Knowledge Bank

A generalized valence bond approach, the G1 method developed by $Goddard1$, has several attractive features. For example, (1) it allows a single particle interpretation, (2) it yields the proper molecular dissociation, (3) it accounts for substantial part of the correlation energy, and (4) it produces an improved spin distribution near the nuclei. The G1 formulation, however, becomes unwieldy for systems with more than six electrons. To treat large systems, we have investigated an approximation to the G1 function. We expand the G1 symmetry operator and retain terms only to first order in electron exchange similar to kaldor’$s2$ treatment of the Hartree-Fock method. The natural orbital $representation3$ for each pair of G1 orbitals improves the convergence of this expansion. Our approximation is in the spirit similar to the Dirac-Van Vleck approach, but more general because our orbitals are nonorthogonal and are obtained variationally. We compare our results with those from exact G1 calculations for small atoms. Since the orbitals are nodeless, the G1 description should lead to unique well founded effective core potentials for application to large molecular structure calculations.