J. Phys. Chem. 1994, 98, 11337-11341
11337
Deviations from Idealized Geometry: An ab Initio Investigation of (CH3)AXz Molecules [A = Si, Ge; X = F, Cl] George Vacek, Vladimir S. MastryukovJ and Henry F. Schaefer III* The Center for Computational Quantum Chemistry, the University of Georgia, Athens, Georgia 30602 Received: March 18, 1994; In Final Form: August 30, 1994@
Four related compounds (CH3)zSiFz (l), (CH3)2SiC12 (2), (CH3)zGeFz (3), and (CH3)zGeClz (4) were studied by a b initio quantum mechanical techniques to examine the deviation from the "ideal" tetrahedral geometry. Basis sets of double-9 (DZ) quality were used, as well as D Z with the addition of a set of d-type functions on all heavy atoms (DZd). These bases were used in conjunction with the Hartree-Fock (HF) self-consistent field method and the single-and-double-excitation configuration interaction (CISD) method. Theoretical predictions corroborate electron diffraction results in that all four molecules have C-A-C bond angles significantly larger than 109'28' but smaller than concluded from some analyses of electron diffraction data. Specifically, at the DZdCISD level of theory, C-A-C bond angles of 115.9, 114.3, 120.9, and 117.6' were found for molecules 1-4, respectively. An analysis also suggests that the 124" experimental C-Ge-C bond angle for (CH3)zGeBrz may be unrealistically large. Additionally, harmonic vibrational analyses at the HF level of theory have been completed to aid future studies of these four molecules.
Introduction The compounds of the elements of group IV with the molecular formula AXzYz (A = C, Si, Ge, Sn, and Pb) are expected to be slightly distorted tetrahedra.' Sometimes, however, large deviations from the ideal tetrahedral angle, 109"28', occur. Schleyer et a1.2a support Mislow's pronouncementZbthat tetrahedral angles are the exception rather than the rule: the bond angle (L) C-C-B in triethylborane, B(CzH5)3, is almost 120°.2a An even larger LC-Pb-C of 135" is postulated on the basis of ab initio calculations for (CH3)zP~Fz.~ Electron diffraction (ED) studies for the MezGeXz (Me = CH3, X = F,4 Cl,516Br7) molecules have revealed the LCGe-C to be in the neighborhood of 120". Similar large angles were also seen with ED studies for the cases MezSiXz (X = F,8 C19). The rough agreement between these isovalent analogs is mutually supportive at first glance. However, the situation is more complex than that. In the cases of MezSiClz and Me?GeC12, for instance, multisolution situations were found in which two different models with significantly different LC-A-C gave virtually equal agreement with the ED experiment. In 1976 Vajda and Hargitta? found two equally valid sets of parameters, with LC-Ge-C 121.7 f 1.4" and 114.5 k 2.1", which fit the ED data for MezGeClz. They preferred the first model slightly due to favorable comparisons of other parameters with those of H2GeC12. Drake, Hencher, and S h e d revisited the problem a year later. They managed to find only a single solution, but difficulty in refining the parameters simultaneously left their value with a rather large uncertainty: 121 f 4". For the case of MeZSiClZ Mastryukov and co-workersg found two different solutions. In the first solution LC-Si-C is 108.9 f 4.0", and in the second it is 122.6 f 3.0". The former value is the more expected value, near tetrahedral, while the latter result corresponds remarkably well with the preferred angle mentioned for the MezGeClz case. The multisolution situation for the MezSiCl2 molecule has been reevaluated in subsequent years. First, microwave (MW) Permanent address: Department of Chemistry, University of Moscow, Moscow 117234, Russia. @Abstractpublished in Advance ACS Abstracts, October 15, 1994.
