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Molecular structure and force field of silicon dichloride and silicon dibromide from joint analysis of vibrational spectroscopic and electron diffraction data
JOURNAL
OF MOLECULAR
SPECTROSCOPY
143,293-303 (1990)
Molecular Structure and Force Field of Silicon Dichloride and Silicon Dibromide from Joint Analysis of Vibrational Spectroscopic and Electron Diffraction Data ALEXANDERG. GERSHIKOV,’ NATALYAYu. SUBBOTINA,* AND MAGDOLNAHARGITTAI~ Structural Chemistry Research Group of the Hungarian Academy of Sciences and Eiitvtis University, f’f I 17. H-1431 Budapest, Hungary
A joint analysis of electron diffraction and vibrational spectroscopic data has been performed for silicon dichloride and silicon dibromide. Various theoretical expressions for the model potentials have been tested. Both molecules appear to be rigid systems with small nuclear displacements and negligible vibrational anharmonicity. The equilibrium geometry and the force constants for both molecules have been determined and reliable deformation frequencies were estimated, viz.. 195 * 13 cm _’ and 130 + 8 cm -’ for SiClz and SiBr,, respectively. o 1990 Academic press, IX INTRODUCTION
Halogenated analogs of carbene are important in synthetic and theoretical chemistry. Their molecular geometry and molecular vibrations have been repeatedly investigated by experimental (Z-8) and computational (9) techniques. The most accurate experimental information on their nuclear configuration has been provided by electron diffraction ( 7). Their electronic structure and energetics have been analyzed by nonempirical quantum-mechanical calculations ( 9). All structural studies have shown unambiguously a bent molecular geometry of point group C2”for both silicon dichloride and silicon dibromide. These findings are consistent with the bond angles, estimated to be in the interval of 102” to 109” from isotopic shifts in absorption infrared spectra (4, 5). The vibrational characteristics of these compounds are not so well determined. Tables I and II contain vibrational frequencies measured in the spectra of gaseous samples ( I, 3) and of solid matrices (2, 4-6, 8), together with those from theoretical calculations ( 9) and those estimated from electron diffraction data ( 7). The frequencies vi and v3 are rather independent of the matrix used in the spectroscopic analyses and are consistent with the results of the theoretical work. On the other hand, the bending frequency of Sic&, reported from a gas-phase UV absorption spectroscopic analysis (3), differs considerably from that obtained in other studies (1, 4). There is no spectroscopic information for the bending frequency of SiBr2, and any estimate from electron diffraction would be especially valuable. ’ On leave from Donetsk State University. 2 On leave from the Ivanovo Institute of Chemical Technology. 3 To whom correspondence should be addressed. 293
0022-2852190 $3.00 Copyright 0
19W by Academic Press, Inc.
All rights of reproduction in any form reserved.
294
GERSHIKOV,
SUBBOTINA, AND HARGITTAI TABLE I
Vibrational Frequencies of SiClz (in cm-‘)’
Yl
"2
3
uv spectrun,
201 512.7 24a(lO) 512.5
Method
202.2
gas
Reference
phase
502.0
IR spectrun, Ar matrix
2
-
uv spectrun, gas phase
3
501.4
IR spectra,
AP matrix
4
518.7
509.4
IR spectra,
Ne matrix
4
509.9
496.3
IR spectra,
N2 matrix
4
512.0
501.2
IR spectrun, Ar mtrix
5
512
502
IR spectrun, Ar matrix
6
510
498
IR spectrun, IF matrix
a
505.5
204.1
501.0
Ab initio computation
9
513(23)
195(13)
502(20)
ED + SP, joint analysis
Present work
a. In all tables parenthesized referring
values are estimated
uncertainties
to the last digit.
Information on the force fields of these molecules is scarce, and the data from different sources display much less consistency than the vibrational frequencies. On the one hand, force constants are rather sensitive to matrix effects, and their determination on the basis of matrix spectra alone cannot be considered reliable enough. On the other hand, stretching force constants obtained from quantum-mechanical calculations in the Hartree-Fock approximation are usually overestimated and are generally basis-dependent. Joint analysis of electron diffraction and vibrational spectroscopic data has proved useful in the determination of potential functions of relatively small polyatomic molecules (10). Accordingly, it was anticipated that such a joint analysis could extend considerably our knowledge of the force fields of SiC12and SiBrz . In the elucidation of vibrational characteristics measured by different techniques the harmonic approximation is most commonly employed (I 1, 12). It usually provides sufficient accuracy. At the same time, it has been shown that consistency between TABLE II Vibrational Frequencies of SiBr, (in cm -‘)
"1
"2
3
402.6
12oa
Reference
Method
399.5
IR spctrun,
Ar matrix
4
-
394.1
IR spectrun, N2 matrix
4
122.5
-
395.9
128.2
404(27)
130(a)
399.9
ED, gas phase
7
394.6
Ab initio cmputatian
9
400(23)
ED + SP, joint analysis
Present work
GEOMETRY
295
AND FORCE FIELD OF WI2 AND SiBr2
electron diffraction and spectroscopic data may be improved by the application of other dynamic models. Thus, for example, a quadratic potential in curvilinear internal coordinates (13, 14) has proved more applicable for the bent molecules SeOz and C102 (IO) than the common harmonic approximation. Accordingly, an additional purpose of the present work was to examine the accuracy and applicability of the harmonic and different anharmonic approximations in a joint analysis of electron diffraction and spectroscopic data. This study was anticipated to be instructive since the diffraction experiments on SiCl* and SiBr, ( 7) have provided electron scattering intensities in relatively large angular ranges for such high-temperature conditions. This has enhanced the expected reliability of these comparisons. THEORY
Harmonic approximation. The potential function of a Y,XY, molecule with CZv point group can be expressed in the harmonic approximation as follows ( I1 ): V = $fr[( ?, - r:)* + (F2 - r$)*] +fil(?, +frolr$(& - a;)[(&
- r3)(f2 - r3)
- r:) + (F2 - r:)]
+ tfa(r3)*(&
- CX%)* (1)
This potential is a quadratic form of the rectilinear internal coordinates ?, , f2, and &. These coordinates are approximately equal to the internuclear distances, rl = r( X Y, ) and r2 = r( X Y,), and to the bond angle, cy = L Y,X Y2 . They can be expressed by expansion of these geometrical parameters into series of Cartesian displacements and truncation of the series at the quadratic terms (II, 13). The rectilinear coordinates are thus linearly related to the Cartesian coordinates. Their use is advantageous, since the vibrational kinetic energy is independent of these rectilinear coordinates (14) which facilitates the solution of the dynamical problem. In Eq. ( 1)) fi, fil, fra, and fa are the usual constants of the quadratic force field. The coefficients r$ and (13)’ in the last two terms allow all force constants to appear in units of mdyn A-‘. The quantities of ri = r;(XY) and CY~= L ;YXY are called “equilibrium geometrical parameters in the harmonic approximation” and they describe the minimum of potential ( 1) in its approximation of the “true” potential energy surface of the molecule. In the solution of the so-called inverse electron diffraction or spectroscopic problems, the parameters of an r; structure are determined by finding the minimum deviation between experimental observables and their theoretical analogs calculated on the basis of the model potential function ( I). The following expression describes the molecular component of the electron scattering intensities, sM( s), in the harmonic approximation ( 15 ) : sM( S) = i
gg( s)( r~,~)-‘exp( -.Y*( Az*)ij/2) [ &sin( s&j) + Q,cos( &$)],
(2)
i#j
where n is the number of nuclei in the molecule, gi,( s) contains the atomic scattering functions, and s is an angular scattering variable. Further, omitting the subscript ij, R = 1 + ( Az*)/(
Q = --s ((Az’)/rZ
r$)* - u/2( rt)* - s*( ( AZ*)* - v/2)/(
- u/2rt)
- s3v/2rb,
r:)*,
296
GERSHIKOV,
u = (Ax*)
SUBBOTINA,
AND HARGITTAI
+ (Ay*),
v = (AxAz)~
+ (AyAz)*.
