skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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

Abstract

We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bond length, with a confidence bound given on all uncertainties.

Authors:
; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; ; more »; ; « less
Publication Date:
Research Org.:
College of William and Mary, Williamsburg, VA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Contributing Org.:
Simons Collaboration on the Many-Electron Problem
OSTI Identifier:
1395398
Alternate Identifier(s):
OSTI ID: 1426200
Grant/Contract Number:  
SC0001303; DOE-SC0008624; ER 46932; ER16391; SC008696; PHY-1314735; hp120174; hp140092; hp160126; hp170079
Resource Type:
Published Article
Journal Name:
Physical Review. X
Additional Journal Information:
Journal Name: Physical Review. X Journal Volume: 7 Journal Issue: 3; Journal ID: ISSN 2160-3308
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Motta, Mario, Ceperley, David M., Chan, Garnet Kin-Lic, Gomez, John A., Gull, Emanuel, Guo, Sheng, Jiménez-Hoyos, Carlos A., Lan, Tran Nguyen, Li, Jia, Ma, Fengjie, Millis, Andrew J., Prokof’ev, Nikolay V., Ray, Ushnish, Scuseria, Gustavo E., Sorella, Sandro, Stoudenmire, Edwin M., Sun, Qiming, Tupitsyn, Igor S., White, Steven R., Zgid, Dominika, Zhang, Shiwei, and Simons Collaboration on the Many-Electron Problem. 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. United States: N. p., 2017. Web. doi:10.1103/PhysRevX.7.031059.
Motta, Mario, Ceperley, David M., Chan, Garnet Kin-Lic, Gomez, John A., Gull, Emanuel, Guo, Sheng, Jiménez-Hoyos, Carlos A., Lan, Tran Nguyen, Li, Jia, Ma, Fengjie, Millis, Andrew J., Prokof’ev, Nikolay V., Ray, Ushnish, Scuseria, Gustavo E., Sorella, Sandro, Stoudenmire, Edwin M., Sun, Qiming, Tupitsyn, Igor S., White, Steven R., Zgid, Dominika, Zhang, Shiwei, & Simons Collaboration on the Many-Electron Problem. 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. United States. doi:10.1103/PhysRevX.7.031059.
Motta, Mario, Ceperley, David M., Chan, Garnet Kin-Lic, Gomez, John A., Gull, Emanuel, Guo, Sheng, Jiménez-Hoyos, Carlos A., Lan, Tran Nguyen, Li, Jia, Ma, Fengjie, Millis, Andrew J., Prokof’ev, Nikolay V., Ray, Ushnish, Scuseria, Gustavo E., Sorella, Sandro, Stoudenmire, Edwin M., Sun, Qiming, Tupitsyn, Igor S., White, Steven R., Zgid, Dominika, Zhang, Shiwei, and Simons Collaboration on the Many-Electron Problem. Thu . "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". United States. doi:10.1103/PhysRevX.7.031059.
@article{osti_1395398,
title = {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},
author = {Motta, Mario and Ceperley, David M. and Chan, Garnet Kin-Lic and Gomez, John A. and Gull, Emanuel and Guo, Sheng and Jiménez-Hoyos, Carlos A. and Lan, Tran Nguyen and Li, Jia and Ma, Fengjie and Millis, Andrew J. and Prokof’ev, Nikolay V. and Ray, Ushnish and Scuseria, Gustavo E. and Sorella, Sandro and Stoudenmire, Edwin M. and Sun, Qiming and Tupitsyn, Igor S. and White, Steven R. and Zgid, Dominika and Zhang, Shiwei and Simons Collaboration on the Many-Electron Problem},
abstractNote = {We present numerical results for the equation of state of an infinite chain of hydrogen atoms. A variety of modern many-body methods are employed, with exhaustive cross-checks and validation. Approaches for reaching the continuous space limit and the thermodynamic limit are investigated, proposed, and tested. The detailed comparisons provide a benchmark for assessing the current state of the art in many-body computation, and for the development of new methods. The ground-state energy per atom in the linear chain is accurately determined versus bond length, with a confidence bound given on all uncertainties.},
doi = {10.1103/PhysRevX.7.031059},
journal = {Physical Review. X},
number = 3,
volume = 7,
place = {United States},
year = {2017},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1103/PhysRevX.7.031059

Citation Metrics:
Cited by: 32 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Size-consistent variational approaches to nonlocal pseudopotentials: Standard and lattice regularized diffusion Monte Carlo methods revisited
journal, April 2010

