 from the final complex is predicted to be facile.
(1) (a) The Challenge of d and f Electrons, Theory and Computation; Salahub, D. R., Zerner, M. C., Eds.; American Chemical Society: Washington, DC, 1989. (b) Quantum Chemistry: The Challenge of Transition Metals and Coordination Chemistry; Veillard, A,, Ed.; NATO AS1 Series, Series C: Mathematical and Physical Sciences; Reidel: Boston, 1986; Vol. 176. (c) Bonding Energetics in Organometallic Compounds; Marks, T. J., Ed.;ACS Symposium Series 428; American Chemical Society: Washington, DC, 1990. (2) Obara, S.; Kitaura, K.; Morokuma, K. J . Am. Chem. SOC.1984, 106, 7482.
(3) Koga, N.;Obara, S.; Kitaura, K.; Morokuma, K. J . Am. Chem. SOC. 1985, 107, 7109. (4) Koga, N.; Morokuma, K. J . Am. Chem. SOC.1986, 108,6136. (5) Koga, N.; Jin, S.-Q.; Morokuma, K. J . Am. Chem. SOC.1988, 110, 3417. (6) Nakamura, S.; Morokuma, K. Organometallics 1988, 7, 1904. (7) Daniel, C.; Koga, N.; Han, J.; Fu, X.-Y.; Morokuma, K. J . Am. Chem. SOC.1988, I IO, 3773. (8) Koga, N.; Morokuma, K . J . Phys. Chem. 1990, 94, 5454. (9) Koga, N.; Morokuma, K. Organometallics 1991, 10, 946.
0022-3654/92/2096-1683%03.00/0 0 1992 American Chemical Society
