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 $Z^{\sim 6}$. 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 $Z^{\sim 5}$ scaling for all-electron DMC calculations. This improvement enables us to apply the DMC technique even for superheavy elements ($Z\ge 104$), such as oganesson ($Z=118)$, which has the highest atomic number of all synthesized elements so far.

• Received 2 September 2019
• Revised 26 November 2019
• Accepted 13 March 2020

DOI:https://doi.org/10.1103/PhysRevB.101.155106

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

©2020 American Physical Society