Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations
Abstract
We present accurate many-body results of the electronic densities in several solid materials, including Si, NaCl, and Cu. These results are obtained using the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a plane-wave basis with norm-conserving, multiple-projector pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation, whose adaption and implementation in the plane-wave basis AFQMC framework are discussed in the present paper. This development allows us to compute correlation functions, electronic densities, and interatomic forces, paving the way for geometry optimizations and calculations of thermodynamic properties in solids. Finite supercell size effects are considerably more subtle in the many-body framework than in independent-electron calculations. We analyze the convergence of the electronic density, and obtain best estimates for the thermodynamic limit. The densities from several typical density functionals are benchmarked against our near-exact results. The electronic densities we obtained can also be used to help construct improved density functionals.
- Authors:
-
- College of William and Mary, Williamsburg, VA (United States)
- Beijing Normal University (China)
- Publication Date:
- Research Org.:
- College of William and Mary, Williamsburg, VA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1850737
- Grant/Contract Number:
- SC0001303
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 103; Journal Issue: 7; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; Materials Science; Physics; First-principles calculations; Density functional theory development; Electronic structure; Quantum Monte Carlo
Citation Formats
Chen, Siyuan, Motta, Mario, Ma, Fengjie, and Zhang, Shiwei. Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations. United States: N. p., 2021.
Web. doi:10.1103/physrevb.103.075138.
Chen, Siyuan, Motta, Mario, Ma, Fengjie, & Zhang, Shiwei. Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations. United States. https://doi.org/10.1103/physrevb.103.075138
Chen, Siyuan, Motta, Mario, Ma, Fengjie, and Zhang, Shiwei. Mon .
"Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations". United States. https://doi.org/10.1103/physrevb.103.075138. https://www.osti.gov/servlets/purl/1850737.
@article{osti_1850737,
title = {Ab initio electronic density in solids by many-body plane-wave auxiliary-field quantum Monte Carlo calculations},
author = {Chen, Siyuan and Motta, Mario and Ma, Fengjie and Zhang, Shiwei},
abstractNote = {We present accurate many-body results of the electronic densities in several solid materials, including Si, NaCl, and Cu. These results are obtained using the ab initio auxiliary-field quantum Monte Carlo (AFQMC) method working in a plane-wave basis with norm-conserving, multiple-projector pseudopotentials. AFQMC has been shown to be an excellent many-body total energy method. Computation of observables and correlation functions other than the ground-state energy requires back-propagation, whose adaption and implementation in the plane-wave basis AFQMC framework are discussed in the present paper. This development allows us to compute correlation functions, electronic densities, and interatomic forces, paving the way for geometry optimizations and calculations of thermodynamic properties in solids. Finite supercell size effects are considerably more subtle in the many-body framework than in independent-electron calculations. We analyze the convergence of the electronic density, and obtain best estimates for the thermodynamic limit. The densities from several typical density functionals are benchmarked against our near-exact results. The electronic densities we obtained can also be used to help construct improved density functionals.},
doi = {10.1103/physrevb.103.075138},
journal = {Physical Review. B},
number = 7,
volume = 103,
place = {United States},
year = {Mon Feb 22 00:00:00 EST 2021},
month = {Mon Feb 22 00:00:00 EST 2021}
}
Free Publicly Available Full Text
Publisher's Version of Record
Other availability
Search WorldCat to find libraries that may hold this journal
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:
Generalized Gradient Approximation Made Simple
journal, October 1996
- Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
- Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
Benchmark study of the two-dimensional Hubbard model with auxiliary-field quantum Monte Carlo method
journal, August 2016
- Qin, Mingpu; Shi, Hao; Zhang, Shiwei
- Physical Review B, Vol. 94, Issue 8
Quantum Monte Carlo Calculations in Solids with Downfolded Hamiltonians
journal, June 2015
- Ma, Fengjie; Purwanto, Wirawan; Zhang, Shiwei
- Physical Review Letters, Vol. 114, Issue 22
Auxiliary-field quantum Monte Carlo calculations with multiple-projector pseudopotentials
journal, April 2017
- Ma, Fengjie; Zhang, Shiwei; Krakauer, Henry
- Physical Review B, Vol. 95, Issue 16
Quantum Monte Carlo simulations of solids
journal, January 2001
- Foulkes, W. M. C.; Mitas, L.; Needs, R. J.