Equation (2) contains, in addition to the harmonic internuclear distance &, the generalized mean-square amplitudes ( Ax~)~, ( AY*)~, ( Az*)~, ( AxAz),, and ( AyAz)o (16). They are related to frequencies, L-matrix elements, and force constants by expressions given in Ref. (16) or in Ref. (12); the latter involves the temperaturedependent Z matrices as well. We have utilized the expressions compiled in Ref. ( 12). Note that a bent XY2 molecule ( C2”) has five such amplitude parameters that are different from zero, ( Az*)~~, uxy, vXy, ( Az*)*~ and uyy, of which four are independent. Note, furthermore, that the initial model potential contains also four force constants. Thus the transition from Eq. ( 1) to Eq. (2) is not accompanied by loss of information about the molecular vibrations, at least not at the theoretical level. Anharmonic approximation. In order to check the validity of different approximations for the potential energy surface of SiC12 and SiBr2 in the joint analysis of electron diffraction and spectroscopic data, two anharmonic models have also been tested. In the first one the potential has the form V= $fr[(r, - r$)’ + (r2 - @)*I +f,r$(a
- a$)[(r,
+_&(r, - r$) (r2 - r$> - r$) + (r2 - r$)]
+ $fa(r$)*(a
- a$)*
(3)
and it is a function of the so-called curvilinear internal coordinates, r, , r2, and (Y.They correspond rigorously to the geometrical parameters, i.e., internuclear distances r( X Y, ) , r( X Y,), and bond angle L Y, X Y2, respectively. In spite of the fact that Eqs. ( 1) and ( 3) look very similar, they differ in their descriptions of the nuclear dynamics of the molecule. Using rectilinear coordinates (Eq. ( 1)) the kinetic energy operator of the vibrational Hamiltonian does not depend on rl , r2, and (Yand it is only a quadratic function of conjugate momenta ( 11). On the other hand, since the curvilinear coordinates are nonlinearly related to the Cartesian coordinates, the kinetic energy operator becomes a function of the curvilinear coordinates in Eq. (3) (14) and includes, among others, cubic and quartic terms which are cross-products of coordinates and momenta. Therefore, the theoretical model, described by Eq. (3)) accounts for the anharmonicity of the nuclear dynamics in a special form: the anharmonic effects are included in the kinetic and not in the potential energy part of the vibrational Hamiltonian. The structural parameters rzh = rzh(XY) and ash = L,YiXY2 describe the minimum position of the model potential ( 3 ) in this approximation of the molecular potential surface. Parameters of rsh structure were first introduced in a study of linear X Y2 molecules with point group Dmh ( 17). The other anharmonic model tested in this study has the expression for the vibrational potential v = M(ri
- r,)* + +
(r2
-
(r2
-
re121+A( rI -
re)(r2
-
re)
+frare(a
-
4[(h
re)l + f_Lrf((-Y - a,12 +.Mre)-‘[(rf - reJ3+ (12
-
-
r,131
re)
(4)
and also uses curvilinear coordinates. In this approximation of the nuclear dynamics the anharmonic effects appear in both the kinetic and the potential energy part of the
GEOMETRY
AND FORCE
FIELD
297
OF SiC12 AND SiBrz
vibrational Hamiltonian. Equation (4) is a simplified form of the anharmonic potential function, since only the diagonal cubic constant, Jrr, is retained in order to limit the number of variables in the joint analysis. The parameters r, and CY,characterize the “true” equilibrium molecular geometry to the extent to which the model function (4) is applicable to the vibrational potential of the nuclear system under investigation. From the computational point of view, the dependence of the kinetic energy on the curvilinear internal coordinates-this is the so-called kinematic anharmonicitycomplicates the direct solution of the dynamic problem. For this reason, it is convenient to change this relationship. A considerable simplification occurs by the nonlinear transformation of the curvilinear coordinates to the conventional rectilinear, dimensionless, normal coordinates, qi ( 13) :
+ Mklld
+ k122qd + h314;
+ b1$?2d + hd
+ ha?:)
(5)
The expressions of cubic constants kuk through the parameters fi, &, Aa, L, and Jrr for bent XY, molecules (C,,) can be found in Ref. ( 13). In the harmonic approximation (cf. Eq. ( 1)) all cubic coefficients, k,, will be zero, since the variables ?i, F2;,and & are linearly related to the normal coordinates. On the other hand, the quadratic potential in curvilinear coordinates (Eq. (3)) will turn into Eq. ( 5 ) , containing all different from zero cubic constants. The expression of electron scattering intensity, sM( s), corresponding to the anharmonic potential function ( 5) was described in Ref. ( 28) in the framework of firstorder perturbation theory. According to this, sM(s) may be expressed with desired accuracy as EM
= i
gii(s)(l~,iJ)~‘exp[(-s2(Az2)i,)/2l[RijSin(SY,,ij) + Q~cos(sre,,)l (6)
i#j
where, omitting subscripts ij, R = 1 + (Az’)/rz Q = s((Az)
- zr/2r: - s2((Az212 - v/2)/r:,
- (Az2>/rp +
u/b,)
- s3(v/2re
-
K).
Comparison with Eq. (2) shows that there are two additional parameters here, both accounting for anharmonicity, viz., ( Az)~ and K~, for each pair of nuclei, ij. The parameters ( Az)~,, and ( Az)~~ can be described by a general equation for an XY2 ( C2v) molecule as
(AZ) = C ai( i=
I
where (4,)
= -( 1/2v,)(%,,t,
+ k,2& + k&3),
(92) = -( 1/2v2)(3kzzztz + k2,,tl + &t3), (q3)
=
0 ti
=
coth(hcv,/2kT),
(7)
298
GERSHIKOV,
SUBBOTINA,
AND HARGITTAI
and T is the temperature of the electron diffraction experiment. The expressions for the expansion coefficients, ai, of the parallel nuclear displacements, AZ, with respect to the normal coordinates may be derived on the basis of relationships given in Ref. ( 13). Accordingly, we obtain a?‘=
(L*,/2a)(2cv*/h)_“2,
ai”’ = (L,2/2a)(2cv,/h)_“2,
a:‘=
(1/7r)[L,,sin(a,/2)
+ 2-“2L2,cos(~,/2)](2c~,/h)-1’2,
a:‘=
( l/7r)[L12sin(a,/2)
+ 2-“2L22~os(~,/2)](2c~2/h)-1’2,
a;’
= 0,
(8)
where L;j are the transformation matrix elements ( I1 ) . In the calculation of the parameters ( Az)~~ and ( Az)~~ by Eq. (7), it is necessary to include the expansion coefficients a”’ and UT’, respectively. A general formula, analogous to Eq. (7)) may be constructed for the parameters K,Y~ and ~~~~ K =
(h/4d(t?
