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

Title: Polynomial-product states: A symmetry-projection-based factorization of the full coupled cluster wavefunction in terms of polynomials of double excitations

Journal Article · · Journal of Chemical Physics
DOI:https://doi.org/10.1063/1.5085314· OSTI ID:1610560

Our goal is to remedy the failure of symmetry-adapted coupled-cluster theory in the presence of strong correlation. Previous work along these lines has taken us from a diagram-level analysis of the coupled-cluster equations to an understanding of the collective modes which can occur in various channels of the coupled-cluster equations to the exploration of non-exponential wavefunctions in efforts to combine coupled-cluster theory with symmetry projection. In this manuscript, we extend these efforts by introducing a new, polynomial product wavefunction ansatz that incorporates information from symmetry projection into standard coupled-cluster theory in a way that attempts to mitigate the effects of the lack of size extensivity and size consistency characteristic of symmetry-projected methods. Finally, we describe the new approach in detail within the context of our previous efforts, explore some illustrative calculations, and consider one route for reducing the computational cost of the new method.

Research Organization:
Rice Univ., Houston, TX (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); Welch Foundation; National Science Foundation (NSF)
Grant/Contract Number:
SC0001474; FG02-09ER16053; C-0036; DGE-1450681
OSTI ID:
1610560
Alternate ID(s):
OSTI ID: 1505882
Journal Information:
Journal of Chemical Physics, Vol. 150, Issue 14; ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 9 works
Citation information provided by
Web of Science

References (77)

