Quantum Chemistry Beyond the Algebraic Approximation with Gaussian Geminals

Abstract

It is very hard to achieve chemical accuracies of 1 mhartree (or about 1 kcal/mole) for molecular energies. The electron correlation methods using expansions in virtual orbitals as computed from some zeroth-order problem usually converge very slowly. This is mainly due to the absence of explicit correlation in these expansions. A valuable remedy is presented in the form of Gaussian type geminal (GTG) expansions for pair functions in perturbation and coupled pair calculations. The combined use of Gaussian type orbitals (GTO) for Hartree-Fock orbitals and GTG’s for pair functions enables the analytic evaluation of all many-electron integrals, regardless of the molecule or the number of electrons. Nonlinear parameters in the GTG’s have been obtained by minimizing a new second-order energy functional which is computationally more efficient than a previous one. Saturated second- and third-order energies for He, Be, H₂ and LiH have been obtained, essentially matching previous accurate atomic results, and superseding decisively diatomic results. Coupled-pair results with the GTG basis obtained at the second-order level match other accurate Be and LiH results, and are far superior for He and H₂, Drastic, yet numerically reliable, approximate treatments for the strong orthogonality were introduced which dramatically reduce the computational efforts. Future developments are discussed.