First derivative of molecular integrals for electronic energy using spherical gaussian type orbitals

Abstract

A complete analytical first derivative (gradient) of molecular integrals for evaluation of electronic energy using spherical gaussian type orbital (FSGO) is presented in this paper. The analytical first derivative for the inverse of the overlap matrix, which is used in FSGO method, is also presented. Analytical gradients of exponents, orbital and nuclear cartesian coordinates, and coefficients are all considered. In order to save more computational time, all the above formulas for gradients are presented in terms of original integrals which are evaluated and stored beforehand. The gradient formulas have been tested for H 2O and CH 2 by FSGO method, and compared with the results of the finite difference method. Besides the high accuracy of analytical gradient, these calculations have shown that considerable computational time is saved.