Evaluation of parameters in semiempirical molecular quantum-mechanical calculations

Abstract

General analytic expressions are given for the partial derivatives of both eigenvalues and eigenvectors with respect to the various molecular integrals, or parameters, which appear in the secular equation in molecular quantum-mechanical problems. Since most physical properties of interest depend upon the various eigenvalues and eigenvectors in a straightforward manner, it is then possible to evaluate analytically the derivatives of the calculated values of these properties with respect to the various parameters associated with the problem. With the aid of nonlinear estimation procedures, it is therefore possible to readily find that set of parameters which gives the "best fit" to a particular set of experimental data. Thus a systematic procedure for evaluating these parameters is available.