Nonlocal pseudopotentials and time-step errors in diffusion Monte Carlo

Anderson, Tyler A.; Umrigar, C. J.

doi:10.1063/5.0052838

Cited by 8 publications

(6 citation statements)

References 16 publications

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“…Note that the T-moves impact comes from sampling the nonlocal term for paths that do not cross the node. Consequently, this suggests that further improvements of the DMC propagator related to the presence of the nonlocal operator might be possible and recent work suggests interesting options in this direction [22]. The DMC method involves the propagation of walkers in position space together with reweighting represented by the local energy factor in Eqn.…”

Section: Discussionmentioning

confidence: 99%

“…These complications have been recognized some time ago and the algorithm was adjusted by a number of additional improvements. This includes, for exmple, the Metropolis rejection step [41,23] and a smooth cut-off of the drift to a finite value beyond certain threshold [22]. These adjustments modify the walker evolution and effectively improve the corresponding Green's function in regions that show either very small wave function amplitudes and/or very large fluctuations of local energy.…”

Section: Discussionmentioning

confidence: 99%

“…For the localization approximation, the situation is not that simple since the numerator is given by the integral, not by the value at the sampling point. However, in practical calculations, the problematic events related to too low local energies are found to be rare and can be handled without significant biases, for example, by using a threshold for large weights [22].…”

Section: Behmentioning

confidence: 99%

“…Here the zero variance is restored indirectly assuming the trial function converges to an exact eigenstate, thus the two approaches appear to be complementary to each other. See also a very recent development that unifies the advantages of both with gains in efficiency [22]. In some cases, the higher accuracy of ccECPs have led to potential functions for particular symmetry channels that are deeper, i.e., closer to the original (screened) Coulomb interaction than in some other commonly used ECP sets.…”

Section: Introductionmentioning

confidence: 99%

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A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

Zhou,

Scemama,

Wang

et al. 2021

Preprint

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We study beryllium dihydride (BeH 2 ) and acetylene (C 2 H 2 ) molecules using real-space diffusion Monte Carlo (DMC) method. The molecules serve as perhaps the simplest prototypes that illustrate the difficulties with biases in the fixednode DMC calculations that might appear with the use of effective core potentials (ECPs) or other nonlocal operators. This is especially relevant for the recently introduced correlation consistent ECPs (ccECPs) for 2s2p elements. Corresponding ccECPs exhibit deeper potential functions due to higher fidelity to all-electron counterparts, which could lead to larger local energy fluctuations. We point out that the difficulties stem from issues that are straightforward to address by upgrades of basis sets, use of T-moves for nonlocal terms, inclusion of a few configurations into the trial function and similar. The resulting accuracy corresponds to the ccECP target (chemical accuracy) and it is in consistent agreement with independent correlated calculations. Further possibilities for upgrading the reliability of the DMC algorithm and considerations for better adapted and more robust Jastrow factors are discussed as well.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Behmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

Zhou,

Scemama,

Wang

et al. 2021

Preprint

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“…A number of strategies for curtailing this error have been proposed, including variations on the use of configuration interaction using a perturbative selection made iteratively (CIPSI) − and birth–death algorithms that require no a priori information about the nodal surface . Some other sources of error in DMC include pseudopotential errors, which may be remedied by stochastic projection-based methods (T-moves) with size-consistent adjustments, and time-step errors, which are controlled by modifying the approximate Green’s function and T-move scheme …”

Section: Methodsmentioning

confidence: 99%

Finite-Size Error Cancellation in Diffusion Monte Carlo Calculations of Surface Chemistry

Iyer

Rubenstein

2022

J. Phys. Chem. A

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The accurate prediction of reaction mechanisms in heterogeneous (surface) catalysis is one of the central challenges in computational chemistry. Quantum Monte Carlo methods�Diffusion Monte Carlo (DMC) in particular�are being recognized as higher-accuracy, albeit more computationally expensive, alternatives to Density Functional Theory (DFT) for energy predictions of catalytic systems. A major computational bottleneck in the broader adoption of DMC for catalysis is the need to perform finitesize extrapolations by simulating increasingly large periodic cells (supercells) to eliminate many-body finite-size effects and obtain energies in the thermodynamic limit. Here, we show that it is possible to significantly reduce this computational cost by leveraging the cancellation of many-body finite-size errors that accompanies the evaluation of energy differences when calculating quantities like adsorption (binding) energies and mapping potential energy surfaces. We analyze the cancellation and convergence of many-body finite-size errors in two well-known adsorbate/slab systems, H 2 O/LiH(001) and CO/Pt(111). Based on this analysis, we identify strategies for obtaining binding energies in the thermodynamic limit that optimally utilize error cancellation to balance accuracy and computational efficiency. Using one such strategy, we then predict the correct order of adsorption site preference on CO/Pt(111), a challenging problem for a wide range of density functionals. Our accurate and inexpensive DMC calculations are found to unambiguously recover the top > bridge > hollow site order, in agreement with experimental observations. We proceed to use this DMC method to map the potential energy surface of CO hopping between Pt(111) adsorption sites. This reveals the existence of an L-shaped top−bridge−hollow diffusion trajectory characterized by energy barriers that provide an additional kinetic justification for experimental observations of CO/Pt(111) adsorption. Overall, this work demonstrates that it is routinely possible to achieve orderof-magnitude speedups and memory savings in DMC calculations by taking advantage of error cancellation in the calculation of energy differences that are ubiquitous in heterogeneous catalysis and surface chemistry more broadly.

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A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

et al. 2022

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Nonlocal pseudopotentials and time-step errors in diffusion Monte Carlo

Cited by 8 publications

References 16 publications

A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

Finite-Size Error Cancellation in Diffusion Monte Carlo Calculations of Surface Chemistry

A quantum Monte Carlo study of systems with effective core potentials and node nonlinearities

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