Multiplicity of Force Constants in the Vibrational Analysis of Molecules

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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.

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