Scale factors as effective parameters for correcting nonempirical force fields

Sources of uncertainties that arise in the search for scale factors used to systematically correct theoretical quantum-mechanical force fields in the harmonic approximation are considered. The special features of various approaches to the traditional procedure for scaling according to Pulay are analyzed. It is suggested that scale factors be determined as quotients obtained by dividing the diagonal elements of the approximation to the exact matrix of force constants by their quantum-mechanical analogues. Using this approach obviates the necessity of solving the inverse problem. Perturbation theory is used to show that, when molecular geometric parameters and scale factors are varied jointly, an exact correlation can appear, which substantiates the effective character of force field corrections with the use of scale factors. The procedure for the scaling of generalized quantum-mechanical force fields based on the transition from the normal-coordinate to natural-coordinate representation is considered.