Vibrational spectrum of disiloxane—theoretical interpretation based on MVFF calculations

I

Spectrochimica Acto. Vol. 35A. pp. I107 to II4 @ Pergamon Press Ltd.. 1979. Printed in Great Britain

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Vibrational spectrum of disiloxane-theoretical based on MVFF calculations

107$02.00/0

interpretation

J. KOPUT and J. KONARSKI Institute of Chemistry, A. Mickiewicz University, 60-780 Poznad, Poland (Received 27 October 1978) Abstract-On the basis of the vibrational frequencies of disiloxane-do and disiloxane-de the valence force field of the molecule has been obtained. Influence of the changes in geometry on assignment and isotope shift of the normal vibration frequencies was considered. The results suggest that in the gas phase the disiloxane molecule exhibits a nearly linear SiOSi skeleton whereas in the crystal phase a bent one.

INTRODUCTION

The i.r. and Raman spectra of disiloxane molecule were investigated many times [l-g]. In the i.r. study, EMELEUS et al. [l] pointed out that the disiloxane was an asymmetric rotor, but LORD ef al. [2] basing his work on the i.r. and Raman spectra of gaseous and liquid disiloxane did not confirm the EMELEUS results. As a satisfactory explanation for the obtained results, a linear model for the SiOSi skeleton was proposed [2]. However, MCKEAN [4] while examining the Raman spectra in the liquid phase observed the r60-‘80 frequency shift of the band near 606cm-’ assigned to the SiOSi symmetric stretch. The investigations of i.r. spectra in argon and nitrogen matrices by CURL et al. [3] and in the crystal phase and solid solution by MCKEAN [51 confirmed the non-linearity of the disiloxane skeleton under such conditions. Recent study of Raman and i.r. spectra of disiloxane in the gaseous and solid state by DURIG et al. [6] showed that the spectra of gaseous disiloxane could be interpreted in terms of a G& double group, this leading to the conclusion that the molecule exhibits a quasilinear SiOSi skeleton. This structure was confirmed in far-i.r. and Raman spectra [6-8, lo] and by electron diffraction study [ 141. The theoretical investigations of the disiloxane vibrational spectra tried to explain the character of the SiOSi bending motion [6-91 and the influence of this motion on other vibrations of the molecule [13]. MCKEAN [l I] and BEATTIE et al. [12] performed simple force constant calculations using the triatomic model of the molecule. In both cases, the calculations were carried out for the point model of SiH, groups, assuming the frequency of the SiOSi bending motion to be equal to 200 cm-‘. The calculated dependencies of normal vibration frequencies [ 11, 121 as well as i.r. * AI,, Ad,, E,d and E2d mean the irreducible representations of the G& double group.

and Raman band inten. ities [ 121 on values of the SiOSi angle led the authors to confirm the quasilinear model of the disiloxane molecule. The aim of the presented paper is to perform the whole analysis of the force field of the disiloxane molecule. On the basis of results, the assignment of observed i.r. and Raman bands will be proposed. The influence of the changes in geometry on frequencies of normal vibrations as well as on isotope shifts and total energy distribution will be discussed. EXPERIMENTAL Geomettical structure of the molecule The geometrical structure and parameters of the disiloxane molecule were obtained by ALMENNINGENet al. [14] from electron diffraction study. The disiloxane geometry, equilibrium bond lengths and valence angles are shown in Fig. 1. It was found [14] that the equilibrium SiOSi angle was equal to 144.1~0.90. On the basis of these results the C,, symmetry of the disiloxane molecule was proposed [14]. The value of the equilibrium SiOSi angle was also determined by DURIG el al. [6] from investigation of the SiOSi bending mode potential function. The obtained potential functions for disiloxane-d,, and disiloxane-dh gave an average equilibrium SiOSi angle of 149 T 2”. Vibrational spectra The first interpretation of the disiloxane-d0 and disiloxane-d6 i.r. and Raman spectra was given by LLIRDet al. [2]. The spectra in gas and liquid phase were interpreted in terms of Dad molecular symmetry. MCKEAN[S] interpreted the i.r. spectra of the molecules in the crystal state and in the mutual solid solution on the basis of Czu symmetry. Recently, the i.r. and Raman spectra of gaseous disiloxane were interpreted by DURIGet al. [6] in terms of G;6 symmetry. In the presented calculations for the disiloxane molecule with the linear SiOSi skeleton, the frequencies observed by DURIG et al. [6] in the spectra of gaseous disiloxane-d,, and disiloxane-d6 were used as the normal vibration frequencies. We did not introduce any corrections for the anharmonicity of the vibrations. The frequency of SiH3 symmetric deformation (A,, mode)* and the frequency of SiD, symmetric deformation (El,+ mode) were not taken into account since: (i) the SiH, symmetric deformation band was not

