Vibrational—Rotational Angular-Momentum Coupling in Spherical-Top Molecules. II. General Zeta Sums

Abstract

General Coriolis zeta sums are derived for all molecules belonging to tetrahedral, octahedral, and icosahedral point groups. For all infrared‐active species, the zeta sum is given by ${\displaystyle \sum }{\zeta }_i{\mathrm{=m}}_0+\frac{1}{2}{\mathrm{(\delta }}_r{\mathrm{+\delta }}_g\text{+1)m−}\frac{1}{2}{\mathrm{(\delta }}_r\text{+2)}$ , where m₀=1 or 0 depending on whether or not a central atom is present; m is the number of sets of equivalent nuclei on threefold or higher symmetry axes, but not on all symmetry elements; δ_r=1 or 0 depending on whether or not the rigid rotations belong to the infrared‐active representation; and δ_g=1 for Point Group T_h and zero for all other point groups. Several related matters are considered, including the definition of the signs of individual zetas. The application of these zeta sums to the analysis of vibrational spectra is treated briefly, especially with regard to the contours of unresolved bands.