Estimating the relativistic energy by diffusion quantum Monte Carlo

Abstract

We report formulas to estimate the relativistic corrections for atoms or molecules (treated as the first order perturbation) by diffusion quantum Monte Carlo (DQMC) simulations. Our formulas involve primarily quantities which are routinely computed in nonrelativistic simulations. Hence our approach entails only minor additional modifications of existing (all electron) DQMC codes. We illustrate our algorithm by estimating various relativistic corrections to the ground state energy of LiH. 3784 J.Since both quantites which appear on the right-hand side of Eq. (4) possess Coulombic singularities, it easily fol-J.

Lowest-order relativistic corrections of helium computed using Monte Carlo methods

“…For smaller atoms (helium, lithium, beryllium) Monte Carlo methods are not as accurate as other explicitly correlated calculations but for larger atoms they are much more competitive and have recovered 99% of the correlation energy with a relatively compact wave function [50][51][52][53][54]. Because all integrals are computed numerically, this method has also been used to determine a variety of properties [55][56][57][58][59][60][61][62] including the relativistic corrections for several singlet S states [63][64][65]. Our ultimate goal is to use these Monte Carlo wave functions to calculate the relativistic corrections for a number of atoms.…”

All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe

“…Numerous all-electron DMC studies have been reported 5,6,7,8,9,10,11,12,13,14,15,16,17 for atoms up to Z = 10, but very few have included heavier atoms. DMC studies of heavier atoms have normally used pseudopotentials to remove the chemically inert core electrons from the problem.…”

Relativistic corrections to atomic energies from quantum Monte Carlo calculations

“…For large numbers of electrons the only practical method for performing the required integrations with accurate many-body wave functions is to use Monte Carlo techniques [5,6]. Variational Monte Carlo (VMC) calculations of this type have been performed by Vrbik, De Pasquale, and Rothstein [7] for the four-electron molecule LiH. In our work we have considered five cases, including the ten-electron atom Ne, which is the heaviest atom to which diffusion Monte Carlo (DMC) techniques have been applied, without the use of approximations to treat the core electrons [8].…”