Evaluation of analytic molecular orbital derivatives and gradients using the effective valence shell Hamiltonian method

Expressions for the analytic energy gradients and the nonadiabatic derivative couplings are derived for the effective valence shell Hamiltonian theory (a variant of degenerate/quasidegenerate many-body perturbation theory) using the diagonal and off-diagonal Hellmann-Feynman formulas and a generalized set of coupled perturbed Hartree-Fock equations to evaluate the derivatives of the molecular orbitals. The method is designed fbr efficiently treating the energy derivatives and nonadiabatic couplings for several states simultaneously. The generalized coupled perturbed Hartree-Fock equations arise because the reference space orbitals are optimized for simultaneously describing the ground and excited states, a feature lost with the traditional partitioning where the virtual orbitals provide a poor choice, for representing the low lying states. A simple correspondence emerges between the new generalized coupled perturbed Hartree-Fock and the traditional coupled-perturbed Hartree-Fock methods enabling the use of the former with straightforward modifications. The derivatives of the second and higher order portions of the effective Hamiltonian are readily obtained using a diagrammatic representation that will be described elsewhere. (C) 1998 American Institute of Physics. [S0021-9606(98)30546-2].