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

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

doi:10.1063/5.0021036

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

Journal Article · Sat Nov 14 00:00:00 EST 2020 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0021036· OSTI ID:1760134

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Argonne National Lab. (ANL), Argonne, IL (United States)
Univ. of Pittsburgh, PA (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Centre National de la Recherche Scientifique (CNRS), Toulouse (France)

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.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC05-00OR22725

OSTI ID:: 1760134

Alternate ID(s):: OSTI ID: 1712502

Journal Information:: Journal of Chemical Physics, Vol. 153, Issue 18; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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