J. Phys. Chem. 1988, 92, 28-33
28
TABLE I: Van Vleck-Weisskopf Parameters for Some Fundamental Bands s ( 10-5) A,,, km/mol "01 -/,
sample cm-' C& 678
CHCI, CHlI CDJ (3.5
cm-I
3.91 1035 5.56 769 6.95 522 5.17 884 16.0 493 3.38 656 11.2 2.34 315 1534 4.39
Dresent Crawford" Present Crawford 151 6.34 280 9.29 15.1 4.27 8.96 15.8 116
103 4.35 198 6.08 10.2 2.8 1 5.99 11.7 80.2
154 15.1 33 1 3.93 18.3 1.61 5.99 4.50 784
105 10.3 234 2.57 12.4 1.06 4.01 3.33 542
the VVW parameters, vo, y, and S , from the optical constants, n and k . The same graphical technique as that described in ref 2 was used. The values of nD for C6H6, CHCI,, CH31 (=CD31), and C6F6 were respectively taken as 1.4979, 1.4429, 1.5270, and 1.3781. Table I shows the results. The present values of the strength factor S are about 1.5 times those previously reported. For a fundamental transition arising from the normal coordinate Q, S becomes
with
"References 1-5. When the VVW model6 is applied to absorption in_ the infrared region, it gives rise directly to an expression for Co:
c,/
=s
[
vo2 -
vov
(vo - v)2
+ y2 + vo2 + vov + y2 + y2
(vo
+ v)2 + y2
]
(4)
where S is the strength factor, vo is the oscillator's resonance frequency, and y is the damping constant. Thus, combinations of eq 2 and 4, and eq 3 and 5, respectively, enable us to determine
Here N is the number of oscillators per unit volume, c is the light velocity, ( d ~ / d Q )is~ the dipole moment derivative, and A,,, represents the absolute band intensity corrected for the internal field. If A,, calculated from the present S is reasonable, it will support the new equation. Such study is now under way and will be reported later in detail. Registry No. Benzene, 7 1-43-2; chloroform,67-66-3; methyl iodide, 74-88-4: methyl iodide& 865-50-9; hexafluorobenzene, 392-56-3.
Vibrational Spectra of Methylstannane: A Molecular Force Field and Dipole Moment Derivatives from ab Initio Second-Order Mraller-Plesset Calculations C. Pouchan,* G . Lespes, and A. Dargelos Laboratoire de Chimie Structurale, UA 474, FacultP des Sciences Exactes et Naturelles, Universitt de Pau et des Pays de I'Adour, 64000 Pau, France (Received: March 24, 1987)
We have predicted the vibrational spectra (frequencies and intensities) and the associated force field for methylstannane using basis sets of double {quality and a pseudopotential treatment for the tin. The calculations were performed by using HF and correlated wave functions via the second-order Merller-Plesset perturbation method. Agreement with experiment is good since most of significant coupling constants agree in sign and magnitude with the experimental data based on the HOFF assumptions. We believe our force field for methylstannane to be the most complete to date and compare it to the chemically similar force field for ethane and methylsilane.
Introduction Ab initio calculations of the force field and vibrational frequencies of a variety of polyatomic molecules have been reported in the last decade.14 Most of these studies were carried out at the Hartree-Fock level by using gradient techniques. Extended to larger molecules these studies have been restricted, however, to compounds containing first- and second-row atoms! With basis sets of double 5 quality, harmonic frequencies typically of around 10-1 5% higher than the experimental values have been obtained in such s t u d i e ~ . ~ -This ~ overestimation is partly due to the harmonic approximation (3-5%) partly to the neglect of electron correlation (7-1 0%)
Data deduced from correlated wave function calculations are also becoming a ~ a i l a b l e ,mostly ~ . ~ from the configuration interaction method,"Sl0 the Maller-Plesset perturbation approach4J1J2 and some from multiconfiguration Hartree-Fock wave funct i o n ~ . ~ Such . ' ~ studies have shown that the calculated frequencies are in much better agreement with experiment than those obtained at the Hartree-Fock level. Most often applied to small systems, these calculations also have examined large molecules with only first- and second-row atoms. The observation that the error in computed vibrational frequencies is quite systematic for a given basis set has led to the suggestion that scale factors be used to correct force constants at S C F (or CI level). It has also been found that basis set and
(1) For an overview, see Pulay, P. In Modern Theoretical Chemistry;
Schaeffer, H. F., IV, Ed.; Plenum: New York, 1977, Vol. 4. (2) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J . Am. Chem. Soc. 1979, 101, 2550, and references cited therein. ( 3 ) Fogarasi, G.; Pulay, P. In Vibrational Spectra and Structure; Durig,
J. P., Ed.; Elsevier: Amsterdam, 1985; Vol. 14. (4) Hess, B. A.; Jr.; Schaad, L. J.; Carsky, P.; Zahradnik, R. Chem. Reo. 1986, 86, 709, and references cited therein.
