Valence-bond theory and the evaluation of electronic energy matrix elements between nonorthogonal Slater determinants

The central practical problem which has impeded the development of the valence-bond theory of molecular electronic structure for the past fifty years has been the so-called nonorthogonality problem. In this article we develop a new method for calculating electronic energy matrix elements between Slater determinants constructed from a set of nonorthogonal orbitals. The method should lead to a reduction in the time needed for the evaluation of the crucially important Hamiltonian and overlap matrix elements needed in valence-bond theory by about 2 orders of magnitude for typical (small) molecular problems. The time required by previously available methods for the evaluation of these matrix elements increases as N⁶, where N is the number of electrons. We show that the time required by our new method increases only as N⁴. .AE