11616
J. Phys. Chem. 1996, 100, 11616-11619
Existence of Two Distinct Isomeric Forms of Me(OH)SiCH2. A Theoretical Confirmation Ramaiyer Venkatraman, Andrzej Nowek, and Jerzy Leszczynski* Department of Chemistry, Jackson State UniVersity, 1400 Lynch Street, Jackson, Mississippi 39217 ReceiVed: February 27, 1996; In Final Form: May 15, 1996X
On the basis of the results of the experimental IR studies of matrix reactions between methylsilanes and oxygen atoms, Withnall and Andrews have postulated the possibility of the existence of equilibrium between two forms of Me(OH)SidCH2. In order to verify their supposition, an ab initio study at various levels of theory was performed. Two hydroxy forms of methylsilaethylene were fully optimized using the gradient procedures at the MP2 and DFT(Becke3LYP) approximations with the standard 6-311G(d,p), 6-311G(2d,2p), and 6-311G(2df,2pd) basis sets. Harmonic vibrational frequencies were calculated at all levels. The MP4(SDQ)/6-311G(2df,2dp)//MP2/6-311G(2df,2pd) + ZPE(MP2) calculations establish the energy difference between cis and trans isomers at 1.9 kcal/mol, which makes both forms experimentally accessible. Vibrational frequencies and shifts of frequencies upon isotopic 18O and deuterium substitutions predicted at the MP2 and DFT levels correlate well with the experimental data, thus supporting assignments of vibrational bands and identifications of reaction products by Withnall and Andrews.
Introduction Interaction between experimental techniques and theoretical predictions is of great importance in identification of new species. In the past decade, the matrix-isolation technique has been used to obtain and, in conjunction with FTIR spectroscopy, to identify a variety of carbon-, silicon-, and germaniumcontaining species produced by irradiation of mixtures of ozone or oxygen and methane (ethane), silane (disilane), and germane derivatives in low-temperature argon matrices. For example, laboratory studies on products and intermediates for the UV photolysis of various halocarbon/ozone mixtures1,2 are of considerable interest, as oxidation of these species may influence stratospheric ozone resources. Also, using matrix-isolation techniques, new species such as silicon and germanium analogues of methanol, formaldehyde, and carbonic acid have been obtained. Studies on the photolytic reactions of germane/ozone mixtures revealed novel species containing GedO and GesOH linkages.3 However, in many cases experimental data are scarce and should be supported by rigorous theoretical studies before definitive conclusions are drawn. An interesting example is the recent studies on products of oxidation of silane and its derivatives. Organosilicon compounds containing SidO and SisOH functional groups were detected as photolytic products obtained by irradiation of mixtures of SiH4 or MenSiH4-n (n ) 1, 2, 3, 4) and ozone or oxygen in low-temperature argon matrices.4-7 Analysis of recorded infrared spectra provides evidence for the resulting photoproducts. Withnall and Andrews7 postulated Me(HO)SidCH2, hydroxymethylsilaethylene (HMSE), as one of the products of Me3SiH/ozone mixture photolysis. In addition, detailed analysis of the recorded spectra allowed them to derive an assumption on the existence of two distinct forms of HMSE (Figure 1). It seems that the above suppositions can be confirmed or excluded by use of rigorous quantum mechanical methods. Due to the moderate size of HMSE, higher correlated levels of theory and saturated basis sets can be applied. In our study, possible cis-trans equilibrium of HMSE is investigated at the correlated second-order MøllerPlesset MP2, fourth-order MP4(SDQ) perturbation theory, and * Author to whom correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, July 1, 1996.
S0022-3654(96)00595-3 CCC: $12.00
Figure 1. Molecular arrangement of cis- and trans-hydroxymethylsilaethylene.
