Toward quantum Monte Carlo forces on heavier ions: Scaling properties

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Quantum Monte Carlo (QMC) methods are crucial for accurate calculations of spectroscopic observables and molecular geometries.
• The development of reliable QMC force estimators is essential for advancing computational materials science and chemistry.

Purpose of the Study:

• To benchmark the accuracy and computational cost of the zero-variance zero-bias (ZVZB) force estimator in Quantum Monte Carlo simulations.
• To assess how the computational cost and accuracy of ZVZB forces scale with the effective pseudopotential valence charge (Zeff).
• To predict the feasibility of using QMC forces for materials with high Zeff, such as transition metal oxides.

Main Methods:

• Utilized standard variational and diffusion Monte Carlo simulations with mean-field trial wavefunctions and atomic pseudopotentials.
• Employed the zero-variance zero-bias (ZVZB) force estimator for QMC calculations.
• Applied a regression technique for statistical force uncertainty estimation in heavy-tailed QMC data.
• Investigated atoms and dimers with effective pseudopotential valence charges (Zeff) ranging from 1 to 20.

Main Results:

• QMC energies and forces exhibit power-law scaling with Zeff.
• Force uncertainty increases rapidly with Zeff, leading to a diffusion Monte Carlo cost scaling of approximately Zeff^6.5(3).
• The accessible system size at a fixed computational cost scales as Zeff^-2, independent of specific model assumptions or variance-reduction techniques.

Conclusions:

• The computational cost of QMC forces increases significantly with the effective pseudopotential valence charge (Zeff).
• Further development of variance-reduction techniques is critical for applying QMC forces to systems with high Zeff elements.
• The findings provide practical cost predictions for QMC force calculations in various materials, including those not yet studied with QMC.