1107

J. KOPUTand J. KONARSKI

1108

Fig. 1. Geometry and internal valence coordinates of the disiloxane. Structural parameters are taken from [14]: r(Si-H) = 1.486 A, R(Si-0) = 1.634 A, p(HSi0) = 109.9”. observed in the Raman spectrum of gaseous disiloxanedo [6]. A weak band in the Raman spectrum of liquid at 1009 cm-’ was assigned to this vibration [2], but the Teller-Redlich product rule gives 1067 cm-’ as an upper limit for this frequency. (ii) the shoulder at 650 cm-’ on the diffuse Raman band was assigned to the symmetric SiDr deformation motion (El, mode) [6]. It seems to us, that this assignment was not well founded. For disiloxane-do, the frequency of the SiH, symmetric deformation (EM mode) of 979 cm-’ estimated from the analysis of the torsional fine structure is close to the frequency of the SiHl symmetric deformation (Ew mode) of 981 cm-’ [6]. One can expect that for disiloxanedn, the omitted frequency will be close to the frequency of the SiD, symmetric deformation (EM mode) of 702 cm-’ [6] too. In the i.r. spectrum of gaseous disiloxane-dh, a strong band at 720cm-’ [2] was attributed to the considered motion. In the initial calculation of the force field for disiloxane with a bent SiOSi skeleton, MCKEAN’S [S] values of the frequencies were used, but obtained results did not give a satisfactory assignment of the observed transitions. Satisfactory results were obtained with DU~UGet of’s [6] values of the frequencies, so in the presented discussion these results have been taken into account. For simplicity, in the calculation of the force field for disiloxane with a bent SiOSi skeleton, it was assumed that the frequencies of the degenerate vibrations of the Eld and E2,, symmetry were not split in the bent molecule.

FORCE FIELD CALCULATION

The GF matrix method [15] was used in the presented calculation ‘of the force field of the disiloxane molecule. The highly anharmonic, large amplitude vibrations are the main problem arising in the normal coordinate analysis. On the basis of the i.r. and Raman spectra analysis, DURIG et al. [6] showed that two anharmonic, large amplitude vibrations existed in the disiloxane molecule. The first one, being the SiOSi bending motion is described by the double minimum potential function with barriers of 112 z 5 and 95 T 5 cm-’ and ground state energy levels at 42.6 and 37.8cm-’ for the disiloxane-do

and disiloxane-dC, respectively. The second large amplitude motion is the internal rotation of the SiHs groups. The analysis of the fine structure of the perpendicular bands of the SiHX stretch and the SiHs deformation indicates that the internal rotation in disiloxane is nearly free [6]. The inclusion of the highly anharmonic vibrations in the normal coordinate analysis is difficult from the computational point of view. However, it is possible to separate these vibrations from other harmonic vibrations and to consider them together with the rotation of the molecule [ 16-181. In such a case, the harmonic force constants and normal coordinates of the disiloxane molecule depend on the coordinates of the large amplitude vibrations, i.e. on the coordinates of the SiOSi bending motion and the SiHJ internal rotation. Two models of the disiloxane molecule were considered in order to elucidate the influence of the bending SiOSi motion on the normal vibrations of the molecule. The first one was the disiloxane molecule with the linear SiOSi skeleton, the second one the disiloxane molecule with the bent skeleton. In the former, the SiOSi angle was taken as 180”, corresponding to the “average” equilibrium position of the SiOSi bending motion. Assuming that the SiHs groups are in the eclipsed configuration, the molecule can be described in terms of the DQ symmetry group. The vibrational representation not including the anharmonic vibrations arises in this symmetry group as I, = 3A{(R) + 3A;‘(i.r.) + 3E’(R,i.r.) + 3.??“(R). In the latter, the value of the SiOSi angle of 144.1” was assumed, this value being determined by electron diffraction study [14] and in agreement with the angle for the minimum of the bending mode potential function [6]. For the configuration with one hydrogen atom from both the SiH3 groups located in the SiOSi plane, the molecular symmetry group is CzU and the vibrational representation not including the anharmonic vibrations arises as r, = 6A,(R, i.r.) + 3Az(R) + 6B,(R, i.r.) +

