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E L S E V I E R Spectrochimica Acta Part A 52 (1996) 1515-1520

SPECTROCHIMICA ACTA

PART A

A general harmonic force field for methyl silane

J . L . D u n c a n * , A . M . F e r g u s o n

Department o] Chemistry, University o[ Aberdeen, Meston Walk, Old Aberdeen AB9 2UE, UK

Received 17 November 1995; accepted 31 January 1996

Abstract

The number of accumulated spectroscopic data sensitive to the harmonic force constants of methyl silane has been augmented recently through high resolution infrared gas-phase studies of t2CH3SiH3, ~3CH3SiH 3 and tZCH3SiD3 species (J.L. Duncan, A.M. Ferguson and D.C. McKean, J. Mol. Spectrosc, 168 (1994) 522). This permits the determination of an empirical harmonic force field, in which 24 A~ and E species force constants out of the total of 36 are independently defined in terms of 72 data across five isotopic species. The empirical constants are compared with those from a scaled ab initio force field using a basis set of double zeta plus polarization quality, where very good agreement is found throughout. Ultimately, a best estimate general harmonic force field is presented in which the 12 undermined and numerically small interaction force constants are constrained to their ab initio predicted scaled values.

Keywords: Harmonic force constants; Methyl silane

I. Introduct ion

Attempts to derive an empirical harmonic force field for methyl silane date back to 1962, when Randi6 determined a simple diagonal potential function from the vibrational wavenumbers as- signed for CH3SiH3 [1]. Later, one of the present authors extended this treatment somewhat [2], by incorporating vibrational data for CH3SiD 3 ob- served by Wilde [3]. Two years later, in 1966, essentially equivalent calculations were reported by Clark and Weber [4], as part of an overall study of methyl and di-silanes and germanes. The

* Corresponding author.

most recent calculations, to our knowledge, are due to Clark and Drake [5], who also estimated the fundamental vibrational wavenumbers of ~2CD3SiH3 and CD3SiD3 from their infrared and Raman spectra, and included these in their data set. In all cases, the sets of force constants pre- sented are very incomplete, with many interaction constants arbitrarily constrained to zero.

Ab initio quantum mechanical calculations on methyl silanes have been carried out by Komor- nicki [6] who used a double zeta with polarization basis to calculate the force field at the SCF level. Calculations at this level have been amply demon- strated to give satisfactory predictions of force constants, even for molecules containing third row elements, e.g. methylene chloride [7]. More

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1516 J .L . Duncan, A . M . Ferguson / Spectrochimica Acta Par t A 52 (1996) 1515-1520

Table 1

Fundamental wavenumbers, small isotopic vibrational displacements, harmonized values, Coriolis coupling ( constants and given by the G H F F of Table 3"

