Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules

Abstract

The phaseless auxiliary-field quantum Monte Carlo (AF QMC) method [S. Zhang and H. Krakauer, Phys. Rev. Lett. 90, 136401 (2003)] is used to carry out a systematic study of the dissociation and ionization energies of second-row group 3A--7A atoms and dimers: Al, Si, P, S, and Cl. In addition, the ${\mathrm{P}}_{2}$ dimer is compared to the third-row ${\mathrm{As}}_{2}$ dimer, which is also triply bonded. This method projects the many-body ground state by means of importance-sampled random walks in the space of Slater determinants. The Monte Carlo phase problem, due to the electron-electron Coulomb interaction, is controlled via the phaseless approximation, with a trial wave function $\ensuremath{\mid}{\ensuremath{\Psi}}_{T}⟩$. As in previous calculations, a mean-field single Slater determinant is used as $\ensuremath{\mid}{\ensuremath{\Psi}}_{T}⟩$. The method is formulated in the Hilbert space defined by any chosen one-particle basis. The present calculations use a plane wave basis under periodic boundary conditions with norm-conserving pseudopotentials. Computational details of the plane wave AF QMC method are presented. The isolated systems chosen here allow a systematic study of the various algorithmic issues. We show the accuracy of the plane wave method and discuss its convergence with respect to parameters such as the supercell size and plane wave cutoff. The use of standard norm-conserving pseudopotentials in the many-body AF QMC framework is examined.