Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

Shepherd, James J.; Henderson, Thomas M.; Scuseria, Gustavo E.

doi:10.1063/1.4942770

Title: Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

Journal Article · Mon Mar 07 00:00:00 EST 2016 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4942770· OSTI ID:1470135

Shepherd, James J. ^[1]; Henderson, Thomas M. ^[1]; Scuseria, Gustavo E. ^[1]

Rice Univ., Houston, TX (United States). Dept. of Chemistry. Dept. of Physics and Astronomy

Over the past few years, pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. In this paper, by modifying the full configuration interaction quantum Monte Carlo algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. Finally, we present evidence for this and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Rice Univ., Houston, TX (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: FG02-04ER15523

OSTI ID:: 1470135

Alternate ID(s):: OSTI ID: 1240474

Journal Information:: Journal of Chemical Physics, Vol. 144, Issue 9; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 23 works

Citation information provided by
Web of Science

References (41)

Symmetry Breaking and Broken Ergodicity in Full Configuration Interaction Quantum Monte Carlo Thomas, Robert E.; Overy, Catherine; Booth, George H. Journal of Chemical Theory and Computation, Vol. 10, Issue 5 https://doi.org/10.1021/ct400835u	journal	April 2014
Efficient description of strongly correlated electrons with mean-field cost Boguslawski, Katharina; Tecmer, Paweł; Ayers, Paul W. Physical Review B, Vol. 89, Issue 20 https://doi.org/10.1103/PhysRevB.89.201106	journal	May 2014
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space Booth, George H.; Thom, Alex J. W.; Alavi, Ali The Journal of Chemical Physics, Vol. 131, Issue 5 https://doi.org/10.1063/1.3193710	journal	January 2009
Accurate Ab Initio Calculation of Ionization Potentials of the First-Row Transition Metals with the Configuration-Interaction Quantum Monte Carlo Technique Thomas, Robert E.; Booth, George H.; Alavi, Ali Physical Review Letters, Vol. 114, Issue 3 https://doi.org/10.1103/PhysRevLett.114.033001	journal	January 2015
An explicitly correlated approach to basis set incompleteness in full configuration interaction quantum Monte Carlo Booth, George H.; Cleland, Deidre; Alavi, Ali The Journal of Chemical Physics, Vol. 137, Issue 16 https://doi.org/10.1063/1.4762445	journal	October 2012
Seniority zero pair coupled cluster doubles theory Stein, Tamar; Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 140, Issue 21 https://doi.org/10.1063/1.4880819	journal	June 2014
Sign problem in full configuration interaction quantum Monte Carlo: Linear and sublinear representation regimes for the exact wave function Shepherd, James J.; Scuseria, Gustavo E.; Spencer, James S. Physical Review B, Vol. 90, Issue 15 https://doi.org/10.1103/PhysRevB.90.155130	journal	October 2014
Full configuration interaction perspective on the homogeneous electron gas Shepherd, James J.; Booth, George; Grüneis, Andreas Physical Review B, Vol. 85, Issue 8 https://doi.org/10.1103/PhysRevB.85.081103	journal	February 2012
ELECTRON PAIRS IN THE BERYLLIUM ATOM ¹ Allen, Thomas L.; Shull, Harrison The Journal of Physical Chemistry, Vol. 66, Issue 12 https://doi.org/10.1021/j100818a001	journal	December 1962
The effect of quantization on the full configuration interaction quantum Monte Carlo sign problem Kolodrubetz, M. H.; Spencer, J. S.; Clark, B. K. The Journal of Chemical Physics, Vol. 138, Issue 2 https://doi.org/10.1063/1.4773819	journal	January 2013
Solutions of the Two-Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms LeBlanc, J. P. F.; Antipov, Andrey E.; Becca, Federico Physical Review X, Vol. 5, Issue 4 https://doi.org/10.1103/physrevx.5.041041	journal	December 2015
Natural Orbitals and Geminals of the Beryllium Atom Smith, Darwin W.; Fogel, Sidney J. The Journal of Chemical Physics, Vol. 43, Issue 10 https://doi.org/10.1063/1.1701519	journal	November 1965
Linearized Coupled Cluster Correction on the Antisymmetric Product of 1-Reference Orbital Geminals Boguslawski, Katharina; Ayers, Paul W. Journal of Chemical Theory and Computation, Vol. 11, Issue 11 https://doi.org/10.1021/acs.jctc.5b00776	journal	October 2015
Comparison between exact and approximate treatments of the pairing interaction for finite Fermi systems Dukelsky, J.; Dussel, G. G.; Hirsch, J. G. Nuclear Physics A, Vol. 714, Issue 1-2 https://doi.org/10.1016/S0375-9474(02)01361-1	journal	February 2003
Semi-stochastic full configuration interaction quantum Monte Carlo: Developments and application Blunt, N. S.; Smart, Simon D.; Kersten, J. A. F. The Journal of Chemical Physics, Vol. 142, Issue 18 https://doi.org/10.1063/1.4920975	journal	May 2015
Error estimates on averages of correlated data Flyvbjerg, H.; Petersen, H. G. The Journal of Chemical Physics, Vol. 91, Issue 1 https://doi.org/10.1063/1.457480	journal	July 1989
Nonvariational Orbital Optimization Techniques for the AP1roG Wave Function Boguslawski, Katharina; Tecmer, Paweł; Bultinck, Patrick Journal of Chemical Theory and Computation, Vol. 10, Issue 11 https://doi.org/10.1021/ct500759q	journal	October 2014
Seniority-based coupled cluster theory Henderson, Thomas M.; Bulik, Ireneusz W.; Stein, Tamar The Journal of Chemical Physics, Vol. 141, Issue 24 https://doi.org/10.1063/1.4904384	journal	December 2014
