DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: High Accuracy Transition Metal Effective Cores for the Many-Body Diffusion Monte Carlo Method

Abstract

Practical applications of the real-space diffusion Monte Carlo (DMC) method require the removal of core electrons, where currently localization approximations of semilocal potentials are generally used in the projector. Accurate calculations of complex solids and large molecules demand minimizing the impact of approximated atomic cores. Prior works have shown that the errors from such approximations can be sizable in both finite and periodic systems. In this work, we show that a class of differential pseudopotentials, known as pseudo-Hamiltonians, can be constructed for the 3d transition metal atoms, entirely removing the need for any localization scheme in the DMC projector. As a proof of principle, we demonstrate the approach for the case of Co. In order to minimize errors in the pseudo-Hamiltonian at the many-body level, we generalize the recently proposed correlation-consistent pseudopotential generation scheme to successively close semilocal representations of the differential potentials. Our generation scheme successfully produces potentials tailored specifically for real space projector quantum Monte Carlo methods with low error at the many-body level, i.e., with many-body scattering properties very close to relativistic all-electron results. In particular, we show that the agreement with respect to atomic and molecular quantities reach chemical accuracy in many cases-on par with themore » most accurate semilocal pseudopotentials available. Further, our pseudo-Hamiltonian generation scheme utilizes standard quantum chemistry codes designed only to work with semilocal pseudopotentials, enabling straightforward generation of pseudo-Hamiltonians for additional elements in future works.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [2]; ORCiD logo [1]
  1. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
  2. North Carolina State Univ., Raleigh, NC (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division
OSTI Identifier:
1842606
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 18; Journal Issue: 2; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Pseudopotentials; Optimization; Energy; Quantum mechanics; Approximation

Citation Formats

Bennett, Chandler, Reboredo, Fernando A., Mitas, Lubos, and Krogel, Jaron. High Accuracy Transition Metal Effective Cores for the Many-Body Diffusion Monte Carlo Method. United States: N. p., 2022. Web. doi:10.1021/acs.jctc.1c00992.
Bennett, Chandler, Reboredo, Fernando A., Mitas, Lubos, & Krogel, Jaron. High Accuracy Transition Metal Effective Cores for the Many-Body Diffusion Monte Carlo Method. United States. https://doi.org/10.1021/acs.jctc.1c00992
Bennett, Chandler, Reboredo, Fernando A., Mitas, Lubos, and Krogel, Jaron. Mon . "High Accuracy Transition Metal Effective Cores for the Many-Body Diffusion Monte Carlo Method". United States. https://doi.org/10.1021/acs.jctc.1c00992. https://www.osti.gov/servlets/purl/1842606.
@article{osti_1842606,
title = {High Accuracy Transition Metal Effective Cores for the Many-Body Diffusion Monte Carlo Method},
author = {Bennett, Chandler and Reboredo, Fernando A. and Mitas, Lubos and Krogel, Jaron},
abstractNote = {Practical applications of the real-space diffusion Monte Carlo (DMC) method require the removal of core electrons, where currently localization approximations of semilocal potentials are generally used in the projector. Accurate calculations of complex solids and large molecules demand minimizing the impact of approximated atomic cores. Prior works have shown that the errors from such approximations can be sizable in both finite and periodic systems. In this work, we show that a class of differential pseudopotentials, known as pseudo-Hamiltonians, can be constructed for the 3d transition metal atoms, entirely removing the need for any localization scheme in the DMC projector. As a proof of principle, we demonstrate the approach for the case of Co. In order to minimize errors in the pseudo-Hamiltonian at the many-body level, we generalize the recently proposed correlation-consistent pseudopotential generation scheme to successively close semilocal representations of the differential potentials. Our generation scheme successfully produces potentials tailored specifically for real space projector quantum Monte Carlo methods with low error at the many-body level, i.e., with many-body scattering properties very close to relativistic all-electron results. In particular, we show that the agreement with respect to atomic and molecular quantities reach chemical accuracy in many cases-on par with the most accurate semilocal pseudopotentials available. Further, our pseudo-Hamiltonian generation scheme utilizes standard quantum chemistry codes designed only to work with semilocal pseudopotentials, enabling straightforward generation of pseudo-Hamiltonians for additional elements in future works.},
doi = {10.1021/acs.jctc.1c00992},
journal = {Journal of Chemical Theory and Computation},
number = 2,
volume = 18,
place = {United States},
year = {Mon Jan 10 00:00:00 EST 2022},
month = {Mon Jan 10 00:00:00 EST 2022}
}