12CH3SiH3 13CHsSiH3 12CHsSiD3

v ~ o 6 Av b A¢o cr e v, Av b 09, A ~ ~7 c

v~ 2926.90 3048.86 30 1.43 3.63 3.36 0.20 0.03 2924.0 3045.71 30

v 2 2169.75 2236.86 22 - 3.82 0.05 0.05 0.20 0.05 1563.9 1598.56 16

v 3 1263.56 1289.35 13 - 2.05 9.38 9.77 0.05 - 0.02 0.49 0.51 0.05

v 4 943.16 957.52 10 - 0 . 3 5 0.10 0.10 0.10 0.10 652.80 661.96 7

v 5 702.99 710.09 7 - 1.12 14.12 14.40 0.05 0.02 741.05 748.95 7

v 7 2981.67 3105.90 31 - 0 . 6 2 9.92 10.76 0.25 - 0 . 3 0 0.00 0.00 0.10

v 8 2165.08 2232.76 22 - 0.75 0.03 0.03 0.05 0.03 1582.49 1617.95 16

v 9 1432.62 1461.86 15 1.82 2.93 3.05 0.50 0.48 0.83 0.85 0.50

vlo 952.5 967.00 10 - 0.30 0.2 0.2 0.50 0.2 687.57 695.10 7

vtl 872.13 889.93 9 - 0 . 3 2 6.28 6.53 0.35 0.22 825.39 841.31 8

vt2 524.00 531.98 5 0.18 0.05 0.05 0.10 0.00 415 420.0 4

( ( (

(7 0.063 0.02 0.006 0.063 0.02 0.016 0.056 0.02

(8 0.009 0.02 0.004 0.011 0.02 0.006 0.088 0.02

(9 - 0 . 3 5 9 0.02 - 0 . 0 2 2 -0 .331 0.02 0.001 - 0 . 3 4 6 0.02

(lo [ -0 .243] d - [ -0 .242] - 0 . 2 7 7 0.02

(11 0.368 0.02 0.006 0.367 0.02 0.006 0.346 0.02

(12 0.243 0.02 - 0 . 0 1 0 0.245 0.02 - 0 . 0 1 0 -

D D D

Dj 10.71 0.53 - 0 . 1 8 10.82 0.66 0.62

DjK 45.55 2.28 -- 1.65 - [43.4] -

O K [137] - [141]

- 1.70

3.85

- 0.05

2.68

- 1.38

- 0.03

3.63 0.44

1.90

- 0 . 3 3 1.71

0.002

0.010

0.003

- 0.008

0.003

[0.253]

[8.15] [41.4] [22.9]

Wavenumber data in cm-~; distortion constants in kHz; ( constants dimensionless. b Av values relative to t2CH3SiH3.

Av values relative to ~2CD3SiH3. a Values in square brackets are predicted values in terms of the G H F F of Table 3.

recent ab initio SCF calculations of comparable sophisitcation have been undertaken by Hein et al. [8] as part of a study of the stability and vibrational spectra of MH4 and MH3CH3 sys- tems (M is Si, Ge, Sn, Pb). Predicted fundamen- tal vibrational wavenumbers are listed, but not the associated harmonic force constants, except for the three MH, MC and CH valence stretch- ing constants. The theoretical force constants are acknowledged to be "quite similar" to those of Komornicki [6], which is the case for the three quoted values.

2. Experimental data

The calculations reported here make use of the results of a recent extensive study of the infrared spectra of 12CHaSiH3, 13CHaSiH3 and 12CHaSiD3 species [9]. These clarify a number of uncertainties in previously reported wavenum- bers of certain fundamentals, and yield valuable small methyl group vibrational shifts, which are known to be highly sensitive functions of inter- action force constants. In addition, new or im- proved Coriolis coupling constants for the

J.L. Duncan, A.M. Ferguson /Spectrochimica Acta Part A 52 (1996) 1515- 1520 1517

centrifugal distortion constants for isotopic methyl silanes; uncertainties allowed in the data and the error vector (c = obs - calc) are

t2CH~SiH~ 12CD3SiDx

v, ~v b ¢!), /~¢O O" /: v, Av e tt), z~¢o ,'7 ~:

v I 2131 2194.8 22 - 3.2 - 2 . 0 - 2.1 2.0 v 2 - 0.25 0.25 1.0 0.05 1562 1596.5 16

v~ 1004 1020.2 10 1.2 1001 1017.1 10

v 4 941 955.3 10 1.4 717 725.3 7

v 5 643 648.9 6 0.2 617 622.5 6

v 7 2235 2304.1 23 0.7 1.0 1. I 1.0

v s 0.8 0.85 1.0 0.24 1580 1615.4 16

v 9 1044 1059.4 11 7.3 ~ 1036 1051.3 20

v,~ ~ 957 971.6 20 2.5 668 677.5 7

VII 773 786.9 8 1.2 693 701.4 7

vt 2 ~ 457 463.0 15 9.0 ~ 389 393.4 15

(7 [ 0.171] (~ [ 0.006]

(9 [-0.385] -~lo [--0.191]

( l l [ 0.273]

(I 2 [ 0.239]

D

Dj [7.5]

DjK [37.9]

D K [65.3]

1.7

2.1

1.3

0.7

1.9

0.4

1.1 2.6

6.1

- 5.(1 13.4

[ 0.172]

[ 0.070]

[ - 0 . 3 9 2 ]

[ - 0 . 1 5 7 ]

[ 0.236]

[ 0.222]

[5.61 [31.01 [16.0]

degenerate fundamentals of the three species are available. To these have been added the funda- mental vibration observations on ~2CD3SiH3 and ~2CD3SiD3 of Clark and Drake [5], and centrifu- gal distortion constants for 12CH3SiH3 of Wong et al. [10]. This gives a total of 72 observed spectroscopic data with which to investigate the harmonic potential function.

