Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets

Abstract

We investigate the use of optimized correlation-consistent Gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second-order Møller–Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely, calculations in the Kohn–Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn–Sham basis and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si, and MgO and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experimentmore » for the systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.« less

Authors:
ORCiD logo;
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1720183
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Name: Journal of Chemical Physics Journal Volume: 153 Journal Issue: 19; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English

Citation Formats

Morales, Miguel A., and Malone, Fionn D.. Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets. United States: N. p., 2020. Web. doi:10.1063/5.0025390.
Copy to clipboard
Morales, Miguel A., & Malone, Fionn D.. Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets. United States. https://doi.org/10.1063/5.0025390
Copy to clipboard
Morales, Miguel A., and Malone, Fionn D.. Thu . "Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets". United States. https://doi.org/10.1063/5.0025390.
Copy to clipboard
@article{osti_1720183,
title = {Accelerating the convergence of auxiliary-field quantum Monte Carlo in solids with optimized Gaussian basis sets},
author = {Morales, Miguel A. and Malone, Fionn D.},
abstractNote = {We investigate the use of optimized correlation-consistent Gaussian basis sets for the study of insulating solids with auxiliary-field quantum Monte Carlo (AFQMC). The exponents of the basis set are optimized through the minimization of the second-order Møller–Plesset perturbation theory (MP2) energy in a small unit cell of the solid. We compare against other alternative basis sets proposed in the literature, namely, calculations in the Kohn–Sham basis and in the natural orbitals of an MP2 calculation. We find that our optimized basis sets accelerate the convergence of the AFQMC correlation energy compared to a Kohn–Sham basis and offer similar convergence to MP2 natural orbitals at a fraction of the cost needed to generate them. We also suggest the use of an improved, method independent, MP2-based basis set correction that significantly reduces the required basis set sizes needed to converge the correlation energy. With these developments, we study the relative performance of these basis sets in LiH, Si, and MgO and determine that our optimized basis sets yield the most consistent results as a function of volume. Using these optimized basis sets, we systematically converge the AFQMC calculations to the complete basis set and thermodynamic limit and find excellent agreement with experiment for the systems studied. Although we focus on AFQMC, our basis set generation procedure is independent of the subsequent correlated wavefunction method used.},
doi = {10.1063/5.0025390},
journal = {Journal of Chemical Physics},
number = 19,
volume = 153,
place = {United States},
year = {2020},
month = {11}
}
Copy to clipboard
Journal Article:
Free Publicly Available Full Text
Accepted Manuscript (Publisher)
Publisher's Version of Record
https://doi.org/10.1063/5.0025390
Copyright Statement
Other availability
Search WorldCat Search WorldCat to find libraries that may hold this journal
Save / Share:
Export Metadata
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Works referenced in this record:

P y SCF: the Python-based simulations of chemistry framework : The PySCF program
journal, September 2017

  • Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S.
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1
  • DOI: 10.1002/wcms.1340

Communications: Accurate and efficient approximations to explicitly correlated coupled-cluster singles and doubles, CCSD-F12
journal, June 2010

  • Hättig, Christof; Tew, David P.; Köhn, Andreas
  • The Journal of Chemical Physics, Vol. 132, Issue 23
  • DOI: 10.1063/1.3442368

Overcoming the Memory Bottleneck in Auxiliary Field Quantum Monte Carlo Simulations with Interpolative Separable Density Fitting
journal, November 2018

  • Malone, Fionn D.; Zhang, Shuai; Morales, Miguel A.
  • Journal of Chemical Theory and Computation, Vol. 15, Issue 1
  • DOI: 10.1021/acs.jctc.8b00944

Møller-plesset calculations taking care of the correlation CUSP
journal, February 1987

Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians
journal, June 2015

Soft self-consistent pseudopotentials in a generalized eigenvalue formalism
journal, April 1990

Daubechies wavelets as a basis set for density functional pseudopotential calculations
journal, July 2008

  • Genovese, Luigi; Neelov, Alexey; Goedecker, Stefan
  • The Journal of Chemical Physics, Vol. 129, Issue 1
  • DOI: 10.1063/1.2949547

Convergence of many-body wave-function expansions using a plane-wave basis: From homogeneous electron gas to solid state systems
journal, July 2012

Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional
journal, November 2005

  • Heyd, Jochen; Peralta, Juan E.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 123, Issue 17
  • DOI: 10.1063/1.2085170

Gaussian Basis Sets for Crystalline Solids: All-Purpose Basis Set Libraries vs System-Specific Optimizations
journal, March 2020