(5) Pouchan, C.; Dargelos, A.; Chaillet, M. J . Chim. Phys. 1978, 75, 595. (6) Blom, C. E.; Altona, C. Mol. Phys. 1976, 31, 1377. (7) Yamaguchi, Y.; Shaeffer, H . F., I11 J . Chem. Phys. 1980, 73, 2310.
0022-3654/88/2092-0028$01 SO10
(8) Almlof, J. In Geometrical Derivatives of Energy Surfaces and Molecular Properties; Jorgensen, p.; Simmons, J., ms.;Reidel: Dordrecht, 1986. (9) For an overview, see Jorgensen, P.; Simmons, J. J . Chem. Phys. 1983, 79, 334; J . Chem. Phys. 1983, 79, 3599. (10)Botschwina, P. Chem. Phys. Left. 1984, 107, 535. (1 1) Hout, R.F., Jr.; Levi, B. A.; Hehre, W. J. J . Comput. Chem. 1982, 3, 234. (12) Hess, B. A,, Jr.; Schaad, L. J. J . Am. Chem. SOC.1985, 107, 865. (13) Dupuis, M.; Wendoloski, J. J. J . Chem. Phys. 1984, 80,5696.
0 1988 American Chemical Society
Vibrational Spectra of Methylstannane
The Journal of Physical Chemistry, Vol. 92, No. 1, 1988 29
electron correlation effects are more important for diagonal force constants than they are for most coupling force constants.I4 Thus, a force field given by theoretical calculations may be improved considerably if the diagonal of the force constant matrix is replaced by data originating from some other experimental source (frequencies derived from isotopic derivatives, intensities, ...).2,15 Ideally, one would adjust the theoretical force field by fitting it to the experimentally determined harmonic frequencies or, if the latter are not known, to the observed frequencies as a first approximation. In this paper we report an ab initio calculation of the vibrational frequencies and the IR intensities of methylstannane, CH3SnH3. Electron correlation effects on the force field are investigated from a second-order Moller-Plesset approach (MP2). The values of scale factors for the diagonal force constants were determined by a least-squares fit of the calculated fundamental frequencies to harmonic vibrational spectra of SnH3CH3and two of its deuteriated forms. The resulting force field is believed to be the best available harmonic force field for SnH3CH3. Methylstannane is an interesting molecule for several reasons: It contains a heavy atom, tin, which is treated by using a relativistic pseudopotential to describe the core electrons. Except for the recent study of Schneider and Thiel16 restricted at the Hartree-Fock level, an approach of this type has not been developed to any great extent for obtaining force fields in large sized systems. Methylstannane is a homologue of ethane and methylsilane, for which force fields have been more or less clearly established. It is thus of interest to determine a complete force field for methylstannane in order to analyze the similarities and differences observed in the series. Finally, experimental data on the vibrational spectrum17taking into account anharmonicity corrections, as well as the determination of structure from microwave spectra analysis,’*are available for methylstannane. These data can be used either for comparison with calculated values or combined with theoretical data to improve the computation. An important objective of this paper is: to evaluate from S C F and MP2 wave functions the a priori force field of SnH3CH3and to discuss discrepancies between the calculated and the experimentally derived force field; to propose from a combination of experimental and theoretical methods the best available harmonic force field for methylstannane; to compare the force field parameters of SnH3CH3with those of SiH3CH3and CH3CH3because of their structural similarity; and to give on the basis of IR intensities and frequencies the vibrational spectrum of SnH,CH, and eventually to remove any remaining doubt in the assignment.
TABLE I: Internal Coordinates for Methylstannane
Calculations
In this work we have located the theoretically predicted equilibrium geometry and evaluated the harmonic force constants at the S C F and second-order Maller-Plesset correlation (MP2) levels of theory. All of the calculations reported here have been carried out with the PSHONDO program systemI9 using the pseudopotential atomic approximation proposed by Durand and BarthelatZ0for tin. Computations have been carried out with Dunning’sz1 [9s5p] Gaussian basis contracted to [4s2p] for the carbon, while the hydrogen basis was the [2s] contraction derived by Dunningz1from (14) Pulay, P.; Lee, J. G.; Boggs, J. E. J . Chem. Phys. 1983, 79, 3382. (15) Pouchan, C.; Liotard, D.; Dargelos, A,; Chaillet, M. J . Chim. Phys. 1976, 73, 1046. (16) Schneider, W.; Thiel, W. J . Chem. Phys. 1987, 86, 923. (17) Kimmel, H.; Dillard, C. R. Spectrochim. Acra, Part A 1968, 24A, 909.
