Extremal properties of force constants. Part I

Abstract

The secular equation (GF)L = LΛ of the vibrational problem of a molecule can be rewritten in the form F = L ̃-1ΛL-1. Given the vibrational wave numbers, ω, the solution F of this equation for the case of a two-dimensional symmetry species is dependent on one arbitrary parameter, e.g., φ{symbol}, 0 ≦ φ{symbol} ≦ 2π. The dependence of the force constants on the parameter φ{symbol} as defined in this paper was investigated for the following molecules: H2O, H2S, H2Se, SO2, NO2, ClO2, as well as NH3, PH3, AsH3, and SbH3. It was found that the force constants, calculated by the usual iteration technique, can be correlated with such values of the angle φ{symbol}, for which the force constant fr exhibits a maximum or the force constant fa shows a minimum depending on whether or not the molecule contains hydrogen. © 1967.