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

Abstract

We report all-electron variational and diffusion quantum Monte Carlo ͑VMC and DMC͒ calculations for the noble gas atoms He, Ne, Ar, Kr, and Xe. The calculations were performed using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. The quality of both the optimized Jastrow factors and the nodal surfaces of the wave functions declines with increasing atomic number Z, but the DMC calculations are tractable and well behaved in all cases. We discuss the scaling of the computational cost of DMC calculations with Z.

Spectroscopic data for the LiH molecule from pseudopotential quantum Monte Carlo calculations

“…[1] Although the scaling of the computational cost of these calculations with particle number N is reasonable (∼N 3 [1]), the cost increases rapidly with Z (∼Z 5.5 [2,3]). It is therefore normal to use pseudopotentials for heavier atoms.…”

The quantum Monte Carlo method

“…which is generally considered to rule out applications to atoms with Z greater than about ten. We have in fact pushed all-electron QMC calculations to Z = 54 using techniques to be described in the next section [55] although we were eventually forced to stop when smoke was observed coming out of the side of the computer [56]. The use of a pseudopotential serves to reduce the effective value of Z and although errors are inevitably introduced, the gain in computational efficiency is sufficient to make applications to heavy atoms feasible.…”

A Quantum Monte Carlo Study of Lanthanum

“…For the atoms heavier than Ne, the situation is more difficult. However, there have been some studies which gave satisfactory results [5][6][7][8]. For our knowledge, it is the first time Qwalk code is to be used in dealing with lanthanides.…”