  • Casula, Michele; Moroni, Saverio; Sorella, Sandro
  • The Journal of Chemical Physics, Vol. 132, Issue 15
  • DOI: 10.1063/1.3380831

Quadratic configuration interaction. A general technique for determining electron correlation energies
journal, November 1987

  • Pople, John A.; Head‐Gordon, Martin; Raghavachari, Krishnan
  • The Journal of Chemical Physics, Vol. 87, Issue 10
  • DOI: 10.1063/1.453520

Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states
journal, September 2014

  • Sharma, Sandeep; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 141, Issue 11
  • DOI: 10.1063/1.4895977

Assessing weak hydrogen binding on Ca + centers: An accurate many-body study with large basis sets
journal, October 2011

  • Purwanto, Wirawan; Krakauer, Henry; Virgus, Yudistira
  • The Journal of Chemical Physics, Vol. 135, Issue 16
  • DOI: 10.1063/1.3654002

Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group
journal, March 2002

  • Chan, Garnet Kin-Lic; Head-Gordon, Martin
  • The Journal of Chemical Physics, Vol. 116, Issue 11
  • DOI: 10.1063/1.1449459

The closed‐shell coupled cluster single and double excitation (CCSD) model for the description of electron correlation. A comparison with configuration interaction (CISD) results
journal, March 1987

  • Scuseria, Gustavo E.; Scheiner, Andrew C.; Lee, Timothy J.
  • The Journal of Chemical Physics, Vol. 86, Issue 5
  • DOI: 10.1063/1.452039

Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: Potential energy curves of low-lying C2 singlet states
journal, March 2009

  • Purwanto, Wirawan; Zhang, Shiwei; Krakauer, Henry
  • The Journal of Chemical Physics, Vol. 130, Issue 9
  • DOI: 10.1063/1.3077920

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


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


Fully self-consistent GW calculations for atoms and molecules
journal, October 2006


Studying Two-Dimensional Systems with the Density Matrix Renormalization Group
journal, March 2012


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

Determinant Diagrammatic Monte Carlo Algorithm in the Thermodynamic Limit
journal, July 2017


Quantum Mechanics of Many-Electron Systems
journal, April 1929

  • Dirac, P. A. M.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 123, Issue 792
  • DOI: 10.1098/rspa.1929.0094

Self-consistent second-order Green’s function perturbation theory for periodic systems
journal, February 2016

  • Rusakov, Alexander A.; Zgid, Dominika
  • The Journal of Chemical Physics, Vol. 144, Issue 5
  • DOI: 10.1063/1.4940900

A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples
journal, February 1982

  • Purvis, George D.; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 76, Issue 4
  • DOI: 10.1063/1.443164

Density Matrix Embedding: A Simple Alternative to Dynamical Mean-Field Theory
journal, November 2012


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
  • DOI: 10.1063/1.443766

Explicitly correlated multireference configuration interaction with multiple reference functions: Avoided crossings and conical intersections
journal, May 2011

  • Shiozaki, Toru; Werner, Hans-Joachim
  • The Journal of Chemical Physics, Vol. 134, Issue 18
  • DOI: 10.1063/1.3587632

Local Hamiltonians for quantitative Green's function embedding methods
journal, November 2014

  • Rusakov, Alexander A.; Phillips, Jordan J.; Zgid, Dominika
  • The Journal of Chemical Physics, Vol. 141, Issue 19
  • DOI: 10.1063/1.4901432

Large-Scale Semidefinite Programming for Many-Electron Quantum Mechanics
journal, February 2011


Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study
journal, December 2011


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

Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule
journal, September 2013

  • Zen, Andrea; Luo, Ye; Sorella, Sandro
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 10
  • DOI: 10.1021/ct400382m

Variational energy functionals tested on atoms
journal, May 2004


Ab initio quantum chemistry using the density matrix renormalization group
journal, March 1999

  • White, Steven R.; Martin, Richard L.
  • The Journal of Chemical Physics, Vol. 110, Issue 9
  • DOI: 10.1063/1.478295

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

Density matrix formulation for quantum renormalization groups
journal, November 1992


The density matrix renormalization group for ab initio quantum chemistry
journal, September 2014


Systematically improvable multiscale solver for correlated electron systems
journal, March 2015


Monte Carlo calculations of coupled boson-fermion systems. I
journal, October 1981


