Perturbation calculation of molecular correlation energy using Gaussian-type geminals. Second-order pair energies of LiH and BH

The second-order pair energies of LiH and BH are calculated using Rayleigh-Schroedinger perturbation theory. The first-order perturbed pair functions are expanded in terms of explicitly correlated Gaussian functions. The nonlinear parameters entering the Gaussian geminals are optimized with reference to crude SCF functions according to the method proposed previously. The final values of the second-order pair energies are then calculated using accurate SCF orbitals. At this final stage only the linear parameters are reoptimized. The calculated second-order correlation energies of LiH and BH are compared with recent diagrammatic many-body perturbation theory results. The basis sets composed of two optimized Gaussian geminals for each spin-adapted pair function are shown to give quite reliable second-order correlation energies. The results obtained with four geminals for each pair function are superior to the most accurate many-body perturbation theory data. It is stressed that the nonlinear parameters of Gaussian geminals can be given a simple physical interpretation which facilitates their reasonable guess. The first-order pair functions represented in terms of Gaussian geminals have a very attractive compact and simple form. If properly optimized they can also provide highly accurate values of the second-order molecular correlation energies.