Faraday Symp. Chem. SOC., 1984 19 39-48 Silacyclobutadiene Singlet and Triplet Geometries Vibrational Frequencies and Electronic Structures E. COLVIN III* BY MICHAEL AND HENRYF. SCHAEFER Department of Chemistry University of California Berkeley California 94720 USA. Received 16th August 1984 The geometries of the lowest singlet and triplet states of silacyclobutadiene have been optimized at the double-zeta (DZ) and double-zeta (DZ + d) self-consistent-field (SCF) level of theory. Silacyclobutadiene has a planar asymmetric closed-shell ground state. The ground-state C-C and C-Si bond lengths are in good agreement with standard values indicating that this state is closely analogous to the ground state of cyclobutadiene. The calculated DZ+d SCF harmonic vibrational frequencies support this analogy.The lowest triplet state of silacyclo- butadiene is found by configuration-interaction calculations to lie only ca. 5 kcal mo1-l above the ground state much lower than the established value of 23 kcal mol-' for the singlet-triplet separation in cyclobutadiene The overall stability and singlet-triplet separation of silacyclo- butadiene are discussed in terms of bond energies and 71-system aromaticity. The last decade has seen a dramatic upsurge in experimental and theoretical interest in organosilicon chemistry. Beginning in 1976 with the synthesis and characterization of the first silicon+arbon double bond,l. this interest has increasingly focused on strained and unsaturated organosilicon c~mpounds.~ In the theoretical study of such species a natural compound to investigate is silacyclobutadiene (SiC3H4).It is a representative model species of conjugated organosilicon systems yet it is small enough to be treated by rigorous ab initio techniques. Moreover silacyclobutadiene has special theoretical relevance because its properties offer insights into the extensively studied problem of the nature of the cyclobutadiene ground state.4 Of course silacyclobutadiene is of interest in its own right. It is a new and virtually unstudied compound and hence its properties are of interest to chemists attempting to characterize it further. EXPERIMENTAL AND THEORETICAL BACKGROUND In 1983 Muetterties and Gentle announced the tentative observation of sila- cyclobutadiene by thermal-desorption mass spectroscopy during a study of the silane surface chemistry of palladi~m.~ While Muetterties' study provides the only experi- mental information on silacyclobutadiene at this time some previous theoretical results are available for this species.In 1980 Gordon reported a self-consistent-field (SCF) full-geometry optimization of silacyclobutadiene using a split-valence 3-21G basis set followed by single-point calculations with an extended 6-31G* basis set.6 He found silacyclobutadiene to be a planar asymmetrical structure stable relative to dissociation to acetylene and sila-acetylene by 56.3 kcal mol-l. Although little is known about silacyclobutadiene the analogous compound cyclobutadiene has certainly been one of the most vigorously pursued molecules of this century.' A particular emphasis of recent experimental and theoretical work on 39 STUDIES ON SILACYCLOBUTADIENE cyclobutadiene has been the elucidation of the ground-state geometry and spin- multiplicity.While it has been known for more than a decade that certain crystalline derivatives of cyclobutadiene have singlet rectangular ground conclusive results for cyclobutadiene itself have proved more elusive. Initial infrared studies of cyclobutadiene detained in an argon matrix led to the conclusion that it possessed a square ground state,12-14 seemingly indicative of a triplet state. However numerous failures to observe an e.s.r. signal argued strongly against a triplet ground state.8 This discrepancy was finally resolved in favour of the rectangular singlet ground state by Masamune using i.r.analysis of cyclobutadiene photosynthesized in an argon matrix.l5 Concurrent with this experimental work has been a tremendous theoretical effort by many groups. For theoreticians cyclobutadiene is of interest not only because of the controversial nature of its ground state but also because it is a model system for the study of bond strain steric hinderance n-conjugation and aromaticity. Theoretical studies of cyclobutadiene have almost unanimously predicted a rec- tangular