- Reviews of Modern Physics, Vol. 73, Issue 1
Auxiliary field Monte-Carlo for quantum many-body ground states
journal, April 1986
- Sugiyama, G.; Koonin, S. E.
- Annals of Physics, Vol. 168, Issue 1
Computation of Ground-State Properties in Molecular Systems: Back-Propagation with Auxiliary-Field Quantum Monte Carlo
journal, October 2017
- Motta, Mario; Zhang, Shiwei
- Journal of Chemical Theory and Computation, Vol. 13, Issue 11
Fixed‐node quantum Monte Carlo for molecules a) b)
journal, December 1982
- Reynolds, Peter J.; Ceperley, David M.; Alder, Berni J.
- The Journal of Chemical Physics, Vol. 77, Issue 11
Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations
journal, November 2017
- Vogiatzis, Konstantinos D.; Ma, Dongxia; Olsen, Jeppe
- The Journal of Chemical Physics, Vol. 147, Issue 18
Analytical derivatives, forces, force constants, molecular geometries, and related response properties in electronic structure theory: Analytical calculation of energy derivatives
journal, September 2013
- Pulay, Peter
- Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 4, Issue 3
Some recent developments in auxiliary-field quantum Monte Carlo for real materials
journal, January 2021
- Shi, Hao; Zhang, Shiwei
- The Journal of Chemical Physics, Vol. 154, Issue 2
Optimized norm-conserving Vanderbilt pseudopotentials
journal, August 2013
- Hamann, D. R.
- Physical Review B, Vol. 88, Issue 8
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
Stability conditions and nuclear rotations in the Hartree-Fock theory
journal, November 1960
- Thouless, D. J.
- Nuclear Physics, Vol. 21
The Compressibility of Media under Extreme Pressures
journal, September 1944
- Murnaghan, F. D.
- Proceedings of the National Academy of Sciences, Vol. 30, Issue 9
CODATA recommended values of the fundamental physical constants: 2014
journal, September 2016
- Mohr, Peter J.; Newell, David B.; Taylor, Barry N.
- Reviews of Modern Physics, Vol. 88, Issue 3
Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981
- Blankenbecler, R.; Scalapino, D. J.; Sugar, R. L.
- Physical Review D, Vol. 24, Issue 8
Phaseless auxiliary-field quantum Monte Carlo calculations with plane waves and pseudopotentials: Applications to atoms and molecules
journal, June 2007
- Suewattana, Malliga; Purwanto, Wirawan; Zhang, Shiwei
- Physical Review B, Vol. 75, Issue 24
On the distribution of points in a cube and the approximate evaluation of integrals
journal, January 1967
- Sobol', I. M.
- USSR Computational Mathematics and Mathematical Physics, Vol. 7, Issue 4
Stripe order in the underdoped region of the two-dimensional Hubbard model
journal, November 2017
- Zheng, Bo-Xiao; Chung, Chia-Min; Corboz, Philippe
- Science, Vol. 358, Issue 6367
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
journal, December 2015
- LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico
- Physical Review X, Vol. 5, Issue 4
Auxiliary-field quantum Monte Carlo calculations of molecular systems with a Gaussian basis
journal, June 2006
- Al-Saidi, W. A.; Zhang, Shiwei; Krakauer, Henry
- The Journal of Chemical Physics, Vol. 124, Issue 22
Ground-State Properties of the Hydrogen Chain: Dimerization, Insulator-to-Metal Transition, and Magnetic Phases
journal, September 2020
- Motta, Mario; Genovese, Claudio; Ma, Fengjie
- Physical Review X, Vol. 10, Issue 3
Density functional theory: Its origins, rise to prominence, and future
journal, August 2015
- Jones, R. O.
- Reviews of Modern Physics, Vol. 87, Issue 3
Quantum Monte Carlo Method using Phase-Free Random Walks with Slater Determinants
journal, April 2003
- Zhang, Shiwei; Krakauer, Henry
- Physical Review Letters, Vol. 90, Issue 13
Pressure-induced diamond to -tin transition in bulk silicon: A quantum Monte Carlo study
journal, December 2009
- Purwanto, Wirawan; Krakauer, Henry; Zhang, Shiwei
- Physical Review B, Vol. 80, Issue 21
Finite-size correction in many-body electronic structure calculations of magnetic systems
journal, October 2011
- Ma, Fengjie; Zhang, Shiwei; Krakauer, Henry
- Physical Review B, Vol. 84, Issue 15
Calculation of Partition Functions
journal, July 1959
- Hubbard, J.
