Full Text
PHYSICS
I. F. KOVALEV
POTENTIAL FUNCTIONS OF MOLECULES IN THE HOMOLOGOUS SERIES
$(\mathrm{CH}_3)_n\mathrm{SiF}_{4-n}$ $(n = 1—4)$
(Presented by Academician I. V. Obreimov, 1 VIII 1962)
-
The study of the vibrational properties of methylfluorosilanes is of considerable interest in connection with the development of the chemistry and physics of organosilicon compounds. Up to the present time, experimental data on Raman and infrared spectra have been obtained for molecules of this series, and, incidentally, only individual particular questions of the mechanical vibrational problem have been solved $({}^{1-3})$.
-
We have considered the entire series $(\mathrm{CH}_3)_n\mathrm{SiF}_{4-n}$ $(n = 1—4)$. Using the methods of M. V. Vol’kenshtein, M. A. El’yashevich, B. I. Stepanov $({}^{4})$ and L. S. Mayants $({}^{5})$, the coefficients of the potential energy (force constants and interaction coefficients) were calculated, the frequencies and forms of normal vibrations were computed, and, for $\mathrm{CH}_3\mathrm{SiF}_3$, the sensitivities of the frequencies to changes in the force constants and the displacements of atoms from equilibrium positions during vibrations were determined. The problem was solved simultaneously for the whole series of methylfluorosilanes, taking into account the results of studies of other halogen-substituted silicon compounds $({}^{6,7})$, as well as $\mathrm{SiF}_4$ $({}^{8})$. The following values for equilibrium bond lengths in the molecules were adopted as the basis ($r$ in Å) $({}^{9})$:
Fig. 1. Equilibrium configuration of the molecule $(\mathrm{CH}_3)_3\mathrm{SiF}$
| $\mathrm{CH}_3\mathrm{SiF}_3$ | $(\mathrm{CH}_3)_2\mathrm{SiF}_2$ | $(\mathrm{CH}_3)_3\mathrm{SiF}$ | |
|---|---|---|---|
| $r(\mathrm{C}—\mathrm{H})$ | 1.10 | 1.09 | 1.093 |
| $r(\mathrm{Si}—\mathrm{C})$ | 1.88 | 1.89 | 0.87 |
| $r(\mathrm{Si}—\mathrm{F})$ | 1.555 | 1.56 | 1.55 |
The angles were taken to be tetrahedral. The notation for the coordinate system introduced is given in Fig. 1. In the present work, the interaction coefficients are presented and discussed as those most fully reflecting the form of the potential functions (Table 1).
- From Table 1 it is seen how the distribution of forces and mutual interactions within the molecules changes in passing from tetramethylsilane to methyltrifluorosilane. Certain regularities are observed. Replacement of methyl groups by fluorine atoms leads to an increase in the strength of the $\mathrm{Si}—\mathrm{C}$ bond by approximately 10%. A similar effect is also characteristic of analogous chlorine- and bromine-substituted compounds and may be associated with the high electronegativity of the halogens, especially fluorine. Attachment of halogen atoms to silicon causes an inductive effect, i.e., a shift of the electron shell of the molecule toward the halogen. As the number of fluorine atoms attached to silicon increases, the value of the coefficient decreases (within 10–15%)
Table 1
Influence coefficients of methylfluorosilanes \((10^6\ \mathrm{cm}^{-2})\)