In the absence of empirical anharmonicity con- stants, observed fundamental vibration wavenum- bers have to be corrected to harmonic values. As in previous studies [11 13], this was accomplished in terms of diatomic-type anharmonicity con- stants x; of 0.040 and 0.020 for CH stretching and bending, 0.030 and 0.015 for Sill stretching and bending, and 0.010 for SiC stretching, and assum- ing Dennison's rule to hold for isotopic species. Thus

~o; = v ? b ~ d / ( 1 - - x ; ) ,

and

x * = x , v * /v,

Coriolis interaction constants and centrifugal dis- tortion constants were used as their experimental values.

No serious major Fermi resonance perturba- tions appear to affect the fundamentals. The ubiq- uitous C H 3 symmetric stretch/deformation overtone resonance will be present, but the defor- mation fundamentals are sufficiently low that the interacting levels are some 80 cm- ~ and 400 cm- apart in the 3000 cm t region. We ignore Fermi resonance perturbation effects, and accept the fundamental wavenumbers uncorrected as data. For the force constant calculations, we have al- lowed uncertainties of 1% on fundamental

1518 J.L. Duncan, A .M. Ferguson / Spectrochimica Acta Part A 52 (1996) 1515 1520

Table 2 Empirically determined force constants ~ for methyl silane; ab initio force constants of Komornicki [6], and the latter scaled to reproduce the harmonized fundamentals b

F,/ Description Empirical Ab initio

Unscaled Scaled b

F U CH 3 stretch 5.340 5.885 5.336 F1,2 0.045 0.128 0.110 Fi,3 0 0.062 0.056 El, 4 0 0.014 0.012 Fi. 5 0 --0.013 --0.012 1:,_.2 CHs def. 0.394 0.490 0.404 F2, 3 -0.158 -0.182 -0.156 Fz. 4 0 -0.023 -0.019 F~,5 0.012 0.013 0.011 F~.~ CSi stretch 3.042 3.216 2.991 F~.4 0 0.098 0.087 F~,5 -0.087 0.090 -0.079 1;'4, 4 Sill 3 stretch 2,946 3,386 2.963 /74,5 0 0.042 0.037 Fs, 5 Sill 3 def. 0.242 0.288 0.248

F7, 7 C H 3 stretch 5.225 5.755 5.218 £'7, 8 -0.120 -0.143 -0.123 F7,9 0.110 0.131 0.113 F7.10 0 --0.013 --0.012 FT.II 0 -0.010 -0.009 F7,12 0 0.026 0.023 Fs, 8 CH 3 def. 0.454 0.556 0.459 Fs, 9 0.019 0.017 0.014 Fs,,o 0 0.000 0.000 Fs.,i 0 -0.006 -0.005 Fs,I 2 - 0.004 0.000 0.000 /79, 9 CH 3 rock 0.339 0.413 0.341 F~, m 0 0.028 0.024 Fg.I1 -0.008 -0.020 -0.017 F9,12 0.090 0.121 0.105 Fro. m Sill 3 stretch 2.835 3.228 2.825 FIo. I 1 -0.040 -0.058 -0.052 Fro,12 0.031 0.058 0.052 F~.~l Sill 3 def. 0.225 0.264 0.227 F I I , I 2 -0.046 -0.044 -0.038 Fi2.12 Sill 3 rock 0.246 0.283 0.243

All values in units of aJ A -2 (mdyn A t). b Five scaling factors were employed: CH stretch 0.907, CSi stretch 0.930, Sill stretch 0.875, CH bend 0.825, Sill bend 0.860. Interaction constants were scaled with the geometric mean of the relevant diagonal force constant scaling factors [8].

wavenumbers , 2% on small i so topic wavenumber

displacements , 0.02 on Cor iol is in terac t ion con-

s tants (or the exper imenta l error , if larger) and 5%

on d is tor t ion cons tan ts [l 1-13]. The da t a set we have used is listed in Table 1.