A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals Limacher, Peter A.; Ayers, Paul W.; Johnson, Paul A. Journal of Chemical Theory and Computation, Vol. 9, Issue 3 https://doi.org/10.1021/ct300902c	journal	February 2013
Stochastic Multiconfigurational Self-Consistent Field Theory Thomas, Robert E.; Sun, Qiming; Alavi, Ali Journal of Chemical Theory and Computation, Vol. 11, Issue 11 https://doi.org/10.1021/acs.jctc.5b00917	journal	October 2015
Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo Cleland, Deidre; Booth, George H.; Alavi, Ali The Journal of Chemical Physics, Vol. 132, Issue 4 https://doi.org/10.1063/1.3302277	journal	January 2010
Insights into the structure of many-electron wave functions of Mott-insulating antiferromagnets: The three-band Hubbard model in full configuration interaction quantum Monte Carlo Schwarz, Lauretta R.; Booth, George H.; Alavi, Ali Physical Review B, Vol. 91, Issue 4 https://doi.org/10.1103/PhysRevB.91.045139	journal	January 2015
Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy Bytautas, Laimutis; Henderson, Thomas M.; Jiménez-Hoyos, Carlos A. The Journal of Chemical Physics, Vol. 135, Issue 4 https://doi.org/10.1063/1.3613706	journal	July 2011
Pair extended coupled cluster doubles Henderson, Thomas M.; Bulik, Ireneusz W.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 142, Issue 21 https://doi.org/10.1063/1.4921986	journal	June 2015
Assessing the Accuracy of New Geminal-Based Approaches Tecmer, Paweł; Boguslawski, Katharina; Johnson, Paul A. The Journal of Physical Chemistry A, Vol. 118, Issue 39 https://doi.org/10.1021/jp502127v	journal	April 2014
Breaking the carbon dimer: The challenges of multiple bond dissociation with full configuration interaction quantum Monte Carlo methods Booth, George H.; Cleland, Deidre; Thom, Alex J. W. The Journal of Chemical Physics, Vol. 135, Issue 8 https://doi.org/10.1063/1.3624383	journal	August 2011
The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method Spencer, J. S.; Blunt, N. S.; Foulkes, W. M. C. The Journal of Chemical Physics, Vol. 136, Issue 5 https://doi.org/10.1063/1.3681396	journal	February 2012
Linear-scaling and parallelisable algorithms for stochastic quantum chemistry Booth, George H.; Smart, Simon D.; Alavi, Ali Molecular Physics, Vol. 112, Issue 14 https://doi.org/10.1080/00268976.2013.877165	journal	January 2014
Towards an exact description of electronic wavefunctions in real solids Booth, George H.; Grüneis, Andreas; Kresse, Georg Nature, Vol. 493, Issue 7432 https://doi.org/10.1038/nature11770	journal	December 2012
Quasiparticle coupled cluster theory for pairing interactions Henderson, Thomas M.; Scuseria, Gustavo E.; Dukelsky, Jorge Physical Review C, Vol. 89, Issue 5 https://doi.org/10.1103/PhysRevC.89.054305	journal	May 2014
Observations on variational and projector Monte Carlo methods Umrigar, C. J. The Journal of Chemical Physics, Vol. 143, Issue 16 https://doi.org/10.1063/1.4933112	journal	October 2015
A new approach to density matrix functional theory Kollmar, Christian; Heß, Bernd A. The Journal of Chemical Physics, Vol. 119, Issue 9 https://doi.org/10.1063/1.1590635	journal	September 2003
Projected seniority-two orbital optimization of the antisymmetric product of one-reference orbital geminal Boguslawski, Katharina; Tecmer, Paweł; Limacher, Peter A. The Journal of Chemical Physics, Vol. 140, Issue 21 https://doi.org/10.1063/1.4880820	journal	June 2014
The influence of orbital rotation on the energy of closed-shell wavefunctions Limacher, Peter A.; Kim, Taewon D.; Ayers, Paul W. Molecular Physics, Vol. 112, Issue 5-6 https://doi.org/10.1080/00268976.2013.874600	journal	January 2014
Singlet ground state actinide chemistry with geminals Tecmer, Paweł; Boguslawski, Katharina; Ayers, Paul W. Physical Chemistry Chemical Physics, Vol. 17, Issue 22 https://doi.org/10.1039/C4CP05293E	journal	January 2015
Complete multi-configuration self-consistent field theory Veillard, A.; Clementi, E. Theoretica Chimica Acta, Vol. 7, Issue 2 https://doi.org/10.1007/BF01151915	journal	January 1967
Partial node configuration-interaction Monte Carlo as applied to the Fermi polaron Kolodrubetz, M.; Clark, B. K. Physical Review B, Vol. 86, Issue 7 https://doi.org/10.1103/PhysRevB.86.075109	journal	August 2012
Generalized Molecular Orbital Theory II Couty, Marc; Hall, Michael B. The Journal of Physical Chemistry A, Vol. 101, Issue 37 https://doi.org/10.1021/jp963953l	journal	September 1997
Unbiased reduced density matrices and electronic properties from full configuration interaction quantum Monte Carlo Overy, Catherine; Booth, George H.; Blunt, N. S. The Journal of Chemical Physics, Vol. 141, Issue 24 https://doi.org/10.1063/1.4904313	journal	December 2014
Reduced Density Matrices of Atoms and Molecules. I. The 2 Matrix of Double‐Occupancy, Configuration‐Interaction Wavefunctions for Singlet States Weinhold, Frank; Wilson, E. Bright The Journal of Chemical Physics, Vol. 46, Issue 7 https://doi.org/10.1063/1.1841109	journal	April 1967
Polynomial similarity transformation theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian Degroote, Matthias; Henderson, Thomas M.; Zhao, Jinmo Physical Review B, Vol. 93, Issue 12 https://doi.org/10.1103/PhysRevB.93.125124	journal	March 2016

