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Ab-initio quantum Monte Carlo (QMC) methods are a state-of-the-artcomputational approach to obtaining highly accurate many-body wave functions.Although QMC methods are widely used in physics and chemistry to computeground-state energies, calculation of atomic forces is still undertechnical/algorithmic development. Very recently, force evaluation has startedto become of paramount importance for the generation of machine-learningforce-field potentials. Nevertheless, there is no consensus regarding whetheran efficient algorithm is available for the QMC force evaluation, namely onethat scales well with the number of electrons and the atomic numbers. In thisstudy, 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 andwithout the so-called space-warp coordinate transformation (SWCT) andappropriate 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 LRDMCenergies give equilibrium bond lengths ($r_{\rm eq}$) and harmonic frequencies($\omega$) very close to the experimental values for all dimers, improving thecorresponding VMC results. The LRDMC forces improve the VMC forces, implyingthat it is worth computing the DMC forces beyond VMC in spite of the highercomputational cost. We find that the ratio of computational costs between QMCenergy and forces scales as $Z^{\sim 2.5}$ without the SWCT. In contrast, theapplication of the SWCT makes the ratio {\it independent} of $Z$. As such, theaccessible QMC system size is not affected by the evaluation of ionic forcesbut governed by the same scaling as the total energy one.

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