singlet ground ~tate.l~-~~ While this result disagreed with the early i.r. studies mentioned above the e.s.r. data (or lack thereof) cast some doubt on the possibility of a triplet ground state.Later semiempirical and more sophisticated two-configuration SCF studies of this problem confirmed the ground state to be a rectangular singlet,18-21v 23 which was consistent with the e.s.r. data but contradicted the available i.r. results. This disagreement instigated a number of fairly extensive configuration- interaction (CI) investigations in an attempt to resolve what for several years appeared to be a major discrepancy between theory and experiment. Although the subsequent i.r. results proved the early experimental conclusions wrong these CI studies were valuable inasmuch as they gave a solid theoretical picture of the lowest states of cyclobutadiene. For example the a+n CI calculation of Jafri and Newton using a 6-3lG* basis predicts a rectangular singlet ground state 23.0 kcal mol-1 more stable than the square triplet state.21 The square singlet transition state was found to lie 12.0 kcal mol-1 above the ground state.The goal of the current study was to establish comparable or perhaps even more reliable theoretical results for the lowest-energy states of silacyclobutadiene. THEORETICAL METHODS The stationary points for the lowest singlet and triplet states of silacyclobutadiene were located and characterized at the self-consistent-field (SCF) level of theory. These theoretical studies were carried out using two basis sets. The first basis set used was the relatively standard double-zeta (DZ) basis of Huzinaga and D~nning~~-~~ with the following contraction scheme Si(l1s 7p/6s 4p) C(9s 5p/4s 2p) H(4s/2s).The second basis set (DZ +d) was the Huzinaga-Dunning DZ basis described above augmented with 6 d-like functions [x2,y2,z2,xy xz yz times exp (-ar2)]centred on silicon (a = 0.6) and carbon (a = 0.75). The starting point for the geometry optimization was the 3-21G SCF structure of Gordon.6 The optimization was facilitated by the use of analytic SCF gradient tech.niques with an optimization criteria that the energy gradients be < hartree bohr-l.? The harmonic vibrational frequencies of the DZ and DZ+d singlet structures were obtained via finite differences of analytic SCF gradients. Similarly the i.r. intensities were evaluated from dipole derivatives determined by finite differences of dipole moments calculated at the displaced geometries.-f 1 hartree = 4.359814 x lo-'* J; 1 bohr = 5.291771 x lo-" m. M. E. COLVIN AND H. F. SCHAEFER I11 H H DZ DZ+d Fig. 1. Predicted one-configuration SCF equilibrium geometries for the silacyclobutadiene ground state. All bond lengths in A. Two-configuration SCF (TCSCF) single-point calculations were carried out on the ground singlet state of silacyclobutadiene at the optimized one-configuration geometry. The two configurations corresponded to the orbital occupancies (2~”~3a”~) and (2~”~4a”~). In addition pi-space and single- and double-(SD) excitation CI calculations were carried out at the SCF equilibrium geometries. The pi-space CI involved single and double CI with all but the valence a’’ orbitals held frozen. Specifically the orbitals held frozen were Si( Is 2s 2px 2py 2pz 3s 3px 3py) C( Is 2s 2px 2p,) and H( 1s) and the corresponding virtual orbitals.This resulted in 9 1 and 435 configurations respectively for the DZ and DZ+d singlet state and in 123 and 627 configurations for the DZ and DZ +d triplet states. In the SDCI calculation the core orbitals on silicon (Is 2s 2ps 2pv 2pz) and carbon (1s) were held frozen. This larger CI involved 25771 and 79603 configurations for the DZ and DZ+d singlet state respectively and 29355 and 91 779 configurations for the DZ and DZ +d triplet state. EQUILIBRIUM STRUCTURES The predicted SCF equilibrium geometries for the lowest singlet and triplet states of silacyclobutadiene are given in fig. 1 and 2. The large differences in silicon-carbon bond lengths in going from the DZ to DZ+d basis sets (up to 0.1 A for the singlet state) illustrate the necessity of including d-functions on the heavy atoms.The predicted DZ +d bond lengths for singlet silacyclobutadiene suggest that this structure should be interpreted in terms of conventional carbon-carbon and silicon- carbon single and double bonds. The two carbon-carbon bond lengths in the singlet are predicted to be 1.539 and 1.346 A in close agreement with the standard values of ca. 1.54 A for a carbon-carbon single bond and ca. 1.34A for a carbon-carbon double bond.29 The longer of the predicted silicon-carbon bonds is 1.866 A in comparison with a value of 1.867 A determined from the microwave spectrum of methyl~ilane.