(18) Durig, J. R.; Whang, C. M.; Attia, G. M.; Li, Y . S . J . Mol. Spectrosc. 1984, 108, 240. (19) (a) Maynau. D.; Daudey, J. P. Chem. Phvs. Lett. 1981.81, 273. (b) Technical Report, Workshop on Pseudopotentiais; Laboratoire de Physique Quantique, UniversitC Paul Sabatier: Toulouse, 1981. (20) Durand, Ph.; Barthelat, J. C. Theor. Chim. Acta 1975, 38, 283. (21) Dunning, T. H., Jr.; Hay, P. J. In Modern Theoretical Chemistry, Schaeffer, H. F., 111, Ed.; Plenum: New York, 1977; Vol. 2
Qis
Q16 Q17 Qi8 e19 Q20
Q2 I Q22 Q23 Q14
Qzs Q26
Q27 Q28
TABLE I 1 Definition of Symmetry Coordinates for Methylstannane
E
SnH, str CH, str SnH, bend CH, bend SnH3 rock
CH3 rock A2
Q23
+
torsion
the [4s] primitive basis. The core electrons of the tin atom are incorporated into the Hamiltonian of the system by an analytical pseudopotential one-electron operator using a relativistic description in order to take account of the high atomic number of tin.2z The valence “ab initio” calculations were undertaken by using a double f basis set23enlarged with d orbitals for the tin atom which is denoted by [2s2pld]. The exponent of these d functions (< = 0.20) was obtained by minimization of the S C F energy on the SnH4 molecule.24 The geometry and force constant calculations were performed by using analytical gradient methods described elsewhere25at H F level and numerical differentiation at MP2 level, with residual forces being less than hartree/bohr. Plus and minus distortions along each symmetry coordinate (Table 11), constructed from the standard set of internal coordinates defined in Table I, were made for the diagonal force constants and appropriate crossed distortions for the off-diagonal terms. Step sizes of 0.01-0.03 A were used for bond lengths and 2-4’ were used for bond and dihedral angles. The choice of this symmetry-adapted internal coordinate representation facilitates the assignment of the spectra and, as the discussion in the next section shows, allows us to focus on the difference and similarities in the bonding environment between methylstannane and methylsilane26 and ethane.27 (22) Barthelat, J. C.; Pelissier, M.; Durand, Ph. Phys. Rev. A 1981, 21, 1773. (23) Barthelat, J. C.; Durand, Ph.; Serafini, A. Mol. Phys. 1977, 33, 159. (24) Fernandez, J.; Lespes, G.; Dargelos, A. Chem. Phys. 1986, 103, 85. (25) (a) Komornicki, A,; Ishida, K.; Morokuma, K.; Ditchfield, R.; Conrad, M. Chem. Phys. Lett. 1977, 45, 595. (b) Dupuis, M.; King, H. K. J . Chem. Phys. 1978, 68, 3998. (c) Trinquier, G.; Daudey, J. P.; Komiha, N. J . Am. Chem. SOC.1985, 107, 7210. (26) Komornicki, A. J . Am. Chem. SOC.1984, 106, 3114.
30
The Journal of Physical Chemistry, Vol. 92, No. I, 1988
Pouchan et al.
internal rotation. This barrier is found to be within the range 0.5-0.6 kcal-mol-', which is consistent with the value (0.6 kcalmol-') determined from the microwave spectra.I8 Daram SCF MP2 exvtl'* The Force Field. The methylstannane force field was calculated r ( S n - H ) , 8, 1.716 1.730 1.708 f 0.001 by considering the following interesting aspects: the effect of 2.140 f 0.001 2.108 2.148 r(C-Sn), A electron correlation on the theoretical force field, the comparison r(C-H), A 1.085 1.108 1.083 f 0.005 with the parameters deduced from experimental data, and finally a ( C S n H ) , deg 110.82 110.57 109.36 f 0.03 the evolution of the force constants in the XH3-CH3 series (X a ( S n C H ) , deg 110.66 110.17 110.36 f 0.04 = C, Si). In order to permit a more detailed comparison of these A, GHz 46.381 45.110 46.069 derived force fields, their harmonic force constants at various levels 7.051 6.81 1 6.892 B, C, G H z are listed in Table IV. The vibrational analysis was performed with the formalism of It should be noted that electron correlation effects appear to Wilson et from the geometry and the force field deduced from be more important for diagonal force constants than they are for our calculations. In order to obtain complementary spectrum most coupling force constants. Except for Sn-C the MP2 diagonal assignment data, dipole moment derivatives with respect to the values are smaller than the H F results by about 2% for the symmetry coordinates have been calculated. The dipole derivatives stretching terms and from 6% up to 13% for the bending ones. The study of the off-diagonal force constants reveals some inwere calculated as finite differences of the dipole moment when teresting features. The inclusion of electron correlation changes the geometries were displaced. The variations of the Cartesian some of the coupling force constants significantly. Mostly, their coordinates used to calculate &/&Si are estimated in such a values decrease in our MP2 calculations. Except for the coupling manner that the nuclear distortions (relative to the reference geometry) satisfy the Eckart condition^.