| Molecule | 1: \((Q_1,\ Q_1)\) | 1: \((q',\ q')\) | 1: \((q_1,\ q_1)\) | 1: \((\alpha_{12},\ \alpha_{12})\) | 1: \((\beta_1,\ \beta_1)\) | 1: \((\beta_2,\ \beta_2)\) | 1: \(k_\delta^{-1}\) | 1: \((\varepsilon_{12},\ \varepsilon_{12})\) | 1: \((\gamma_1,\ \gamma_1)\) | 2: \((q_1,\ q_2)\) | 2: \((Q_1,\ q_1)\) | 2: \((q_1,\ \alpha_{12})\) | 2: \((q_1,\ \alpha_{23})\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I \(\mathrm{CH_3SiF_3}\) | 0,205 | 0,112 | 0,127 | 1,228 | 1,370 | — | 0,831 | — | 1,112 | −0,003 | −0,002 | −0,033 | 0,035 |
| II \((\mathrm{CH_3})_2\mathrm{SiF_2}\) | 0,207 | 0,124 | 0,128 | 1,229 | 1,287 | 1,279 | 0,824 | 1,118 | 1,132 | −0,003 | −0,002 | −0,034 | 0,035 |
| III \((\mathrm{CH_3})_3\mathrm{SiF}\) | 0,209 | 0,141 | 0,128 | 1,227 | 1,262 | 1,273 | — | 1,129 | 0,930 | −0,003 | −0,002 | −0,034 | 0,035 |
| IV \((\mathrm{CH_3})_4\mathrm{Si}\) | 0,231 | — | 0,129 | 1,226 | 1,256 | — | — | 1,123 | — | −0,003 | −0,002 | −0,034 | 0,034 |
| Molecule | 2: \((q_1,\ \beta_1)\) | 2: \((q_1,\ \beta_2)\) | 2: \((Q_1,\ \beta_1)\) | 2: \((Q_1,\ \beta_2)\) | 2: \((Q_1,\ \alpha_{12})\) | 2: \((\alpha_{12},\ \alpha_{13})\) | 2: \((\alpha_{12},\ \beta_1)\) | 2: \((\beta_2,\ \beta_3)\) | 2: \((\beta_1,\ \beta_2)\) | 2: \((\alpha_{12},\ \beta_3)\) | 3: \((q'_1,\ q'_2)\) | 3: \((Q_1,\ q')\) | 3: \((Q_1,\ Q_2)\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | −0,041 | 0,036 | −0,055 | — | 0,055 | −0,236 | −0,211 | −0,308 | — | −0,333 | −0,009 | −0,004 | — |
| II | −0,037 | 0,035 | −0,051 | −0,046 | 0,049 | −0,229 | −0,220 | −0,256 | −0,251 | −0,333 | −0,008 | −0,006 | 0 |
| III | −0,036 | 0,035 | −0,046 | −0,039 | 0,042 | −0,226 | −0,222 | −0,251 | −0,244 | −0,331 | — | −0,006 | −0,004 |
| IV | −0,036 | 0,035 | −0,038 | — | 0,038 | −0,221 | −0,225 | −0,237 | — | −0,334 | — | — | −0,010 |
| Molecule | 3: \(a_\delta^{-1}\) | 3: \(b_\delta^{-1}[q',\ \varepsilon_{12}]\) | 3: \((b',\ \gamma)\) | 3: \(b_\gamma^{-1}\) | 3: \((Q_1,\ \gamma_1)\) | 3: \((Q_1,\ \gamma_2)\) | 3: \(B_\delta^{-1}[Q_1,\ \varepsilon_{23}]\) | 3: \((Q_1,\ \varepsilon_{13})\) | 3: \(l_{\delta\delta}^{-1}[\varepsilon_{12},\ \varepsilon_{13}]\) | 3: \(l_{\gamma\gamma}^{-1}\) | 3: \(l_{\gamma\gamma}^{a-1}\) | 3: \(O_{\gamma\delta}^{-1}[\gamma_1,\ \gamma_2]\) | 3: \((\gamma_1,\ \varepsilon_{13})\) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | −0,040 | 0,045 | −0,071 | 0,053 | −0,030 | — | 0,030 | — | −0,211 | −0,172 | −0,351 | −0,065 | — |
| II | −0,049 | [0,063] | −0,057 | 0,050 | −0,049 | 0,053 | 0,038 | −0,044 | — | −0,155 | −0,204 | [−0,404] | −0,228 |
| III | — | [0,062] | −0,062 | — | −0,038 | 0,038 | [0,048] | −0,043 | [−0,281] | — | — | [−0,182] | −0,209 |
| IV | — | — | — | — | — | — | [0,042] | −0,042 | [−0,249] | — | — | — | — |
Table 1 (continued)
| Molecule | $O_{\gamma\gamma}^{-1}[\gamma_1,\varepsilon_{23}]$ | $O_{\delta\varepsilon}^{-1}$ | $(Q_1,\beta_4)$ | $(Q_1,\beta_5)$ | $(Q_1,\beta_6)$ | $(Q_1,\alpha_{46})$ | $(Q_1,\alpha_{56})$ | $(q',\beta_1)$ | $(q',\beta_2)$ | $(\beta_1,\beta_8)$ | $(\beta_2,\beta_9)$ | $\left(\begin{matrix}\beta_1,\beta_7\\ \beta_2,\beta_6\end{matrix}\right)$ | $l_{\alpha\delta}^{-1}(\beta_1,\beta_5)$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | — | — | — | — | — | — | — | 0 | 0,002 | — | — | — | 0,012 |
