Quantitative estimation of localization errors of 3 d transition metal pseudopotentials in diffusion Monte Carlo

The necessarily approximate evaluation of non-local pseudopotentials in diffusion Monte Carlo (DMC) introduces localization errors. We estimate these errors for two families of non-local pseudopotentials for the first-row transition metal atoms Sc-Zn using an extrapolation scheme and multideterminant wavefunctions. Sensitivities of the error in the DMC energies to the Jastrow factor are used to estimate the quality of two sets of pseudopotentials with respect to locality error reduction. The locality approximation and T-moves scheme are also compared for accuracy of total energies. After estimating the removal of the locality and T-moves errors, we present the range of fixed-node energies between a single determinant description and a full valence multideterminant complete active space expansion. The results for these pseudopotentials agree with previous findings that the locality approximation is less sensitive to changes in the Jastrow than T-moves yielding more accurate total energies, however not necessarily more accurate energy differences. For both the locality approximation and T-moves, we find decreasing Jastrow sensitivity moving left to right across the series Sc-Zn. The recently generated pseudopotentials of Krogel et al. [Phys. Rev. B 93, 075143 (2016)] reduce the magnitude of the locality error compared with the pseudopotentials of Burkatzki et al. [J. Chem. Phys. 129, 164115 (2008)] by an average estimated 40% using the locality approximation. The estimated locality error is equivalent for both sets of pseudopotentials when T-moves is used. For the Sc-Zn atomic series with these pseudopotentials, and using up to three-body Jastrow factors, our results suggest that the fixed-node error is dominant over the locality error when a single determinant is used

Machine Learning Diffusion Monte Carlo Energies

We present two machine learning methodologies that are capable of predicting diffusion Monte Carlo (DMC) energies with small datasets (~60 DMC calculations in total). The first uses voxel deep neural networks (VDNNs) to predict DMC energy densities using Kohn-Sham density functional theory (DFT) electron densities as input. The second uses kernel ridge regression (KRR) to predict atomic contributions to the DMC total energy using atomic environment vectors as input (we used atom centred symmetry functions, atomic environment vectors from the ANI models, and smooth overlap of atomic positions). We first compare the methodologies on pristine graphene lattices, where we find the KRR methodology performs best in comparison to gradient boosted decision trees, random forest, gaussian process regression, and multilayer perceptrons. In addition, KRR outperforms VDNNs by an order of magnitude. Afterwards, we study the generalizability of KRR to predict the energy barrier associated with a Stone-Wales defect. Lastly, we move from 2D to 3D materials and use KRR to predict total energies of liquid water. In all cases, we find that the KRR models are more accurate than Kohn-Sham DFT and all mean absolute errors are less than chemical accuracy

Ab initio quantum Monte Carlo calculations of spin superexchange in cuprates: the benchmarking case of Ca2_2CuO3_3

In view of the continuous theoretical efforts aimed at an accurate microscopic description of the strongly correlated transition metal oxides and related materials, we show that with continuum quantum Monte Carlo (QMC) calculations it is possible to obtain the value of the spin superexchange coupling constant of a copper oxide in a quantitatively excellent agreement with experiment. The variational nature of the QMC total energy allows us to identify the best trial wave function out of the available pool of wave functions, which makes the approach essentially free from adjustable parameters and thus truly ab initio. The present results on magnetic interactions suggest that QMC is capable of accurately describing ground state properties of strongly correlated materials.Comment: Published in Physical Review