^^ In these conditions, SnH, stretch/CH3 stretch, the sign is preserved for all coupling the rotational contribution to the IR intensities will be c a n ~ e l e d ~ . ) ~ terms even if the predicted force constants are small. In all cases the H F force constants of methylstannane are improved in taking and the intensities are, in the hypothesis of electrical and meinto account correlation effects through MP2 calculations. chanical harmonicity, expressed in terms of the integrated abA force field given by H F or MP2 calculations may therefore sorption coefficient: be improved considerably if the diagonal of the force constant matrix is fitted by data originating from some other source, such as experimental frequencies. In this way, with the MP2 coupling where N A is Avogadro's number, C the speed of light, gk the values and harmonic frequencies, it seems worthwhile combining degeneracy of the mode under consideration, and Llk the [L] these data in order to determine the best available harmonic force matrix elements which relates the symmetry coordinates [SI to field for methylstannane. The adjusted force field thus obtained the normal coordinates [ Q ] . by a fitting procedure allows us to propose scale factors for S C F and MP2 diagonal terms (Table V). Except for the SnC stretch, Results and Discussion these values show that the diagonal stretching and bending force constants are similarly overestimated at the MP2 level, which is Molecular Structure. Our results for the structure of mecontrary to the H F level where the bending terms are more ovthylstannane are given at H F and MP2 levels in Table I11 and erestimated than the stretching ones. are compared to the data deduced by Durig et al.'* from the A comparison of the H F force constants in the series XH3-CH3 microwave spectra. It is generally accepted that electron corre(X = C, Si, Sn) reveals that the Sn-C stretch diagonal force lation increases the bond lengths relative to the value predicted constant is much smaller than the one corresponding to the Si-C at the S C F level. Indeed, MP2 results yield bond lengths that stretch in methylsilane and this latter is again much smaller than are slightly longer than those found at the S C F level, the biggest the C-C stretch in ethane. This trend can be explained by the change being in the C-Sn distance. Electron correlation causes increase of the central bond length in the series. The same obfor CSn a significant bond lengthening by 0.04 A and gives a Sn-C servations for the SnH3 group are true in the SnH3 stretching, distance (2.148 A) in perfect agreement with the experimental deformation, bending, and rocking descriptions compared to the value (2.140 A). The equilibrium S n H distance from S C F calSiH, and CH, groups in methylsilane and ethane. The methyl culations (1.716 A) also agrees with the experimental values (ro part in methylstannane looks very much like the CH, portion of = 1.708 A; rs = 1.713 A) and is identical with that previously methylsilane leading, at the H F level, to comparable diagonal and calculated by one of us for SnH4.24This Sn-H distance, reduced interaction force constants. Furthermore, within the A , and E by about 0.02 A as the relativistic effect is introduced, remains symmetry blocks we do observe that the methyl group stretching slightly above the value found in the microwave experiment. is nearly the same for the three molecules, with the CH, asymInclusion of electron correlation at the MP2 level lengthens the metric stretch being much smaller than the symmetric one. Thus Sn-H bonds which were overestimated by 0.017 8, in comparison for a number of modes the methyl group force constants appear to the microwave data. The trends observed for Sn-H are reto be insensitive to the presence of SnH, group on the other end produced for C H bonds and suggest that the presence of p poof the molecule. larization functions on the hydrogen atoms could be important As in methylsilane, we do find that the methyl rock diagonal for an improved prediction of bond lengths. force constant in methylstannane is smaller than the methyl bend All calculated bond angles agree very well with experimental in contrast to the one observed in ethane. If we turn our attention data and appear to be practically insensitive to the electron to the interaction force constants, we find that they are in general correlation effect. At MP2 level, no calculated bond angle deviates comparable in SnH,-CH, and SiH,-CH, but generally smaller by more than 0.2' from experiment. Calculations of the B rothan in ethane. Surprisingly, it should be noted that the XH, tational constants give values (7.051 and 6.81 1 GHz at S C F and rock/CH, rock interaction is important and similar in magnitude MP2 levels) in good agreement with experiment (6.892 G H z ) , ' ~ for the three molecules in spite of an increased X-C distance in corroborating the quality of the calculated structural parameters. the series. This accuracy between calculated and experimental data is conA detailed comparison of the calculated and experimentally firmed by the S C F and MP2 results obtained for the barrier to derived force field can be made since Kimmel and Dillard17 have proposed a harmonic force field from the study of fundamentals, (27) Duncan, J. L.; Kelly, K. A.; Nivellini, G. D.; Tullini, F. J . Mol. overtones, and combination bands for three isotopic molecules. Spectrosc. 1983, 98, 87. Based on the assumptions of the hybrid orbital force field (HO(28) Wilson, E. B.; Decius, J . C.; Cross, P.C . Molecular Vibrations: McGraw-Hill: New York, 1955. FF),,l which provides relationships between stretch-bend interTABLE 111: Calculated Geometries and Rotational Constants for Methylstannane
~~~
~~
(29) Eckart, C. Phys. Rev. 1935, 45, 552. (30) Lakdar, T. B.; Suard, M.: Taillandier, E.; Berthier, G. Mol. Phys. 1978, 36, 509.
