Speeding up ab initio diffusion Monte Carlo simulations by a smart lattice regularization

One of the most significant drawbacks of the all-electron ab initio diffusion Monte Carlo (DMC) is that its computational cost drastically increases with the atomic number (Z), which typically scales with Z^6. In this study, we introduce a very efficient implementation of the lattice regularized diffusion Monte Carlo (LRDMC), where the conventional time discretization is replaced by its lattice space counterpart. This scheme enables us to conveniently adopt a small lattice space in the vicinity of nuclei, and a large one in the valence region, by which a considerable speedup is achieved, especially for large atomic number Z. Indeed, the computational performances of the improved LRDMC can be theoretically established based on the Thomas-Fermi model for heavy atoms, implying the optimal Z^5 scaling for all-electron DMC calculations. This improvement enables us to apply the DMC technique even for superheavy elements (Z104), such as oganesson (Z=118), which has the highest atomic number of all synthesized elements so far.