Effect of scaling of a quantum mechanical force field on the frequencies and forms of molecular vibrations

Abstract

The effect of scaling of an ab initio quantum mechanical force field on the frequencies and forms of normal vibrations are studied in terms of first- and second-order perturbation theory. Scaling the force constant matrix according to Pulay using certain assumptions in first-order perturbation theory is equivalent to scaling vibration frequencies and does not modify the form of vibrations. In this case, the second-order corrections to the frequencies and forms of vibrations become zero. The first-order perturbation theory formulas are used to verify the assumptions by calculating the frequencies and matrices of transition to perturbed forms of vibrations of ethane, propane, ethylene, cyclopropene, and isobutene molecules from quantum mechanical force fields found with the 6-31G basis set. It is shown that the vibration frequencies calculated by the formulas of first-order perturbation theory are in good agreement with exact values; the matrix of transition to perturbed eigenvectors is rarefied, with only ≈1% of its elements being markedly nonzero.