  • Daga, Loredana Edith; Civalleri, Bartolomeo; Maschio, Lorenzo
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 4
  • DOI: 10.1021/acs.jctc.9b01004

Ab-initio simulations of materials using VASP: Density-functional theory and beyond
journal, October 2008

  • Hafner, Jürgen
  • Journal of Computational Chemistry, Vol. 29, Issue 13
  • DOI: 10.1002/jcc.21057

Auxiliary-field quantum Monte Carlo calculations of the structural properties of nickel oxide
journal, October 2018

  • Zhang, Shuai; Malone, Fionn D.; Morales, Miguel A.
  • The Journal of Chemical Physics, Vol. 149, Issue 16
  • DOI: 10.1063/1.5040900

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009

  • Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola
  • Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502
  • DOI: 10.1088/0953-8984/21/39/395502

Second-Order Møller–Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach
journal, September 2012

  • Del Ben, Mauro; Hutter, Jürg; VandeVondele, Joost
  • Journal of Chemical Theory and Computation, Vol. 8, Issue 11
  • DOI: 10.1021/ct300531w

In pursuit of the ab initio limit for conformational energy prototypes
journal, June 1998

  • Császár, Attila G.; Allen, Wesley D.; Schaefer, Henry F.
  • The Journal of Chemical Physics, Vol. 108, Issue 23
  • DOI: 10.1063/1.476449

Fast local-MP2 method with density-fitting for crystals. II. Test calculations and application to the carbon dioxide crystal
journal, August 2007

Fast local-MP2 method with density-fitting for crystals. I. Theory and algorithms
journal, August 2007

An error analysis for Hartree-Fock crystal orbital calculations
journal, July 1982

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153

Momentum-space formalism for the total energy of solids
journal, November 1979

General orbital invariant MP2-F12 theory
journal, April 2007

  • Werner, Hans-Joachim; Adler, Thomas B.; Manby, Frederick R.
  • The Journal of Chemical Physics, Vol. 126, Issue 16
  • DOI: 10.1063/1.2712434

Explicitly Correlated Electrons in Molecules
journal, December 2011

  • Hättig, Christof; Klopper, Wim; Köhn, Andreas
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200168z

Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions
journal, May 1992

  • Kendall, Rick A.; Dunning, Thom H.; Harrison, Robert J.
  • The Journal of Chemical Physics, Vol. 96, Issue 9
  • DOI: 10.1063/1.462569

Improved hybrid functional for solids: The HSEsol functional
journal, January 2011

  • Schimka, Laurids; Harl, Judith; Kresse, Georg
  • The Journal of Chemical Physics, Vol. 134, Issue 2
  • DOI: 10.1063/1.3524336

Coulombic potential energy integrals and approximations
journal, May 1973

  • Whitten, J. L.
  • The Journal of Chemical Physics, Vol. 58, Issue 10
  • DOI: 10.1063/1.1679012

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

Auxiliary-field quantum Monte Carlo calculations with multiple-projector pseudopotentials
journal, April 2017

Approaching the theoretical limit in periodic local MP2 calculations with atomic-orbital basis sets: The case of LiH
journal, June 2011

  • Usvyat, Denis; Civalleri, Bartolomeo; Maschio, Lorenzo
  • The Journal of Chemical Physics, Vol. 134, Issue 21
  • DOI: 10.1063/1.3595514

Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon
journal, January 1993

  • Woon, David E.; Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 98, Issue 2
  • DOI: 10.1063/1.464303

QWalk: A quantum Monte Carlo program for electronic structure
journal, May 2009

  • Wagner, Lucas K.; Bajdich, Michal; Mitas, Lubos
  • Journal of Computational Physics, Vol. 228, Issue 9
  • DOI: 10.1016/j.jcp.2009.01.017

Iterative minimization techniques for ab initio total-energy calculations: molecular dynamics and conjugate gradients
journal, October 1992

RPA natural orbitals and their application to post-Hartree-Fock electronic structure methods
journal, December 2019

  • Ramberger, Benjamin; Sukurma, Zoran; Schäfer, Tobias
  • The Journal of Chemical Physics, Vol. 151, Issue 21
  • DOI: 10.1063/1.5128415

Density functional theory is straying from the path toward the exact functional
journal, January 2017

  • Medvedev, Michael G.; Bushmarinov, Ivan S.; Sun, Jianwei
  • Science, Vol. 355, Issue 6320
  • DOI: 10.1126/science.aah5975

Second-order Møller–Plesset perturbation theory applied to extended systems. II. Structural and energetic properties
journal, August 2010

  • Grüneis, Andreas; Marsman, Martijn; Kresse, Georg
  • The Journal of Chemical Physics, Vol. 133, Issue 7
  • DOI: 10.1063/1.3466765

