| 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.
Moscow State University. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 2, pp. 210–216, March–April, 1998.
This work was supported by RFFR grant No. 96-03-34085. |
