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 kth 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 3O 2 molecule using the present theory agree well with the observed quantities.
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