Works referenced in this record:

Monte-Carlo solution of Schrödinger's equation
journal, February 1971


The Electronic Spectrum of Gaseous CoO in the Visible Region
journal, December 1997

  • Barnes, M.; Clouthier, D. J.; Hajigeorgiou, P. G.
  • Journal of Molecular Spectroscopy, Vol. 186, Issue 2
  • DOI: 10.1006/jmsp.1997.7456

High Accuracy Transition Metal Effective Cores for Many-body Diffusion Monte Carlo
dataset, January 2021

  • Bennett, M. Chandler; Reboredo, Fernando A.; Mitas, Lubos
  • Materials Data Facility
  • DOI: 10.18126/j7cm-wh84

Soft pseudopotentials for efficient quantum Monte Carlo calculations: From Be to Ne and Al to Ar
journal, May 2001

  • Ovcharenko, Ivan; Aspuru-Guzik, Alán; Lester, William A.
  • The Journal of Chemical Physics, Vol. 114, Issue 18
  • DOI: 10.1063/1.1364680

Towards a systematic assessment of errors in diffusion Monte Carlo calculations of semiconductors: Case study of zinc selenide and zinc oxide
journal, December 2015

  • Yu, Jaehyung; Wagner, Lucas K.; Ertekin, Elif
  • The Journal of Chemical Physics, Vol. 143, Issue 22
  • DOI: 10.1063/1.4937421

Molpro: a general-purpose quantum chemistry program package: Molpro
journal, July 2011

  • Werner, Hans-Joachim; Knowles, Peter J.; Knizia, Gerald
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 2
  • DOI: 10.1002/wcms.82

A data ecosystem to support machine learning in materials science
journal, October 2019

  • Blaiszik, Ben; Ward, Logan; Schwarting, Marcus
  • MRS Communications, Vol. 9, Issue 4
  • DOI: 10.1557/mrc.2019.118

Quantum Monte Carlo simulations of solids
journal, January 2001


Coupled cluster theory for high spin, open shell reference wave functions
journal, October 1993

  • Knowles, Peter J.; Hampel, Claudia; Werner, Hans‐Joachim
  • The Journal of Chemical Physics, Vol. 99, Issue 7
  • DOI: 10.1063/1.465990

Compact effective potentials and efficient shared‐exponent basis sets for the first‐ and second‐row atoms
journal, December 1984

  • Stevens, Walter J.; Basch, Harold; Krauss, Morris
  • The Journal of Chemical Physics, Vol. 81, Issue 12
  • DOI: 10.1063/1.447604

Smooth relativistic Hartree–Fock pseudopotentials for H to Ba and Lu to Hg
journal, May 2005

  • Trail, J. R.; Needs, R. J.
  • The Journal of Chemical Physics, Vol. 122, Issue 17
  • DOI: 10.1063/1.1888569

Hybridizing pseudo-Hamiltonians and non-local pseudopotentials in diffusion Monte Carlo
journal, September 2020

  • Krogel, Jaron T.; Reboredo, Fernando A.
  • The Journal of Chemical Physics, Vol. 153, Issue 10
  • DOI: 10.1063/5.0016778

A new generation of effective core potentials from correlated calculations: 2nd row elements
journal, September 2018

