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 s...

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Bibliographic Details
Published in:The Journal of chemical physics 2021-05, Vol.154 (20), p.204111-204111
Main Authors: Tiihonen, Juha, Clay, Raymond C., Krogel, Jaron T.
Format: Article
Language:English
Subjects:
Accuracy
Computational efficiency
Computing costs
Diffusion
Dimers
Optimization
Physics
Pseudopotentials
Statistical analysis
Transition metal oxides
Uncertainty
Variance
Wave functions
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Summary: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 ≤ Zeff ≤ 20), we assess the accuracy and the computational cost of ZVZB forces as the effective pseudopotential valence charge, Zeff, increases. We find that the costs of QMC energies and forces approximately follow simple power laws in Zeff. The force uncertainty grows more rapidly, leading to a best case cost scaling relationship of approximately Zeff6.5(3) for diffusion Monte Carlo. We find that the accessible system size at fixed computational cost scales as Zeff−2, insensitive to model assumptions or the use of the “space warp” variance-reduction technique. Our results predict the practical cost of obtaining forces for a range of materials, such as transition metal oxides where QMC forces have yet to be applied, and underscore the importance of further developing force variance-reduction techniques, particularly for atoms with high Zeff.
ISSN:0021-9606
1089-7690
DOI:10.1063/5.0052266