Excited-state gradients viaCPHF equations

Abstract

A detailed derivation of the equations for the energy gradients for excited-state wave functions is presented. These excited states are generated by singles-only CI (CIS) from the Hartree–Fock ground-state wave function. The gradients are obtained from direct differentiation of the CIS energy expression. Since this expression contains explicit terms involving the derivative of the Hartree–Fock orbital coefficients, coupled perturbed Hartree–Fock (CPHF) equations are used to eliminate the need to evaluate these terms. The final equations are then transformed to the atomic orbital basis to avoid costly AO-to-MO transformations. © 1995 John Wiley & Sons, Inc.