  • Bennett, M. Chandler; Wang, Guangming; Annaberdiyev, Abdulgani
  • The Journal of Chemical Physics, Vol. 149, Issue 10
  • DOI: 10.1063/1.5038135

Nonlocal pseudopotentials and diffusion Monte Carlo
journal, September 1991

  • Mitáš, Luboš; Shirley, Eric L.; Ceperley, David M.
  • The Journal of Chemical Physics, Vol. 95, Issue 5
  • DOI: 10.1063/1.460849

Influence of pseudopotentials on excitation energies from selected configuration interaction and diffusion Monte Carlo
journal, January 2019


Structural stability and defect energetics of ZnO from diffusion quantum Monte Carlo
journal, April 2015

  • Santana, Juan A.; Krogel, Jaron T.; Kim, Jeongnim
  • The Journal of Chemical Physics, Vol. 142, Issue 16
  • DOI: 10.1063/1.4919242

Energy-consistent pseudopotentials for quantum Monte Carlo calculations
journal, June 2007

  • Burkatzki, M.; Filippi, C.; Dolg, M.
  • The Journal of Chemical Physics, Vol. 126, Issue 23
  • DOI: 10.1063/1.2741534

An efficient internally contracted multiconfiguration–reference configuration interaction method
journal, November 1988

  • Werner, Hans‐Joachim; Knowles, Peter J.
  • The Journal of Chemical Physics, Vol. 89, Issue 9
  • DOI: 10.1063/1.455556

A fifth-order perturbation comparison of electron correlation theories
journal, May 1989


Energy‐adjusted a b i n i t i o pseudopotentials for the first row transition elements
journal, January 1987

  • Dolg, M.; Wedig, U.; Stoll, H.
  • The Journal of Chemical Physics, Vol. 86, Issue 2
  • DOI: 10.1063/1.452288

QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo
journal, May 2020

  • Kent, P. R. C.; Annaberdiyev, Abdulgani; Benali, Anouar
  • The Journal of Chemical Physics, Vol. 152, Issue 17
  • DOI: 10.1063/5.0004860

A new generation of effective core potentials from correlated calculations: 3d transition metal series
journal, October 2018

  • Annaberdiyev, Abdulgani; Wang, Guangming; Melton, Cody A.
  • The Journal of Chemical Physics, Vol. 149, Issue 13
  • DOI: 10.1063/1.5040472

Coupled-cluster theory in quantum chemistry
journal, February 2007


Nexus: A modular workflow management system for quantum simulation codes
journal, January 2016


The pure rotational spectrum of CoO(X4Δi): Identifying the high-spin components
journal, October 2005


Improved a b i n i t i o effective core potentials for molecular calculations
journal, December 1979

  • Christiansen, Phillip A.; Lee, Yoon S.; Pitzer, Kenneth S.
  • The Journal of Chemical Physics, Vol. 71, Issue 11
  • DOI: 10.1063/1.438197

Self-Consistent Equations Including Exchange and Correlation Effects
journal, November 1965


An efficient method for the evaluation of coupling coefficients in configuration interaction calculations
journal, April 1988


Relativistic effective potentials in quantum Monte Carlo calculations
journal, January 1987

  • Hurley, M. M.; Christiansen, P. A.
  • The Journal of Chemical Physics, Vol. 86, Issue 2
  • DOI: 10.1063/1.452294

Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods
journal, February 1990


A new generation of effective core potentials for correlated calculations
journal, December 2017

  • Bennett, M. Chandler; Melton, Cody A.; Annaberdiyev, Abdulgani
  • The Journal of Chemical Physics, Vol. 147, Issue 22
  • DOI: 10.1063/1.4995643

A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach
journal, May 1980


Valence quantum Monte Carlo with a b i n i t i o effective core potentials
journal, July 1987

  • Hammond, Brian L.; Reynolds, Peter J.; Lester, William A.
  • The Journal of Chemical Physics, Vol. 87, Issue 2
  • DOI: 10.1063/1.453345

