8pectrochimica Acts, 1964, ¥ol. 20, pp. 1807 to 1814. Pergamon Press Ltd. Printed in Northern Ireland

The calculation el lorce constants and normal coordinatesmVI.

Force constants of the sflyl group

J . L. D u n c A n * Department of Chemistry, University of Reading, England

(Received 13 2~arch 1964)

Abstract--Normal coordinate calculations have been carried out for a number of molecules of three-fold symmetry containing the silyl group. All available data on frequencies and Coriolis interaction constants for all isotopic species (where possible) were used in force constant re- finement calculations. Since these data were not sufficient to fix the general harmonic force field (GFF), the silyl group force field was constrained according to the model which has been successfully applied to the methyl group in previous papers in this series. In general, the refinements were made independently for each molecule, and the results show a pleasing degree of uniformity for the silyl group when the nature of the fourth atom attached to the Si atom is taken into account. On the basis of the transferability of force constants in almost identical molecules, some assignments for silyl acetylene and methyl silyl acetylene are questioned, and alternative assignments proposed.

INTRODUCTION

IN RECENT yea r s high reso lu t ion in f ra red s pec t r a h a v e been o b t a i n e d for a large n u m b e r of s imple molecules con ta in ing the silyl g roup . This, a long wi th R a m a n s p e c t r a in some of the eases, has enab led defini te a s s ignmen t s to be m a d e for the v i b r a t i o n s of the; molecules concerned. I n addi t ion , the ana lys i s of pe rpend i cu l a r bands u n d e r h igh reso lu t ion has enab led the ca lcu la t ion of m a n y Coriolis v i b r a t i o n - r o t a t i o n ~ c o n s t a n t s to be car r ied out . I t was fel t t h a t the re were sufficient d a t a ava i l ab le for a large enough select ion of silyl molecules to m e r i t i n d e p e n d e n t n o r m a l coord ina te ana lyses to be carr ied out on each molecule , in order to see if a r e a s o n a b l y cons i s ten t force field for the silyl g r o u p could be ob ta ined , a lways keep ing in mind t h a t the differences in e lect ronic d i s t r i bu t ion due to the n a t u r e of the fou r th a t o m would cause small , qua l i t a t i ve ly pred ic tab le , dev ia t ions f r o m a c o n s t a n t force field. This p a p e r gives the resul ts of such calculat ions.

The ca lcu la t ions were p e r f o r m e d b y means of an e lect ronic c o m p u t e r , us ing an i t e r a t i ve p rocedu re to refine an init ial set of force c o n s t a n t s to the bes t se t cons i s ten t wi th the e x p e r i m e n t a l da ta . This m e t h o d has been ful ly descr ibed in P a r t s I I a n d I I I of th is series [1]. All d a t a h a v e been t a k e n f r o m the l i t e ra tu re , a l t h o u g h in a few cases ~ c o n s t a n t s h a v e boon reca lcu la t ed when more accu ra t e molecu la r g e o m e t r y or b a n d cent res h a v e m a d e this necessary . Refe rences to the sources of all d a t a are g iven in the r e spec t i ve tables .

R E S U L T S

The s y m m e t r y coord ina tes used for the molecules cons idered are def ined br ief ly in Tab l e 1, in t e r m s of those for silyl ace ty lene , which are g iven in full. F o r an

* I.C.I. Research Fellow, University of Reading. Permanent address: Department of Chemistry, University of Aberdeen, Old Aberdeen,

Scotland. [1] J. A~novs and I. M. MILLS, Spectrochim. Acts 18, 1073 (1962); 19, 1567 (1963).

1807

1808 J . L . DUNCAN

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T h e c a l c u l a t i o n o f f o r c e c o n s t a n t s a n d n o r m a l c o o r d i n a t e s - - V I 1 8 0 9

exact description of the latter, the reader is referred to Fig. l(a) of Par t V of this series [2].

The data used to converge on the best set of force constants in each case are given in Table 2 (silyl halides), Table 3 (silyl cyanide, silyl acetylene, methyl silyl acetylene, disilyl acetylene), and Table 4 (disilane, methyl silane). In every case tha t it was possible, use has been made of the data for the fully deuterated silyl isotope. In Tables 2, 3 and 4, the data calculated from the final sets of force constants are bracketed alongside the observed data, in order to demonstrate the fit obtained.