density functional (DFT) levels using relatively large, splitvalence triple-ζ plus sets of polarization functions basis sets. Method The ab initio LCAO-MO method8 was used for study of the title species. The calculations were carried out with the GAUSSIAN92 set of programs.9 All geometries were optimized © 1996 American Chemical Society
Two Distinct Isomeric Forms of Me(OH)SiCH2
J. Phys. Chem., Vol. 100, No. 28, 1996 11617
TABLE 1: Optimized Bond Lengths (Å) and Bond Angles (deg) for cis- and trans-Hydroxymethylsilaethylenea MP2/6-311G(d,p)
DFT/6-311G(d,p)
cis
trans
cis
trans
Si1-C2 C2-H3 C2-H4 Si1-O5 O5-H6 Si1-C7 C7-H8 C7-H9 C7-H10
1.6984 1.0844 1.0853 1.6507 0.9592 1.8522 1.0919 1.0928 1.0928
1.6950 1.0835 1.0849 1.6505 0.9573 1.8646 1.0922 1.0938 1.0938
1.6972 1.0834 1.0834 1.6551 0.9606 1.8590 1.0916 1.0927 1.0927
Si1-C2-H3 Si1-C2-H4 Si1-O5-H6 C2-Si1-O5 C2-Si1-C7 Si1-C7-H8 Si1-C7-H9 Si1-C7-H10
124.59 119.15 116.06 126.22 126.57 110.40 110.47 110.47
123.48 119.49 116.45 122.44 125.08 109.45 111.43 111.43
124.06 120.22 117.75 125.19 127.37 110.34 110.31 110.76
a
DFT/6-311G(2d,2p) cis
MP2/6-311G(2df,2pd)
trans
cis
1.6937 1.0821 1.0833 1.6543 0.9587 1.8706 1.0920 1.0936 1.0936
Bond Lengths 1.6940 1.6908 1.0806 1.0795 1.0810 1.0807 1.6459 1.6455 0.9594 0.9593 1.8557 1.8656 1.0887 1.0891 1.0900 1.0908 1.0900 1.0908
1.6953 1.0800 1.0813 1.6407 0.9584 1.8494 1.0871 1.0883 1.0883
123.20 120.34 118.95 121.32 125.81 109.51 111.56 111.56
Bond Angles 123.97 123.55 120.44 119.95 116.38 117.65 125.01 121.21 127.33 125.96 110.19 109.49 110.65 111.41 110.65 111.41
124.7 119.0 116.2 126.1 126.5 110.2 110.5 110.5
trans
DFT/6-311G(2df,2pd) cis
trans
1.6923 1.0792 1.0810 1.6406 0.9566 1.8587 1.0877 1.0892 1.0892
1.6937 1.0812 1.0818 1.6428 0.9593 1.8557 1.0891 1.0905 1.0905
1.6905 1.0800 1.0813 1.6426 0.9575 1.8654 1.0894 1.0912 1.0912
124.4 118.7 116.9 122.2 125.1 109.4 111.4 111.4
124.21 120.10 117.39 125.22 127.08 110.23 110.77 110.77
123.97 119.78 118.35 121.41 125.69 109.53 111.50 111.50
For atom numbering, see Figure 1.
TABLE 2: Calculated Total Electronic Energies, Dipole Moments, and Relative Energies for cis- and trans-Hydroxymethylsilaethylenea MP2/6-311G(d,p) DFT/6-311G(d,p) MP2/6-311G(2d,2p) DFT/6-311G(2d,2p) MP2/6-311G(2df,2pd) DFT/6-311G(2df,2pd)
E(cis)
µ
E(trans)
µ
E(trans) w E(cis)
-443.664 402 -444.617 659 -443.723 985 -444.632 045 -443.792 578 -443.827 051c -444.638 839
0.79 0.78 0.97 0.92 1.06
-443.659 612b -444.613 596 -443.720 274 -444.628 551 -443.789 031 -443.823 608c -444.635 457
3.40 3.39 3.34 3.29 3.34
-3.00 -2.35 -2.05 -2.02 -1.96 -1.90 -2.03
1.00
3.29
Energies in au, µ in debye; E(trans) w E(cis) corrected for ZPE × 0.95 (kcal/mol). One imaginary frequency 112i related to the almost pure (95%) OH torsional mode. c MP4(SDQ) at the MP2-optimized geometry. a
within unconstrained C1 symmetry of the system at the secondorder Møller-Plesset perturbation theory (MP2) and density functional theory (DFT) with Becke’s three-parameter exchange functionals and the gradient-corrected functional of Lee, Yang, and Parr (DFT(B3-LYP)).10 The standard split-valence triple-ζ 6-311G basis sets augmented by five-component d (heavy) and p (hydrogen atoms) polarization functions (6-311G(d,p) and 6-311G(2d,2p)) and an additional set of seven-component f polarization functions on Si, O, and C, and d polarization functions on hydrogen atoms (6-311G(2df,2pd)) were applied.11 At all levels, the order of the stationary point was checked by an analysis of the harmonic vibrational frequencies. Transformation