-
2/3)U;
+ {(k,22W&l]4r,(v! + {&,,daz)l[4
+
(k222/4~)(l?
- 2/3)&
- 4VZ)]} [2V:( 1 - t:> + v:t: - 2u,vg,t*]
lJ2 ( v: - 4u:)]}[2V:(
1 - t:> + v:t: - 2v,v2t,t*]
+ {(~,3+W:)l]4~,(~:
- 4V:)]}[2V:( 1 - t:> + u:t: - 2v,vg,t3]
+
-
{(k&Z~U:)/[h’&‘;
4~:)]}[2v:(
1 - t:) + v;t: - %‘$‘$2tj].
This general formula is valid in the absence of anharmonic vibrational resonances expressed by vi - 2vj. Such resonances have not been observed for silicon dichloride and silicon dibromide. Note that in the solution of the inverse electron diffraction problem on the basis of Eq. (6), the variables to be refined are the constants of the initial potential functions (3) and (4). The application of the quadratic model (3) requires substitution of the symbols r, and CY,by r$ and agh in Eqs. (6) and (8). The refinement of molecular constants for silicon dichloride and silicon dibromide was carried out according to Ref. ( 10). The generalized quantity to minimize is given by the expression G = C pi[siMeXP(Si) - ySiMCa’C(Si)]2+ 2 pj(V/exp- v?‘~)~,
(9)
where y is a scale factor. The weight coefficients pi and pj were assumed to be inversely proportional to the squares of estimated experimental errors of SiMeXP(Si)and vJexp, respectively. For optimization of function G the direct search method of Hooke and Jeeves was used ( 19). STRUCTURE
ANALYSIS
The electron diffraction experimental data from Ref. 7 were used in the joint analysis. These data were recorded at 1470 K. The relative error in obtaining the molecular
299
GEOMETRYAND FORCE FIELD OF SiC12 AND SiBrz
component of electron scattering intensities, sM( s), from the total experimental intensities, P”(s), was estimated to be 9% for SiC12 and 12% for SiBrz. The atomic electron scattering functions were taken from the usual sources (20). Vibrational frequencies compiled in Table III were used in the spectroscopic part of Eq. ( 9). Standard deviations of 10 cm -’ were assumed for all frequencies, vj ( j = 1, 2, 3 ). This assumption was supposed to take into account possible matrix effects (4) and uncertainty of the quantum mechanical calculations ( 9). An alternative value of 248( 10) cm -’ for v2 of Sic12 was also tried from Ref. ( 3 ) . The analysis was carried out on the basis of the model potential functions ( 1 ), ( 3 ), and (4). In the harmonic approximation the variables were ri(XY), L$YXY, and force constantsf,, Ar, fra, and fa. The theoretical function &f(s) was calculated according to Eq. ( 2 ) . When the quadratic model ( 3 ) was used in curvilinear coordinates, in addition to the above mentioned force constants, the parameters r$‘(XY) and LzhYXY were refined. Finally, for the anharmonic potential (4), the set of paand f,, was refined. For the last two dynamic rameters r,(XY), &YXYJX,fra,fa, models the function sM( s) was calculated according to Eq. (6). No appreciable correlations have been observed among the various parameters in the joint analysis. We note here a few correlation coefficients, p, that are the largest in these refinements, viz., ~(&lfu)
0.6 1
and
~(_&Jfa)
0.46
for Sic4
~(frrlfa)
0.65
and
~(fralfa)
0.67
for SiBr2.
The largest correlations appeared in the refinements with the anharmonic approximation (4) for the parameters r, and&, p( r,/Jr,) 0.82 and 0.74 for Sic12 and SiBr2, TABLEIII Experimental and Optimized Values of Observables for SiCIZand SiBrz Observable
Experimental
Experimental
Optimized value a
(cm-‘)
SiBr2
Sic12
Optimized
c
b
B
value c
b
512.5(lOO)d
514(26)
513(23)
513(23)
402.6(100)d
404(27)
403(27)
v2 (cm-l)
202.2(100)d
193(13)
194(13)
195(13)
128.2(loo)e
129(B)
129(B)
130(B)
"3 (cm“)
501.4(lOO)d
502(22)
502(20)
502(20)
399.5(100)d
399(23)
401(23)
400(23)
Y,
404(27)
Rl oaf
6.34
6.58
5.72
4.47
4.59
4.30
If2 (%)f
8.71
8.92
8.75
15.78
16.10
14.20
91.8
95.9
76.9
56.3
Bming
a. Based on the analysis
in terms of the harmonic potential
in terss of the quadratic analysis
potential
function in curvilinear
in terms of the anharmonic potential
diffraction
reliability
of tte Least-squares
50.7
59.7
function, Eq. (1). coordinates,
function, Eq. (4).
d. Ref. 4.
factors for two angular ranges of the scattering
residual function, Eq. (9).
b. Based on the analysis
Eq. (3).
c. Based on the
e. Ref. 9.
intensity.