(31) Mills, I. M. Sperfrochim. Acta 1963, 19, 1585
The Journal of Physical Chemistry, Vol. 92, No. I , 1988 31
Vibrational Spectra of Methylstannane
TABLE I V Calculated Harmonic Force Constants at Different Levels of Theory for MethylstannaneO description exptl” SCF MP2 adj val Sn-C str 2.124 2.870 2.895 2.139 AI Fl.1 2.237 2.241 2.524 2.458 SnH, str F2,2 5.424 5.895 5.391 5.760 CH, str F3,3 0.434 0.431 0.561 0.511 SnH, def F4,4 0.474 0.453 0.605 0.557 CH, def F5.5 0.056 0.086 0.056 Fl,2 -0.016 -0.019 -0.016 Fl,3 -0.115 -0.119 -0.115 -0.046 Fl,4 -0.229 -0.224 -0.229 -0.282 FI.5 -0.0 10 0.01 1 -0.0 10 F2,3 0.061 0.062 0.062 0.054 F2,4 -0.022 -0.018 -0.018 F2,5 -0.020 -0.025 -0.020 F3,4 0.186 0.205 0.101 0.186 F3.5 0.024 0.020 0.020 F4,5 2.217 2.217 2.437 2.396 SnH, str E F6.6 5.377 5.366 9.843 5.789 CH, str F7.7 0.398 0.332 0.493 0.426 SnH, bend F8,8 0.669 0.576 0.551 0.624 CH, bend F9,9 0.504 0.473 0.407 0.456 SnH, rock FI0,lO 0.456 0.41 3 0.395 0.426 CH, rock Fll,ll -0.01 1 -0.004 -0.004 F6,7 -0.075 -0.062 -0.086 -0.062 F6,8 0.007 0.007 0.002 F6.9 0.066 0.075 0.090 0.066 F6.10 0.03 1 0.031 0.029 F6,11 -0.003 -0.012 -0.003 F7,8 -0.197 -0.143 -0.197 -0.194 F7,9 0.033 0.029 0.033 F7.10 0.142 0.137 0.143 0.142 F7,11 -0.002 -0.002 -0.005 F8,9 -0.087 -0.053 -0.053 0.029 F8.10 -0.034 -0.027 -0.027 F8.11 -0.003 -0.002 -0.002 F9,10 0.018 0.008 0.012 0.008 F9,11 0.176 0.158 0.087 0.158 FIOJ I 0.0021 0.0027 0.0021 torsion A2 F12.12
SiH,CH326 3.216 3.386 5.885 0.634 0.589 0.098 0.062 -0.134 -0.199 0.014 0.063 -0.025 -0.020 0.140 0.022 3.228 5.755 0.581 0.668 0.623 0.496 -0.013 -0.086 0.0 0.086 0.031 -0.0 16 -0.157 0.042 0.144 -0.009 -0.097 -0.032 0.0 0.020 0.197 0.0018
c2H626 4.950 5.833 5.833 0.67 1 0.671 0.138 0.138 -0.325 -0.325 0.010 0.135 -0.027 -0.027 0.135 0.032 5.670 5.670 0.693 0.693 0.782 0.782 -0.029 -0.162 -0.006 0.115 0.057 -0.006 -0.162 0.057 0.115 -0.005 -0.023 0.004 0.004 -0.023 0.175
“Stretching, bending, and stretch-bend force constants are in aJ A-2,aJ, and aJ A-I, respectively. TABLE V Calculated Scale Factors for SCF and MP2 Diagonal Terms
diag force const SnC str SnH, str CH, str SnH, def CH, def
0.745 0.886 0.920 0.774 0.783
MP2 0.739 0.910 0.942 0.849 0.851
SnH, str CH, str SnH, bend CH, bend SnH, rock CH, rock
0.910 0.920 0.807 0.861 0.938 0.866
0.925 0.929 0.934 0.923 1.037 0.927
SCF
action force constants and their corresponding principal stretching terms, this experimental force field reduces the number of unknown parameters. The six stretch-bend interaction force constants were thus calculated by Dillard et a].” from the equations derived by Mills.31 Concerning the diagonal force constants, our “adjusted values” are in excellent agreement with those reported by Dillard et al.” The slight differences noted for FsnHlbend and FsnH,rock are due to the difficulty of the experimental determination since these two modes are strongly coupled. The study of the off-diagonal force constants reveals that the assumptions of the HOFF model are corroborated for most terms, especially at the MP2 level. The most glaring difference concerns (SnC,,/SnH, der) and F35(CH3,,/CH3 der) terms, which the FL4 are twice as large as the values quoted by Dillard et a1.I’ The experimental predictions are certainly underestimated in this case since these constants are then smaller than in ethane and in
m e t h y l ~ i l a n eDillard ~ ~ ~ ~ et ~ al. have also suggested that there is a possible correlation between the asymmetric deformation-rocking interaction force constant and the corresponding bond angle. On the basis of these assumptions, these constants were assumed to have a value of 0.012 and 0.029 a J for the CH, and SnH, groups, respectively, in the experimental determination. Our MP2 results value (0.008 aJ) but are agree very well with the FCHlkn,j/cH,rock incompatible (-0.053 aJ) with the experimentally derived FSnH3bend/SnH, rock value. The negative value found in our calculations is in agreement with the one obtained for the homologous term in methylsilane. Except for the interaction between the CH, and SnH, rocking, all the interaction force constants between the CH3 and SnH, groups