Local-density-functional calculations of the energy of atoms
journal, January 1997

  • Kotochigova, Svetlana; Levine, Zachary H.; Shirley, Eric L.
  • Physical Review A, Vol. 55, Issue 1
  • DOI: 10.1103/PhysRevA.55.191

Variational configuration interaction methods and comparison with perturbation theory
journal, January 1977

  • Pople, J. A.; Seeger, R.; Krishnan, R.
  • International Journal of Quantum Chemistry, Vol. 12, Issue S11
  • DOI: 10.1002/qua.560120820

Pseudopotentials and modelpotentials
journal, February 2011

  • Cao, Xiaoyan; Dolg, Michael
  • WIREs Computational Molecular Science, Vol. 1, Issue 2
  • DOI: 10.1002/wcms.28

A new generation of effective core potentials from correlated calculations: 4s and 4p main group elements and first row additions
journal, October 2019

  • Wang, Guangming; Annaberdiyev, Abdulgani; Melton, Cody A.
  • The Journal of Chemical Physics, Vol. 151, Issue 14
  • DOI: 10.1063/1.5121006

Guided ion-beam studies of the reactions of Con+ (n=2–20) with O2: Cobalt cluster-oxide and -dioxide bond energies
journal, August 2005

  • Liu, Fuyi; Li, Feng-Xia; Armentrout, P. B.
  • The Journal of Chemical Physics, Vol. 123, Issue 6
  • DOI: 10.1063/1.1998836

Zur Quantentheorie der Molekeln
journal, January 1927


Diffusion Monte Carlo Method with Lattice Regularization
journal, September 2005


Inhomogeneous Electron Gas
journal, November 1964


Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas–Kroll–Hess transformation up to arbitrary order
journal, January 2004

  • Reiher, Markus; Wolf, Alexander
  • The Journal of Chemical Physics, Vol. 121, Issue 22
  • DOI: 10.1063/1.1818681

Proof for an upper bound in fixed-node Monte Carlo for lattice fermions
journal, May 1995

  • ten Haaf, D. F. B.; van Bemmel, H. J. M.; van Leeuwen, J. M. J.
  • Physical Review B, Vol. 51, Issue 19
  • DOI: 10.1103/PhysRevB.51.13039

Exact decoupling of the Dirac Hamiltonian. I. General theory
journal, August 2004

  • Reiher, Markus; Wolf, Alexander
  • The Journal of Chemical Physics, Vol. 121, Issue 5
  • DOI: 10.1063/1.1768160

Erratum: Local-density-functional calculations of the energy of atoms [Phys. Rev. A 55 , 191 (1997)]
journal, December 1997


The statistical error of green's function Monte Carlo
journal, June 1986

  • Ceperley, D. M.
  • Journal of Statistical Physics, Vol. 43, Issue 5-6
  • DOI: 10.1007/BF02628307

QMCPACK : an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids
journal, April 2018

  • Kim, Jeongnim; Baczewski, Andrew D.; Beaudet, Todd D.
  • Journal of Physics: Condensed Matter, Vol. 30, Issue 19
  • DOI: 10.1088/1361-648X/aab9c3

Magnitude of pseudopotential localization errors in fixed node diffusion quantum Monte Carlo
journal, June 2017

  • Krogel, Jaron T.; Kent, P. R. C.
  • The Journal of Chemical Physics, Vol. 146, Issue 24
  • DOI: 10.1063/1.4986951

Energy-consistent small-core pseudopotentials for 3d-transition metals adapted to quantum Monte Carlo calculations
journal, October 2008

  • Burkatzki, M.; Filippi, Claudia; Dolg, M.
  • The Journal of Chemical Physics, Vol. 129, Issue 16
  • DOI: 10.1063/1.2987872

The Materials Data Facility: Data Services to Advance Materials Science Research
journal, July 2016


Beyond the locality approximation in the standard diffusion Monte Carlo method
journal, October 2006