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

Title: Benchmark of correlation matrix renormalization method in molecule calculations

Abstract

In this paper, we report benchmark calculations of the correlation matrix renormalization (CMR) approach for 23 molecules in the well-established G2 molecule set. This subset represents molecules with spin-singlet ground state in a variety of chemical bonding and coordination environments. The QUAsi-atomic minimal basis-set orbitals (QUAMBOs) are used as local orbitals in both CMR and full configuration interaction (FCI) calculations for comparison. The results obtained from the calculations are also compared with available experimental data. It is shown that the CMR method produces binding and dissociation energy curves in good agreement with the QUAMBO-FCI calculations as well as experimental results. Finally, the CMR benchmark calculations yield a standard deviation of 0.09 Å for the equilibrium bond length and 0.018 Hartree/atom for the formation energy, with a gain of great computational efficiency which scales like Hartree–Fock method.

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [2];  [2]
  1. Qingdao University, Shandong (China)
  2. Ames Lab. and Iowa State Univ., Ames, IA (United States)
Publication Date:
Research Org.:
Ames Lab., Ames, IA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
OSTI Identifier:
1498685
Report Number(s):
IS-J-9890
Journal ID: ISSN 0953-8984
Grant/Contract Number:  
AC02-07CH11358; 21773132
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Physics. Condensed Matter
Additional Journal Information:
Journal Volume: 31; Journal Issue: 19; Journal ID: ISSN 0953-8984
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Zhang, Han, Lu, Wen-Cai, Yao, Yong-Xin, Wang, Cai-Zhuang, and Ho, Kai-Ming. Benchmark of correlation matrix renormalization method in molecule calculations. United States: N. p., 2019. Web. doi:10.1088/1361-648X/ab05b3.
Zhang, Han, Lu, Wen-Cai, Yao, Yong-Xin, Wang, Cai-Zhuang, & Ho, Kai-Ming. Benchmark of correlation matrix renormalization method in molecule calculations. United States. https://doi.org/10.1088/1361-648X/ab05b3
Zhang, Han, Lu, Wen-Cai, Yao, Yong-Xin, Wang, Cai-Zhuang, and Ho, Kai-Ming. Fri . "Benchmark of correlation matrix renormalization method in molecule calculations". United States. https://doi.org/10.1088/1361-648X/ab05b3. https://www.osti.gov/servlets/purl/1498685.
@article{osti_1498685,
title = {Benchmark of correlation matrix renormalization method in molecule calculations},
author = {Zhang, Han and Lu, Wen-Cai and Yao, Yong-Xin and Wang, Cai-Zhuang and Ho, Kai-Ming},
abstractNote = {In this paper, we report benchmark calculations of the correlation matrix renormalization (CMR) approach for 23 molecules in the well-established G2 molecule set. This subset represents molecules with spin-singlet ground state in a variety of chemical bonding and coordination environments. The QUAsi-atomic minimal basis-set orbitals (QUAMBOs) are used as local orbitals in both CMR and full configuration interaction (FCI) calculations for comparison. The results obtained from the calculations are also compared with available experimental data. It is shown that the CMR method produces binding and dissociation energy curves in good agreement with the QUAMBO-FCI calculations as well as experimental results. Finally, the CMR benchmark calculations yield a standard deviation of 0.09 Å for the equilibrium bond length and 0.018 Hartree/atom for the formation energy, with a gain of great computational efficiency which scales like Hartree–Fock method.},
doi = {10.1088/1361-648X/ab05b3},
journal = {Journal of Physics. Condensed Matter},
number = 19,
volume = 31,
place = {United States},
year = {2019},
month = {2}
}

Works referenced in this record:

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

Coupled-cluster theory in quantum chemistry
journal, February 2007


Multireference Nature of Chemistry: The Coupled-Cluster View
journal, December 2011

  • Lyakh, Dmitry I.; Musiał, Monika; Lotrich, Victor F.
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr2001417

The Construction and Interpretation of Mcscf Wavefunctions
journal, October 1998


Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications
journal, December 2011

  • Szalay, Péter G.; Müller, Thomas; Gidofalvi, Gergely
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr200137a