3. Symmetry coordinates and molecular geometry

The symmet ry coord ina tes used are the conven- t ional ones employed for X Y 3 symmetr ic top molecu la r systems. The are defined in the previous

calcula t ions o f one o f the au thors [2]. The angle redundanc ies have been explici t ly removed, and angle de fo rma t ion coord ina tes are scaled with their co r respond ing C H or S i l l bond lengths. The molecu la r geomet ry employed is the r o s t ructure de te rmined f rom a s imul taneous fit to 30 g round state ro ta t iona l cons tants over 19 different iso- topic conformers [14], given by r ( C H ) = 1.0957/k, r (CSi) = 1.8686 A, r ( S i H ) = 1.4832 A, / H C S i =

110.88 ° and / H S i C = 110.50 °.

4. Empirical force constant calculations

There are a to ta l o f 36 force cons tan ts between the A 1 and E species o f the molecu la r C3v po in t g roup for methyl silane. (We ignore the unique A2 species tors ional v ib ra t ion in this work, for which a purely ha rmon ic force cons tan t is not par t icu- lar ly meaningful . ) Of these, many in terac t ion con- s tants are expected to be small , and a p ropo r t i on o f these are b o u n d to be unde te rmined by the da ta at our disposal . As a start , we set out to explore the sensit ivity o f the var ious force con- s tants to the accumula ted da ta , in o rder to choose sensibly which cons tan ts to constrain . The Cor i - olis in terac t ion ~" cons tan ts and small displace- ments in the fundamenta l s on ~3C subst i tu t ion are well known to be sensitive funct ions o f certain in terac t ion force cons tan ts [11-13]. However , we also found here that the small d isp lacements in XH3 fundamenta l s on deu te ra t ion at the oppos i te end o f the molecule were equal ly sensitive to cer ta in in terac t ion constants . This is not really surprising, because they are accura te ly known da t a and a lmos t free f rom anha rmon ic i ty effects, exact ly as for ~3C isotopic shifts. However , their use as such does not seem to have been exploi ted in any ca lcula t ions to date.

J.L. Duncan, A .M. Ferguson /Spectrochimica Acta Part A 52 (1996) 1515 1520 1519

Table 3 C o m b i n e d empir ical /scaled ab initio general ha rm on ic force field for methyl silane, which fits the da ta of Table l according to the

error vector shown

Force cons tan t Value Uncer ta in ty Force cons tan t Value Uncer ta in ty

FL, I (CH~ str.) 5.349 0.033 FT, v (CH~ str.) 5.204 0.029 F1.2 0.035 0.033 FT. s - 0.133 0.007 F~.~ [0.056] ~ FT. 9 0.081 0.020 FI. 4 [0.012] FT.a, [ 0.012] F., 5 [ 0.012] F7.~, [ - 0 . 0 0 9 ] F2. 2 (CH~ def.) 0.395 0.003 F7,~2 [0.023] ~ - 0.158 0.004 Fs. ~ (CH 3 def.) 0.462 0.008 F2, 4 [ - 0 . 0 1 9 ] Fs. 9 0.018 0.008 /;2.5 0.013 0.005 F~.lo [0.000] F~,, 3 (CSi str.) 3.038 0.014 Fs.lt [ - 0 . 0 0 5 ] F~.4 [0.0871 Fs,,2 - 0.005 0.010 F~. 5 - 0.089 0.005 F9. 9 (CH 3 rock) 0.347 0.009 F4. 4 (Sill 3 str.) 2.947 0.014 F~. m [0.024] F4, 5 [0.037] Fg.~t - 0.011 0.002 Fs. 5 (Sill3 def.) 0.243 0.002 F9,12 0.066 0.007

Fio, lo (Sill3 str.) 2.836 0.015 Ftl),tl - 0.039 0.004 F~o.12 0.036 0.005 Fil,i I (Sill 3 def.) 0.225 0.001 Fll,i 2 -- 0.043 0.002 Fi2,12 (Sill 3 rock) 0.248 0.004

a Values in square brackets cons t ra ined to scaled ab initio values of Table 2.

