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 (1 ≤ Z ≤ 35, where Z is the atomic number). 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 (req) and harmonic frequencies (ω) very close to the experimental values for all dimers, improving the corresponding VMC results. The LRDMC forces with the RE approximation improve the VMC forces, implying that it is worth computing the DMC forces beyond VMC despite the higher computational cost. The LRDMC forces with the VD approximations also show improvement, which unfortunately comes at a much higher computational cost in all-electron calculations. We find that the ratio of computational costs between QMC energy and forces scales as Z∼2.5 without the SWCT. In contrast, the application of the SWCT makes the ratio 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.
Highlights
The quantum Monte Carlo (QMC) technique1 is one of the state-of-the-art numerical methods for evaluating the expectation values of many-body wave functions, and it provides extremely accurate energetics
All our calculations were carried out by considering all the electrons of the corresponding atomic species, we do not expect—nor do we have evidence that—the main conclusions of our work will depend on the presence of pseudopotentials, which are often used in QMC to remove the chemically inert core electrons
The variational Monte Carlo (VMC) and lattice-regularized diffusion Monte Carlo (LRDMC) forces were calculated in combination with the space-warp coordinate transformation (SWCT) and appropriate regularization techniques to remove the infinite variance problem
Summary
The quantum Monte Carlo (QMC) technique is one of the state-of-the-art numerical methods for evaluating the expectation values of many-body wave functions, and it provides extremely accurate energetics. To avoid the well-known signproblem instability, the projection to the ground state is restricted to leave the nodal surface of the initial trial wave function unchanged, and this is usually given by the best available VMC variational guess Despite this approximation, the FNDMC method provides results that are usually of much higher quality than the VMC results. Tiihonen et al. showed that the scaling of QMC atomic force calculations with pseudopotentials is worse than that of energy calculations, remarkably by orders of magnitude In detail, they claimed that, at constant computational cost and constant statistical resolution, the accessible system size scales as Ze−ff, where Zeff is the effective valence charge. The accessible system size is not affected by QMC force calculations when the SWCT variance-reduction technique is applied
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