spectra of this molecule were studied and an LC-Si-C of 114.7 f 0.3" was reported.1° Second, the previously reported ED datag were jointly analyzed with the rotational constants of the MW spectroscopy reportlo and calculated amplitudes of vibration. This resulted in an LC-Si-C determination of 114.2 f 0.2".11 Additionally, the two-solution problem was analyzed in detail and shown to be a consequence of limitations inherent to ED. ED does not distinguish the difference between two models which interchange the major nonbonded contributions, C-Cl and Cl-Cl, responsible for the magnitude of the bond angles around the silicon atom (see Figure 1 of ref 11). In principle, such a phenomenon does not depend on the nature of the central atom; i.e., it is applicable to all MezAX2 cases because it is caused by nonbonded X-X, C-X, and C-C interactions. In all the ED results mentioned above, if there is not a double solution, then the single solution has a very large margin for error. Only combination of ED studies with other techniques allows for better resolution. Some of these molecules (X = C1) were the subject of a recent ab initio study by Jonas, Frenking, and Reetz.12 Sine the goal of their research was more broad, including study of a total of 25 species with the formula Me,ACL-" (A is an element of group IV), they did not address this issue of C-A-C bond angles. Moreover, they report only LC-A-C1 values, which are always close to the tetrahedral value, and the independent LC-A-C can not be determined from the given information. Frenking was kind enough to send us the complete geometrical information.lZ For their basis set III, they calculated LC-A-C to be 114.2" and 117.3" for MezSiClZ and MezGeClz. The first is identical with the current experimental value mentioned above." However, the second is in disagreement by more than 4" from the preferred experimental value (121.7",5 121" 6, and agrees better with the discarded ED solution of 114.5".5 The purpose of this study is to perform more sophisticated ab initio calculations for the four related compounds MezSiFz (l),MezSiClz (2), MezGeFZ (3), and MezGeClz (4) to examine the deviations from the "ideal" tetrahedral geometry and draw attention to any experimental determinations which may be in error. Furthermore, calculated rotational constants, dipole moments, harmonic vibrational frequencies and infrared (IR)
0022-365419412098-11337$04.50/0 0 1994 American Chemical Society
11338 J. Phys. Chem., Vol. 98, No. 44, 1994
Vacek et al.
TABLE 1: Optimized Geometries for (CH3)AXz Where A = Si or Ge and X = F or CIa
molecule X=F
X=C1
theory
r(A-C)
r(C-H’)
r(C-H”)
r(A-X)
a(C-A-C)
DUSCF DZEVSCF DUCISD DZEVCISD DZ/SCF DZdSCF DZlCISD DZdCISD
1.8642 1.8544 1.8766 1.8474 1.8729 1.8602 1.8871 1.8537
1.0834 1.0871 1.0978 1.0932 1.0821 1.0859 1.0985 1.0929
1.0835 1.0873 1.0980 1.0933 1.0837 1.0872 1.1OOO 1.0939
A = Si 1.6749 1.5864 1.6969 1.6001 2.1827 2.0622 2.1967 2.0545
DZlSCF DZEVSCF DUCISD DZdCISD DUSCF DZdSCF DUCISD DZEVCISD
1.9269 1.9359 1.9336 1.9246 1.9364 1.9436 1.9446 1.9333
1.0823 1.0844 1.0950 1.0895 1.0814 1.0837 1.0958 1.0895
1.0828 1.0851 1.0956 1.0901 1.0831 1.0852 1.0975 1.0909
1.7592 1.7227 1.7771 1.7344 2.2334 2.1748 2.2426 2.1647
a(X-A-X)
a(A-C-H’)
a(A-C-H”)
119.5 115.8 119.3 115.9 118.0 114.5 117.3 114.3
103.9 105.6 104.2 105.7 107.3 108.0 107.9 108.4
110.3 111.0 110.3 111.0 110.9 111.3 110.9 111.2
111.3 111.5 111.2 111.5 110.6 110.9 110.5 110.9
122.3 120.4 122.2 120.9 119.2 117.7 118.6 117.6
103.0 103.5 103.3 103.7 106.9 106.5 107.4 106.9
109.6 109.7 109.6 109.5 110.2 110.0 110.2 109.8
110.7 110.7 110.6 110.6 110.0 110.2 110.0 110.2
A=Ge X=F
X=C1
a Bond lengths are in 8, and angles are in deg. All structures are in to the paired hydrogens (pointing up).