Vibrational

spectrum

of disiloxane-theoretical

interpretation

based on MVFF calculations

1109

The force field of the disiloxane molecule was calculated in the MVFF scheme using the least squares refinement technique [19]. In the first step only the diagonal force constants were determined and then the non-diagonal force constants having the greatest influence on the calculated frequencies were introduced up to obtaining the total energy distribution consistent with the assignment of the observed bands. For the disiloxane with the linear skeleton, the interaction force constants between the SiH, groups depending on the torsional angle y were calculation using the into introduced relation [ 17,201:

3&(R, i.r.). The other structural parameters were taken from electron diffraction study 1141. In the calculation of the force field the internal valence coordinates shown in Fig. 1 were used. For both the models under consideration, these coordinates were transformed into the symmetry coordinates shown in Table 1. For the disiloxane with the linear skeleton, the coordinates are similar to the symmetry BUNKER'S [17] symmetry coordinates for the dimethylacetylene. With such a choice of coordinates, the G matrix elements do not depend on the torsional angle between the SiH, groups. For the second model, the symmetry coordinates are equivalent to the local C,, symmetry coordinates of both the SiH, groups transformed according to symmetry group. In both the CzU molecular models, the redundant coordinates of the A,, and Ads symmetry were dropped, since the initial calculation had shown that the influence of these coordinates on the final results had been negligibly small. The relationships between the irreducible representations of the G&, D,h and Czv symmetry groups are shown in Fig. 2.

fii = dii + kij COS (6~ + 6),

6 = 0,72~/3.

The di, constants describe the static interaction and the /ri constants the dynamic interaction between the ith and jth internal valence coordinates of the SiH, groups, respectively. It was assumed, that for disiloxane with a bent skeleton, with a large SiOSi angle, the same relationship holds. RESULTSANDDISCUSSION

Symmetry

group

D3h

G6

C2”

’ -/“I

A,.

Al

A48

A2

A2

Eld

E’

5,

Ezd

E”

62

“55

Fig. 2. Correlation diagram of the irreducible representations of G&, &, and CzO groups to which i.r. and Raman active vibrations belong.

Table 1. Symmetry Symmetry

Species

4h

Ai A;

coordinates

coordinatest

C2” A, St = rl + r2+ r, + r4+ r, + r6 A,

Ai

Al

A; AI A:: JZ ~‘3 E: EL E: E; E; Eii E: EL! E:: E:

B, B, B, A, Bz A, Bz A, Bz B, A? B, AI B, A2

Sz=cul+az+a,-B,-8*-8,+~4+as+a~-~4-~s-~6

R,+R2 S4 = r, + r2 + r, - r4 - r, - r, Ss=al+a2+n,-p,-B*-P,-a4-(1J-a6+84+B~+P6 S, = R, - Rz ST = 2r, - r2 - r, + 2r4 - r, - r, s, = I.2- r, + r, - I.6 S9=2a,-a2-cr,i2P4-a~-a6 S,o=a*-a,+cr,-a6 S,=

s,l=28,-P2-P,+284_P~-Ba s*z = 02 - B, + PI - 86 S,, = 2r, - r2 - r, - 2r4 + r, + r, S14 = r2 - r, - r5 f r6 S,~=2a,-crz-cr,-2a4+a~+as

* Redundant coordinates not included. t Not normalized. In calculations normalized SAA Vol. 3SA. No. !9-G

Force constants and vibrational assignments The calculated internal valence force constants for disiloxane with linear and bent skeletons are collected in Table 2 under columns D,,, and Cz,, respectively. It can be seen that the diagonal and non-diagonal force constants depend on the SiOSi angle. In the case of disiloxane with a linear skeleton, the interaction force constants between the SiO stretching vibrations, the HSiO bending vibrations, the SiH stretching and HSiO bending vibrations, the SiH stretching and the HSiH bending vibraof disiloxane* Description

SiH, sym str SiH, sym def SiOSi sym str SiH, sym str SiH, sym def SiOSi antisym str SiH, antisym str SiH, antisym str SiH, antisym def SiH, antisym def SiH, in-plane rock SiH, out-of-plane rock SiH, antisym str SIH, antisym str SiH, antisvm def SiHJ ant&m def SiH, in-plane rock SiH, out-of-plane rock

in usual manner. Refer to Fig. 1 for notation.

