1
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Dutta R, Gao F, Khamoshi A, Henderson TM, Scuseria GE. Correlated pair ansatz with a binary tree structure. J Chem Phys 2024; 160:084113. [PMID: 38421064 DOI: 10.1063/5.0185375] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2023] [Accepted: 02/02/2024] [Indexed: 03/02/2024] Open
Abstract
We develop an efficient algorithm to implement the recently introduced binary tree state (BTS) ansatz on a classical computer. BTS allows a simple approximation to permanents arising from the computationally intractable antisymmetric product of interacting geminals and respects size-consistency. We show how to compute BTS overlap and reduced density matrices efficiently. We also explore two routes for developing correlated BTS approaches: Jastrow coupled cluster on BTS and linear combinations of BT states. The resulting methods show great promise in benchmark applications to the reduced Bardeen-Cooper-Schrieffer Hamiltonian and the one-dimensional XXZ Heisenberg Hamiltonian.
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Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Fei Gao
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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2
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Henderson TM, Tabrizi SG, Chen GP, Scuseria GE. Hartree-Fock-Bogoliubov theory for number-parity-violating fermionic Hamiltonians. J Chem Phys 2024; 160:064103. [PMID: 38341776 DOI: 10.1063/5.0188155] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2023] [Accepted: 01/15/2024] [Indexed: 02/13/2024] Open
Abstract
It is usually asserted that physical Hamiltonians for fermions must contain an even number of fermion operators. This is indeed true in electronic structure theory. However, when the Jordan-Wigner (JW) transformation is used to map physical spin Hamiltonians to Hamiltonians of spinless fermions, terms that contain an odd number of fermion operators may appear. The resulting fermionic Hamiltonian thus does not have number parity symmetry and requires wave functions that do not have this symmetry either. In this work, we discuss the extension of standard Hartree-Fock-Bogoliubov (HFB) theory to the number-parity-nonconserving case. These ideas had appeared in the literature before but, perhaps for lack of practical applications, had, to the best of our knowledge, never been employed. We here present a useful application for this more general HFB theory based on coherent states of the SO(2M + 1) Lie group, where M is the number of orbitals. We also show how using these unusual mean-field states can provide significant improvements when studying the JW transformation of chemically relevant spin Hamiltonians.
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Affiliation(s)
- Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | | | - Guo P Chen
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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3
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Papastathopoulos-Katsaros A, Henderson TM, Scuseria GE. Symmetry-projected cluster mean-field theory applied to spin systems. J Chem Phys 2023; 159:084107. [PMID: 37610020 DOI: 10.1063/5.0155765] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/23/2023] [Accepted: 07/11/2023] [Indexed: 08/24/2023] Open
Abstract
We introduce Sz spin-projection based on cluster mean-field theory and apply it to the ground state of strongly correlated spin systems. In cluster mean-fields, the ground state wavefunction is written as a factorized tensor product of optimized cluster states. In previous work, we have focused on unrestricted cluster mean-field, where each cluster is Sz symmetry adapted. We here remove this restriction by introducing a generalized cluster mean-field (GcMF) theory, where each cluster is allowed to access all Sz sectors, breaking Sz symmetry. In addition, a projection scheme is used to restore global Sz, which gives rise to the Sz spin-projected generalized cluster mean-field (SzGcMF). Both of these extensions contribute to accounting for inter-cluster correlations. We benchmark these methods on the 1D, quasi-2D, and 2D J1 - J2 and XXZ Heisenberg models. Our results indicate that the new methods (GcMF and SzGcMF) provide a qualitative and semi-quantitative description of the Heisenberg lattices in the regimes considered, suggesting them as useful references for further inter-cluster correlations, which are discussed in this work.
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Affiliation(s)
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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4
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Harsha G, Henderson TM, Scuseria GE. Thermofield Theory for Finite-Temperature Electronic Structure. J Phys Chem A 2023; 127:3063-3071. [PMID: 37017308 DOI: 10.1021/acs.jpca.2c08418] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/06/2023]
Abstract
Wave function methods have offered a robust, systematically improvable means to study ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the energy landscape at a reasonable computational cost. Analogues of such methods to study thermal properties, though highly desirable, have been lacking because evaluating thermal properties involve a trace over the entire Hilbert space, which is a formidable task. Besides, excited-state theories are generally not as well studied as ground-state ones. In this mini-review, we present an overview of a finite-temperature wave function formalism based on thermofield dynamics to overcome these difficulties. Thermofield dynamics allows us to map the equilibrium thermal density matrix to a pure state, i.e., a single wave function, albeit in an expanded Hilbert space. Ensemble averages become expectation values over this so-called thermal state. Around this thermal state, we have developed a procedure to generalize ground-state wave function theories to finite temperatures. As explicit examples, we highlight formulations of mean-field, configuration interaction, and coupled cluster theories for thermal properties of Fermions in the grand-canonical ensemble. To assess the quality of these approximations, we also show benchmark studies for the one-dimensional Hubbard model, while comparing against exact results. We will see that the thermal methods perform similarly to their ground-state counterparts, while merely adding a prefactor to the asymptotic computational cost. They also inherit all the properties, good or bad, from the ground-state methods, signifying the robustness of our formalism and the scope for future development.
