Impact of electron density on the fixed-node errors in Quantum Monte Carlo of atomic systems

We analyze the effect of increasing charge density on the fixed-node errors in diffusion Monte Carlo (FNDMC). We compare FNDMC ground state energies of 4-electron atomic systems with nuclear charge Z using Hartree–Fock and restricted Configuration Interaction trial wave functions. We perform these calculations for several different values of the nuclear charge, and we analyze the systematic trends of the recovered correlation energies as a function of Z . For this testing system we demonstrate that the fixed-node error of the Hartree–Fock trial wave functions increases linearly with increasing the nuclear charge.