Ill0

J. KOPUTand J. KONARSKI Table 2. Internal valence force constants of the disiloxane molecule with linear and bent SiOSi skeleton Force constant*

Valuet, mdyn/A 4h C2”

Description

k

Si-H str HSiH bend HSiO bend Si-0 str Si-0 str/Si-0 str Si-0 str/HSiO bend

2.608 0.619 0.803 5.558 1.018 0.041 0.330

2.515 0.669 0.886 6.110 1.222 0.302 0.660

i

Si-H str/Si-H Si-H str/HSiO str str/HSiH bend

-0.330 -0.021 0.188

-0.435 -0.045 0.260

k

Si-H str/Si-0 HSiH bend/HSiH str bend HSiO bend/HSiO bend HSiH bend/HSiO bend

0.038 0.048 0.136 0.050

0.140 0.051 0.205 0.064

HSiH bend/HSiH bend/HSiO bend HSiO bend/HSiO bend HSiO bend/HSiO bend

-0.041 -0.001 0.026 0.019 -0.004

-0.007 -0.003 -0.014 0.005 -0.001

f.Q fitR

fae

f UP f;;; :,

f;laW fW)

* Prime at vibration coordinate indicates the interaction force constant between non-adjacent internal coordinates. Prime at force constant indicates the interaction force constant between the SiH, groups. t All bending coordinates weighted by 1 A.

reach a large value. For disiloxane with a bent skeleton, the interaction force constant between the SiO stretching and HSiO bending of the opposite SiH, group vibrations has a much higher value than for the one with the linear skeleton. In both cases, the interaction between the SiHs groups is small. The static interaction force constants, described by the dij constants, are much more important then the dynamic ones, described by the kij constants. The same situation exists in the interaction of the HSiO bending vibrations as well as in the interaction of the HSiH bending vibrations. The observed and calculated values of the no+ma1 vibration frequencies and total energy dis-

tions

tribution (TED) for the disiloxane-do and disiloxane-d6 molecules are listed in Tables 3-6. The total energy distribution among the symmetry coordinates was calculated according to the ALIX et al. [21] method. The calculated force field for the disiloxane molecule with the linear SiOSi skeleton reproduce very well the observed frequencies. For the disiloxane-do and disiloxane-d6, the total energy distribution is in a good agreement with the assignment for the gas phase [6]. The investigation on the relationship [22] between the G matrix diagonal elements and the corresponding L transformation matrix elements proves that each of the normal vibrations of the disiloxane molecule is

Table 3. Comparison of observed and calculated frequencies and TED for the disiloxane-du with the linear SiOSi skeleton (Dw, symmetry) Species

Obs

Calc

TED*

‘4;

2188 599

2187.0 1068.2 599.0

SiH9 sym str (90). SiH, sym def (10) SiHa sym def (91). SiH, sym str (10) SiOSi sym str (101)

A;

2179 1106 959

2181.2 1108.7 962.1

SiH, sym str (91), SiH, sym def (9) SiOSi antisym str (92), SiHp sym def (8) SiH, sym def (83), SiH, sym str (9), SiOSi antisym str (8)

E’

(2194) (979) 760

2194.0 979.0 761.3

SiH3 antisym str (96) SiH3 antisym def (97) SiH, rock (101)

E”

(2194) 981 717

2193.8 981.1 714.8

SiH3 antisym str (96) SiH, antisym dif (%) SiHs rock (101)

* Only contributions greater then 5% are presented. estimated from the fine structure analysis [6].

Band not observed. ( ) Frequency

Vibrational spectrum of disiloxane-theoretical

interpretation

based on MVFF calculations

1111

Table 4. Comparison of observed and calculated frequencies and TED for the disiloxane-&, with the linear SiOSi skeleton (I&,, symmetry)* Species

Obs

Calc

TED

Ai

1579 779

1579.3 779.1

569

569.0

SiD, sym str (87), SiD, sym def (12) Sib sym def (82), SiD, sym str (13) SiOSi sym str (95). SiD, sym def (6)

1575

1572.9

SiD, sym str (88). SiD, sym def (11)

1093 709

1090.2 704.7

SiOSi antisym str (100) SiD> sym def (W), SiDJ sym str (11)

E

1593 WOI 595

1593.3 701.6 593.4

SiD, antisym str (95) SiD, antisym def (95) SiDJ rock (101)

E”

1593 702 527

1593.0 701.8 529.8

SiD3 antisym str (95) SiDs antisym def (96) SiDXrock (101)

A::

* Refer to Table 3 for notation. [ ] Frequency in the calculations.