| II | $-0,141$ | $-0,206$ | 0 | $-0,005$ | — | $-0,002$ | $-0,002$ | 0,002 | $-0,006$ | 0 | 0,011 | 0 | 0,009 |
| III | [$-0,150$] | — | 0,002 | 0,007 | $-0,005$ | $-0,002$ | $-0,001$ | 0,004 | $-0,004$ | 0,004 | 0,012 | 0[0,002] | [$-0,005$] |
| IV | — | — | 0,008 | $-0,003$ | — | $-0,002$ | $-0,001$ | — | — | 0,003 | 0,012 | 0,001 | [$-0,006$] |
| Molecule | $(\gamma_1,\beta_1)$ | $(\gamma_1,\beta_2)$ | $(\gamma_1,\beta_4)$ | $(\gamma_1,\beta_5)$ | $(\gamma_1,\beta_8)$ | $(\varepsilon_{12},\alpha_{13})$ | $(\varepsilon_{12},\alpha_{23})$ | $(\varepsilon_{12},\alpha_{46})$ | $(\varepsilon_{12},\beta_1)$ | $(\varepsilon_{12},\beta_5)$ | $n_{\beta\gamma}^{1-1}[\varepsilon_{12},\beta_2]$ | $(q_1,\gamma_1)$ | $(q_2,\gamma_1)$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | 0,033 | 0,001 | — | — | — | — | — | — | — | — | — | $-0,001$ | 0,001 |
| II | 0,031 | 0,040 | 0,010 | $-0,030$ | $-0,024$ | — | 0,007 | 0,018 | 0,039 | $-0,110$ | 0,004 | 0,001 | 0,002 |
| III | 0,017 | 0,027 | 0,009 | $-0,023$ | 0,001 | 0,001 | 0,004 | 0,014 | 0,029 | $-0,119$ | [0,071] | 0,001 | 0,001 |
| IV | — | — | — | — | — | — | $-0,002$ | 0,011 | 0,058 | $-0,123$ | — | — | — |
| Molecule | $(q_7,\gamma_1)$ | $(q_1,\varepsilon_{13})$ | $(q_2,\varepsilon_{13})$ | $(\alpha_{13},\gamma_1)$ | $(\alpha_{13},\gamma_2)$ | $(\alpha_{13},\gamma_3)$ | $(\alpha_{23},\gamma_1)$ | $p_{\beta\delta}^{-1}[\varepsilon_{12},\beta_1]$ | $r_{\beta\delta}^{-1}[\varepsilon_{12},\beta_8]$ | $(\alpha_{89},\gamma_2)$ | $(\alpha_{13},\varepsilon_{23})$ | $(\alpha_{13},\beta_9)$ | $(q',\alpha_{13})$ | $(q',\alpha_{23})$ |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| I | — | — | — | $-0,011$ | — | — | $-0,014$ | $-0,011$ | $-0,013$ | — | — | * | $-0,001$ | $-0,001$ |
| II | $-0,002$ | $-0,003$ | 0,004 | $-0,026$ | 0,016 | 0,016 | $-0,025$ | 0,012 | $-0,020$ | 0,013 | — | $-0,002$ | 0 | 0 |
| III | 0,001 | $-0,002$ | 0,005 | $-0,024$ | 0,024 | 0,003* | $-0,023$ | [$-0,030$] | [0,011] | 0,006 | 0,002 | $-0,003$ | 0,001 | 0,001 |
| IV | — | $-0,003$ | 0,006 | — | — | — | — | [$-0,008$] | [0,008] | — | $-0,003$ | $-0,001$ | — | — |
Notes. 1. Order of arrangement of the coefficients: 1—diagonal influence coefficients, 2—mutual influences of the coordinates of the Si—CH$_3$ group, 3—groups C(SiF$_n$)C$_{3-n}$ ($n=0$–3), 4—interactions of the coordinates of the indicated groups with one another.
-
Brackets denote interactions as applied to the equilibrium scheme of the molecule (CH$_3$)$_3$SiF. Mutual interactions of another type: $k_\delta^{-1}$—(F$_i$SiF$_j=\delta$), $a_\delta^{-1}$—(Si—F$_k$, F$_k$SiF$_j$), $b_\delta^{-1}$—(Si—F$_k$, F$_j$SiF$_m$), $b_\gamma^{-1}$—(Si—F$_k$, F$_j$SiC), $B_\delta^{-1}$—(Si—C, FSiF), $l_{ij}^{-1}$ refers to interactions of angles $i$ and $j$ having a common side, $O_{ij}^{-1}$—of “opposite” angles (having a common vertex), $n_{\beta\gamma}^{\prime -1}$—(FSiC$_k$, SiC$_k$H) (the angles do not lie in one plane), $p_{\beta\delta}^{-1}$ and $r_{\beta\delta}^{-1}$—(FSiF, SiCH); in the case of $p_{\beta\delta}^{-1}$ the plane SiCH bisects the angle $\delta$.
-
Numbers in square brackets refer to coefficients written in the same brackets.
-
The influence coefficients of SiF$_4$ are: $(q',q')=0,100$, $(q_1',q_2')=0,003$, $k_\delta^{-1}=0,798$, $a_\delta^{-1}=-0,028$, $l_{\delta\delta}^{-1}=-0,200$, $b_\delta^{-1}=0,028$, $o_{\delta\delta}^{-1}=0$.
influence \((q', q') = k_{g'}^{-1}\), and consequently the strength of the Si—F bond increases. The influence of the interaction of coordinates in the SiF\(_j\) group with one another and with the coordinates of the SiC\(_k\) group is manifested.
The values of the coefficients \(k_{g'}^{1}\)(Si—Hal) decrease strongly in the direction Br → Cl → F substitution. In contrast to the chloro and bromo derivatives, the accumulation of F atoms has almost no effect on the stiffness of the CSiC angles. The stiffness of the C—H bonds and of the HCH angles changes practically not at all in the molecules of all methylhalosilanes; the stiffness of the HCSi angles decreases somewhat. The mutual influences of coordinates within the methyl group are quantitatively identical for all the compounds considered. The interactions of these coordinates with the remaining ones, corresponding to deformations of other parts of the molecules, differ by no more than 5–10%. The valence \(\nu(\mathrm{C—H})\) and internal deformation \(\delta(\mathrm{CH}_3)\) vibrations of types \(A_1\) and \(A_2\) in methylhalosilanes are quite characteristic both in frequency and in form. The same may be said of the symmetric \(\nu(\mathrm{C—H})\) and \(\delta(\mathrm{CH}_3)\) vibrations of the methyl group of type E. In rocking vibrations \(\rho(\mathrm{CH}_3)\), the amplitudes of change of the molecular parameters not belonging to the methyl group differ appreciably. A comparison of the calculated displacements of atoms from their equilibrium positions in normal vibrations in the molecules CH\(_3\)SiHal\(_3\) shows that the \(\nu\)- and \(\delta\)-vibrations of the CH\(_3\) group are also characteristic in terms of displacements.
The changes in the length of the silicon—carbon bond in vibrations of type \(A_1\) in these molecules are equal (in Å):
| \(\nu(\mathrm{C—H})\) | \(\delta(\mathrm{CH}_3)\) | \(\nu(\mathrm{Si—C})\) | \(\nu(\mathrm{Si—Hal})\) | \(\delta(\mathrm{SiHal}_3)\) | |
|---|---|---|---|---|---|
| CH\(_3\)SiF\(_3\) | 0.0036 | 0.0134 | 0.0395 | 0.0263 | 0.0035 |
| (CH\(_3\))\(_2\)SiF\(_2\) | 0.0034 | 0.0139 | 0.0471 | 0.0096 | 0.0009 |
| (CH\(_3\))\(_3\)SiF | 0.0034 | 0.0139 | 0.0477 | 0.0035 | 0.0022 |
A particularly sharp difference is characteristic of the valence vibrations \(\nu(\mathrm{Si—Hal})\).
The author expresses deep gratitude to Academician I. V. Obreimov for his interest in the work and for a number of suggestions.
Saratov State Pedagogical Institute
Received 1 VIII 1962
CITED LITERATURE
\(^1\) R. L. Collins, J. R. Nielsen, J. Chem. Phys., 23, 351 (1955).
\(^2\) H. Kriegsmann, Zs. Electrochem., Ber. Bunsenges. phys. Chem., 62, 1033 (1958).
\(^3\) H. Kriegsmann, Zs. anorg. allg. Chem., 294, 113 (1958).
\(^4\) M. V. Vol’kenshtein, M. A. El’yashevich, B. I. Stepanov, Molecular Vibrations, 1, Moscow, 1949.
\(^5\) L. S. Mayants, Theory and Calculation of Molecular Vibrations, 1960.
\(^6\) I. F. Kovalev, DAN, 136, 1313 (1961); Optics and Spectroscopy, 12, 11 (1962).
\(^7\) I. F. Kovalev, DAN, 142, 1069 (1962).
\(^8\) I. N. Godnev, A. S. Sverdlvin, N. I. Ushanova, Optics and Spectroscopy, 2, 704 (1957).
\(^9\) M. J. M. Bowen et al., Tables of Interatomic Distances and Configuration in Molecules and Ions, London, 1958.