Role and Treatment of Zero Eigenvalues of Rotation in the Cartesian Force Constant Matrix Along Reaction Path

Abstract

Rotational vectors in chemistry appear as eigenvectors associated with three zero eigenvalues of the force constant matrix at an equilibrium configuration of an isolated molecule. Another set of three zero eigenvalues of the force constant matrix is related with translational motions of the center of mass. Accordingly, for N-nucleus molecular system, f = 3N - 6 degrees of freedom are necessary to describe the vibra- tional vectors at the equilibrium configuration. In GF theory of molecular vibrations, internal coordinate systems have been introduced for describing the vibrational motions of a molecule at a stable equilibrium point [1]. The internal coordinates consists of the f independent configurational parameters q ¹,... q ², . . . , q ^f such as bond lengths, valence angles, angles between a bond and the plane determined by three nuclei, and angles between two planes.