Molecular vibrations in the representation of generalized forces

Abstract

An iterative procedure based on a first order perturbation treatment is described for the calculation of the quadratic force field of a polyatomic molecule in the representation of generalized forces conjugate to vibrational coordinates. In this procedure the elements of the inverse potential constant matrix, or compliance matrix, are adjusted with the aid of Jacobian matrices with respect to experimental vibrational data. A simple extension of this method makes it possible to use to advantage mean square vibrational amplitudes and/or centrifugal distortion constants in a least squares computation. Only symmetrical characteristic matrices are involved in the calculation and inversion of the kinematic G matrix is not required. The converged set of constants may easily be transformed in the vibrational coordinate representation. Programs have been written for an automatic digital computer which will carry out a fully automatic calculation of the force field; sample calculations have been made for the molecules of NO 2 and PCl 3 for which the most general quadratic force field was obtained from vibrational frequencies and mean square amplitudes.