were assumed to be zero in the experimental approach. Our MP2 results show that the FCH, rock/SnH, r,& is larger in our determination (0.158 aJ) than in the empirical one (0.087 aJ) and confirm the very small values of the other off-diagonal terms. Use of the presently reported theoretical values would be a good starting point for a more realistic analysis of the experimental data. Vibrational Analysis: Frequencies and Intensities. The resulting harmonic vibrational frequencies obtained at different levels of theory (HF, MP2, adjusted) are listed in Table VI. Harmonic frequencies derived from experimental isotopic studies by Kimmel and Dillardl’ are also listed for comparison. It is well-known that single-determinant H F theory using a double polarization basis set is moderately successful in reproducing the harmonic vibrational frequencies. Although deviations of calculated from measured frequencies are sizable, the errors are relatively constant, allowing systematic corrections by about 10%. At the MP2 level, the mean absolute deviation is roughly half that obtained at the corresponding H F level for molecules involving single bonds. This appears to be also true in our pseudopotential calculations. Indeed, the mean absolute per-
32 The Journal of Physicat Chemistry, Vol. 92, No. 1, 1988
Pouchan et al.
TABLE VI: Calculated Harmonic Vibrational Frequencies (cm-') for Methylstannane and Isotopic Derivatives: PED Analysis exptl16 SCF MP2 adj PED (7%)
SnH,CH, AI
CH, str SnH, str CH, def SnH, def SnC str
3058 1935 1242 716 527
3195 2066 1455 827 600
3156 2038 1354 780 603
3062 1944 1236 719 516
CH, str (100) SnHp str (100) CH, def (97) + SnC str (3) SnH, def (100) SnC str (97) + SnH, def (3)
CHI str SnH, str CH, def CH3 rock SnH, def SnH, rock
3157 1935 1481 796 755 430
3291 2038 1613 872 820 454
3276 2020 1526 827 766 430
3156 1943 1466 806 741 431
CH, str (100) SnH, str (100) CHI def (97) + CH, rock (3) CH, rock (76) + SnH, rock (15) + SnH, def (8) + CH, def (3) SnH, def (91) + CH, rock (11) + SnH, rock (3) SnH, rock (69) + CH, rock (30) + SnH, def (1)
1I O
134
118
109
E
A2
torsion
torsion Sn D CH
AI
,
CH, str SnD, str CH, def SnD, def SnC str
3055 1383 1237 504 509
3195 1469 1449 586 606
3156 1444 1353 555 605
3062 1378 1235 502 529
CH, str (100) SnD, str (100) CH, def (97) + SnC str (3) SnD, def (60) + SnC str (40) SnC str (63) + SnD, def (37)
CH, str SnD, str CH, def CH, rock SnD, def SnD, rock
3151 1383 1462 786 509 324
3291 1448 1613 848 583 344
3276 1436 1526 804 546 325
3156 1381 1466 779 528 327
CH, str (100) SnD, str (100) CH, def (97) + CH, rock (3) CH, rock (92) + SnD, rock (4) + CH, def (3) SnD, def (93) + SnD, rock (7) SnD, rock (7?) + CH, rock (23)
101
123
109
101
E
A1
torsion
torsion
SnH3CD, AI
CD, str SnH, str CD, def SnH, def SnC str
2210 1950 939 726 478
2292 2065 1126 827 547
2263 2038 1052 780 548
2194 1944 949 7 19 475
CD, str (100) SnH, str (100) CD, def (90) + SnC str (10) SnH, def (100) SnC str (96) + SnH, def (2.5) + CD, def (1.5)
CD, str SnH, str CD3 def CD, rock SnH, def SnH, rock
2339 1950 1049 643 75 I 404
2435 2037 1168 707 821 414
2423 2020 1107 663 77 1 394
2333 1943 1063 653 748 390
CD, str (100) SnH, str (100) CD, def (99) + CD, rock ( I ) CD3 rock (61) + SnH, rock (30) + SnH, def (9) SnH, def (88) + SnH, rock (10) + CD3 rock (1) SnH, rock (53) + CD, rock (45)
88
107
95
88
E
'42
torsion
centage deviations of the theoretical frequencies from experimental harmonic values are respectively 9.7%, 10.6%, and 9.2% at the HF level for SnH3CH3,SnD3CH3,and SnH3CD3. These deviations are reduced substantially to 5.3%, 6.3%, and 5.4% at the MP2 level. All MP2 calculated frequencies remain smaller than the corresponding HF quantities. This is consistent with the fact that the correlated calculated bond lengths are significantly longer than the corresponding H F distances. In all cases, the calculated MP2 frequencies are larger than the experimental values. When the fitting procedure carried out by using the experimental harmonic frequencies and the MP2 off-diagonal force constants is used as a starting point for calculations, the mean deviations decrease to 0.7%, 