Estimating the relativistic energy by diffusion quantum Monte Carlo

Abstract

Abstract Heavy atoms are problematic in QMC calculations for several reasons. Their energies are large, they have many electrons, and the time scales for core and valence electron motions are widely different. Larger local energy fluctuations are associated with higher energies. More electrons require longer computational efforts. Different time scales require short steps in one region and long equilibration times in others. The result is an estimated scaling of computational effort with zB-7, the sixth to seventh power of the nuclear charge Z. The Z-dependence can be reduced with the use of pseudopotentials, and this approach has been pursued with success, but not without introducing uncertainties. This paper describes an entirely different method which retains all the electrons, but treats core and valence electrons in different ways. The basic idea is that of treating core electrons by Metropolis sampling and valence electrons by diffusion with drift. Separate trial functions t/JT,core and were chosen orthogonal such that the valence electrons were prevented from collapsing into the core. For the core electrons the Metropolis walks were taken without branching and produced a distribution of walkers. For the valence electrons normal diffusion walks with drift produced a distribution. A smooth transition between regions was obtained with a damping function to eliminate branching as valence electrons approached the core.