Combining Internally Contracted States and Matrix Product States To Perform Multireference Perturbation Theory
journal, January 2017

  • Sharma, Sandeep; Knizia, Gerald; Guo, Sheng
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 2
  • DOI: 10.1021/acs.jctc.6b00898

A direct atomic orbital driven implementation of the coupled cluster singles and doubles (CCSD) model
journal, September 1994


Efficient Temperature-Dependent Green’s Function Methods for Realistic Systems: Using Cubic Spline Interpolation to Approximate Matsubara Green’s Functions
journal, April 2016

  • Kananenka, Alexei A.; Welden, Alicia Rae; Lan, Tran Nguyen
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 5
  • DOI: 10.1021/acs.jctc.6b00178

Coupled-cluster theory in quantum chemistry
journal, February 2007


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
  • DOI: 10.1103/PhysRevX.5.041041

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


Self‐Consistent Orbitals for Radicals
journal, March 1954

  • Pople, J. A.; Nesbet, R. K.
  • The Journal of Chemical Physics, Vol. 22, Issue 3
  • DOI: 10.1063/1.1740120

Resonating valence bond wave function with molecular orbitals: Application to first-row molecules
journal, October 2009

  • Marchi, Mariapia; Azadi, Sam; Casula, Michele
  • The Journal of Chemical Physics, Vol. 131, Issue 15
  • DOI: 10.1063/1.3249966

Stability, Energetics, and Magnetic States of Cobalt Adatoms on Graphene
journal, October 2014


Bond breaking with auxiliary-field quantum Monte Carlo
journal, October 2007

  • Al-Saidi, W. A.; Zhang, Shiwei; Krakauer, Henry
  • The Journal of Chemical Physics, Vol. 127, Issue 14
  • DOI: 10.1063/1.2770707

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
  • DOI: 10.1063/1.2200885

Fractional charge and spin errors in self-consistent Green’s function theory
journal, May 2015

  • Phillips, Jordan J.; Kananenka, Alexei A.; Zgid, Dominika
  • The Journal of Chemical Physics, Vol. 142, Issue 19
  • DOI: 10.1063/1.4921259

Diagrammatic Monte Carlo
journal, January 2010


Density Matrix Embedding: A Strong-Coupling Quantum Embedding Theory
journal, February 2013

  • Knizia, Gerald; Chan, Garnet Kin-Lic
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 3
  • DOI: 10.1021/ct301044e

The ab-initio density matrix renormalization group in practice
journal, January 2015

  • Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki
  • The Journal of Chemical Physics, Vol. 142, Issue 3
  • DOI: 10.1063/1.4905329

Application of systematic sequences of wave functions to the water dimer
journal, April 1992

  • Feller, David
  • The Journal of Chemical Physics, Vol. 96, Issue 8
  • DOI: 10.1063/1.462652

Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms
journal, July 2016

  • Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki
  • The Journal of Chemical Physics, Vol. 145, Issue 1
  • DOI: 10.1063/1.4955108

Quantum-information analysis of electronic states of different molecular structures
journal, January 2011


Intrinsic Atomic Orbitals: An Unbiased Bridge between Quantum Theory and Chemical Concepts
journal, October 2013

  • Knizia, Gerald
  • Journal of Chemical Theory and Computation, Vol. 9, Issue 11
  • DOI: 10.1021/ct400687b

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


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


Finite temperature quantum embedding theories for correlated systems
journal, February 2017


Calculation of Partition Functions
journal, July 1959


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


Multireference explicitly correlated F12 theories
journal, March 2013


Levels of self-consistency in the GW approximation
journal, March 2009

  • Stan, Adrian; Dahlen, Nils Erik; van Leeuwen, Robert
  • The Journal of Chemical Physics, Vol. 130, Issue 11
  • DOI: 10.1063/1.3089567

Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method
journal, July 2010

  • Sinitskiy, Anton V.; Greenman, Loren; Mazziotti, David A.
  • The Journal of Chemical Physics, Vol. 133, Issue 1
  • DOI: 10.1063/1.3459059

Communication: The description of strong correlation within self-consistent Green's function second-order perturbation theory
journal, June 2014

  • Phillips, Jordan J.; Zgid, Dominika
  • The Journal of Chemical Physics, Vol. 140, Issue 24
  • DOI: 10.1063/1.4884951

Polynomial complexity despite the fermionic sign
journal, April 2017


Communication: Towards ab initio self-energy embedding theory in quantum chemistry
journal, December 2015