f. Electron
glhe minimm
value
300
GERSHIKOV,
SUBBOTINA,
AND HARGITTAI
respectively. This may be explained by the fact that the influence of the anharmonic force constant on the vibrational frequencies of these molecules is weaker than the experimental error or the estimated standard deviation for these frequencies. Thusf,, is determined here exclusively from the electron scattering intensities on the basis of the minute changes in the periods of the oscillating function sM(s) with increasing scattering angle. RESULTS
The results of this analysis are presented in Tables III and IV. Data of Table III illustrate the consistency of observed and refined vibrational frequencies and sM(s) values for all model potential functions involved in the calculations. Table IV compiles all molecular constants determined in this analysis along with available literature data (2, 4, 5, 7, 9). The estimated total errors parenthesized in these tables were obtained from the expression
The scale error was assumed to be 0.2%, 4%, and 20% for the geometrical parameters, quadratic force constants, and cubic coefficient, fr,.r, respectively. As shown by Table III, the harmonic approximation for molecular vibrations provides satisfactory description for all experimental data of SiC12and SiBr2. The application of the quadratic expression (3) in curvilinear coordinates produces no appreciable change in Gmin, and it does not result in higher accuracy of the determined parameters in these cases. Curiously, for Se02 and C102, which have the same C2, point group, the joint analysis has shown improvement with the quadratic potential in curvilinear internal coordinates (10). The reason for this difference may be not only in the peculiarities of the “true” potential surfaces, but also in the vibrational frequencies and rotational constants, AO,Bo, and CO,used in the analysis of Se02 and C102, wherein these constants originated from different isotopomers. Whereas the parameters of potential functions expressed in curvilinear coordinates are invariant to isotopic substitution, this invariance is lost in the application of model potentials expressed in linear vibrational variables ( 14). Thus the potential function ( 3 ) is convenient for treating experimental data for which assignment to isotopic substitution is available. In the absence of such an assignment, model (3) may not be preferable over the harmonic approximation, as shown by our experience with SiC12and SiBr2. Inclusion of anharmonicity in the description of potential (4), as a whole, improves the approximation of M(s) as well as that of the vibrational frequencies while also lowers slightly the standard deviations of the determined force constants. The fact that it has proved possible to estimate the cubic coefficient, J&, on the basis of electron diffraction may be explained by the availability of experimental electron scattering data through relatively large values of the scattering angle; s,,,,, is 29.0 A-’ and 22.5 A -’ for SiC12and SiBr2, respectively ( 7). By the same token, the somewhat decreased accuracy in the determination of the parameters r, and frrr for SiBr2, as compared with those for SiC12, may be explained by the somewhat smaller amount of experimental electron scattering data. Comparison of the geometrical parameters (Table IV) shows very small differences in the bond length parameters rg/&rzh/re, hardly exceeding the experimental errors.
TABLE IV Structural (r in A, Angles in Degrees) and Force Field (in mdyn k’ ) Parameters of WI2 and SiBr2 Parameter
ED, SP and
Present work
computed data s
b
c
SiCL2
r(Si-Cl)
rg 2.mw4)d
reh 2.080(4)
rech 2.081(4)
r,2.076(4)
< Cl-Si-Cl
ra
reh 104.6(6)
rech 104.6(6)
re 104.2(6)
102.8(6)d 2.39ae
fr
1.91(9)
1.91(9)
1.91(9)
-0.13(9)
-0.13(9)
-0.14(7)
-o.ia(3)
-o.la(3)
-o.i8(2)
0.38(s)
0.38(s)
0.38(s)
2.661f 2.19 2.293h 0.3aie o.2aof -0.219 0.230h 0.0645=
f Icy
0.0631f -0.0879 0.0145h 0.2384~ 0.2a4f 0.359 0.239h
-0.9(4)
f t77 SiBr2
r(Si-Br)
rg 2.249(5)d
reh 2.239(S)
rp
< Br-Si-Br
rn lo2.7(3)d
reh 103.6(4)
r,Ch103.7,4,
fr
1.955=
2.239(S)
re 2.227(6) re 103.1(4)
1.55(a)
1.54(a)
1.58(a)
-O.ll(ll)
-0.13(11)
-0.09(10)
-0.09(3)
-0.09(3)
-0.08(3)
0.32(4)
0.33(4)
0.32(4)
2.146f 0.3814= 0.261f 0.00a9e 0.0543f
-1.8(6)
a,b,c. See footnotes a,b,c to Table 111. e. Ref. 4. md~n.A*~,
f. Ref. 9. the tmd
distances
2.227 i. respectively. footnote
In converting
d. Electron diffraction,
the angular force cmstants
Ref. 7. to
of SiC12 and SiBr2 nere taken as 2.076 i and
9. Ref. 2. h. Ref. 5.
f.
301
See also comsnt
to
302
GERSHIKOV,
SUBBOTINA, AND HARGITTAI
For bond angles, the differences between the average and equilibrium values are more noticeable. As a whole, however, the vibrational effects, harmonic or anharmonic, seem to have little if any influence over the geometrical parameters, and both SiC12 and SiBr* can be characterized as rigid systems with small nuclear displacements. The absolute values of the cubic coefficients, fill (Table IV), fully support this conclusion. The quadratic force constants of SiC12 and SiBrz were obtained with acceptable standard deviations in the joint analysis. Those determined for Sic4 are consistent with the parameters of the force field determined from spectroscopic data (2). Noteworthy is that negative values were obtained for the nondiagonal force constants, frr andf,, for both molecules. We were especially interested in the bending frequencies u2. For silicon dichloride both values available from spectroscopic studies (202 versus 248 cm-‘) have been tested in the joint analysis with an assumed standard deviation of 50 cm-’ which exceeds the difference between the two values. In both cases the refined value was 190( 16) cm -‘. Thus the lowest of the two reported frequencies is preferred (it was reported in Refs. (I, 4)). For silicon dibromide the present electron diffraction result supports the data from nonempirical calculations (9), and it is also in agreement with previous estimates (4, 7). CONCLUSIONS
The halogenated carbene analogs silicon dichloride and silicon dibromide are typical rigid molecules. Their vibrations are characterized by small nuclear displacements and negligible anharmonic effects. The parameters of equilibrium geometry and force field of these molecules could be determined by a joint analysis of electron diffraction and vibrational spectroscopic data. Reliable bending frequencies could be estimated for both molecules. ACKNOWLEDGMENTS N. Yu. Subbotina is grateful to the Hungarian Ministry of Education and A. G. Gershikov to the Hungarian Academy of Sciences for generous support. We thank Professor Istvan Hargittai for advice and consultation.
Received: May 1, 1990 REFERENCES 1. R. K. ASUNDI, M. S. KARIM, AND R. SAMUEL,Proc. Phys. Sot. (London) 50, 581-598 ( 1938). 2. D. E. MILLIGANAND M. E. JACOX,J. Chem. Phys. 49, 1938-1942 (1968). 3. J. W. HASTIE,R. H. HAUGE, AND J. L. MARGRAVE,J. Mol. Spectrosc. 29, 152-162 ( 1969). 4. G. MAASS,R. H. HAUGE, AND J. L. MARGRAVE,Z. Anorg. Allg. Chem. 392,295-302 ( 1972). 5. V. A. SVYATKIN,A. K. MALTSEV,AND 0. M. NEFEDOV,Isv. Akad. Nauk SSSR Ser. Khim. 2236-2242 (1977). 6. J. H. MILLERAND L. ANDREW& J. Mol. Struct. 71, 65-73 ( 198 I). 7. I. HARGI?TAI,GY. SCHULTZ,J. TREMMEL,N. D. KAGRAMANOV,A. K. MALTSEV,AND 0. M. NEFEDOV, J. Amer. Chem. Sot. 105,2895-2896 (1983). 8. I. V. OVCHINNIKOV,A. V. GOLOVKIN,N. G. KOMALENKOVA,E. A. CHERNISHEV, AND V. S. NIKITIN, Zh. Obshch. Khim. 57, 1421-1422 (1987). 9. J. M. COFFIN,T. P. HAMILTON,P. PULAY, AND I. HARGITTAI,Inorg. Chem. 28, 4092-4094 ( 1989). IO. V. P. SPIRID~NOVANDA. G. GERSHIKOV,J. Mol. Sfruct. 140, 173-191 (1986).