Applying the Coupled-Cluster Ansatz to Solids and Surfaces in the Thermodynamic Limit
journal, May 2018

Perspective: Explicitly correlated electronic structure theory for complex systems
journal, February 2017

  • Grüneis, Andreas; Hirata, So; Ohnishi, Yu-ya
  • The Journal of Chemical Physics, Vol. 146, Issue 8
  • DOI: 10.1063/1.4976974

Accelerating Auxiliary-Field Quantum Monte Carlo Simulations of Solids with Graphical Processing Units
journal, May 2020

  • Malone, Fionn D.; Zhang, Shuai; Morales, Miguel A.
  • Journal of Chemical Theory and Computation, Vol. 16, Issue 7
  • DOI: 10.1021/acs.jctc.0c00262

Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants
journal, April 2003

CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals
journal, January 2005

  • Dovesi, Roberto; Orlando, Roberto; Civalleri, Bartolomeo
  • Zeitschrift für Kristallographie - Crystalline Materials, Vol. 220, Issue 5/6
  • DOI: 10.1524/zkri.220.5.571.65065

Self-consistent molecular Hartree—Fock—Slater calculations I. The computational procedure
journal, September 1973

Systematically convergent basis sets for transition metals. I. All-electron correlation consistent basis sets for the 3d elements Sc–Zn
journal, August 2005

  • Balabanov, Nikolai B.; Peterson, Kirk A.
  • The Journal of Chemical Physics, Vol. 123, Issue 6
  • DOI: 10.1063/1.1998907

Gaussian-Based Coupled-Cluster Theory for the Ground-State and Band Structure of Solids
journal, February 2017

  • McClain, James; Sun, Qiming; Chan, Garnet Kin-Lic
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 3
  • DOI: 10.1021/acs.jctc.7b00049

Frozen-Orbital and Downfolding Calculations with Auxiliary-Field Quantum Monte Carlo
journal, October 2013

  • Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 11
  • DOI: 10.1021/ct4006486

Gaussian basis sets for use in correlated molecular calculations. IV. Calculation of static electrical response properties
journal, February 1994

  • Woon, David E.; Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 100, Issue 4
  • DOI: 10.1063/1.466439

Wave functions with terms linear in the interelectronic coordinates to take care of the correlation cusp. I. General theory
journal, February 1991

  • Kutzelnigg, Werner; Klopper, Wim
  • The Journal of Chemical Physics, Vol. 94, Issue 3
  • DOI: 10.1063/1.459921

Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases
journal, September 2007

  • VandeVondele, Joost; Hutter, Jürg
  • The Journal of Chemical Physics, Vol. 127, Issue 11
  • DOI: 10.1063/1.2770708

Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space
journal, January 2009

  • Booth, George H.; Thom, Alex J. W.; Alavi, Ali
  • The Journal of Chemical Physics, Vol. 131, Issue 5
  • DOI: 10.1063/1.3193710

Excited state calculations in solids by auxiliary-field quantum Monte Carlo
journal, September 2013

Duality of Ring and Ladder Diagrams and Its Importance for Many-Electron Perturbation Theories
journal, October 2019

The heat of formation of NCO
journal, September 1993

  • East, Allan L. L.; Allen, Wesley D.
  • The Journal of Chemical Physics, Vol. 99, Issue 6
  • DOI: 10.1063/1.466062

Accurate Bulk Properties from Approximate Many-Body Techniques
journal, July 2009

Gaussian basis sets for use in correlated molecular calculations. V. Core‐valence basis sets for boron through neon
journal, September 1995

  • Woon, David E.; Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 103, Issue 11
  • DOI: 10.1063/1.470645

Random-phase approximation and its applications in computational chemistry and materials science
journal, June 2012

  • Ren, Xinguo; Rinke, Patrick; Joas, Christian
  • Journal of Materials Science, Vol. 47, Issue 21
  • DOI: 10.1007/s10853-012-6570-4

Assessing the quality of the random phase approximation for lattice constants and atomization energies of solids
journal, March 2010

The correlation-consistent composite approach: Application to the G3/99 test set
journal, September 2006

  • DeYonker, Nathan J.; Grimes, Tom; Yockel, Scott
  • The Journal of Chemical Physics, Vol. 125, Issue 10
  • DOI: 10.1063/1.2236116

Atomic orbital Laplace-transformed second-order Møller–Plesset theory for periodic systems
journal, December 2001

  • Ayala, Philippe Y.; Kudin, Konstantin N.; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 115, Issue 21
  • DOI: 10.1063/1.1414369

Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules
journal, June 2007

From plane waves to local Gaussians for the simulation of correlated periodic systems
journal, August 2016

  • Booth, George H.; Tsatsoulis, Theodoros; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 145, Issue 8
  • DOI: 10.1063/1.4961301

Optimized norm-conserving Vanderbilt pseudopotentials
journal, August 2013

Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo
journal, January 2010

  • Cleland, Deidre; Booth, George H.; Alavi, Ali
  • The Journal of Chemical Physics, Vol. 132, Issue 4
  • DOI: 10.1063/1.3302277

Assessment of correlation energies based on the random-phase approximation
journal, April 2012

Electron repulsion integral approximations and error bounds: Molecular applications
journal, September 1974

  • Jafri, J. A.; Whitten, J. L.
  • The Journal of Chemical Physics, Vol. 61, Issue 5
  • DOI: 10.1063/1.1682222

Exact-exchange Hartree-Fock calculations for periodic systems. I. Illustration of the method
journal, March 1980

  • Pisani, C.; Dovesi, R.
  • International Journal of Quantum Chemistry, Vol. 17, Issue 3
  • DOI: 10.1002/qua.560170311

Exascale applications: skin in the game
journal, January 2020

  • Alexander, Francis; Almgren, Ann; Bell, John
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 378, Issue 2166
  • DOI: 10.1098/rsta.2019.0056

Periodic local Møller–Plesset second order perturbation theory method applied to molecular crystals: Study of solid NH3 and CO2 using extended basis sets
journal, April 2010

  • Maschio, Lorenzo; Usvyat, Denis; Schütz, Martin
  • The Journal of Chemical Physics, Vol. 132, Issue 13
  • DOI: 10.1063/1.3372800

Towards an exact description of electronic wavefunctions in real solids
journal, December 2012

  • Booth, George H.; Grüneis, Andreas; Kresse, Georg
  • Nature, Vol. 493, Issue 7432
  • DOI: 10.1038/nature11770

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

First principles methods using CASTEP
journal, January 2005

  • Clark, Stewart J.; Segall, Matthew D.; Pickard, Chris J.
  • Zeitschrift für Kristallographie - Crystalline Materials, Vol. 220, Issue 5/6
  • DOI: 10.1524/zkri.220.5.567.65075

Optimization algorithm for the generation of ONCV pseudopotentials
journal, November 2015

Second-order Mo̸ller–Plesset perturbation theory applied to extended systems. I. Within the projector-augmented-wave formalism using a plane wave basis set
journal, January 2009

  • Marsman, M.; Grüneis, A.; Paier, J.
  • The Journal of Chemical Physics, Vol. 130, Issue 18
  • DOI: 10.1063/1.3126249

Natural Orbitals for Wave Function Based Correlated Calculations Using a Plane Wave Basis Set
journal, August 2011

  • Grüneis, Andreas; Booth, George H.; Marsman, Martijn
  • Journal of Chemical Theory and Computation, Vol. 7, Issue 9
  • DOI: 10.1021/ct200263g

Constrained path Monte Carlo method for fermion ground states
journal, March 1997

Pressure-induced diamond to β -tin transition in bulk silicon: A quantum Monte Carlo study
journal, December 2009

An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas
journal, May 2019

  • Mihm, Tina N.; McIsaac, Alexandra R.; Shepherd, James J.
  • The Journal of Chemical Physics, Vol. 150, Issue 19
  • DOI: 10.1063/1.5091445

Explicitly correlated plane waves: Accelerating convergence in periodic wavefunction expansions
journal, August 2013

  • Grüneis, Andreas; Shepherd, James J.; Alavi, Ali
  • The Journal of Chemical Physics, Vol. 139, Issue 8
  • DOI: 10.1063/1.4818753

Particle-particle ladder based basis-set corrections applied to atoms and molecules using coupled-cluster theory
journal, September 2019

  • Irmler, Andreas; Grüneis, Andreas
  • The Journal of Chemical Physics, Vol. 151, Issue 10
  • DOI: 10.1063/1.5110885

cp2k: atomistic simulations of condensed matter systems
journal, June 2013

  • Hutter, Jürg; Iannuzzi, Marcella; Schiffmann, Florian
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 1
  • DOI: 10.1002/wcms.1159

Recent developments in the P y SCF program package
journal, July 2020

  • Sun, Qiming; Zhang, Xing; Banerjee, Samragni
  • The Journal of Chemical Physics, Vol. 153, Issue 2
  • DOI: 10.1063/5.0006074
    Sort by:
    [ × clear filter / sort ]

    Similar Records in DOE PAGES and OSTI.GOV collections: