Anharmonic force constant calculations

Abstract

The relationship of the anharmonic force constants in curvilinear internal coordinates to the observed vibration-rotation spectrum of a molecule is reviewed. A simplified method of setting up the required non-linear coordinate transformations is described: this makes use of an L tensor, which is a straightforward generalization of the L matrix used in the customary description of harmonic force constant calculations. General formulae for the L tensor elements, in terms of the familiar L matrix elements, are presented. The use of non-linear symmetry coordinates and redundancies are described. Sample calculations on the water and ammonia molecules are reported.