  • Lan, Tran Nguyen; Kananenka, Alexei A.; Zgid, Dominika
  • The Journal of Chemical Physics, Vol. 143, Issue 24
  • DOI: 10.1063/1.4938562

Dynamical Mean-Field Theory for Quantum Chemistry
journal, March 2011


Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group
journal, October 2006

  • Hachmann, Johannes; Cardoen, Wim; Chan, Garnet Kin-Lic
  • The Journal of Chemical Physics, Vol. 125, Issue 14
  • DOI: 10.1063/1.2345196

r 12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l
journal, December 1985


Stability of Dirac Liquids with Strong Coulomb Interaction
journal, January 2017


C RYSTAL14 : A program for the ab initio investigation of crystalline solids
journal, March 2014

  • Dovesi, Roberto; Orlando, Roberto; Erba, Alessandro
  • International Journal of Quantum Chemistry, Vol. 114, Issue 19
  • DOI: 10.1002/qua.24658

Self-Consistent Approximations in Many-Body Systems
journal, August 1962


Efficient Temperature-Dependent Green’s Functions Methods for Realistic Systems: Compact Grids for Orthogonal Polynomial Transforms
journal, January 2016

  • Kananenka, Alexei A.; Phillips, Jordan J.; Zgid, Dominika
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 2
  • DOI: 10.1021/acs.jctc.5b00884

Self-consistent G W : All-electron implementation with localized basis functions
journal, August 2013


Coulomb and electron-phonon interactions in metals
journal, October 2016


Variational second-order Møller–Plesset theory based on the Luttinger–Ward functional
journal, April 2004

  • Dahlen, Nils Erik; von Barth, Ulf
  • The Journal of Chemical Physics, Vol. 120, Issue 15
  • DOI: 10.1063/1.1650307

Basis-set convergence of correlated calculations on water
journal, June 1997

  • Helgaker, Trygve; Klopper, Wim; Koch, Henrik
  • The Journal of Chemical Physics, Vol. 106, Issue 23
  • DOI: 10.1063/1.473863

Explicitly correlated multireference configuration interaction: MRCI-F12
journal, January 2011

  • Shiozaki, Toru; Knizia, Gerald; Werner, Hans-Joachim
  • The Journal of Chemical Physics, Vol. 134, Issue 3
  • DOI: 10.1063/1.3528720

Ground-State Energy of a Many-Fermion System. II
journal, June 1960


New perspectives in multireference perturbation theory: the n-electron valence state approach
journal, December 2006

  • Angeli, Celestino; Pastore, Mariachiara; Cimiraglia, Renzo
  • Theoretical Chemistry Accounts, Vol. 117, Issue 5-6
  • DOI: 10.1007/s00214-006-0207-0

Variational Total Energies from Φ- and Ψ- Derivable Theories
journal, March 1999

  • Almbladh, C. -O.; Barth, U. Von; Leeuwen, R. Van
  • International Journal of Modern Physics B, Vol. 13, Issue 05n06
  • DOI: 10.1142/S0217979299000436

Bold Diagrammatic Monte Carlo Technique: When the Sign Problem Is Welcome
journal, December 2007


Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins
journal, February 2013


Rigorous Ab Initio Quantum Embedding for Quantum Chemistry Using Green’s Function Theory: Screened Interaction, Nonlocal Self-Energy Relaxation, Orbital Basis, and Chemical Accuracy
journal, September 2016

  • Nguyen Lan, Tran; Kananenka, Alexei A.; Zgid, Dominika
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 10
  • DOI: 10.1021/acs.jctc.6b00638

Strong correlations via constrained-pairing mean-field theory
journal, September 2009

  • Tsuchimochi, Takashi; Scuseria, Gustavo E.
  • The Journal of Chemical Physics, Vol. 131, Issue 12
  • DOI: 10.1063/1.3237029

A Practical Guide to Density Matrix Embedding Theory in Quantum Chemistry
journal, May 2016

  • Wouters, Sebastian; Jiménez-Hoyos, Carlos A.; Sun, Qiming
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 6
  • DOI: 10.1021/acs.jctc.6b00316

Perturbative correction for the basis set incompleteness error of complete-active-space self-consistent field
journal, November 2010

  • Kong, Liguo; Valeev, Edward F.
  • The Journal of Chemical Physics, Vol. 133, Issue 17
  • DOI: 10.1063/1.3499600