Removal of Redundant Coordinates from the Vibrational Problem

Abstract

A numerical technique for the removal of redundant vibrational coordinates has been developed. This method is based on matrix calculations and is applicable to any choice of coordinates or molecules. First the exact zero coordinates are calculated using the transformation (B matrix) from internal coordinates to cartesian displacements. Second a full set of independent coordinates—preferably symmetry adapted—is constructed by an orthogonalization procedure. Retaining the character of group motions like rocking, wagging, twisting can be taken care of. A description of the method is supplemented by a numerical appendix for an easy (CH₂O) and a complicated (C₆H₁₂) example.

Keywords

Vibrational coordinates Redundancy Removal

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