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Title: Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond

Abstract

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimatedmore » experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.« less

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2];  [1]; ORCiD logo [1]; ORCiD logo [3]; ORCiD logo [3]; ORCiD logo [4]; ORCiD logo [3]; ORCiD logo [5]; ORCiD logo [5]; ORCiD logo [5]
+ Show Author Affiliations
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Univ. of Pittsburgh, PA (United States)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  4. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  5. Centre National de la Recherche Scientifique (CNRS), Toulouse (France)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1760134
Alternate Identifier(s):
OSTI ID: 1712502
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 153; Journal Issue: 18; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Materials; Electronic structure methods; Full configuration interaction; Density functional theory; Computational methods; Monte Carlo methods; Slater determinant

Citation Formats

Benali, Anouar, Gasperich, Kevin, Jordan, Kenneth D., Applencourt, Thomas, Luo, Ye, Bennett, M. Chandler, Krogel, Jaron T., Shulenburger, Luke, Kent, Paul C., Loos, Pierre-François, Scemama, Anthony, and Caffarel, Michel. Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond. United States: N. p., 2020. Web. doi:10.1063/5.0021036.
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Benali, Anouar, Gasperich, Kevin, Jordan, Kenneth D., Applencourt, Thomas, Luo, Ye, Bennett, M. Chandler, Krogel, Jaron T., Shulenburger, Luke, Kent, Paul C., Loos, Pierre-François, Scemama, Anthony, & Caffarel, Michel. Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond. United States. https://doi.org/10.1063/5.0021036
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Benali, Anouar, Gasperich, Kevin, Jordan, Kenneth D., Applencourt, Thomas, Luo, Ye, Bennett, M. Chandler, Krogel, Jaron T., Shulenburger, Luke, Kent, Paul C., Loos, Pierre-François, Scemama, Anthony, and Caffarel, Michel. Sat . "Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond". United States. https://doi.org/10.1063/5.0021036. https://www.osti.gov/servlets/purl/1760134.
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@article{osti_1760134,
title = {Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids—A case study in diamond},
author = {Benali, Anouar and Gasperich, Kevin and Jordan, Kenneth D. and Applencourt, Thomas and Luo, Ye and Bennett, M. Chandler and Krogel, Jaron T. and Shulenburger, Luke and Kent, Paul C. and Loos, Pierre-François and Scemama, Anthony and Caffarel, Michel},
abstractNote = {While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater–Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.},
doi = {10.1063/5.0021036},
journal = {Journal of Chemical Physics},
number = 18,
volume = 153,
place = {United States},
year = {Sat Nov 14 00:00:00 EST 2020},
month = {Sat Nov 14 00:00:00 EST 2020}
}
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