Cited By (3)

Method for making 2-electron response reduced density matrices approximately N -representable Lanssens, Caitlin; Ayers, Paul W.; Van Neck, Dimitri The Journal of Chemical Physics, Vol. 148, Issue 8 https://doi.org/10.1063/1.4994618	journal	February 2018
Pair 2-electron reduced density matrix theory using localized orbitals Head-Marsden, Kade; Mazziotti, David A. The Journal of Chemical Physics, Vol. 147, Issue 8 https://doi.org/10.1063/1.4999423	journal	August 2017
Polynomial-product states: A symmetry-projection-based factorization of the full coupled cluster wavefunction in terms of polynomials of double excitations Gomez, John A.; Henderson, Thomas M.; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 150, Issue 14 https://doi.org/10.1063/1.5085314	journal	April 2019

Similar Records

Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

Journal Article · Mon Mar 07 00:00:00 EST 2016 · Journal of Chemical Physics · OSTI ID:1470135

Henderson, Thomas M.; Scuseria, Gustavo E.

Seniority-based coupled cluster theory

Journal Article · Sun Dec 28 00:00:00 EST 2014 · Journal of Chemical Physics · OSTI ID:1470135

Henderson, Thomas M.; Scuseria, Gustavo E.; Bulik, Ireneusz W.; +1 more

Understanding and improving the efficiency of full configuration interaction quantum Monte Carlo

Journal Article · Mon Mar 07 00:00:00 EST 2016 · Journal of Chemical Physics · OSTI ID:1470135

Vigor, W. A.; Bearpark, M. J.; Spencer, J. S.; +1 more

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
stochastic processes
density-matrix
band gap
Hilbert space
coupled-cluster methods
configuration interaction
correlation energy
Monte Carlo methods
many electron systems
zero point energy

Title: Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

Citation Formats

References (41)

Cited By (3)

Similar Records

Related Subjects