Table 5. Comparison

not taken into account

of observed and calculated frequencies and TED for the disiloxane-do with the bent SiOSi skeleton (Czu symmetry)*

Species

Obs

Calc

TED

A1

(2194) 2188 (979) 760 599

2194.0 2180.8 981.8 976.8 768.5 610.5

SiHJ antisym str (93), SiH, antisym def (7) SiH, sym str (85), SiHl sym def (15) SiHl sym def (53). SiH, antisym def (30), SiOSi sym str (13) SiHJ antisym def (41), SiH3 sym def (38), SiOSi sym str (10) SiHz in-plane rock (84), SiHl sym def (9) SiOSi sym str (76), SiH, in-plane rock (13), SiH, sym def (8)

A2

(2194) 981 717

2193.5 983.1 714.9

SiH, antisym str (93), SiH, antisym def (7) SiH3 antisym def (93), SiH9 antisym str (7) SiHl out-of-plane rock (100)

BI

(2194) 2179 1106 981 959 717

2193.6 2190.5 1106.5 983.0 959.0 713.1

SiHp antisym str (92), Siti, antisym def (7) SiH, sym str (83), SiHl sym def (16) SiOSi antisym str (92), SiH, sym def (5) SiHj antisym def (93) SiHJ sym def (88), SiOSi antisym str (6) SiH, in-plane rock (99)

&

(2194) (979) 760

2194.0 979.6 762.6

SiHj antisym str (93), SiHS antisym def (7) SiHs antisym def (93), SiH, antisym str (7) SiHj out-of-plane rock (100)

* Refer to Tables 3 and 4 for notation.

nearly completely characterized by the symmetry coordinate having the greafest contribution to the total energy distribution. The small miiing is observed between the SiH, symmetric stretching and SiHs symmetric deformation vibrations of the AI and A; symmetry. For the disiloxane-do, the frequency of the SiH, symmetric deformation (Ai mode) of 106%2cmand for the disiloxane-ds, the frequency of the SiD, symmetric deformation (E’ mode) of 701.6 cm-’ were calculated. For the disiloxane molecule with the bent SiOSi skeleton, the calculated force field reproduces satisfactory the observed frequencies, but the total energy distribution is in the full agreement neither with the one calculated for the disiloxane with the linear skeleton nor with the vibrational assignment

for the solid state [5]. The large mixing is observed among the totally symmetric vibrations (A, modes) for the disiloxane-do and disiloxane-ds molecules. The other normal vibrations are nearly completely characteristic; only a small mixing is observed among the A2 symmetry and among the *B1 symmetry vibrations of the disiloxane-do arid amdng the B, symmetry vibrations of the disiloxane-de. The large interaction force constants between the SiO stretching and DSiO bending of both the SiD, groups vibrations cause a large mixing between the SiOSi symmetric stretching, SiD3 inplane rocking and SiD3 symmetric deformation vibrations in the disiloxane-ds molecule. The contributions of the symmetry coordinates which should characterize suitable normal vibrations, according to the assignment of the spectra [6], are

Ill2

J. KOPUTand J. KONARSKI Table 6. Comparison of observed and calculated frequencies and TED for the disiloxane-d, with the bent SiOSi skeleton (Cz, symmetry)* Species

Obs

talc

TED

Al

1593 1579 779 595 569

1593.9 1570.5 778.9 699.3 597.6 532.2

SiD, antisym str (92), SiD, antisym def (8) SiDr sym str (84), SiD, sym def (16) SiOSi sym str (61), SiDr sym def (25). SiD, in-plane rock (12) Si4 antisym def (91), SiDr antisym str (8) SiDr sym def (52), SiD, in-plane rock (34). SiD, sym str (10) Si4 in-plane rock (55), SiOSi sym str (36), SiD, sym def (7)

‘42

1593 702 527

1593.3 702.1 530.6

SiDr antisym str (92), SiD, antisym def (8) SiD, antisym def (93). SiD, antisym str (8) SiDr out-of-plane rock (100)

SI

1593 1575 1093 709 702 527

1593.4 1582.3 1091.8 702.8 697.7 530.3

SiDr antisym str (92), SiD, antisym def (8) SiDr sym str (82), SiDr sym def (19) SiOSi antisym str (100) SiD, sym def (92), SiDr antisym def (6) SiDr antisym def (92), SiD, sym def (6) SiD, in-plane rock (95)

&

1593 W-J1 595

1593.9 701.2 594.9

SiDr antisym str (92), SiD, antisym def (8) SiD, antisym def (92), SiDr antisym str (8) SiDr out-of-plane rock (100)

16501

* Refer to Tables 3 and 4 for notation.

25% of the SiD, symmetric deformation, 34% of the SiDs in-plane rock, and 36% of the SiOSi symmetric stretch for the bands at 779, 595 and 569 cm-‘, respectively. The calculated frequency of the SiHp symmetric deformation (A, mode) of 981.8 cm-’ corresponds to the frequencies of the bands observed in the Raman spectrum of liquid disiloxane-do 121 at 1009 cm-’ and in the .i.r. spectra of crystalline disiloxane-do [2,5] at 1012 cm-‘. For the disiloxane-ds, the calculated frequencies of the SiD, antisymmetric deformation (A, mode) of 699.3 cm-’ and (& mode) of 701.2cm-’ are related to the shoulders at 680 and 685 cm-’ observed in spectrum of the solid solution [5]. The comparison of the corresponding calculated frequencies of the A, and Bz symmetry vibrations as well as the A2 and B, symmetry vibrations leads to the conclusion that a small splitting of the degenerated vibrations of the El* and EW symmetry occurs on passing from the disiloxane molecule with the linear SiOSi skeleton to the one with the bent skeleton. The theoretically predicted splitting of about 8 cm-’ is comparable with the accuracy of the frequency fit. Investigation of the effects of the changes in geometry The calculated force field, the frequencies of normal vibrations and the total energy distribution-they all depend on the large amplitude vibration coordinates, the SiOSi bending mode and the SiHa internal rotation coordinates. For the disiloxane molecule with the linear SiOSi skeleton, the above-mentioned dependence on the SiHp internal rotation coordinate originates from interaction force constants, these constants depending on the torsional angle. As it has been

concluded the force constants describing the dynamic interaction of the SiH, groups are negligibly small. Both the frequency and total energy distribution dependence on the SiOSi bending mode coordinate originate from the force constants as well as from the kinetic energy coefficients. Assuming that the force constants weakly depend on the SiOSi bending mode coordinate, the normal vibration frequencies were calculated for various values of the SiOSi angle. It was supposed that for large SiOSi angles the force field of the bent disiloxane molecule could be approximated by the force field obtained in calculation for the linear disiloxane molecule. For the disiloxane molecule with the bent skeleton, the change of the SiOSi angle influences only the A, and B, vibrations according to molecular symmetry considerations. The frequencies and TED of the A, vibrations-the SiOSi stretch and the SiH, in-plane rock are strongly affected by the SiOSi angle changes. Especially strong changes of the frequencies and TED have been observed for disiloxane-de. For the BI vibrations, only the frequency of the SiOSi antisymmetric stretch changes with the SiOSi angle. The frequencies and TED of other AI and B1 vibrations have been almost unaffected. The dependences of the SiOSi symmetric and antisymmetric stretch frequencies on the values of the SiOSi angle for various isotopically substituted disiloxane molecules are plotted in Figs. 3 and 4, respectively. The dependence of the total energy distribution of the SiOSi symmetric stretch on the SiOSi angle values is presented in Table 7. The comparison of the calculated frequencies of the SiOSi antisymmetric stretch for various SiOSi angle values and those observed under different

1113

Vibrational spectrum of disiloxane- theoretical interpretation based on MVFF calculations

(St H,),

-----

(SIH~),'~O (Si II,),

-me

\

650

-

‘60

E 2.4 ir

550

I

I

I

160

140 SiOSl

180

angle

Fig. 3. Dependence of the SiO symmetric stretch frequency on the SiOSi angle calculated for force field of the disiloxane with the linear SiOSi skeleton.

/

Angle, o

TED SiOSi sym str

TED SiH, in-plane rock

(SiH&‘60

144.1 160.0 170.0 180.0

70 93 99 100

30 8 2 0

(SiH&‘*O

144.1 160.0 170.0 180.0

74 94 99 100

27 7 2 0

(SiD&‘60

144.1 160.0 170.0 180.0

24 41 62 94

76 57 35 6

Molecule

\

600

stituted disiloxane molecules

I60

\

”

Table 7. Dependence of TED for the SiOSi symmetric stretch on the SiOSi angle values for isotopically sub-

/

// I

I

140

I

160 SiOSi

I80

angle

Fig. 4. Dependence of the SiO antisymmetric’ stretch frequency on the SiOSi angle calculated for force field of the disiloxane with the linear SiOSi skeleton.

conditions leads to the conclusion that the geometry of the disiloxane molecule changes on passing from the gaseous to the crystalline phase. According to the Boltzmann distribution for in the gaseous phase, a room temperature, majority of the disiloxane molecules occupy states with nearly linear or linear SiOSi skeletons. In the i.r. spectra of gaseous disiloxane the bands at 1105 [5], 1060 [5] and 1093 cm-’ [6] were assigned to the SiOSi antisymmetric stretch for the disiloxane-do, ‘“0 substituted disiloxane-do and dis-

iloxane-da, respectively. For the SiOSi angle of 170”, the calculated frequencies of this vibration are equal 1105.9, 1060.0 and 1087.2 cm-‘, respectively. From these data, the ‘“O-‘“0 frequency shift of 45.9cm-’ on the SiOSi antisymmetric stretch is calculated, this shift being well comparable with the experimental one of 45.2cm-‘[5]. For the above given SiOSi angle, the frequencies of the SinSi symmetric stretch were calculated to be 604.6, 604.2 and 560.0cm-’ for the disiloxanedo, ‘*O substituted disiloxane-do and disiloxane-ds, respectively. The calculated “0 isotope shift of 0.4cm-’ on this vibration for the disiloxane-do is lower than the one of 3.5 cm-’ estimated by MCKEAN [5] from the effect of “0 substitution on the i.r. bands at 1105 and 1706 cm-‘. The medium, polarized band observed in the Raman spectrum of gaseous disiloxane-d6 at 569 cm-’ has been assigned [6] to the SiOSi symmetric stretch. The intensity and polarization of this band indicates that the normal vibration corresponding to it should be nearly completely characteristic of it. Such a situation exists only for large SiOSi angles as it can be seen from -data collected in Table 7. For the SiOSi angle of 170“, the normal vibration at a frequency of 560.0cm-’ is characterized by the SiOSi symmetric stretch 62% of the time. According to the Boltzmann distribution for low temperatures, in the solid state, a majority of the disiloxane molecules occupy the lowest energy state with the bent SiOSi skeleton. The SiOSi antisymmetric stretch was assigned to the bands at 1077 151 (1084 [6]), 1035 [5] and 1077 cm-’ [51 (1067 cm-’ 161) observed in the i.r. spectra of crystalline disiloxane-do, “0 substituted disiloxane-do and disiloxane-de, respectively. The calculations carried out for the SiOSi angle of 146” (151’) lead to the frequencies of this vibration of 1077.4 (1086.0), 1036.0 (1043.2) and 1055.7 cm-’ (1065.1 cm-‘), respectively. Thus, the calculated ‘sO-‘aO frequency shift of 41.4 cm-’ (42.8 cm-‘) is well comparable with the one of 42.0 cm-’ esti-

1114

J. KOPUT and J. KONARSKI

mated from the i.r. spectra [5]. For the above given angles, the frequencies of the SOS symmetric stretch were calculated to be 648.8 (637.1), 646.6 (635.5) and 539.9cm-’ (543.5) cm-’ for the disiloxane-do, I80 substituted disiloxane-d,, and disiloxane-de, respectively. Except for the disiloxaneds, the calculated frequencies are not comparable with the frequencies of bands observed in spectra. In the i.r. spectra of cryst+lline didoxane-d0 and 180 substituted disiloxane-do [5,6] no bands near 640 cm-’ were observed. A very weak band at 538 cm-’ in the i.r. spectrum of the disiloxane-& solid solution was observed and the possibility of the assignment of this band to the SiOSi symmetric stretch was also considered by MCKEAN

[51.

Acknowledgement-We would like to express our thanks to Professor JAMES R. DURIG from University of South Carolina for his critical remarks and stimulating discussion of the problem in time of his visit in Institute of Chemistry, A. Mickiewicz University of Poznafi.

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