- Physical Review Letters, Vol. 3, Issue 2
Constrained path Monte Carlo method for fermion ground states
journal, March 1997
- Zhang, Shiwei; Carlson, J.; Gubernatis, J. E.
- Physical Review B, Vol. 55, Issue 12
Vibrational states of nuclei in the random phase approximation
journal, January 1961
- Thouless, D. J.
- Nuclear Physics, Vol. 22, Issue 1
Zur Quantentheorie der Molekeln
journal, January 1927
- Born, M.; Oppenheimer, R.
- Annalen der Physik, Vol. 389, Issue 20
Perspective: Fifty years of density-functional theory in chemical physics
journal, May 2014
- Becke, Axel D.
- The Journal of Chemical Physics, Vol. 140, Issue 18
Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods
journal, September 2017
- Motta, Mario; Ceperley, David M.; Chan, Garnet Kin-Lic
- Physical Review X, Vol. 7, Issue 3
Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
journal, May 2018
- Motta, Mario; Zhang, Shiwei
- Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 5
Commentary: The Materials Project: A materials genome approach to accelerating materials innovation
journal, July 2013
- Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy
- APL Materials, Vol. 1, Issue 1
Inhomogeneous Electron Gas
journal, November 1964
- Hohenberg, P.; Kohn, W.
- Physical Review, Vol. 136, Issue 3B, p. B864-B871
Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
journal, April 2008
- Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gábor I.
- Physical Review Letters, Vol. 100, Issue 13
Mechanical and Thermal Properties of Certain Optical Crystalline Materials*
journal, January 1951
- Combes, Lewis S.; Ballard, Stanley S.; McCarthy, Kathryn A.
- Journal of the Optical Society of America, Vol. 41, Issue 4
Mean-Value Point in the Brillouin Zone
journal, June 1973
- Baldereschi, A.
- Physical Review B, Vol. 7, Issue 12
Studies of NaCl-KCl Solid Solutions. I. Heats of Formation, Lattice Spacings, Densities, Schottky Defects and Mutual Solubilities 1,2
journal, January 1954
- Barrett, W. T.; Wallace, W. E.
- Journal of the American Chemical Society, Vol. 76, Issue 2
Ground State of the Electron Gas by a Stochastic Method
journal, August 1980
- Ceperley, D. M.; Alder, B. J.
- Physical Review Letters, Vol. 45, Issue 7, p. 566-569
Simulation of Electrostatic Systems in Periodic Boundary Conditions. I. Lattice Sums and Dielectric Constants
journal, October 1980
- de Leeuw, S. W.; Perram, J. W.; Smith, E. R.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, Issue 1752
Simulation of Electrostatic Systems in Periodic Boundary Conditions. II. Equivalence of Boundary Conditions
journal, October 1980
- de Leeuw, S. W.; Perram, J. W.; Smith, E. R.
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 373, Issue 1752
Die Berechnung optischer und elektrostatischer Gitterpotentiale
journal, January 1921
- Ewald, P. P.
- Annalen der Physik, Vol. 369, Issue 3
Rationale for mixing exact exchange with density functional approximations
journal, December 1996
- Perdew, John P.; Ernzerhof, Matthias; Burke, Kieron
- The Journal of Chemical Physics, Vol. 105, Issue 22, p. 9982-9985
On Achieving High Accuracy in Quantum Chemical Calculations of 3 d Transition Metal-Containing Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules
journal, March 2019
- Shee, James; Rudshteyn, Benjamin; Arthur, Evan J.
- Journal of Chemical Theory and Computation, Vol. 15, Issue 4
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields
journal, November 1994
- Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.
- The Journal of Physical Chemistry, Vol. 98, Issue 45, p. 11623-11627
Perspective on density functional theory
journal, April 2012
- Burke, Kieron
- The Journal of Chemical Physics, Vol. 136, Issue 15