of the force constant matrix in internal symmetry coordinates allowed ordinary normal coordinate calculations to be performed as described by Schachtschneider.12 The standard nonredundant symmetry coordinates were defined according to Pulay et al.13 (see also ref 14). The potential energy distribution (PED) analysis was performed using the PACK program.15 The same program was also used to calculate isotopic shifts of the studied species using the force constant matrices from the MP2 and DFT calculations for main cis and trans isotopomers. Final estimation of the total electronic energies for the studied systems was performed at the second-order Møller-Plesset perturbation theory through single-point fourth-order (MP4(SDQ)) with the 6-311G(2df,2pd) basis set using the MP2/6311G(2df,2dp) reference geometry. The frozen-core approximation was kept throughout. The final relative energies were corrected for the zero-point energy (ZPE) differences (scaled by a factor of 0.95). Results and Discussion The DFT- and MP2-optimized molecular parameters of cis and trans forms of hydroxymethylsilaethylene (Figure 1) are
b
listed in Table 1. At all applied levels of theory, the planar arrangement of the molecular skeleton, except for the H10 (below) and H9 (above) plane, was recovered. As could be expected, the calculated bond lengths and angles of the cis and trans forms are virtually the same. The largest differences are noted for the Si-C2 bond lengths (few thousandths of an angstrom) and C2-Si-C7 bond angles (ca. 1.4°). Also there are only minor differences among molecular parameters calculated using the MP2 and DFT methods, except the Si-O bond distance, which shortened by ca. 0.01 Å in both DFT and MP2 approximations when the 6-311G(d,p) basis set was replaced by the 6-311G(2df,2pd) one. Recently, we noticed very good agreement of the MP2/TZP and DFT/TZP approximations in predictions of molecular parameters for X2H6 and XYH6 (X, Y ) Si, Ge) species.16 We are not aware of any experimental molecular parameters available for HMSE. The cis conformer is predicted to be lower in energy than the trans species at all applied levels of theory. Its relative energy varies only slightly with the applied method, from -2.35 kcal/mol at the DFT/6-311(d,p) level to -1.90 at our highest MP4(SDQ)/6-311G(2df,2pd)//MP2/6-311G(2df,2pd) + 0.95 ZPE(MP2) level (Table 2). Generally, higher levels of theory stabilize the trans form. The trans form could be also stabilized by interaction with polar solvents, as indicated by the magnitude of its dipole moments (ca. three times larger than that predicted for the cis form). Our estimation of the small gas-phase energy difference between the cis and trans forms elucidates an existence of the trans conformer in the IR matrix spectrum recorded by Withnall and Andrews. The most striking difference among the various approximations used is a classification of the trans form. At the MP2/6311G(d,p) level, this conformer is a first-order transition
11618 J. Phys. Chem., Vol. 100, No. 28, 1996
Venkatraman et al.
TABLE 3: Calculated (MP2/6-311G(2df,2pd) and DFT/6-311G(2df,2pd)) Harmonic Vibrational Frequencies (cm-1), IR Absolute Intensities (km/mol), Isotopic Shifts, and Potential Energy Distribution (PED) for trans- and cis-Hydroxymethylsilaethylenea MP2
MP2
symmetry
freq
int
assgnmt
PED
18O
A′ A′ A′ A′ A′′ A′ A′ A′′ A′ A′ A′
3760 3135 3037 3032 3015 2930 1401 1394 1313 1227 1037
128 0 0 1 1 2 3 5 17 18 85
865
96
A′
812
195
100+ 99+ 97+ 96+ 100+ 99+ 95+ 95+ 92+ 97+ 57+ 2049+ 18+ 1571+
-13 0 0 0 0 0 0 0 1 0 -4
A′
1 OH str 2 CH2 a-str 3 CH2 s-str 4 Me a-str 5 Me def-str 6 Me s-str 7 Me a def1 8 ro Me out 9 CH2 sciss 10 Me s-def 11 SiC(2) str SiO str 12 SiO str SiC(2) str SiC(7) str 13 SiOH be
A′ A′ A′ A′ A′′ A′ A′ A′′ A′ A′ A′
3736 3126 3040 3031 3026 2937 1400 1391 1313 1228 1020
112 0 1 0 0 0 3 5 18 19 120
907
64
A′
806
175
100+ 100+ 100+ 99+ 100+ 100+ 95+ 95+ 93+ 97+ 66+ 203566+ 11+ 41+ 29+
-12 0 0 0 0 0 0 0 0 0 -5
A′
1 OH str 2 CH2 a-str 3 Me a-str 4 CH2 s-str 5 Me def-str 6 Me s-str 7 Me a def1 8 ro Me out 9 CH2 sciss 10 Me s-def 11 SiC(2) str SiO str 12 SiO str SiC(2) str SiC(7) str 13 SiOH be Me a-def1
-12 -7
-9 -6
2H
symmetry
trans-HMSE -790 A′ -25 A′ -165 -176 -240 A′ -337 -74 A′ -74 -70 -65 A′ -64 A′′ A′′ -50 A′′ A′ A′′ -87 A′′ cis-HMSE -1016 -803 A′′ -790 A′ -793 -824 -828 A′ -308 -352 -309 A′ -249 -116 A′′ A′′ -93 A′′ A′ A′′ -154 A′ A′′
freq
int
assgnmt
PED
18O
758 755
0 28
-40 -112
36
-8
-53
619
1
0
-66
588 512 253 215 207 135 109
70 0 7 24 5 2 80
81+ 58+ 1212+ 53+ 14+ 58+ 24+ 10+ 101+ 90+ 87+ 97+ 85+ 93+ 92+
0 -5
648
14 Me a-def2 15 ro Me in SiO str CH2 rock 16 SiC(7) str SiO str 17 CH2 rock SiC(7) str Me-a def1 18 CH2 wag 19 to CH2 20 SiO be 21 inv Si 22 C(7)SiC(2)be 23 to Me 24 to OH
0 -1 -6 -2 -1 0 0
-49 -31 -24 -12 -13 -8 -32
759 759
2 26
-139 -172
18
-4
-85
617
22
0
-135
582 500 288 255 216 205 126
49 23 94 19 40 4 0
1075+ 41+ 23+ 1463+ 12+ 11+ 68+ 14102+ 86+ 96+ 87+ 103+ 86+ 100+
0 -13
660
SiC(2) str 14 Me a-def2 15 ro Me in SiO str SiOH be str 16 SiC(7) str SiC(2) str SiO str 17 CH2 rock SiC(7) str 18 CH2 wag 19 to CH2 20 to OH 21 SiO be 22 inv Si 23 C(7)SiC(2)be 24 to Me
0 -1 -1 -6 -2 -1 -1
-136 -132 -64 -41 -19 -32 -35
DFT
DFT
symmetry
freq
int
assignment
PED
18O
A′ A′ A′ A′ A′′ A′ A′ A′′ A′ A′ A′
3719 3082 2998 2966 2943 2883 1390 1386 1315 1229 1027
107 0 0 4 4 4 3 5 20 14 90
857
101
A′ A′′ A′
816 762 761
205 0 18
100+ 99+ 98+ 99+ 100+ 98+ 96+ 95+ 93+ 98+ 60+ 1848+ 18+ 1372+ 81+ 55+
-12 0 0 0 0 0 0 0 0 0 -3
A′
1 OH str 2 CH2 a-str 3 CH2 s-str 4 Me a-str 5 Me def-str 6 Me s-str 7 Me a def1 8 ro Me out 9 CH2 sciss 10 Me s-def 11 SiC(2) str SiO str 12 SiO str SiC(2) str SiC(7) 13 SiOH be 14 Me a-def2 15 ro Me in
A′ A′ A′ A′ A′′ A′ A′ A′′ A′ A′ A′
3692 3070 2991 2971 2953 2891 1390 1384 1316 1236 1010
90 2 1 4 2 2 3 5 20 15 128
894
71
A′
801
133
100+ 100+ 99+ 100+ 100+ 99+ 95+ 95+ 93+ 98+ 67+ 1838+ 30+ 1144+
-12 0 0 0 0 0 0 0 0 0 -4
A′
1 OH str 2 CH2 a-str 3 CH2 s-str 4 Me a-str 5 Me def-str 6 Me s-str 7 Me a-def1 8 ro Me out 9 CH2 sciss 10 Me s-def 11 SiC(2) str SiO str 12 SiO str SiOH be SiC(7) str 13 Me a-def1
a
2H
-11 -8 0 -6
-9 -4
2H
symmetry
trans-HMSE -637 -84 -32 A′ -23 0 0 0 A′ 0 0 A′′ 0 A′′ -9 A′ A′ -4 A′′ -45 -91 -74
freq
int
654
29
619
4
602 504 261 216 211
23 0 6 5 53
A′′
182
49
A′′
103
0
767 758
0 59
653
31
625
8
597 494 259 256 213 211 116
57 15 21 97 2 2 0
cis-HMSE -622 -79 A′′ -20 A′ -18 -62 -203 A′ 0 0 A′ 0 -1 A′′ -1 A′′ A′′ -24 A′ A′′ A′ -25 A′′
assignment
PED
SiO str CH2 rock 16 CH2 rock Me a-def1 SiOH be SiC(7) str 17 SiC(7) str CH2 rock 18 CH2 wag 19 to CH2 20 SiO be 21 C(7) SiC(2)be 22 inv Si to OH 23 to OH inv Si 24 to Me
16+ 1248+ 12+ 11+ 1070+ 18+ 101+ 90+ 87+ 85+ 81+ 1977+ 18+ 98+
SiOH be 14 Me a-def2 15 SiO str ro Me in SiOH be 16 CH2 rock SiC(7) str 17 SiC(7) str CH2 rock 18 CH2 wag 19 to CH2 20 SiO be 21 to OH 22 C(7) SiC (2) be 23 inv Si 24 to Me
32+ 83+ 33+ 28+ 2536+ 2853+ 36+ 102+ 89+ 85+ 97+ 85+ 103+ 99+
18O
2H
-3
-35
-3
-18
0 0 -5 -2 -2
-25 -5 -10 -2 -5
0
-44
0
-1
0 -16
-1 -65
-2
-27
-1
-28
0 -1 -4 -2 -2 -1 0