~~ The shorter of the silicon-carbon bonds in silacyclobutadiene is predicted to have a length of 1.688 A in good agreement with the result of 1.698 A reported for the silaethylene silicon-carbon bond by an earlier theoretical study using a similar basis set and level of theory.31 Similarly the reported theoretical cyclobutadiene structures show strong agreement of the carbon-carbon bond lengths STUDIES ON SILACYCLOBUTADIENE H .H DZ DZ+d Fig.2. Predicted SCF equilibrium geometries for the lowest triplet state of silacyclobutadiene. All bond lengths in A. with the standard Thus it is reasonable to conclude on structural grounds that the singlet ground state of silacyclobutadiene is closely analogous to the ground state of cyclobutadiene. The SCF equilibrium structures of the lowest triplet state of silacyclobutadiene (fig.2) do not allow as clear an interpretation. Nevertheless a few obvious points are interesting to note. First the effect of the added d-functions is much less pronounced in the triplet state (maximum DZ to DZ + d change 0.051 A) than in the singlet state (maximum change 0.096 A). Secondly the triplet state does not have a diagonal axis of symmetry so that structurally it is not exactly analogous to the square lowest triplet state of cyclobutadiene. Thirdly the shortest carbon-carbon and carbon-silicon bonds are not on opposite sides of the ring as they are in the singlet indicating a dramatic difference in the electron distributions between the two states. The differences in the lengths for the comparable bonds in the singlet and triplet states offer some insight into the nature of the 3A’ state.The most dramatic changes in going from the lA’ to the 3A’ state are in the silicon-carbon ‘double bond’ which expands by 0.158 to1.846 A and in the carbon-carbon ‘single bond’ which shrinks by 0.102 A to 1.437 A. In contrast the carbon-carbon ‘double bond’ expands by only 0.036 A to 1.382 A and the silicon-carbon ‘single bond’ shrinks by only 0.037 A to 1.829 A. The overall result of these changes is that the silacyclobutadiene 3A’ state silicon-carbon bonds have lengths comparable to a Si-C single bond (1.846 and 1.829 A as compared with 1.867 A in methyl~ilane),~~ while carbon-carbon bond lengths are closer to that of a carbon-carbon double bond (1.437 and 1.382 A as compared with 1.339 in ethylene).32 As noted earlier the silicon substitution rules out a truly square structure for triplet silacyclobutadiene.Nevertheless the triplet structure is much more ‘square-like ’ in geometry than is singlet silacyclobutadiene. VIBRATIONAL FREQUENCIES The DZ + d SCF harmonic vibrational frequencies (cm-l) and the corresponding infrared intensities D (A2a.m.u.)-l for the lA‘ ground state are given in table 1 along with descriptive assignments. A comparison of the predicted frequencies of the normal modes corresponding to the various heavy-atom bond stretches with the experimental stretching frequencies of similar bonds yields more information about the nature of these bonds. While making these comparisons it should be kept in mind that several studies of DZ and DZ + d SCF harmonic vibrational frequencies have found that the M.E. COLVIN AND H. F. SCHAEFER I11 Table 1. Vibrational frequencies for the singlet ground state of silacyclobutadiene predicted at the DZ +d SCF level of theory symmetry frequency/cm-l intensity/DZ(A~a.m.u.1-1 description U’ 3485 0.0 C-H stretch U’ 3462 0.1 C-H stretch U’ 3353 0.7 C-H stretch U’ 2424 3.9 Si-H stretch U’ 1621 2.2 C=C stretch U’ 1360 0.2 C-H in-plane rock U’ 1228 1.4 C-H in-plane rock U’ 1150 1.4 C-PI in-plane rock U’ 1090 0.2 Si=C stretch a’’ 1042 0.1 C-H out-of-plane wag U’ 888 2.0 C-C stretch U’ 861 0.9 C-H Si-H rock U’ 762 0.3 C-H out-of-plane wag U“ 694 2.7 Si-H in-plane rock a’’ 541 0.1 C-H out-of-plane wag U’ 522 0.2 Si-C stretch U” 503 2.3 ring fold U” 306 1.o Si-H out-of-plane wag Table 2.Comparison of selected DZ +d SCF harmonic vibrational frequencies with analogous experimental results frequencies/cm-] ~ ~~~~ mode predicted experimental C-C stretch 888 ca. 1000 (cy~lobutadiene)’~ 995 (ethane)37 C=C stretch 1621 1523 (cy~lobutadiene)’~ Si-C stretch 523 cu. 700 (methyl~ilane)~~ Si=C stretch 1090 1001 1003 (1,l -dimethyl~ilaethylene)~~? 