GEOMETRY I1 12. 13. 14. 15.
AND FORCE FIELD OF SIC& AND
SiBr,
303
E. B. WILSON,JR ., J. C. DECIUS,AND P. C. CROSS,“Molecular Vibrations,” McGraw-Hill, New York, 1955. S. J. CYVIN, “Molecular Vibrations and Mean Square Amplitudes,” Elsevier, Amsterdam/New York, 1968. K. KUCHITSUANDY. MORINO, Bull. Chem. Sec. Japan 38, 814-824 ( 1965). A. R. HOY, I. M. MILLS, AND G. STREY, Mol. Phys. 24, 1265-1290 (1972). V. P. SPIRIDONOV,A. G. GERSHIKOV,E. Z. ZASORIN,AND B. S. BUTAYEV,in “Diffraction Studies on Non-Crystalline Substances” (I. Hargittai and W. J. Orville-Thomas, Eds.), Akadkmiai Kiadb, Budapest
and Elsevier, Amsterdam /New York, I98 I. 16. Y. MORINOAND E. HIROTA, J. Chem. Phys. 23,737-747 (1955). 17. A. G. GERSHIKOV,Zh. Strukt. Khim. 25 (4). 30-34 ( 1984). 18. A. G. GERSHIKOV,Khim. Fiz. 1,587-593 (1982). 19. R. H~~KE AND T. A. JEEVES,J. Assoc. Comput. Math. 8,2 12-229 ( 1961). 20. R. A. BONHAMAND L. SCHAFER,“International Tables for X-ray Crystallography, Vol. IV,” Kynoch, Birmingham, 1974; C. TAVARD, D. NICOLAS,AND M. ROUAULT, J. Chim. Phys. Phys.-Chim. Biol. 64,540-554 (1967).
OF MOLECULAR
SPECTROSCOPY
143,293-303 (1990)
Molecular Structure and Force Field of Silicon Dichloride and Silicon Dibromide from Joint Analysis of Vibrational Spectroscopic and Electron Diffraction Data ALEXANDERG. GERSHIKOV,’ NATALYAYu. SUBBOTINA,* AND MAGDOLNAHARGITTAI~ Structural Chemistry Research Group of the Hungarian Academy of Sciences and Eiitvtis University, f’f I 17. H-1431 Budapest, Hungary
A joint analysis of electron diffraction and vibrational spectroscopic data has been performed for silicon dichloride and silicon dibromide. Various theoretical expressions for the model potentials have been tested. Both molecules appear to be rigid systems with small nuclear displacements and negligible vibrational anharmonicity. The equilibrium geometry and the force constants for both molecules have been determined and reliable deformation frequencies were estimated, viz.. 195 * 13 cm _’ and 130 + 8 cm -’ for SiClz and SiBr,, respectively. o 1990 Academic press, IX INTRODUCTION
Halogenated analogs of carbene are important in synthetic and theoretical chemistry. Their molecular geometry and molecular vibrations have been repeatedly investigated by experimental (Z-8) and computational (9) techniques. The most accurate experimental information on their nuclear configuration has been provided by electron diffraction ( 7). Their electronic structure and energetics have been analyzed by nonempirical quantum-mechanical calculations ( 9). All structural studies have shown unambiguously a bent molecular geometry of point group C2”for both silicon dichloride and silicon dibromide. These findings are consistent with the bond angles, estimated to be in the interval of 102” to 109” from isotopic shifts in absorption infrared spectra (4, 5). The vibrational characteristics of these compounds are not so well determined. Tables I and II contain vibrational frequencies measured in the spectra of gaseous samples ( I, 3) and of solid matrices (2, 4-6, 8), together with those from theoretical calculations ( 9) and those estimated from electron diffraction data ( 7). The frequencies vi and v3 are rather independent of the matrix used in the spectroscopic analyses and are consistent with the results of the theoretical work. On the other hand, the bending frequency of Sic&, reported from a gas-phase UV absorption spectroscopic analysis (3), differs considerably from that obtained in other studies (1, 4). There is no spectroscopic information for the bending frequency of SiBr2, and any estimate from electron diffraction would be especially valuable. ’ On leave from Donetsk State University. 2 On leave from the Ivanovo Institute of Chemical Technology. 3 To whom correspondence should be addressed. 293
0022-2852190 $3.00 Copyright 0
19W by Academic Press, Inc.
All rights of reproduction in any form reserved.
294
GERSHIKOV,
SUBBOTINA, AND HARGITTAI TABLE I
Vibrational Frequencies of SiClz (in cm-‘)’
Yl
"2
3
uv spectrun,
201 512.7 24a(lO) 512.5
Method
202.2
gas
Reference
phase
502.0
IR spectrun, Ar matrix
2
-
uv spectrun, gas phase
3
501.4
IR spectra,
AP matrix
4
518.7
509.4
IR spectra,
Ne matrix
4
509.9
496.3
IR spectra,
N2 matrix
4
512.0
501.2
IR spectrun, Ar mtrix
5
512
502
IR spectrun, Ar matrix
6
510
498
IR spectrun, IF matrix
a
505.5
204.1
501.0
Ab initio computation
9
513(23)
195(13)
502(20)
ED + SP, joint analysis
Present work
a. In all tables parenthesized referring
values are estimated
uncertainties
to the last digit.
