Calculation of shrinkage corrections in harmonic approximation

Abstract The classical spectral problem is analyzed on the level of the harmonic force field approximation to determine the vector describing the mean atomic displacements from the equilibrium positions, x &> =Σ k x &> =— 1 2 B(O) −1 Σ k ΔB k , where B(O) is the transformation matrix between the internal and Cartesian coordinates defined for the equilibrium configuration, ΔB k is the variation in the transformation matrix caused by molecular motion along the k th eigenvector and the summation is over all molecular modes. A simple procedure for determining the ΔB k quantities without explicitly calculating the ΔB k matrices is described. The vectors x and k enter nto the expressions for the shrinkage corrections and the mean square vibrational amplitudes. The harmonic amplitudes calculated for the C 3 O 2 molecule using the present theory agree well with the observed quantities.