40 986 (m~nomethylsilaethylene)~~ predicted frequencies are systematically ca. 10% higher than the experimentally measured This error arises because correlation and anharmonic effects are not included at such levels of theory. The predicted frequencies of selected normal modes and the bond stretches they correspond to are given in table 2 along with the comparable experimental results for various molecules.For the modes corresponding to the stretching of the carbon+arbon single and double bonds and the siliconsarbon double bond the qualitative agreement is good (including the anticipated 10% error). The predicted frequency for the silacyclobutadiene silicon5arbon single bond stretch is 523 cm-l ca. 100 cm-l short of what it should be to agree well with the experimental result of 7OOcm-l for methyl~ilane.~~ This discrepancy is probably a result of some mixing of the predicted mode with other low-frequency ring modes so that it does not correspond to a simple STUDIES ON SILACYCLOBUTADIENE Table 3.Total energies for singlet and triplet silacyclobutadiene (in hartree) singlet triplet level of theory DZ DZ+d DZ DZ+d single configuration two-configuration SCF -404.607 25 -404.626 70 -404.699 96 - -404.625 71 - -404.707 60 - pi-space CI single- and double-excitation CI -404.682 13 -404.913 76 -404.755 40 -405.1 19 87 -404.666 60 -404.913 83 -404.9 13 83 Table 4. Singlet-triplet energy separations in silacyclobutadiene ~ level of theory relative energies/kcal mol-l singlet triplet DZ DZ+d single configuration single configuration -1 1.58 -4.79 two-configuration single-configuration 9.58 -pi-space CI pi-space CI 9.75 -CISD CISD 0.0 1.7 Davidson Davidson 3.3 3.5 Si-C stretch. The overall good agreement of these predicted frequencies with the experimental frequencies for the free bonds corroborates the result derived from structural considerations that the carbon+arbon and silicon-carbon single and double bonds in the lA’ ground state of silacyclobutadiene are not greatly perturbed by ring strain or conjugation effects.SINGLET-TRIPLET ENERGY SEPARATION The total and relative energies for the lowest singlet and triplet states of sila- cyclobutadiene are given in tables 3 and 4. For comparison some predicted singlet- triplet separations for cyclobutadiene are given in table 5. At the single-configuration SCF level of theory the silacyclobutadiene 3A’ state is predicted to be 11.6 and 4.8 kcal mol-1 more stable than the lA’ for the DZ and DZ +d basis sets respectively.This result closely matches the cyclobutadiene single- determinant 6-31G* singlet-triplet separation of 5.8 kcal mol-1 predicted by Hehre and Pop1e.l’ The fact that single-determinant SCF theory predicts the triplet state to be lower in energy is not surprising. A one-determinant RHF wavefunction includes in a certain sense some electron correlation for triplet states due to the ‘Fermi hole’ between the triplet-coupled electron~.~~ Moreover the low-lying 4a”orbital (occupied in the triplet state) is neglected in the one-configuration treatment of the closed-shell lA’ state. To describe better the singlet state a two-configuration wavefunction was employed with the second configuration corresponding to the 3a”2-P 4a”2 excitation. The weights for these two configurations are 0.94 (2aN23d2) and -0.33 (2a”24a”2).The relatively large coefficient of the second configuration demonstrates the importance of this configuration in describing the singlet state. Numerous studies have demonstrated the veracity of singlet-triplet energy separations M. E. COLVIN AND H. F. SCHAEFER 111 Table 5. Published singlet-triplet energy separations in cyclobutadiene singlet-triplet theoretical method separation /kcal mol-l ref. 6-31 G* single configuration SCF -5.8 17 STO-3G pi-space CI 6-31G* U+Z CI 22.4 23.O 22 21 predicted by comparing a two-configuration closed-shell singlet with the corresponding single-configuration triplet ~tate.