Calculation of the Frequencies of the Symmetrical Modes of Vibration for Molecules with Various Types of Symmetry

Abstract

The secular equations for the frequencies of the symmetrical modes of vibration for molecules with various types of symmetry have been developed. The types of symmetry considered include a center of symmetry, and twofold, threefold, and fourfold axes of symmetry. Application to the problem of the configuration of oximes indicates that acetoxime has the following structural formula: $\begin{array}{c}\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\mathrm{CH}}_3\\ \mathrm{\hspace{0.17em}\hspace{0.17em}–\hspace{0.17em}\hspace{0.17em}–}\\ {126}^{\circ }\mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\mathrm{C}=\mathrm{N}-\mathrm{OH}.\\ \mathrm{\hspace{0.17em}\hspace{0.17em}–\hspace{0.17em}\hspace{0.17em}–}\\ \mathrm{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{\mathrm{CH}}_3\end{array}$ .