Domain-Based Local Pair Natural Orbital Version of Mukherjee’s State-Specific Coupled Cluster Method journal January 2018
A size-consistent approach to strongly correlated systems using a generalized antisymmetrized product of nonorthogonal geminals journal January 2013
Behind the success of modified coupled-cluster methods: addition by subtraction journal July 2018
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 March 2016
Multireference coupled-cluster theory: The easy way journal March 2011
An efficient reformulation of the closed‐shell coupled cluster single and double excitation (CCSD) equations journal December 1988
Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian journal June 2017
Correlation problems in atomic and molecular systems. V. Spin‐adapted coupled cluster many‐electron theory journal July 1977
Coupled-Cluster Valence-Bond Singles and Doubles for Strongly Correlated Systems: Block-Tensor Based Implementation and Application to Oligoacenes journal January 2017
Many – Body Methods in Chemistry and Physics book January 2009
Coupled Cluster Approach journal January 1980
Communication: An adaptive configuration interaction approach for strongly correlated electrons with tunable accuracy journal April 2016
Multi-component symmetry-projected approach for molecular ground state correlations journal November 2013
Towards numerically robust multireference theories: The driven similarity renormalization group truncated to one- and two-body operators journal April 2016
Seniority-based coupled cluster theory journal December 2014
Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations journal September 2016
Single-reference coupled cluster theory for multi-reference problems journal November 2017
Seniority and orbital symmetry as tools for establishing a full configuration interaction hierarchy journal July 2011
Pair extended coupled cluster doubles journal June 2015
Combinations of coupled cluster, density functionals, and the random phase approximation for describing static and dynamic correlation, and van der Waals interactions journal November 2015
Assessing the Accuracy of New Geminal-Based Approaches journal April 2014
Targeting excited states in all-trans polyenes with electron-pair states journal December 2016
Attenuated coupled cluster: a heuristic polynomial similarity transformation incorporating spin symmetry projection into traditional coupled cluster theory journal January 2017
Projected quasiparticle theory for molecular electronic structure journal September 2011
Coupled Cluster Valence Bond Method: Efficient Computer Implementation and Application to Multiple Bond Dissociations and Strong Correlations in the Acenes journal April 2014
Alternative single-reference coupled cluster approaches for multireference problems: The simpler, the better journal June 2011
Can Single-Reference Coupled Cluster Theory Describe Static Correlation? journal June 2015
Projected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory journal May 2017
Automated Construction of Molecular Active Spaces from Atomic Valence Orbitals journal August 2017
Singlet-paired coupled cluster theory for open shells journal June 2016
Polynomial similarity transformation theory: A smooth interpolation between coupled cluster doubles and projected BCS applied to the reduced BCS Hamiltonian journal March 2016
Recoupling the singlet- and triplet-pairing channels in single-reference coupled cluster theory journal October 2016
Orbital-invariant spin-extended approximate coupled-cluster for multi-reference systems journal July 2018
Perspective: Multireference coupled cluster theories of dynamical electron correlation journal July 2018
Amplitude Determinant Coupled Cluster with Pairwise Doubles journal November 2016
Bridging Single- and Multireference Domains for Electron Correlation: Spin-Extended Coupled Electron Pair Approximation journal March 2017
Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian journal February 2017
Seniority zero pair coupled cluster doubles theory journal June 2014
Influence of broken-pair excitations on the exact pair wavefunction journal September 2017
Spin-projected generalized Hartree-Fock method as a polynomial of particle-hole excitations journal August 2017
Spin polynomial similarity transformation for repulsive Hamiltonians: interpolating between coupled cluster and spin-projected unrestricted Hartree–Fock journal January 2017
Localized Atomic and Molecular Orbitals journal July 1963
Selection of active spaces for multiconfigurational wavefunctions journal June 2015
A New Mean-Field Method Suitable for Strongly Correlated Electrons: Computationally Facile Antisymmetric Products of Nonorthogonal Geminals journal February 2013
An Introduction to Coupled Cluster Theory for Computational Chemists book January 2000
Exploring Copper Oxide Cores Using the Projected Hartree–Fock Method journal September 2012
Variational principles and linked-cluster exp S expansions for static and dynamic many-body problems journal December 1983
Projected Hartree–Fock theory journal April 2012
Efficient description of strongly correlated electrons with mean-field cost journal May 2014
Actinide chemistry using singlet-paired coupled cluster and its combinations with density functionals journal December 2015
Predicting Singlet–Triplet Energy Splittings with Projected Hartree–Fock Methods journal July 2013
Tensor-structured coupled cluster theory journal November 2017
Electron correlations in narrow energy bands journal November 1963
On the Correlation Problem in Atomic and Molecular Systems. Calculation of Wavefunction Components in Ursell‐Type Expansion Using Quantum‐Field Theoretical Methods journal December 1966
Entanglement and Polyradical Character of Polycyclic Aromatic Hydrocarbons Predicted by Projected Hartree–Fock Theory journal May 2013
Excited states from modified coupled cluster methods: Are they any better than EOM CCSD? journal April 2017
Cheap and Near Exact CASSCF with Large Active Spaces journal October 2017
A dynamic correlation dressed complete active space method: Theory, implementation, and preliminary applications journal December 2017
Accurate thermochemistry from a parameterized coupled-cluster singles and doubles model and a local pair natural orbital based implementation for applications to larger systems journal February 2012
pCCSD: Parameterized coupled-cluster theory with single and double excitations journal November 2010
Zur Theorie der Metalle: Erwiderung auf eine Arbeit von A. H. Wilson journal September 1933
Multi-component symmetry-projected approach for molecular ground state correlations text January 2013
Efficient description of strongly correlated electrons with mean-field cost text January 2014
Quasiparticle Coupled Cluster Theory for Pairing Interactions text January 2014
Seniority-based coupled cluster theory text January 2014
Can single-reference coupled cluster theory describe static correlation? text January 2015
Combinations of coupled cluster, density functionals, and the random phase approximation for describing static and dynamic correlation, and van der Waals interactions text January 2015
Actinide chemistry using singlet-paired coupled cluster and its combinations with density functionals text January 2015
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 text January 2016
Bridging single- and multireference domains for electron correlation: spin-extended coupled electron pair approximation preprint January 2016
Automated construction of molecular active spaces from atomic valence orbitals text January 2017
Projected Hartree-Fock as a Polynomial of Particle-Hole Excitations and Its Combination With Variational Coupled Cluster Theory text January 2017
Combining symmetry collective states with coupled cluster theory: Lessons from the Agassi model Hamiltonian text January 2017
Spin-Projected Generalized Hartree-Fock as a Polynomial of Particle-Hole Excitations text January 2017
Influence of broken-pair excitations on the exact pair wavefunction text January 2017
Cheap and near exact CASSCF with large active spaces text January 2017
Targeting excited states in all-trans polyenes with electron-pair states text January 2019

Cited By (2)