~~-~~ Such a DZ calculation for sila- cyclobutadiene finds the TCSCF singlet 9.6 kcal mol-1 more stable than the triplet.In light of the dramatic effect of the second configuration on the singlet-state energy we decided to investigate further the singlet-triplet energy separation using configuration interaction. Studies of cyclobutadiene have found that the results of larger CI calculations could be accurately anticipated with a much smaller pi-space CI calculation considering only excitations among valence a’’ orbitals.22,24 Single-point pi-space CI calculations on the lowest singlet and triplet states of silacyclobutadiene (at the SCF equilibrium geometries) are in good agreement with the results using the two-configuration singlet/one-configuration triplet scheme (see table 4). A large SDCI calculation of the singlet-triplet energy separation somewhat decreases the pi-space CI results and leads to a final predicted singlet-triplet splitting of ca.5 kcal mol-l. For comparison the most reliable predictions of the singlet-triplet separation in cyclobutadiene are 21 kcal (Kollmar and Staemmlerls) 22 kcal (Borden et aZ.22)and 23 kcal (Jafri and Newton21). That the singlet-triplet energy separation for silacyclobutadiene is ca. 17 kcal mol-1 less than that for cyclobutadiene can be understood in terms of bond-energy considerations. As discussed earlier the rectangular singlet ground states of cyclo- butadiene and silacyclobutadiene contain essentially conventional single and double covalent bonds. Thus it is reasonable to consider these species in terms of the energies of the individual bonds.Several earlier studies have shown that silicon+arbon and carbon*arbon single-bond energies are very similar (ca.88 kcal mol-l for Si-C47 and ca. 85 kcalmol-l for C-C49. However this similarity does not hold for the com- parable n-bonds. On the basis of bond strength and kinetic data Walsh recommends a silicon-carbon n-bond energy of 39 5 kcal m~l-’,~~ nearly 20 kcal mol-l less than the well established carbon-carbon n-bond energy of ca. 57 kcal11101-~.~~ This means that the disruption of the cyclobutadiene n-system in going from the singlet to the triplet state comes at greater energetic cost than in silacyclobutadiene and hence the greater singlet-triplet energy gap. The same result is seen in the relative singlet-triplet energy separations of ethylene and silaethylene.In the 1978 paper of Hood and Schaefer and the more recent CEPA study of Kohler and Lischka the silaethylene singlet-triplet splitting was predicted to be 38.5 and 35.2 kcal mol-l respectively in comparison with a much higher value of 62.8 kcal mol-1 for ethylene.49 A question of interest in the study of cyclobutadiene is whether the square closed-shell singlet state lies at a sufficiently low energy to act as a transition state between the two possible identical rectangular forms of cyclobutadiene (i.e. the two possible orientations of the double bonds). As mentioned earlier the square singlet tran- sition state is found to be more stable than the corresponding triplet state by STUDIES ON SILACYCLOBUTADIENE ca.11 kcalmol-l. In an attempt to determine whether an analogous state of silacyclobutadiene lies below the first triplet state we carried out a single-point DZ TCSCF energy calculation for the lA’ state at the optimized ,A‘ geometry. The ‘square’ singlet was found to be 0.8 kcal mol-1 more stable than the corresponding triplet state. Note however that full optimization of the singlet transition state may either increase or decrease this square singlet-triplet gap. SILACYCLOBUTADIENE STABILITY Although silacyclobutadiene has been shown to be a relative minimum on the potential surface (there are no imaginary vibrational frequencies) the overall thermo- dynamic stability of silacyclobutadiene is still open to question. One of the goals of Gordon’s study of silacyclobutadiene was to determine if this species was stable with respect to dissociation to acetylene and sila-acetylene.Gordon6 carried out this calculation at the SCF level of theory using 6-31G* basis sets at the 3-21G equilibrium geometries. He found silacyclobutadiene to be 56.3 kcal mol-1 more stable than the separated products. We repeated this calculation with a DZ basis set and found a somewhat lower result of 44.8 kcal mol-I. While these results are in qualitative agreement with the results of Trinquier50 and others51 that when possible the preferred forms of unsaturated organosilicon compounds are rings the question of the silacyclobutadiene