-26 -4 -12 -40 -1 -25 0
For atom numbering, see Figure 1. Harmonic wavenumbers scaled by 0.95. In a PED analysis contributions of less than 10% are disregarded. Signs + and - show the phase of the coordinate mixing. Abbreviations: str, stretching; s, symmetric; a, asymmetric; def, bending vibrations of HCH combined with rotation of Me group against the rest of molecule; def1, bending vibrations of HCH; def2, rotation of Me group against the rest of molecule; inv, inversion; in, in-plane; out, out-of-plane; ro, rocking; wa, wagging; sciss, scissoring; to, torsion; be, bending. Shifts correspond to hydroxyl group isotopic substitutions. b Assigned experimental frequencies:7 3737 to 3726 (OH str), 899 (SiC str), 777.5 and 781 (SiO), 729.7 (SiOH bend), 285.1 cm-1 (CSiC bend).
Two Distinct Isomeric Forms of Me(OH)SiCH2 structure characterized by an imaginary frequency of 112 cm-1. When the basis set is saturated by the second and third set of polarization functions, this imaginary frequency becomes a real one of 117 and 109 cm-1 at the MP2/6-311G(2d,2p) and MP2/ 6-311G(2df,2pd) levels, respectively. At the DFT and HF (not given in the paper) levels the trans form is predicted independently of the applied basis set to be a local minimum species. Calculated vibrational frequencies and their shifts upon isotopic substitutions could deliver a conclusive confirmation for the Withnall and Andrews predicted existence of two hydroxy forms of HMSE. Since the calculated harmonic vibrational frequencies are compared to the experimental anharmonic data, we multiplied predicted frequencies by a uniform scaling factor of 0.95, which mainly compensates for the anharmonicity of the experimental data and limited electron correlation contributions included in our calculations. In Table 3, the results of our MP2/6-311G(2df,2pd) and DFT/6-311G(2df,2pd) calculations are presented. Two OH stretching vibrations observed by Withnall and Andrews at 3715 and 3737 cm-1 correspond well with the strong, highest-energy frequencies predicted at 3736 and 3760 cm-1 (MP2) and 3692 and 3719 cm-1 (DFT) for cis and trans isomeric forms, respectively. Even better agreement is obtained if one compares their difference. The experimental νOH(trans) - νOH(cis) is 22 cm-1, very close to the values of 24 and 27 cm-1 at the MP2 and DFT levels, respectively. The experimental 18O red shift of these two bands by 11.0 and 11.6 cm-1 corresponds to the calculated shifts of 12 and 13 cm-1 (MP2 level) and 12 and 12 cm-1 (DFT level). As is also evident from the comparison of data in Table 3, other observed shifts of vibrational frequencies upon 18O and deuterium substitution are qualitatively in agreement with our predictions and with the PED analysis of modes. In addition, 759 (cis-HMSE) and 755 cm-1 (trans-HMSE) modes with a significant SisO stretching component calculated at the MP2 level correspond well to the experimentally observed doublet of 781.5 and 777.5 cm-1, showing an 18O shift of 16 cm-1. The corresponding shift predicted for the cis form amounts to 13 cm-1, while for the trans form it corresponds to 5 cm-1. Thus, our data strongly support the assigned position of the SisO stretching mode in HMSE. It should be pointed out that the result of the MP2 and DFT calculations with the same basis sets are very similar. Such agreement has been noted already in a recent study on molecular parameters of Si2H6 and SiGeH6.16 In the present study, in addition to the agreement observed for predicted molecular parameters, vibrational frequencies and intensities from the DFT level also match closely those obtained using the MP2 approximation. Conclusions The existence, proposed by Withnall and Andrews, of two hydroxy forms of methylsilaethylene was confirmed by rigorous ab initio calculations. Our results indicate that the difference in their energies is within ca. 2 kcal/mol, with the cis form being
