Multiplicity of Force Constants in the Vibrational Analysis of Molecules

Abstract

Double roots for the force constants arise in the solution of the secular equation because of the symmetry of the force constant matrix. If the F matrix is of order m, there are 1 2 m (m − 1) sets of such double roots. These roots correspond to a difference in “phase” of the normal‐coordinate composition. The set of single roots applicable to the molecular force field can be in principle found by solving 1 2 m (m + 1) linear equations: Tr λ i = Tr (GF) = Σ ijα s iα s jα u α F ij using isotopic substitutions on the α sets of symmetrically equivalent atoms. Application is made to HCN.