stability requires closer scrutiny. A recent study of one of these dissociation products sila-acetylene has shown that it is a stationary point but not a minimum on the potential surface.52 Instead linear sila-acetylene is predicted to have a degenerate imaginary mode corre- sponding to bending to yield the shallow trans bent minimum.At the Davidson- corrected SDCI level of theory silylidene is reported to be 43 kcal mot1 more stable than sila-acetylene with a barrier to interconversion of 49 kcal mol-l. Taking this into account silacyclobutadiene is predicted to be ca. 5 kcal mol-l less stable than the dissociation products acetylene and silylidene. However since the initial concerted reaction of silacyclobutadiene to form acetylene and sila-acetylene is symmetry f~rbidden,~, the barrier to unimolecular dissociation should be considerable.SILACYCLOBUTADIENE AROMATICITY Since silacyclobutadiene is essentially an annulene the possibility of aromatic stabilization or destabilization by n-electron conjugation should be considered. The thermochemical concept of aromaticity is derived from the observation that certain annulenes with (4n +2) n-electrons (e.g.benzene) possess special stability because of their conjugated n-~ystems.~ Associated with this concept of aromatic stabilization is the idea that 4n n-electron annulenes are destabilized by cyclic conjugation (so-called antiaromaticity). However note that there is no specific evidence that disruption of the cyclic conjugation would stabilize such annulenes. In fact experimental studies of one 4n annulene 1,5-bisdihydroannulene (n = 3) indicate that this system prefers a nearly planar conformation even at the expense of increased angular It is difficult to judge the exact role of aromatic effects on silacyclobutadiene.While the ground state is planar and stable with respect to out-of-phase distortions the geometry would seem to preclude significant n-conjugation (see structure section). In his study of silacyclobutadiene Gordon predicted what he called the ‘anti- aromaticity ’ using the bond-separation formula55 SiC,H +3CH +SiH,-+CH SiH +CH CH +CH SiH +CH CH,. (1) M. E. COLVIN AND H. F. SCHAEFER 111 47 Gordon calculates AE for the above reaction to be -53.5 kcal mol-1 and states that this 'is an indication of strong antiaromaticity in silacyclobutadiene. ' By comparison cyclobutadiene is found to have a corresponding AE of -67.9." Using eqn (1) we calculate the DZ SCF silacyclobutadiene antiaromaticity to be 49.1 kcal mol-l.These results indicate strong antiaromatic destabilization but they are not entirely unambiguous. In particular an obvious shortcoming of this bond-separation scheme is its inability to distinguish destabilizing conjugation effects from angle 57 and 1,3 interaction^^^ known to be important in four-membered ring systems. CONCLUDING REMARKS The ground state of silacyclobutadiene has been determined to be planar closed-shell singlet analogous to the rectangular ground state of cyclobutadiene. The bond lengths and vibrational frequencies of the singlet indicate little n-conjugation in the silacyclobutadiene ring.The lowest triplet state lies ca. 5 kcal mol-1 above the ground state. This research was supported by the U.S.National Science Foundation Chemistry Division grant no. CHE-8218785. We are also grateful to Energy Conversion Devices Inc. for an unrestricted grant in support of this research. Helpful discussions with Drs Jozef Bicerano and John de Neufville (ECD) and Mark Gordon (North Dakota) were much appreciated as was theoretical help from Dr Michel Dupuis. 0. L. Chapman C. C. Chang J. Kolc M. E. Jung J. A. Lowe T. J. Barton and M. L. Tumey J. Am. Chem. Soc. 1976,98 7844. M. R. Chedekel M. Skoglund R. L. Kreeger and M. Shechter J. Am. Chem. SOC.,1976 98 7846. For a review of experimental work see L. E. Gusel'nikov N. S. Nametkon and V.Vdovin Acc. Chem. Res. 1975 8 18. For recent reviews see G. Maier Angew. Chem. 1974 86 491; Angew. Chem. Int. Ed. Engl. 1974 13,425; T. Balley and S. Masamune Tetrahedron Rep. 1980,36,343; M. P. Cava and M. J. Mitchell Cyclobutadiene and Related Compounds (Academic Press New York 1967). T. M. Gentle and E. L. Muetterties J. Am. Chem. SOC.,1983 105 304. M. S. Gordon J. Chem. Soc. Chem. Commun. 1980 1131. ' Beginning with A. 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