We have amended our force constant refine- ment program so that we can choose to refine either to an absolute vibrational wavenumber, or to a vibrational wavenumber shift, within a single isotopic species; the latter is calculated relative to the corresponding vibration in a previous iden- tified isotopic species in the current cycle of refin- ement. Thus small CH3 fundamental vibrational displacements in CH3SiD 3 relative to CH3SiH3 have been used, as have Sill3 displacements in CD3SiH3 relative to CH3SiH3. These data are much more discriminatory than the absolute vi- brational wavenumbers, because they carry a very much smaller uncertainty. They are included in Table 1.

Our calculations would refine to a maximum of 24 force constants out of the total of 36 (11 diagonal and 13 independent interaction con- stants), the remaining 12 constants being con- strained to be zero. Our empirical set of force constants is listed in Table 2. Reproduction of the input data was very good, in general, all values

being comfortably reproduced within the uncer- tainties allowed. The necessity to include 12 parameters arbitrarily set to zero, however, is not very satisfactory.

5. Combined empirical/ab initio general harmonic force field for methyl silane

The availability of comparatively high quality double zeta plus polarization ab initio calcula- tions for methyl silane by Komornicki [6] allowed us to compare our empirical force constants with their theoretical equivalents (see Table 2). Because such HF-SCF ab initio calculations overestimate the absolute magnitude of the force constants, we have scaled the quoted values down to best fit the estimated fundamental harmonic wavenumbers, using the minimum number of five scaling factors [8]. The scaled ab initio force constants for methyl silane and the scaling factors used are included in Table 2. The agreement between the determined empirical constants and their scaled ab initio

1520 J.L. Duncan, A.M. Ferguson /Spectrochimica Acta Part A 52 (1996) 1515-1520

counterparts is enormously encouraging, and yet again demonstrates the quality of such theoreti- cal predictions [6, 8]. It is also most pleasing to note that all undetermined empirical constants are predicted to take small values. Their impor- tance, however, should not be undervalued.

We undertook a final refinement to the data in Table 1, in which all interaction force con- stants, previously undetermined empirically, were constrained to their predicted scaled ab initio values. Although this made only marginal changes to most of the determined constants, the overall reproduction of the spectroscopic data was considerably improved. Our finally ac- cepted combined empirical/ab initio general har- monic force field for methyl silane is presented in Table 3, and the reproduction of data achieved using this is given in terms of the error vector e in Table 1.

Acknowledgements

A.M.F. thanks the Science and Engineering Research Council for a postdoctoral research

fellowship, during the tenure of which the calcu- lations described in this paper were carried out.

References

[l] M. Randi6, Spectrochim. Acta, 18 (1962) 115. [2] J.L. Duncan, Spectrochim. Acta, 20 (1964) 1807. [3] R.E. Wilde, J. Mol. Spectrosc., 8 (1962) 427. [4] E.A. Clark and A. Weber, J. Chem. Phys., 65 (1966)

1759. [5] A.J.F. Clark and J.E. Drake, Can. J. Spectrosc., 22 (1977)

79. [6] A. Komornicki, J. Am. Chem. Soc., 106 (1984) 3114. [7] J.U Duncan, A.M. Ferguson, K.H. Tonge and J. Harper,

Mol. Phys., 63 (1988) 647. [8] T.A. Hein, W. Thiel and T.J. Lee, J. Phys. Chem., 97

(1993) 4381. [9] J.L. Duncan, A.M. Ferguson and D.C. McKean, J. Mol.

Spectrosc., 168 (1994) 522. [10] M. Wong, I. Ozier and W.L. Meerts, J. Mol. Spectrosc.,

102 (1983) 89. I11] J.L. Duncan and E. Hamilton, J. Mol. Struct., 76 (1981)

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Mol. Spectrosc., 98 (1983) 87. [13] J.L. Duncan, J. Harper, E. Hamilton and G.D. Nivellini,

J. Mol. Spectorsc., 102 (1983) 416. [14] J.L. Duncan, J.L. Harvie, D.C. McKean and S. Cradock,

J. Mol. Struct., 145 (1986) 225.