1.195, and 0.8% for the three isotopic molecules, leading to a very satisfactory agreement with experiment. The assignment then performed, based on the analysis of the potential energy distribution, is complemented by the calculation of integrated absorption intensities. These latter calculations require the determination of the dipole moment derivatives with respect to the symmetry coordinates (Table VII). As previously noted by KomornickiZ6for methylsilane, our calculations suggest that the electric dipole moment of methylstannane points toward the tin atom, Le., +CSn-, as resultant values of the vector sum of -CH +, +SnH-, and +SnC- bond dipoles. Moreover, our calculated dipole moment (0.73 D) appears to agree well with the
torsion
TABLE VII: Dipole Moment Derivatives &/as, and Integrated Intensities for Methylstannane
A,
vI v2 u3 v4
v5
E
v6 v, v8 v9
vIo vI1
description CH, str SnH, str CH, def SnH, def CSn str CH, str SnH, str
CH, def CH, rock SnH, def SnH, rock
A!,
-0.410 0.598 -0.1 11 -1.333 -0.679 0.518 -1.368 -0.257 0.526 -1.261 1.316
(S,) (S,) (S,) (S,) (SI) (S,) (S,) (S,)
(SI') (S,) (Si0)
km-mol-'
obsd
2.62 5.18 1.01 22.47 2.1 1 6.49 67.39 1.74 13.92 41.36 11.54
W 5
W 5
m W 5
W
m m m
In D.A-I or Darad-' for stretch or bend coordinates.
experimental value (0.68 D) reported by Lide.32 The integrated absorption intensities obtained from the dipole moment derivatives with respect to the symmetry coordinates and the L matrix derived from the normal-coordinate analysis after (32) Lide, D. R., Jr. J . Chem. Phys. 1951, 19, 1605.
J . Phys. Chem. 1988, 92, 33-36 the fitting procedure are given in Table VII. Generally, there is reasonable agreement between the calculated values and the qualitative observations of band intensities, which are of course subjective and affected by band type. The largest intensities are found for the Sn-H stretching [ v 2 ( A 1and ) u7(E)],and the next most intense are the SnH, deformation bands [u4(A1)and vlo(E)] followed by the CH, and SnH, rocking modes [v,(E) and v l l ( E ) ] . The corresponding motions are also the strongest bands in the recorded spectra. The very low intensities of the CH3 deformations [ Y ~ ( Aand I ) vs(E)]are also supported by our calculations. The only disagreement is found for the Sn-C stretching, where the calculated intensities appear to be widely underestimated relative to the qualitative observation although ap/aS, is important. Concerning the vibrational assignments based on the analysis of the potential energy distribution, our calculations show that except for the SnD, deformation and the SnC stretch modes of the A , symmetry species in SnD3CH3,the concept of characteristic group frequencies can be applied to the SnH3CH3and SnH3CD3 species in A I symmetry. In the case of the E symmetry species it appears that the CH, rocking, SnH, rocking, and SnH, deformation modes show a significant amount of mixing for CH3SnH, and CD3SnH3whereas the CH, rocking and SnH, deformation become relatively pure in CH3SnD3. The theoretical sequence of band positionning agrees with the experimental sequence obtained by Kimmel and Dillard.I7 Even in the relatively restricted spectral range between 700 and 800 cm-' our final calculations confirm the fact that the degenerate SnH, deformation is located between the degenerate CH3 rock and the symmetric SnH, deformation and has a higher intensity than the latter two. Nevertheless, it should be emphasized that this sequence is not exactly reproduced a t S C F and MP2 levels, where the degenerate SnH, deformation is found to be lower than the corresponding A I mode by about 10 cm-I. In all cases the
33