T a b l e 2. D a t a t o w h i c h t h e f o r c e c o n s t a n t s a r e f i t t e d f o r t h e s i l y l h a l i d e s . F r e -

q u e n c i e s i n c m -1 , ~ c o n s t a n t s d i m e n s i o n l e s s . O b s e r v e d d a t a u n b r a c k e t e d , c a l c u -

l a t e d d a t a b r a c k e t e d

SiHaF (a) SiHaC1 (a) SiHaBr (a) Si t taI (b)

Yl 2206 (2209) 2201 (2211) 2200 (2211) 2192 (2202) v~ 990 (990) 949 (950) 930 (930) 903 (905) v a 872 (872) 551 (552) 430 (430) 362 (363) ~4 2196 (2214) 2195 (2215) 2196 (2213) 2206 (2214) ~5 956(c) (954) 954 (952) 950 (950) 941 (939) • e 728 (729) 664 (662) 633 (633) 592 (595) ~4 0.025 (0.028) 0.006 (0.006) 0.011 (0.010) 0.015 (0.031) ~5 - -0 .160 (c) (--0-157) - -0 .179 (--0.180) - -0 .185 (--0.185) - -0 .196 (--0.172) ~ 0.205 (0.213) 0.214 (0.213) 0.200 (0.200) 0.199 (0.160)

SiDaF (d) SiD3C1 (d) SiDaBr SiDaI (e)

V 1 1577 (1574) 1581 (1574) - - 1575 (1567) v 2 704 (704) 702 (701) - - 664 (663) v 3 888 (888) 538 (537) - - 352 (351) V 4 1615 (1602) 1616 (1601) - - 1607 (1601) v 5 * (692) - - (686) - - ,~675 (678) v 6 549 (549) 488 (489) - - 435 (433) ~4 - - (0.092) - - (0.067) - - - - (0.092) ~5 - - (--0"149) - - (--0"200) - - --0"197 (--0"202) ~6 - - (0"20I) - - (0'202) - - - - (0"145)

rs i H 1.480 (a) 1.480 (a) 1-480 (a) 1.480 (b) rBi X 1.594 (a) 2'049 (a) 2.210 (a) 2.435 (b) ce 110"2 ° (a) 110'2 ° (a) 110"2 ° (a) 110"2 ° (b)

* NEWMAn, POLO and WILSON [5] give a wrong value here, duo to the use of an erroneous p roduc t rule value . (a) Ref. [3]; (b) Ref. [4]; (e) Author ' s re -es t imat ion of band centre and ~ cons tan t ; (d) Ref. [5]; (e) Ref. [6].

In Table 5, the force fields for the molecules considered are given in terms of the scaled valence symmet ry coordinate representations of Table 1, where they are compared with the force field of silane, t ransformed to C3,: symmetry . For silane, it has been shown that frequency and ~-data are sufficient to completely

[3] C. N ~ w ' s ~ w , J . K . O ' L o A , ~ . , S. R . P o L o a n d M. K . WrLSO~¢, J. Chem. Phys. 2 5 , 8 5 5 ( 1 9 5 6 ) . [4] R . N . D I x o ~ a n d N . SI~PPA_~D, Trans. Faraday Soc. 53, 2 8 2 ( 1 9 5 7 ) .

[5] C. N E w ~ 2 ¢ , S. R . POLO a n d M. K . W I L S O n , Spectrochim. Acta 1 5 , 793 ( 1 9 5 9 ) . [6] H . R . Li~c~ozq a n d E . R . N I x o ~ , Spectrochim. Acta 12 , 41 ( 1 9 5 8 ) .

1 8 1 0 g . L . D U N C A N

Table 3. Data to which the force constants are fitted for silyl cyanide, silyl acetylene, methyl silyl acetylene and disilyl acetylene. Frequencies in cm -1,

constants dimensionless. Observed data unbracketed, calculated data bracketed

SiHaCN (a) S iHsCCH (b) SiHaC~--CCH a (c) S i H a C ~ C S i H a (d)

~ 2212 (2223) y~ 3314 (3315) v~ 2205 (2208) v~ 2193 (2217) v 3 920 (926) v a 2056 (2055) v4 608 (612) va 936 (935) v 5 2227 (2235) v 5 ?679 (627) v~ ~ 9 4 1 (938) Y6 2193 (2199) v~ 682 (684) v~ 928 (932) v s ~ 2 3 5 (237) v s 696 (693) ~5 0.04 (0.04) ~ ?684 (638) ~ - - 0 . 1 6 ( - -0 .16) v~o ~-~220 (220) ~ - - (0 .30) ~ 0.01 (0 .02) ~s - - (0.86) ~7 - - 0 . 2 6 ( - -0-23)

~s 0"36 (0.36) ~ - - (0.98) ~10 - - ( 0 ' 9 0 )

SiDaCN (a) SiDaCCH (b)

vl 2212 (2209) v 1 3315 (3315) v 2 1588 (1580) v~ 1595 (1577) v a 701 (696) v a 2055 (2055) va 592 (588) Pa 709 (710) v 5 1624 (1618) v 5 ?679 (597) v 6 675 (679) V 6 1595 (1591) v~ 542 (540) v 7 679 (668) vs ~ 2 2 0 (218) v s 537 (539) ~5 - - (0.10) % ?684 (640) ~6 - - ( - -0 .16) ~ o 206 (206) ~ - - (0 .38) ~o - - (0 .08) ~ - - (0 .74) ~ - 0 . 2 2 ( - 0 - 2 3 )

~ 0.41 (0 .41) ~ - - (0.97) ~ o - - (0.82)

~1 2942 (2951) Vl 2187 (2196) v 2 2170 (2184) v 2 2132 (2132) v a ?2050 (2197) v a ~ 9 2 0 (920) ~4 1365 (1363) ~4 420 (420) v 5 1038 (1025) r e 2170 (2177) v 6 937 (938) v~ 912 (912) v 7 7481 (518) ~s 807 (807) v 9 2975 (2986) ~9 2190 (2196) VlO 2182 (2193) v19 946 (946) v l l 1455 (1460) ~11 682 (682) vl~ ~ 1 0 3 8 (1041) v12 - - (103) Y13 948 (951) Via 2187 (2200) v14 699 (698) v14 946 (946) v15 358 (360) vl~ ?607 (663) vie - - (137) v16 297 (297) ~ - - (o .o6) ~ - - (O-Ol) ~1o 0.00 (0"01) ~1o - - 0 ' 2 2 ( - -0 .22) ~11 - - ( - -0"29) ~11 - - (0.32) ~12 - - (0"38) ~12 - - (0"89) ~13 - - 0 . 2 3 ( - -0"21) ~1s - - (0.01) ~14 0 '34 (0-35) ~13 - - ( - -0 ' 19 ) ~15 - - (0'83) ~18 - - (0-33) ~ 6 - - (o-88) ~ 6 - - (0 .86)

rsilt 1.480 (e) rs iR 1'480 r s l~ 1.480 rsi t t 1"480 (f) rsie 1"848 (e) rsi c 1"840 rsl 0 1.848 rsi c 1.848 (f) r e ) r 1"157 (e) rcc 1"207 rc= C 1.207 rcc 1.207 (f) ¢¢ 110.9 ° (e) rcrI 1-056 r e -o 1.458 m 109.5 ° (f)

111"0° rcIt 1.100 0¢ 109"5 °

(a) l~ef. [7]; (b) F requenc ies f rom Ref. [8], ~'s a n d m o l e c u l a r g e o m e t r y r eca l cu l a t ed b y the a u t h o r us ing MUENTER a n d LAUI%IE'S [9] B-va lue ; (c) R e f [10]; (d) Ref. [11]; (e) Ref. [12]; (f) A u t h o r ' s e s t ima te .

[7 ] I f . R . L I N T O N a n d E . R . N I x o N , Spectrochim. Acta 1 0 , 2 9 9 ( 1 9 5 8 ) .

[8 ] R . B . R E E V E S , R . E . W I L D E a n d D . W . R O B I N S O N , J . Chem. Phys. 40, 1 2 5 ( 1 9 6 4 ) .

[9 ] J . S . M U E N T E R a n d V . W . L A U R I E , J . Chem. Phys. 3 9 , 1 1 8 1 ( 1 9 6 3 ) .

[ 1 0 ] D . ~V. R O B I N S O N a n d R . B . R E E V E S , J . Chem. Phys. 3 7 , 2 6 2 5 ( 1 9 6 2 ) .

[ 1 1 ] 1~. C . L O R D , D . W . M A Y O , H . E . O P I T Z a n d J . S . ~:)EAKE, Spectroehim. Acta 1 2 , 1 4 7 ( 1 9 5 8 ) .

[ 1 2 ] J . S H E R I D A N a n d A . C . T U R N E R , Proc. Chem. Soc. 2 1 ( 1 9 6 0 ) .

T h e ca l cu la t ion o f force c o n s t a n t s a n d n o r m a l c o o r d i n a t e s - - V I 1811

T a b l e 4. D a t a t o w h i c h t h e force c o n s t a n t s a re f i t t ed fo r d is i lane a n d m e t h y l s i lane. F r e q u e n c i e s in c m -1, ~ c o n s t a n t s d ime ns ion l e s s . O b s e r v e d d a t a u n -

b r a c k e t e d , c a l cu l a t ed d a t a b r a c k e t e d

Si2H ~ (a) Si2D~ (a) SiHaCH a (b) SiDaCtt 3 (b)

v I 2152 (2162) 1548 (1540) Yl 2929 (2939) 2923 (2939) v~ 909 (910) 683 (682) ~ 2169 (2178) 1558 (1552) v a 434 (435) 408 (408) v a 1264 (1263) 1262 (1262) v 5 2154 (2164) 1549 (1542) ~4 946 (945) 741 (740) V6 843 (846) 625 (623) v 5 701 (702) 652 (651) v7 2180 (2186) 1585 (1581) ~ 2982 (2991) 2982 (2991) ~s 946 (946) 682 (678) v s 2166 (2176) 1577 (1573) ~9 379 (383) 277 (274) ~9 1403 (1396) 1401 (1395) Yl0 ~2155 (2162) 1569 (1564) ~10 ~950 (962) 668 (680) Vll 929 (935) 667 (662) YH 871 (866) 825 (829) ~12 625 (623) 475 (477) V12 545 (545) ~ 4 3 0 (435) ~7 0"03 (0"04) - - (0"10) ~7 0'06 (0'06) - - (0"06) ~s --0.31 (--0.29) - - (--0.33) ~s 0-01 (O-01) - - (0-07) ~9 0.24 (0.25) - - (0.23) ~9 - - (--0.33) - - (--0.33) ~,0 - - (0.04) - - (0.10) ~10 --0.24 (--0.26) - - (--0"27) ~H - - (--0'33) - - (--0.34) ~11 0"35 (0"36) - - (0-33) ~1~ - - (0"35) - - (0'34) ~12 0'24 (0-25) - - (0.27)

~'SiH ~'SiSi

1-480 rsiH 1"480 (c) 2.32 rsic 1.867 (c) 109 .5o rcIt 1"100 (c)

~(HSiH) 108-3 ° (c) ~(HCH) 107"7 ° (c)

(a) Refs. [13] and L14]; (b) Refs. [15] and [16]; (c) Ref. [17].

de te rmine the GFF [18]. For the other molecules in the table, however, it was necessary to use constrained force fields. In each case a hybrid orbital force field (HOFF) has been assumed (see Ref. [19] and Par t I I I of this series [1]): this implies tha t the interaction force constants F67 and F68 of the degenerate species

are equal and opposite, and that F12 of the total ly symmetric species is --1/V~2 of its degenerate counterpart [2], i.e.

1 F6~(E ) = --F68(E ) -- ~/~ F12(A1)"

This s tate of affairs applies exactly on transforming the force field of any molecule of T~ symmet ry to Ca~ symmetry, and so applies exactly to the case of silane (see Table 5). To the approximation of the hybrid orbital model, the nature of the fourth a tom at tached to the central a tom is immaterial (Ref. [19], eqn. (13)), and so this s tate of affairs applies to any molecule of more than 4 atoms which has Car(or Dab, Dad ) symmetry . All force constants insensitive to the data used have been constrained equal to zero and have been omitted from Table 5.

[13] G. W . BETHEE a n d M. K . WILSON, J. Chem. Phys. 26, 1107 (1957). [14] H . S. GUTOWSK¥ a n d E . O. STEJSKAL, J. Chem. Phys. 22, 939 (1954). [15] R . E . WILDE, J. Mol. Spectrosc. 8, 427 (1962).

[16] M. RANDIC, Speetrochim. Acta 1S, 115 (1962). [17] R . W . KILB a n d L. PIERCE, J. Chem. Phys. 27, 108 (1957). [18] J . L. DUNCAN a n d I . M. MILLS, Spectrochim. Acta 20, 523 (1964). [19] I . M. MILLS, Spectrochim. Acta 19, 1585 (1963).