Quantum Monte Carlo and Related Approaches
journal, December 2011

  • Austin, Brian M.; Zubarev, Dmitry Yu.; Lester, William A.
  • Chemical Reviews, Vol. 112, Issue 1
  • DOI: 10.1021/cr2001564

Sign-Problem-Free Quantum Monte Carlo of the Onset of Antiferromagnetism in Metals
journal, December 2012


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

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


Band theory and Mott insulators: Hubbard U instead of Stoner I
journal, July 1991

  • Anisimov, Vladimir I.; Zaanen, Jan; Andersen, Ole K.
  • Physical Review B, Vol. 44, Issue 3, p. 943-954
  • DOI: 10.1103/PhysRevB.44.943

First-principles calculations of the electronic structure and spectra of strongly correlated systems: the LDA + U method
journal, January 1997

  • Anisimov, Vladimir I.; Aryasetiawan, F.; Lichtenstein, A. I.
  • Journal of Physics: Condensed Matter, Vol. 9, Issue 4, p. 767-808
  • DOI: 10.1088/0953-8984/9/4/002

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
journal, January 1996

  • Georges, Antoine; Kotliar, Gabriel; Krauth, Werner
  • Reviews of Modern Physics, Vol. 68, Issue 1
  • DOI: 10.1103/RevModPhys.68.13

Correlated electrons in δ-plutonium within a dynamical mean-field picture
journal, April 2001

  • Savrasov, S. Y.; Kotliar, G.; Abrahams, E.
  • Nature, Vol. 410, Issue 6830
  • DOI: 10.1038/35071035

Electronic structure calculations with dynamical mean-field theory
journal, August 2006


LDA + Gutzwiller method for correlated electron systems
journal, July 2008


Self-interaction correction in the LDA + U method
journal, July 2007


Double counting in LDA+DMFT—The example of NiO
journal, July 2010

  • Karolak, M.; Ulm, G.; Wehling, T.
  • Journal of Electron Spectroscopy and Related Phenomena, Vol. 181, Issue 1
  • DOI: 10.1016/j.elspec.2010.05.021

Covalency in transition-metal oxides within all-electron dynamical mean-field theory
journal, August 2014


Correlation Matrix Renormalization Theory: Improving Accuracy with Two-Electron Density-Matrix Sum Rules
journal, September 2016

  • Liu, C.; Liu, J.; Yao, Y. X.
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 10
  • DOI: 10.1021/acs.jctc.6b00570

Efficient and accurate treatment of electron correlations with Correlation Matrix Renormalization theory
journal, August 2015

  • Yao, Y. X.; Liu, J.; Liu, C.
  • Scientific Reports, Vol. 5, Issue 1
  • DOI: 10.1038/srep13478

New Functional Integral Approach to Strongly Correlated Fermi Systems: The Gutzwiller Approximation as a Saddle Point
journal, September 1986


Multiband Gutzwiller wave functions for general on-site interactions
journal, March 1998


Equivalence of Gutzwiller and slave-boson mean-field theories for multiband Hubbard models
journal, November 2007


Assessment of Gaussian-2 and density functional theories for the computation of enthalpies of formation
journal, January 1997

  • Curtiss, Larry A.; Raghavachari, Krishnan; Redfern, Paul C.
  • The Journal of Chemical Physics, Vol. 106, Issue 3
  • DOI: 10.1063/1.473182

Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals
journal, February 2004

  • Lu, W. C.; Wang, C. Z.; Schmidt, M. W.
  • The Journal of Chemical Physics, Vol. 120, Issue 6
  • DOI: 10.1063/1.1638731

Molecule intrinsic minimal basis sets. II. Bonding analyses for Si4H6 and Si2 to Si10
journal, February 2004

  • Lu, W. C.; Wang, C. Z.; Schmidt, M. W.
  • The Journal of Chemical Physics, Vol. 120, Issue 6
  • DOI: 10.1063/1.1638732

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

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

Projector augmented-wave method
journal, December 1994


From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999


Accurate ab initio potential energy curve of F2. II. Core-valence correlations, relativistic contributions, and long-range interactions
journal, November 2007

  • Bytautas, L.; Matsunaga, N.; Nagata, T.
  • The Journal of Chemical Physics, Vol. 127, Issue 20
  • DOI: 10.1063/1.2801989