J. Phys. Chem., Vol. 100, No. 28, 1996 11619 a lower energy conformer at all applied levels of theory. The MP2- and DFT-level molecular parameters and vibrational frequencies agree well, and both closely reproduce available experimental data. Augmention of the basis set by polarization functions has an insignificant effect on predicted molecular geometries, except for the length of the polar Si-O bond. The DFT method is a cost-effective and reliable computational alternative in the study of molecular structures and vibrational frequencies of the hydroxymethylsilaethylenes. Acknowledgment. We thank Prof. J. S. Kwiatkowski for illuminating discussion and a reviewer for helpful comments and corrections. This study was supported in part by ARPANaval Regional Contract NOO174-93-RC-00004, the National Science Foundation Grant RII-8902064, and a contract (DAAL 03-89-0038) between the Army Research Office and the University of Minnesota for the Army High Performance Computing Research Center under the auspices of the Department of the Army, Army Research Laboratory Cooperative Agreement No. DAAH04-95-2-0003/Contract No. DAAH0495-C-008, the policy of the government, and no official endorsement should be inferred. The Mississippi Center for Supercomputing Research is acknowledged for a generous allotment of computer time. References and Notes (1) Schriver, L.; Abdelaoui, O.; Schriver, A. J. Phys. Chem. 1992, 96, 8069. (2) Lugez, C.; Schriver, A.; Schriver-Mazzuoli, L.; Lasson, E.; Nielsen, C. J. J. Phys. Chem. 1993, 97, 11617. (3) Whitnal, R.; Andrews, L. J. Phys. Chem. 1990, 94, 2351. (4) Whitnal, R.; Andrews, L. J. Am. Chem. Soc. 1986, 108, 8118. (5) Whitnal, R.; Andrews, L. J. Am. Chem. Soc. 1985, 107, 2567. (6) Whitnal, R.; Andrews, L. J. Phys. Chem. 1995, 89, 2361. (7) Whitnal, R.; Andrews, L. J. Phys. Chem. 1988, 92, 594. (8) See, for example: Hehre, W. H.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; John Wiley and Sons: New York, 1986. (9) Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schelgel, H. B.; Robb, M.; Replogle, E. S.; Gomperts, R.; Anders, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. I.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A GAUSSIAN92, Revision A; Gaussian, Inc.: Pittsburgh, PA, 1992. (10) (a) Kohn, W.; Sham, L. J. Phys. ReV. 1965, A140, 1133. (b) Lee, C.; Yang, W.; Parr, R. Phys. ReV. 1988, B37, 789. (c) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (11) (a) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. (b) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, 3265. (12) Schachtschneider, J. H. Technical Report, Shell Development Co.: Emeryville, CA, 1969. (13) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J. Am. Chem. Soc. 1979, 101, 2550. (14) Fogarasi, G.; Pulay, P. In Vibrational Spectra and Structure; Durig, J. R., Ed.; Elsevier: Amsterdam, 1985; Vol. 14, p 125. (15) (a) KuBulat, K. Ph.D. Dissertation, University of Florida, 1989. (b) Person, W. B. Personal communication. (16) Leszczynski, J.; Huang, J. Q.; Schreiner, P. R.; Vacek, G.; Kapp, J.; Schleyer, P. v R.; Schaefer, H. F., III. Chem. Phys. Lett. 1995, 244, 252.
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