The Rotation-Vibration Energies of Tetrahedrally Symmetric Pentatomic Molecules. I

Abstract

A complete theory for the rotation-vibration energies of tetrahedrally pentatomic molecules has been derived to second degree of approximation for certain vibration states. In this discussion the elements of the matrix $H$ are given for the states ${V}_{1}{\ensuremath{\nu}}_{1}$, ${\ensuremath{\nu}}_{2}$, ${V}_{1}{\ensuremath{\nu}}_{1}+{\ensuremath{\nu}}_{3}$, ${V}_{1}{\ensuremath{\nu}}_{1}+{\ensuremath{\nu}}_{4}$, ${\ensuremath{\nu}}_{2}+{\ensuremath{\nu}}_{3}$ and ${\ensuremath{\nu}}_{2}+{\ensuremath{\nu}}_{4}$. The selection rules governing what transitions may take place have been determined with relations for the intensities.