ACCURATE RELATIVISTIC ENERGIES OF ONE-ELECTRON AND 2-ELECTRON SYSTEMSUSING GAUSSIAN WAVE-FUNCTIONS

Gaussian wave functions with optimized nonlinear variational parameter s are applied to evaluate clamped-nucleus nonrelativistic energies as well as the lowest order relativistic corrections for the ground state s of the hydrogen atom, hydrogen molecular ion H-2(+), helium atom, an d hydrogen molecule. The two-electron functions used depend explicitly on the interelectronic distance r(12) but do not describe the cusp pr operly. Despite this, for H-2(+) and H-2 the results are more accurate than ever reported, and for He they are inferior only to the best cal culations employing Hylleraas-type expansions. It is demonstrated that , contrary to a common opinion, Gaussian wave functions are very well suited for high-accuracy relativistic computations even in the Breit-P auli approximation, provided that the nonlinear parameters are optimiz ed with respect to the nonrelativistic energy. (C) 1996 American Insti tute of Physics.