Information on the force fields of these molecules is scarce, and the data from different sources display much less consistency than the vibrational frequencies. On the one hand, force constants are rather sensitive to matrix effects, and their determination on the basis of matrix spectra alone cannot be considered reliable enough. On the other hand, stretching force constants obtained from quantum-mechanical calculations in the Hartree-Fock approximation are usually overestimated and are generally basis-dependent. Joint analysis of electron diffraction and vibrational spectroscopic data has proved useful in the determination of potential functions of relatively small polyatomic molecules (10). Accordingly, it was anticipated that such a joint analysis could extend considerably our knowledge of the force fields of SiC12and SiBrz . In the elucidation of vibrational characteristics measured by different techniques the harmonic approximation is most commonly employed (I 1, 12). It usually provides sufficient accuracy. At the same time, it has been shown that consistency between TABLE II Vibrational Frequencies of SiBr, (in cm -‘)
"1
"2
3
402.6
12oa
Reference
Method
399.5
IR spctrun,
Ar matrix
4
-
394.1
IR spectrun, N2 matrix
4
122.5
-
395.9
128.2
404(27)
130(a)
399.9
ED, gas phase
7
394.6
Ab initio cmputatian
9
400(23)
ED + SP, joint analysis
Present work
GEOMETRY
295
AND FORCE FIELD OF WI2 AND SiBr2
electron diffraction and spectroscopic data may be improved by the application of other dynamic models. Thus, for example, a quadratic potential in curvilinear internal coordinates (13, 14) has proved more applicable for the bent molecules SeOz and C102 (IO) than the common harmonic approximation. Accordingly, an additional purpose of the present work was to examine the accuracy and applicability of the harmonic and different anharmonic approximations in a joint analysis of electron diffraction and spectroscopic data. This study was anticipated to be instructive since the diffraction experiments on SiCl* and SiBr, ( 7) have provided electron scattering intensities in relatively large angular ranges for such high-temperature conditions. This has enhanced the expected reliability of these comparisons. THEORY
Harmonic approximation. The potential function of a Y,XY, molecule with CZv point group can be expressed in the harmonic approximation as follows ( I1 ): V = $fr[( ?, - r:)* + (F2 - r$)*] +fil(?, +frolr$(& - a;)[(&
- r3)(f2 - r3)
- r:) + (F2 - r:)]
+ tfa(r3)*(&
- CX%)* (1)
This potential is a quadratic form of the rectilinear internal coordinates ?, , f2, and &. These coordinates are approximately equal to the internuclear distances, rl = r( X Y, ) and r2 = r( X Y,), and to the bond angle, cy = L Y,X Y2 . They can be expressed by expansion of these geometrical parameters into series of Cartesian displacements and truncation of the series at the quadratic terms (II, 13). The rectilinear coordinates are thus linearly related to the Cartesian coordinates. Their use is advantageous, since the vibrational kinetic energy is independent of these rectilinear coordinates (14) which facilitates the solution of the dynamical problem. In Eq. ( 1)) fi, fil, fra, and fa are the usual constants of the quadratic force field. The coefficients r$ and (13)’ in the last two terms allow all force constants to appear in units of mdyn A-‘. The quantities of ri = r;(XY) and CY~= L ;YXY are called “equilibrium geometrical parameters in the harmonic approximation” and they describe the minimum of potential ( 1) in its approximation of the “true” potential energy surface of the molecule. In the solution of the so-called inverse electron diffraction or spectroscopic problems, the parameters of an r; structure are determined by finding the minimum deviation between experimental observables and their theoretical analogs calculated on the basis of the model potential function ( I). The following expression describes the molecular component of the electron scattering intensities, sM( s), in the harmonic approximation ( 15 ) : sM( S) = i
gg( s)( r~,~)-‘exp( -.Y*( Az*)ij/2) [ &sin( s&j) + Q,cos( &$)],
(2)
i#j
where n is the number of nuclei in the molecule, gi,( s) contains the atomic scattering functions, and s is an angular scattering variable. Further, omitting the subscript ij, R = 1 + ( Az*)/(
Q = --s ((Az’)/rZ
r$)* - u/2( rt)* - s*( ( AZ*)* - v/2)/(
- u/2rt)
- s3v/2rb,
r:)*,
296
GERSHIKOV,
u = (Ax*)
SUBBOTINA,
AND HARGITTAI
+ (Ay*),
v = (AxAz)~
+ (AyAz)*.
Equation (2) contains, in addition to the harmonic internuclear distance &, the generalized mean-square amplitudes ( Ax~)~, ( AY*)~, ( Az*)~, ( AxAz),, and ( AyAz)o (16). They are related to frequencies, L-matrix elements, and force constants by expressions given in Ref. (16) or in Ref. (12); the latter involves the temperaturedependent Z matrices as well. We have utilized the expressions compiled in Ref. ( 12). Note that a bent XY2 molecule ( C2”) has five such amplitude parameters that are different from zero, ( Az*)~~, uxy, vXy, ( Az*)*~ and uyy, of which four are independent. Note, furthermore, that the initial model potential contains also four force constants. Thus the transition from Eq. ( 1) to Eq. (2) is not accompanied by loss of information about the molecular vibrations, at least not at the theoretical level. Anharmonic approximation. In order to check the validity of different approximations for the potential energy surface of SiC12 and SiBr2 in the joint analysis of electron diffraction and spectroscopic data, two anharmonic models have also been tested. In the first one the potential has the form V= $fr[(r, - r$)’ + (r2 - @)*I +f,r$(a
- a$)[(r,
+_&(r, - r$) (r2 - r$> - r$) + (r2 - r$)]
+ $fa(r$)*(a
- a$)*
(3)
and it is a function of the so-called curvilinear internal coordinates, r, , r2, and (Y.They correspond rigorously to the geometrical parameters, i.e., internuclear distances r( X Y, ) , r( X Y,), and bond angle L Y, X Y2, respectively. In spite of the fact that Eqs. ( 1) and ( 3) look very similar, they differ in their descriptions of the nuclear dynamics of the molecule. Using rectilinear coordinates (Eq. ( 1)) the kinetic energy operator of the vibrational Hamiltonian does not depend on rl , r2, and (Yand it is only a quadratic function of conjugate momenta ( 11). On the other hand, since the curvilinear coordinates are nonlinearly related to the Cartesian coordinates, the kinetic energy operator becomes a function of the curvilinear coordinates in Eq. (3) (14) and includes, among others, cubic and quartic terms which are cross-products of coordinates and momenta. Therefore, the theoretical model, described by Eq. (3)) accounts for the anharmonicity of the nuclear dynamics in a special form: the anharmonic effects are included in the kinetic and not in the potential energy part of the vibrational Hamiltonian. The structural parameters rzh = rzh(XY) and ash = L,YiXY2 describe the minimum position of the model potential ( 3 ) in this approximation of the molecular potential surface. Parameters of rsh structure were first introduced in a study of linear X Y2 molecules with point group Dmh ( 17). The other anharmonic model tested in this study has the expression for the vibrational potential v = M(ri
- r,)* + +
(r2
-
(r2
-
re121+A( rI -
re)(r2
-
re)
+frare(a
-
4[(h
re)l + f_Lrf((-Y - a,12 +.Mre)-‘[(rf - reJ3+ (12
-
-
r,131
re)
(4)
and also uses curvilinear coordinates. In this approximation of the nuclear dynamics the anharmonic effects appear in both the kinetic and the potential energy part of the
GEOMETRY
AND FORCE
FIELD
297
OF SiC12 AND SiBrz
vibrational Hamiltonian. Equation (4) is a simplified form of the anharmonic potential function, since only the diagonal cubic constant, Jrr, is retained in order to limit the number of variables in the joint analysis. The parameters r, and CY,characterize the “true” equilibrium molecular geometry to the extent to which the model function (4) is applicable to the vibrational potential of the nuclear system under investigation. From the computational point of view, the dependence of the kinetic energy on the curvilinear internal coordinates-this is the so-called kinematic anharmonicitycomplicates the direct solution of the dynamic problem. For this reason, it is convenient to change this relationship. A considerable simplification occurs by the nonlinear transformation of the curvilinear coordinates to the conventional rectilinear, dimensionless, normal coordinates, qi ( 13) :
+ Mklld
+ k122qd + h314;
+ b1$?2d + hd
+ ha?:)
(5)
The expressions of cubic constants kuk through the parameters fi, &, Aa, L, and Jrr for bent XY, molecules (C,,) can be found in Ref. ( 13). In the harmonic approximation (cf. Eq. ( 1)) all cubic coefficients, k,, will be zero, since the variables ?i, F2;,and & are linearly related to the normal coordinates. On the other hand, the quadratic potential in curvilinear coordinates (Eq. (3)) will turn into Eq. ( 5 ) , containing all different from zero cubic constants. The expression of electron scattering intensity, sM( s), corresponding to the anharmonic potential function ( 5) was described in Ref. ( 28) in the framework of firstorder perturbation theory. According to this, sM(s) may be expressed with desired accuracy as EM
= i
gii(s)(l~,iJ)~‘exp[(-s2(Az2)i,)/2l[RijSin(SY,,ij) + Q~cos(sre,,)l (6)
i#j
where, omitting subscripts ij, R = 1 + (Az’)/rz Q = s((Az)
- zr/2r: - s2((Az212 - v/2)/r:,
- (Az2>/rp +
u/b,)
- s3(v/2re
-
K).
Comparison with Eq. (2) shows that there are two additional parameters here, both accounting for anharmonicity, viz., ( Az)~ and K~, for each pair of nuclei, ij. The parameters ( Az)~,, and ( Az)~~ can be described by a general equation for an XY2 ( C2v) molecule as
(AZ) = C ai( i=
I
where (4,)
= -( 1/2v,)(%,,t,
+ k,2& + k&3),
(92) = -( 1/2v2)(3kzzztz + k2,,tl + &t3), (q3)
=
0 ti
=
coth(hcv,/2kT),
(7)
298
GERSHIKOV,
SUBBOTINA,
AND HARGITTAI
and T is the temperature of the electron diffraction experiment. The expressions for the expansion coefficients, ai, of the parallel nuclear displacements, AZ, with respect to the normal coordinates may be derived on the basis of relationships given in Ref. ( 13). Accordingly, we obtain a?‘=
(L*,/2a)(2cv*/h)_“2,
ai”’ = (L,2/2a)(2cv,/h)_“2,
a:‘=
(1/7r)[L,,sin(a,/2)
+ 2-“2L2,cos(~,/2)](2c~,/h)-1’2,
a:‘=
( l/7r)[L12sin(a,/2)
+ 2-“2L22~os(~,/2)](2c~2/h)-1’2,
a;’
= 0,
(8)
where L;j are the transformation matrix elements ( I1 ) . In the calculation of the parameters ( Az)~~ and ( Az)~~ by Eq. (7), it is necessary to include the expansion coefficients a”’ and UT’, respectively. A general formula, analogous to Eq. (7)) may be constructed for the parameters K,Y~ and ~~~~ K =
(h/4d(t?
-
2/3)U;
+ {(k,22W&l]4r,(v! + {&,,daz)l[4
+
(k222/4~)(l?
- 2/3)&
- 4VZ)]} [2V:( 1 - t:> + v:t: - 2u,vg,t*]
lJ2 ( v: - 4u:)]}[2V:(
1 - t:> + v:t: - 2v,v2t,t*]
+ {(~,3+W:)l]4~,(~:
- 4V:)]}[2V:( 1 - t:> + u:t: - 2v,vg,t3]
+
-
{(k&Z~U:)/[h’&‘;
4~:)]}[2v:(
1 - t:) + v;t: - %‘$‘$2tj].
This general formula is valid in the absence of anharmonic vibrational resonances expressed by vi - 2vj. Such resonances have not been observed for silicon dichloride and silicon dibromide. Note that in the solution of the inverse electron diffraction problem on the basis of Eq. (6), the variables to be refined are the constants of the initial potential functions (3) and (4). The application of the quadratic model (3) requires substitution of the symbols r, and CY,by r$ and agh in Eqs. (6) and (8). The refinement of molecular constants for silicon dichloride and silicon dibromide was carried out according to Ref. ( 10). The generalized quantity to minimize is given by the expression G = C pi[siMeXP(Si) - ySiMCa’C(Si)]2+ 2 pj(V/exp- v?‘~)~,
(9)
where y is a scale factor. The weight coefficients pi and pj were assumed to be inversely proportional to the squares of estimated experimental errors of SiMeXP(Si)and vJexp, respectively. For optimization of function G the direct search method of Hooke and Jeeves was used ( 19). STRUCTURE
ANALYSIS
The electron diffraction experimental data from Ref. 7 were used in the joint analysis. These data were recorded at 1470 K. The relative error in obtaining the molecular
299
GEOMETRYAND FORCE FIELD OF SiC12 AND SiBrz
component of electron scattering intensities, sM( s), from the total experimental intensities, P”(s), was estimated to be 9% for SiC12 and 12% for SiBrz. The atomic electron scattering functions were taken from the usual sources (20). Vibrational frequencies compiled in Table III were used in the spectroscopic part of Eq. ( 9). Standard deviations of 10 cm -’ were assumed for all frequencies, vj ( j = 1, 2, 3 ). This assumption was supposed to take into account possible matrix effects (4) and uncertainty of the quantum mechanical calculations ( 9). An alternative value of 248( 10) cm -’ for v2 of Sic12 was also tried from Ref. ( 3 ) . The analysis was carried out on the basis of the model potential functions ( 1 ), ( 3 ), and (4). In the harmonic approximation the variables were ri(XY), L$YXY, and force constantsf,, Ar, fra, and fa. The theoretical function &f(s) was calculated according to Eq. ( 2 ) . When the quadratic model ( 3 ) was used in curvilinear coordinates, in addition to the above mentioned force constants, the parameters r$‘(XY) and LzhYXY were refined. Finally, for the anharmonic potential (4), the set of paand f,, was refined. For the last two dynamic rameters r,(XY), &YXYJX,fra,fa, models the function sM( s) was calculated according to Eq. (6). No appreciable correlations have been observed among the various parameters in the joint analysis. We note here a few correlation coefficients, p, that are the largest in these refinements, viz., ~(&lfu)
0.6 1
and
~(_&Jfa)
0.46
for Sic4
~(frrlfa)
0.65
and
~(fralfa)
0.67
for SiBr2.
The largest correlations appeared in the refinements with the anharmonic approximation (4) for the parameters r, and&, p( r,/Jr,) 0.82 and 0.74 for Sic12 and SiBr2, TABLEIII Experimental and Optimized Values of Observables for SiCIZand SiBrz Observable
Experimental
Experimental
Optimized value a
(cm-‘)
SiBr2
Sic12
Optimized
c
b
B
value c
b
512.5(lOO)d
514(26)
513(23)
513(23)
402.6(100)d
404(27)
403(27)
v2 (cm-l)
202.2(100)d
193(13)
194(13)
195(13)
128.2(loo)e
129(B)
129(B)
130(B)
"3 (cm“)
501.4(lOO)d
502(22)
502(20)
502(20)
399.5(100)d
399(23)
401(23)
400(23)
Y,
404(27)
Rl oaf
6.34
6.58
5.72
4.47
4.59
4.30
If2 (%)f
8.71
8.92
8.75
15.78
16.10
14.20
91.8
95.9
76.9
56.3
Bming
a. Based on the analysis
in terms of the harmonic potential
in terss of the quadratic analysis
potential
function in curvilinear
in terms of the anharmonic potential
diffraction
reliability
of tte Least-squares
50.7
59.7
function, Eq. (1). coordinates,
function, Eq. (4).
