The Normal Vibrations of Molecules of the Tetramethylmethane Type

The normal modes of a tetrahedral A(CH3)4 molecule have been investigated. For fixed orientations of the methyl groups, there are two configurations in which the molecule as a whole possesses the symmetry group Td. The group theory analysis has been applied to one of these configurations, referred to as the eclipsed form, and on the basis of Redlich's theorem a set of symmetry coordinates has been derived for each set of equivalent points. Every symmetry coordinate is associated with an irreducible representation of the group, and, as a consequence, the secular determinant is factored to the maximum extent possible on symmetry considerations alone. Using a simple valence potential, the secular equations for the totally symmetric and doubly degenerate modes have been developed. Calculations have been made for tetramethylmethane, C(CH3)4, tetramethylsilane, Si(CH3)4, and the tetramethylammonium ion, N+(CH3)4, assuming in every case that the force constants associated with the methyl groups are the same as in ethane. The results are in reasonable agreement with frequencies observed in the Raman spectra and a tentative assignment of the latter is suggested.