Perturbative relativistic calculations for one-electron systems in a Gaussian basis

Abstract

The “direct perturbation theory” of relativistic corrections (in which singularities of the traditional relativistic perturbation theory are avoided) is applied in a basis of atom-centered Gaussian orbitals to several states of the H atom and the ions H + 2 and HeH 2+. Almost exponential convergence with the basis size is achieved for the non-relativistic energy as well as for the relativistic corrections E 2, E 4, E 6, respectively. An overall 9-figure accuracy of the relativistic energies of the 1σ g and 1σ u states of H + 2 is achieved. The Pauli—Hamiltonian, that only furnishes E 2, is much inferior to direct perturbation theory even for E 2 (at least for states with non-vanishing electron density of the nuclei).