Valence quantum Monte Carlo with ab initio effective core potentials

Abstract

Abstract This paper reports a more elaborate treatment than either of the other papers reporting effective potentials in QMC calculations in 1987 and 1988. Although justified here as a means to avoid the higher computational requirements of heavy (large Z) atoms, the advantages of eliminating core electrons apply equally well for systems of lighter atoms such as carbon, nitrogen, and oxygen. The treatment in this paper begins with a valence-electron Schrödinger equation in which core electrons are missing. The nuclear charges are replaced by reduced effective nuclear charges, and the corevalence electron-electron repulsions are replaced by a nonlocal effective core potential uECP. This term is a relatively complicated expression which incorporates the core-valence orthogonality condition and is a function of valence electron positions. It is obtained in the course of Hartree-Fock calculations for the atoms involved. The implementation in QMC calculations required a number of minor approximations, along with a lengthy set of derivations, finally resulting in an expression for uECP compatible with QMC. Calculations were carried out in fixed-node diffusion QMC for several systems: Li/Li-, Na/Na+, Mg/Mg+, NaH/(Na+H), and Na2/(Na+Na). These produced electron affinities, ionization potentials, and binding energies which could be compared with experimental values. Statistical uncertainties were typically 0.02 eV for these values, and all agreed with experimental values within their uncertainties. Such accuracies would have required much greater computational efforts for all-electron calculations.