Optimization of variational trial functions

Abstract

It is shown that the first and second partials of an upper or lower bound with respect to an arbitrary set of nonlinear parameters may be exactly calculated from the corresponding partials of the defining matrix elements after one variational determination of the trial function. A stable and quadratically convergent minimization procedure is presented which efficiently exploits the availability of the partials to permit optimization of the trial functions with respect to the nonlinear parameters. The formalism for applications in the area of atomic and molecular theory including Hartree-Fock and variational-perturbation techniques is explicitly developed. Results for optimizations of atomic orbital exponents and molecular geometries are presented.