d. Ref. 4.
factors for two angular ranges of the scattering
residual function, Eq. (9).
b. Based on the analysis
Eq. (3).
c. Based on the
e. Ref. 9.
intensity.
f. Electron
glhe minimm
value
300
GERSHIKOV,
SUBBOTINA,
AND HARGITTAI
respectively. This may be explained by the fact that the influence of the anharmonic force constant on the vibrational frequencies of these molecules is weaker than the experimental error or the estimated standard deviation for these frequencies. Thusf,, is determined here exclusively from the electron scattering intensities on the basis of the minute changes in the periods of the oscillating function sM(s) with increasing scattering angle. RESULTS
The results of this analysis are presented in Tables III and IV. Data of Table III illustrate the consistency of observed and refined vibrational frequencies and sM(s) values for all model potential functions involved in the calculations. Table IV compiles all molecular constants determined in this analysis along with available literature data (2, 4, 5, 7, 9). The estimated total errors parenthesized in these tables were obtained from the expression
The scale error was assumed to be 0.2%, 4%, and 20% for the geometrical parameters, quadratic force constants, and cubic coefficient, fr,.r, respectively. As shown by Table III, the harmonic approximation for molecular vibrations provides satisfactory description for all experimental data of SiC12and SiBr2. The application of the quadratic expression (3) in curvilinear coordinates produces no appreciable change in Gmin, and it does not result in higher accuracy of the determined parameters in these cases. Curiously, for Se02 and C102, which have the same C2, point group, the joint analysis has shown improvement with the quadratic potential in curvilinear internal coordinates (10). The reason for this difference may be not only in the peculiarities of the “true” potential surfaces, but also in the vibrational frequencies and rotational constants, AO,Bo, and CO,used in the analysis of Se02 and C102, wherein these constants originated from different isotopomers. Whereas the parameters of potential functions expressed in curvilinear coordinates are invariant to isotopic substitution, this invariance is lost in the application of model potentials expressed in linear vibrational variables ( 14). Thus the potential function ( 3 ) is convenient for treating experimental data for which assignment to isotopic substitution is available. In the absence of such an assignment, model (3) may not be preferable over the harmonic approximation, as shown by our experience with SiC12and SiBr2. Inclusion of anharmonicity in the description of potential (4), as a whole, improves the approximation of M(s) as well as that of the vibrational frequencies while also lowers slightly the standard deviations of the determined force constants. The fact that it has proved possible to estimate the cubic coefficient, J&, on the basis of electron diffraction may be explained by the availability of experimental electron scattering data through relatively large values of the scattering angle; s,,,,, is 29.0 A-’ and 22.5 A -’ for SiC12and SiBr2, respectively ( 7). By the same token, the somewhat decreased accuracy in the determination of the parameters r, and frrr for SiBr2, as compared with those for SiC12, may be explained by the somewhat smaller amount of experimental electron scattering data. Comparison of the geometrical parameters (Table IV) shows very small differences in the bond length parameters rg/&rzh/re, hardly exceeding the experimental errors.
TABLE IV Structural (r in A, Angles in Degrees) and Force Field (in mdyn k’ ) Parameters of WI2 and SiBr2 Parameter
ED, SP and
Present work
computed data s
b
c
SiCL2
r(Si-Cl)
rg 2.mw4)d
reh 2.080(4)
rech 2.081(4)
r,2.076(4)
< Cl-Si-Cl
ra
reh 104.6(6)
rech 104.6(6)
re 104.2(6)
102.8(6)d 2.39ae
fr
1.91(9)
1.91(9)
1.91(9)
-0.13(9)
-0.13(9)
-0.14(7)
-o.ia(3)
-o.la(3)
-o.i8(2)
0.38(s)
0.38(s)
0.38(s)
2.661f 2.19 2.293h 0.3aie o.2aof -0.219 0.230h 0.0645=
f Icy
0.0631f -0.0879 0.0145h 0.2384~ 0.2a4f 0.359 0.239h
-0.9(4)
f t77 SiBr2
r(Si-Br)
rg 2.249(5)d
reh 2.239(S)
rp
< Br-Si-Br
rn lo2.7(3)d
reh 103.6(4)
r,Ch103.7,4,
fr
1.955=
2.239(S)
re 2.227(6) re 103.1(4)
1.55(a)
1.54(a)
1.58(a)
-O.ll(ll)
-0.13(11)
-0.09(10)
-0.09(3)
-0.09(3)
-0.08(3)
0.32(4)
0.33(4)
0.32(4)
2.146f 0.3814= 0.261f 0.00a9e 0.0543f
-1.8(6)
a,b,c. See footnotes a,b,c to Table 111. e. Ref. 4. md~n.A*~,
f. Ref. 9. the tmd
distances
2.227 i. respectively. footnote
In converting
d. Electron diffraction,
the angular force cmstants
Ref. 7. to
of SiC12 and SiBr2 nere taken as 2.076 i and
9. Ref. 2. h. Ref. 5.
f.
301
See also comsnt
to
302
GERSHIKOV,
SUBBOTINA, AND HARGITTAI
For bond angles, the differences between the average and equilibrium values are more noticeable. As a whole, however, the vibrational effects, harmonic or anharmonic, seem to have little if any influence over the geometrical parameters, and both SiC12 and SiBr* can be characterized as rigid systems with small nuclear displacements. The absolute values of the cubic coefficients, fill (Table IV), fully support this conclusion. The quadratic force constants of SiC12 and SiBrz were obtained with acceptable standard deviations in the joint analysis. Those determined for Sic4 are consistent with the parameters of the force field determined from spectroscopic data (2). Noteworthy is that negative values were obtained for the nondiagonal force constants, frr andf,, for both molecules. We were especially interested in the bending frequencies u2. For silicon dichloride both values available from spectroscopic studies (202 versus 248 cm-‘) have been tested in the joint analysis with an assumed standard deviation of 50 cm-’ which exceeds the difference between the two values. In both cases the refined value was 190( 16) cm -‘. Thus the lowest of the two reported frequencies is preferred (it was reported in Refs. (I, 4)). For silicon dibromide the present electron diffraction result supports the data from nonempirical calculations (9), and it is also in agreement with previous estimates (4, 7). CONCLUSIONS
The halogenated carbene analogs silicon dichloride and silicon dibromide are typical rigid molecules. Their vibrations are characterized by small nuclear displacements and negligible anharmonic effects. The parameters of equilibrium geometry and force field of these molecules could be determined by a joint analysis of electron diffraction and vibrational spectroscopic data. Reliable bending frequencies could be estimated for both molecules. ACKNOWLEDGMENTS N. Yu. Subbotina is grateful to the Hungarian Ministry of Education and A. G. Gershikov to the Hungarian Academy of Sciences for generous support. We thank Professor Istvan Hargittai for advice and consultation.
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GEOMETRY I1 12. 13. 14. 15.
AND FORCE FIELD OF SIC& AND
SiBr,
303
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