intensities are presented, since similar data has proven useful in the resolution of the geometry of MezSiClz, as described above. Preliminary results were presented in the 15th Austin Symposium on Molecular Structure.13 Theoretical Methods The basis sets for C, F, Si, C1, and W were fairly standard sets. The fist, DZ, consisted of a standard Huzinaga-Dunning double-c set14-16 of contracted Gaussian functions [designated (9s5p/4s2p) for first-row elements, (1 ls7p/6s4p) for secondrow elements, and (4s/2s) for hydrogen]. This basis was further augmented with a single set of d-like polarization functions on heavy atoms with orbital exponents Q(C) = 0.75, h ( F ) = 1.00, & % a) = 0.50, and m(C1) = 0.75. We refer to this basis set as DZd. Our Ge DZ basis set was obtained by contracting Partridge’s (15s12p7d) primitive basis” to (8s6p2d). The corresponding Ge DZd basis was created by adding a set of d functions with Q(Ge) = 0.28.18 In an investigation of basis set quality for Ge, some examinations were made of the MezGeX2 potential energy surfaces using DZ and DZd bases for Ge, as advocated by Grev.Ig This is a (14sl lp5d7s5p2d) segmented contraction of Dunning’s primitive setz0 and the same augmented with a set of d-like polarization functions, Q(Ge) = 0.25. The results were qualitatively the same and in rather good quantitative agreement as well. There is little reason to choose either Grev’s basis or ours over the other. For the sake of brevity, we present only the results obtained from our Ge basis set. The molecular structures were fully optimized using analytic gradient techniques for restricted H@1*22and C123*24wave functions. In all cases, the residual Cartesian and internal coordinate gradients were less than lod6au. The HF quadratic force constants were evaluated via analytic second-derivative procedure^.*^-^^ With CI methods all single and double excitations (SD) from the HF reference configuration were
CZ,symmetry. H’ refers to the lone hydrogens (pointing down); H” refers included (CISD), with the exception that only the valence electrons were explicitly correlated. The lowest-lying corelike MO’s (orbital energies below -5.0 hartrees) were held doubly-occupied (frozen cores) while the highest virtual orbitals (orbital energies above 5.0 hartrees) were kept unoccupied. With the DZd basis set, this correlation scheme involved 141 257, 141 257, 313 591, and 313 591 configurations for the C2”symmetry wave functions of molecules 1-4, respectively. The shape-driven graphical unitary group approachz8 was used to obtain CISD wave functions. All calculations were performed using the PSI suit of codes29on an IBM RS6000 workstation.
Results Optimized geometries for Me2AX2 molecules (where A = Si or Ge, and X = F or Cl) are displayed in Table 1. Note that these were optimized under Cz,-symmetry constraints and that the individual methyl groups show C,symmetry. The hannonic vibrational frequencies (as shown in Table 2 along with total energies, dipole moments, and rotational constants) are all real for all structures, indicating that the structures are true minima. For the case of MezGeFz only, attempts to find stationary points with other symmetries were made on the DZd/HF surface. First, a search was made under overall Cz,-symmetry constraints but with the methyl groups constrained to C3,-symmetry with respect to the Ge-C axis. No stationary point was found. In their low-level studies of MezSiC12 and MeaGeClz, Jonas et a1.l2 used similar symmetry constraints and found stationary points which were true minima under their vibrational analysis. Although no attempt was made here to study such “highsymmetry” structures for those two molecules, it seems likely that they would disappear on our higher-level surfaces. Next, searches were made under overall C2- and C,-symmetry constraints to look for other stationary points along the two methyl-rotation internal coordinates. The only stationary points found (results not presented here) were transition states between
J. Phys. Chem., Vol. 98, No. 44, 1994 11339
Geometry of (CH3)zAXz Molecules TABLE 2: Theoretical Predictions for (CH&AX2 with the DZd Basis SeP A = Si x = c1 X=F - 1287.242 777 E(SCF)b -567.265 776 -1287.793 922 E(C1SD) -567.880 805 -1287.878 470 E(CISD+Q) -567.966 145 2.506 52.22 0.085 38 0.060 44 0.053 71
2.477 53.47 0.1272 0.1156 0.1117
P
ZPVEb
A,b B,b C,b
A=Ge X=F
x = c1
-2353.534 635 -2354.293 982 -2354.402 380 3.636 52.17 0.1142 0.1019 0.1004
-3073.559 453 -3074.250 550 -3074.356 949 3.235 51.16 0.075 19 0.054 99 0.048 35
A = Si
A=Ge
x = c1
X=F
x = c1
X=F
W,b
IRb
Web
IRb
Web
IRb
W,b
IRb
CH' stre CHdstre HCH' bend HCHdumbrella HCA' bend AX stre AC stre XAX bend CAC bend
3278 3198 1596 1468 987 875 679 348 206
23 4 5 33 214 30 '1 29
