Toward quantum Monte Carlo forces on heavier ions: Scaling properties

Quantum Monte Carlo (QMC) forces have been studied extensively in recent decades because of their importance with spectroscopic observables and geometry optimization. Here, we benchmark the accuracy and computational cost of QMC forces. The zero-variance zero-bias (ZVZB) force estimator is used in standard variational and diffusion Monte Carlo simulations with mean-field based trial wavefunctions and atomic pseudopotentials. Statistical force uncertainties are obtained with a recently developed regression technique for heavy tailed QMC data [P. Lopez Rios and G. J. Conduit, Phys. Rev. E 99, 063312 (2019)]. By considering selected atoms and dimers with elements ranging from H to Zn (1≤Z_eff≤20), we assess the accuracy and the computational cost of ZVZB forces as the effective pseudopotential valence charge, Z_eff, increases. We find that the costs of QMC energies and forces approximately follow simple power laws in Z_eff. The force uncertainty grows more rapidly, leading to a best case cost scaling relationship of approximately Z^6.5(3)_eff for diffusion Monte Carlo. We find that the accessible system size at fixed computational cost scales as Z^-2_eff, insensitive to model assumptions or the use of the "space warp" variance-reduction technique.