EFFECT OF SCALING OF A QUANTUM-MECHANICAL FORCE-FIELD ON THE FREQUENCIES AND FORMS OF MOLECULAR VIBRATIONS

The effect of scaling of an ab initio quantum mechanical force field o n the frequencies and forms of normal vibrations are studied in terms of first- and second-order perturbation theory. Scaling the force cons tant matrix according to Pulay using certain assumptions in first-orde r perturbation theory is equivalent to scaling vibration frequencies a nd does not modify the form of vibrations. In this case, the second-or der 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, cyclopr opene, and isobutene molecules from quantum mechanical force fields fo und with the 6-31G basis set. It is shown that the vibration frequenci es calculated by the formulas of first-order perturbation theory are i n good agreement with exact values; the matrix of transition to pertur bed eigenvectors is rarefied with only approximate to 1% of its elemen ts being markedly nonzero.