Gaussian functions in hylleraas-CI calculations. I. Ground state energies for H2, HeH+, and H+3

Abstract
Gaussian basis functions have been used in explicitly correlated configuration interaction calculations for the ground states of H2, HeH+, and H+3. Due to the use of rij, the polarization functions are found to be much less important in comparison with their effectiveness in the convectional CI methods. Our lowest ground state energies for H2 and HeH+ are 1.8 and 8 cm1, respectively, above the best literature values obtained by using generalized James–Coolidge expansion in terms of confocal elliptical coordinates. With 10s and 2p contracted functions, the calculated ground state energy for H+3 is −1.343 500 hartrees, which is believed to be the lowest variational energy in the literature.