Orbital-Correction Method

Abstract

A method for calculating the total energy of complex systems, such as molecules, is proposed. It is a perturbation expansion with two novel features. First, the starting point is an approximate state (rather than an approximate Hamiltonian) and the expansion is in the orbital correction to that state (rather than in a perturbing Hamiltonian). This permits application to complicated molecules where there is no soluble unperturbed Hamiltonian resembling the real system. The second feature is the evaluation of the total energy without the diagonalization of a Hamiltonian matrix. This is accomplished in a way analogous to, but basically different from, the use of the invariance of a trace under a similarity transformation. This permits the treatment of arbitrarily large systems. The principal approximations in the theory are a self-consistent-field approximation to the electron-electron interaction and the truncation at second order of an expansion which would be exact if carried to all orders. If the method were applied to metals, with the approximate starting states taken as orthogonalized plane waves, the theory becomes rigorous nonlocal pseudopotential theory. In molecules linear-combination-of-atomic-orbitals (LCAO) starting states are envisaged and the theory is a systematic improvement upon (as well as simplification of) LCAO theory. Pseudopotentials do not play a central role in the application to molecules, though their use will improve the accuracy and the improvement may be an important one. The results of application of the method to the central hydrides, methane and hydrogen fluoride, by Meserve are given.