CH3 rock can be predicted close to 800 cm-l, in good agreement with the experimental value ( e 7 9 6 cm-I), comparable to the E , frequency (822 cm-I) found in ethane. The degenerate CH, deformation is a t a higher wavenumber than the symmetric one: this latter can be predicted to lie at 1236 cm-', somewhat lower than the values observed at 1264 cm-' in methylsilaneZ6and the harmonic values found in ethanes2' For these two modes it should be noted that the excessive weakness of the calculated intensities is in perfect agreement with the qualitative observations. The asymmetric and symmetric CH, stretchings are respectively predicted at 3156 and 3062 cm-', which is consistent with the observed values. For both calculations (SCF and MP2), the difference between the two bands which is found to be about 100 cm-' in CH3SnH3is widely increased in CD,SnH3 according to the infrared data. The antisymmetric and the symmetric SnH, stretches form a close group at about 1944 cm-I; their calculated splitting decreases when the level of theory is improved in our calculations. These bands shift in the spectra of SnD3CH3to about 1380 cm-' but remain unchanged in their assignments. In the low reginn of the IR spectra, the Sn-C stretch is found around 520 cm-' while the SnH, rock is expected at 430 cm-I, in good agreement with the experimental values. Furthermore, we find some mixing of the SnH, deformation or CH3 rock with these modes in agreement with the experimentally observed effect of deuterium isotope substitution. The lowest vibrational frequency of the molecule is the infrared-inactive torsional mode. Our MP2 calculations indicate that this stannyl torsion should appear at 118, 109, and 95 cm-' for the three isotopic species. These values are consistent with those estimated at 110, 101, and 88 cm-' by Kimmel and Dillard, based on the study of combination bands in the infrared spectra. Registry No. Methylstannane, 1631-78-3.
Pyramidal Inversion in Silyl Anions James R. Damewood, Jr.,* and Christopher M. Hadad Department of Chemistry, University of Delaware, Newark, Delaware 1971 6 (Received: April 3, 1987)
The barrier to pyramidal inversion in the silyl anion, SiH3- (l),the disilanyl anion, SiH,SiH,- (2), the formylsilyl anion, HCOSiH2- (3), and the borylsilyl anion, BH2SiH2-(4), are obtained by ab initio methods at the 6-31G* level of sophistication. The pyramidal inversion barriers calculated for these compounds are 34.7, 26.6, 23.8, and 0.7 kcalfmol, respectively. A comparison is made between the inversion barriers at silicon in the silyl anions and those at phosphorus in the isoelectronic phosphines.
Introduction Like their isoelectronic analogues from group 15 (Va), the anions of group 14 (IVa) are tricoordinate with a lone pair of electrons and have the potential to undergo the process of pyramidal inversion.' The parent compound in this series, the methyl anion, has received considerable theoretical and experimental attention2 and (if bound) is believed to reside in a very shallow potential energy well with an inversion barrier of only ca. 1-2 (1) For reviews of pyramidal inversion, see: Rauk, A.; Allen, L. C.; Mislow, K. Angew Chem., Int. Ed. Engl. 1970, 9, 400. Lambert, J. B. Top. Stereochem. 1971, 6, 19.
(2) For example, see: Dykstra, C. E.; Hereld, M.; Lucchese, R. R.; Schaefer, H. F. 111; Meyer, W.J . Chem. Phys. 1977, 67, 4071 (theoretical). Ellison, G. B.; Engelking, P. C.; Lineberger, W. C. J. Am. Chem. SOC.1978, 100, 2556 (experimental).
kcal/mol. Unlike the methyl anion, relatively little information is available on the higher homologues from this series., The static and dynamic stereochemistry of silyl anions, for example, is particularly poorly characterized even though these species are some of the more common reagents in modern silicon chemistry. We have performed the ab initio calculations reported in this paper in order to provide information on the pyramidal inversion process in silyl anions. These data will allow for comparisons between (3) For example, see: (a) Rauk, A,; Andose, J. D.; Frick, W. G.; Tang, R.; Mislow, K. J . Am. Chem. SOC.1971, 93, 6507 and references therein. (b)
Keil, F.; Ahlrichs, R. Chem. Phys. 1975, 8, 384. (c) Lambert, J. B.; Urdaneta-Ptrez, M. J . Am. Chem. Soc. 1978,100, 157. (d) Eades, R. A,; Dixon, D. A. J . Chem. Phys. 1980, 72, 3309 and references therein. ( e ) Hopkinson, A. C.; Lien, M. H. Tetrahedron 1981,37, 1105. (0 Gordon, M. S.; Boudjouk, P.; Anwari, F. J . Am. Chem. SOC.1983, 105, 4972. (g) Damewood, J. R., Jr. J . Org. Chem. 1986, 51, 5028 and references therein.
0022-_1~654/88/2092-0033$01.50/0 0 1988 American Chemical Society