The description of N 2 and F 2 potential energy surfaces using multireference coupled cluster theory
journal, January 1987

  • Laidig, William D.; Saxe, Paul; Bartlett, Rodney J.
  • The Journal of Chemical Physics, Vol. 86, Issue 2
  • DOI: 10.1063/1.452291

Full potential energy curve for N2 by the reduced multireference coupled-cluster method
journal, August 2008

  • Li, Xiangzhu; Paldus, Josef
  • The Journal of Chemical Physics, Vol. 129, Issue 5
  • DOI: 10.1063/1.2961033

Potential energy curves for P 2 and P 2 + constructed from a strictly N-representable natural orbital functional
journal, February 2016


Seniority number description of potential energy surfaces: Symmetric dissociation of water, N 2 , C 2 , and Be 2
journal, September 2015

  • Bytautas, Laimutis; Scuseria, Gustavo E.; Ruedenberg, Klaus
  • The Journal of Chemical Physics, Vol. 143, Issue 9
  • DOI: 10.1063/1.4929904

Full configuration interaction potential energy curves for the X 1Σg+, B 1Δg, and B′ 1Σg+ states of C2: A challenge for approximate methods
journal, November 2004

  • Abrams, Micah L.; Sherrill, C. David
  • The Journal of Chemical Physics, Vol. 121, Issue 19
  • DOI: 10.1063/1.1804498

First Principle Calculations of the Potential Energy Curves for Electronic States of the Lithium Dimer
journal, February 2014

  • Musiał, Monika; Kucharski, Stanisław A.
  • Journal of Chemical Theory and Computation, Vol. 10, Issue 3
  • DOI: 10.1021/ct401076e

Comparison of spectroscopic potentials and an a priori analytical function. The potential energy curve of the ground state of the sodium dimer, X 1Σg+ Na2
journal, March 2004

  • Matsunaga, Nikita; Zavitsas, Andreas A.
  • The Journal of Chemical Physics, Vol. 120, Issue 12
  • DOI: 10.1063/1.1648637

The electronic spectrum of F 2
journal, July 1976

  • Colbourn, E. A.; Dagenais, M.; Douglas, A. E.
  • Canadian Journal of Physics, Vol. 54, Issue 13
  • DOI: 10.1139/p76-159

Theoretical study of the UV photodissociation of Cl2: Potentials, transition moments, extinction coefficients, and Cl * /Cl branching ratio
journal, June 2004

  • Kokh, Daria B.; Alekseyev, Aleksey B.; Buenker, Robert J.
  • The Journal of Chemical Physics, Vol. 120, Issue 24
  • DOI: 10.1063/1.1753554

Molecular Spectra and Molecular Structure
book, January 1979


The low‐lying states of hydrogen fluoride: Potential energy curves for the x   1 Σ + , 3 Σ + , 3 Π, and 1 Π states
journal, November 1976

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 65, Issue 10
  • DOI: 10.1063/1.432901

Multiphoton Ionization and Fragmentation of Hydrogen Chloride: A Diatomic Still Good for a Surprise
journal, January 2011

  • Maul, Christof; Chichinin, Alexey I.; Gericke, Karl-Heinz
  • Journal of Atomic, Molecular, and Optical Physics, Vol. 2011
  • DOI: 10.1155/2011/410108

Reducing Dzyaloshinskii-Moriya interaction and field-free spin-orbit torque switching in synthetic antiferromagnets
journal, May 2021


Electronic structure of AlFeN films exhibiting crystallographic orientation change from c- to a-axis with Fe concentrations and annealing effect
journal, February 2020


Molecular Spectra and Molecular Structure
journal, November 1929

  • Garner, W. E.; Lennard-Jones, J. E.
  • Nature, Vol. 124, Issue 3133
  • DOI: 10.1038/124762b0

Molecular Spectra and Molecular Structure
journal, October 1929

  • Garner, W. E.; Lennard-Jones, J. E.
  • Nature, Vol. 124, Issue 3128
  • DOI: 10.1038/124584a0

Gutzwiller density functional theory for correlated electron systems
text, January 2007


Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
text, January 2012


Covalency in transition metal oxides within all-electron Dynamical Mean Field Theory
text, January 2013


Multi-band Gutzwiller wave functions for general on-site interactions
text, January 1997