Simple derivation of the potential energy gradient for an arbitrary electronic wave function

Abstract

An analytical expression for the potential energy gradient was first given by Bratoi [I] in 1958 for the closed-shell Hartree-Fock case. Over the last few years analytically calculated gradients [2-131 have been extensively used for studying molecular potential energy surfaces, and much credit for this development goes to Pulay [ 14,151. The purpose of this letter is to present a very simple derivation of the expression for the gradient for an arbitrary electronic wave function. Consider an arbitrary wave function \E(p,) which is uniquely determined by then parameters b,}. The expectation value of the energy E has been minimized with respect to the first m parameters subject to the constraints