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The calculation of force constants and normal coordinates--VI 1813

I t can be seen tha t a consistent force field is obtained. The results obtained for the silyl halides arc exactly analogous to those obtained by ALDOUS and MILLS [1] for the methyl halides*, and the force constants follow smooth trends through the series. Comparison of the results for the other molecules in Table 5 with those for the silyl halides shows tha t the same conclusions may be arrived at as in the analogous methyl cases, viz. tha t the variations in the force constants are qualita- t ively entirely consistent with the substi tution of terminal atoms (X) of decreasing electronegativity in the order F >> C1 > Br > C > I >> Si, as found experi- mentally.

In order to obtain realistic and transferable sets of force constants in all cases, it appears tha t two bands have been wrongly assigned for silyl acetylene, and two for methyl silyl acetylene. The values reported are queried in Table 3. For silyl acetylene, REEVES et al. [8] report, from the evidence of argon matrix spectra, tha t the Si--C stretch occurs at 679 cm -1 and the CCH angle bend occurs at 684 cm -1 for both the light and heavy molecules. This assignment leaves un- accounted a strong band at 636 cm -1 in the SiH3CCH spectrum. As can be seen from Table 5, the S i - - C ~ stretch force constant (when the C atom is sp hybridised), has an average value of 3.3 ± 0.1 m d y n A -x. Insertion of this value in the force field for silyl acetylene leads to the values bracketed in Table 5, i.e. 627 em -1 and 597 cm -~. Only by increasing this force constant to a quite unreasonably high va lue- -not shown for any other Si--C molecule--can the reported stretching frequencies be tolerably well reproduced. The assignation of a frequency of 684 cm -1 to the CCH angle bend vibration cannot be reproduced in conjunction with the rest of the data by a realistic force field. However, inclusion of the well- eharacterised force constants for the same portion of the methyl acetylene molecule [2] leads to a good fit of all other data and a prediction of the CCH angle bend frequency of 638 cm -1 for the light and 640 cm -~ for the heavy molecules (see Table 3). The corresponding vibration frequency in CH3CCH and CD3CCH is 633 cm -1 in each case. I t seems most likely, therefore, tha t the band at 636 cm -I unaccounted for in the argon matrix spectrum of SiH3CCH is due to the CCH angle bend. The only remaining puzzling feature is the fact tha t a corresponding band is not reported in the matrix spectrum of the heavy isotope [8].

The spectrum of methyl silyl acetylene has been interpreted by ROBnCSON and RE~vEs [9]. They assign a weak shoulder occurring at 2050 cm -1 on the strong, overlapping parallel and perpendicular Sill 3 stretching vibrations as due to the C~---C stretch. In all acetylenic molecules, the C ~ C stretch force constant remains invariant at 15.7 =£ 0.2 mdyn A -1. This value gives a frequency of 2197 cm -1 for the C~-C stretch in methyl silyl acetylene, implying tha t it is buried in amongst the two Sill 3 stretching vibrations, and tha t the weak shoulder at 2050 cm -1 (which exhibits parallel characteristics) is due to an overtone or combination band, perhaps 2v 5 (2 x 1038 cm-1). Only by reducing the value of this force constant to a considerably lower value can the assigned frequency be reproduced.

Of several low frequency bands, Robinson and Reeves choose tha t a t 481 cm -I

* This is not perfectly true. ALDOUS and MILLS constrain F12 = 0, thus not making full use of their hybrid orbital model.

1814 J . L . DUNCAN

as being due to the Si--C stretch. Again, this frequency cannot be reproduced except by reducing the Si--C-~ stretching force constant considerably below 3.3 mdyn /~-1, whereas with this la t ter value, a frequency of 518 cm -1 is predicted. The most intense of the four low frequency bands observed by the authors is quoted as occurring at 526 cm -1. F rom force constant calculations, it seems more probable tha t this band is due to the Si--C stretch vibration, and tha t the 481 cm -1 band may be due to the combination v15 ~ v16 (358 + 137), the parallel component of which could be in Fermi resonance with the Si--C stretch frequency.

Acknowledgement--The author wishes to thank Dr. I. M. MILLS for reading the manuscript of this paper, and for suggesting several improvements.