Space-warp coordinate transformation for efficient ionic force calculations in quantum Monte Carlo

Abstract

Ab-initio quantum Monte Carlo (QMC) methods are a state-of-the-art computational approach to obtaining highly accurate many-body wave functions. Although QMC methods are widely used in physics and chemistry to compute ground-state energies, calculation of atomic forces is still under technical/algorithmic development. Very recently, force evaluation has started to become of paramount importance for the generation of machine-learning force-field potentials. Nevertheless, there is no consensus regarding whether an efficient algorithm is available for the QMC force evaluation, namely one that scales well with the number of electrons and the atomic numbers. In this study, we benchmark the accuracy of all-electron variational Monte Carlo (VMC) and lattice-regularized diffusion Monte Carlo (LRDMC) forces for various mono- and heteronuclear dimers. The VMC and LRDMC forces were calculated with and without the so-called space-warp coordinate transformation (SWCT) and appropriate regularization techniques to remove the infinite variance problem. The LRDMC forces were computed with the Reynolds (RE) and variational-drift (VD) approximations. The potential energy surfaces obtained from the LRDMC energies give equilibrium bond lengths ($r_{\mathrm{eq}}$) and harmonic frequencies ($\omega$) very close to the experimental values for all dimers, improving the corresponding VMC results. The LRDMC forces improve the VMC forces, implying that it is worth computing the DMC forces beyond VMC in spite of the higher computational cost. We find that the ratio of computational costs between QMC energy and forces scales as $Z^{\sim 2.5}$ without the SWCT. In contrast, the application of the SWCT makes the ratio {\it independent} of $Z$. As such, the accessible QMC system size is not affected by the evaluation of ionic forces but governed by the same scaling as the total energy one.

31 pages

References in corpus (11)

• Weak binding between two aromatic rings: feeling the van der Waals attraction by quantum Monte Carlo methods
• Stable liquid Hydrogen at high pressure by a novel ab-initio molecular dynamics
• Phase diagram of hydrogen and a hydrogen-helium mixture at planetary conditions by Quantum Monte Carlo simulations
• Resonating valence bond wave function with molecular orbitals: Application to first-row molecules
• On Achieving High Accuracy in Quantum Chemical Calculations of 3d Transition Metal Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules
• Phase Stability of TiO${}_2$ Polymorphs from Diffusion Quantum Monte Carlo
• Energetics and Dipole Moment of Transition Metal Monoxides by Quantum Monte Carlo
• All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe
• Accurate, efficient and simple forces with Quantum Monte Carlo methods
• Shape and Energy Consistent Pseudopotentials for Correlated Electron systems
• Total forces in the diffusion Monte Carlo method with nonlocal pseudopotentials

Cited by in corpus (10)

• High pressure hydrogen by machine learning and quantum Monte Carlo
• Diffusion Monte Carlo Study on Relative Stabilities of Boron Nitride Polymorphs
• Principal deuterium Hugoniot via Quantum Monte Carlo and $\Delta$-learning
• TurboGenius: Python suite for high-throughput calculations of ab initio quantum Monte Carlo methods
• Training models using forces computed by stochastic electronic structure methods
• Efficient calculation of unbiased atomic forces in ab initio Variational Monte Carlo
• Deep learning quantum Monte Carlo for solids
• Self-consistency error correction for accurate machine learning potentials from variational Monte Carlo
• Fast Evaluation of Unbiased Atomic Forces in ab initio Variational Monte Carlo via the Lagrangian Technique
• A Denser Hydrogen Inferred from First-Principles Simulations Challenges Jupiter's Interior Models