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Affiliation(s)
- Gaurav Harsha
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48105, United States
| | - Thomas M Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
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Papastathopoulos-Katsaros A, Jiménez-Hoyos CA, Henderson TM, Scuseria GE. Coupled Cluster and Perturbation Theories Based on a Cluster Mean-Field Reference Applied to Strongly Correlated Spin Systems. J Chem Theory Comput 2022; 18:4293-4303. [PMID: 35729717 DOI: 10.1021/acs.jctc.2c00338] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
We introduce perturbation and coupled-cluster theories based on a cluster mean-field reference for describing the ground state of strongly correlated spin systems. In cluster mean-field, the ground state wave function is written as a simple tensor product of optimized cluster states. The cluster language and the mean-field nature of the ansatz allow for a straightforward improvement which uses perturbation theory and coupled-cluster to account for intercluster correlations. We present benchmark calculations on the 1D chain and 2D square J1-J2 Heisenberg model, using cluster mean-field, perturbation theory, and coupled-cluster. We also present an extrapolation scheme that allows us to compute thermodynamic limit energies accurately. Our results indicate that, with sufficiently large clusters, the correlated methods (cPT2, cPT4, and cCCSD) can provide a relatively accurate description of the Heisenberg model in the regimes considered, which suggests that the methods presented can be used for other strongly correlated systems. Some ways to improve upon the methods presented in this work are discussed.
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Affiliation(s)
| | - Carlos A Jiménez-Hoyos
- Department of Chemistry, Wesleyan University, Middletown, Connecticut 06459, United States
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, United States.,Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, United States.,Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
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6
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Song R, Henderson TM, Scuseria GE. A power series approximation in symmetry projected coupled cluster theory. J Chem Phys 2022; 156:104105. [DOI: 10.1063/5.0080165] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Projected Hartree–Fock theory provides an accurate description of many kinds of strong correlations but does not properly describe weakly correlated systems. On the other hand, single-reference methods, such as configuration interaction or coupled cluster theory, can handle weakly correlated problems but cannot properly account for strong correlations. Ideally, we would like to combine these techniques in a symmetry-projected coupled cluster approach, but this is far from straightforward. In this work, we provide an alternative formulation to identify the so-called disentangled cluster operators, which arise when we combine these two methodological strands. Our formulation shows promising results for model systems and small molecules.
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Affiliation(s)
- Ruiheng Song
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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Henderson TM. How Accountable to the Public Is Funding for Graduate Medical Education? The Case for State Medicaid GME Payments. Am J Public Health 2021; 111:1216-1219. [PMID: 34370538 DOI: 10.2105/ajph.2021.306246] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/04/2022]
Affiliation(s)
- Thomas M Henderson
- Thomas (Tim) M. Henderson recently retired full time from the Department of Health Administration and Policy, College of Health and Human Services, George Mason University, Fairfax, VA. He continues to work on an adjunct basis and serves as a medical workforce consultant on public policy matters
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Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Guo P. Chen
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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9
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Affiliation(s)
- Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Guo P. Chen
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
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10
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Harsha G, Henderson TM, Scuseria GE. Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems. J Chem Phys 2020; 153:124115. [DOI: 10.1063/5.0022702] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Gaurav Harsha
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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11
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Affiliation(s)
- Rishab Dutta
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
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12
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Affiliation(s)
- Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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13
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Affiliation(s)
- Armin Khamoshi
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
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14
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Affiliation(s)
- Gaurav Harsha
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
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15
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Affiliation(s)
- Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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16
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Gomez JA, Molla M, Garza AJ, Henderson TM, Scuseria GE. Assessing combinations of singlet-paired coupled cluster and density functional theory for treating electron correlation in closed and open shells. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1615144] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- John A. Gomez
- Department of Chemistry, Rice University, Houston, TX, USA
- Applied Physics Graduate Program, Rice University, Houston, TX, USA
| | - Mahlet Molla
- Department of Chemistry, Rice University, Houston, TX, USA
| | | | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
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17
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Affiliation(s)
- Gaurav Harsha
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
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18
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Gomez JA, Henderson TM, Scuseria GE. Polynomial-product states: A symmetry-projection-based factorization of the full coupled cluster wavefunction in terms of polynomials of double excitations. J Chem Phys 2019; 150:144108. [PMID: 30981260 DOI: 10.1063/1.5085314] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
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. 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.
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Affiliation(s)
- John A Gomez
- Applied Physics Graduate Program, Rice University, Houston, Texas 77005, USA
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19
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Qiu Y, Henderson TM, Zhao J, Scuseria GE. Projected coupled cluster theory: Optimization of cluster amplitudes in the presence of symmetry projection. J Chem Phys 2018; 149:164108. [DOI: 10.1063/1.5053605] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Affiliation(s)
- Yiheng Qiu
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Jinmo Zhao
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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20
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Affiliation(s)
- Lena C. Jake
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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21
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Affiliation(s)
- Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
| | - Carlos A. Jiménez-Hoyos
- Department of Chemistry, Wesleyan University, Middletown, Connecticut 06459-0180, United States
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, United States
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, United States
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22
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Affiliation(s)
- Roman Schutski
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
| | - Jinmo Zhao
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
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23
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Affiliation(s)
| | - Thomas M. Henderson
- Department of Physics Astronomy, Rice University, Houston, TX, USA
- Department of Chemistry, Rice University, Houston, TX, USA
| | - Gustavo E. Scuseria
- Department of Physics Astronomy, Rice University, Houston, TX, USA
- Department of Chemistry, Rice University, Houston, TX, USA
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24
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Affiliation(s)
- Yiheng Qiu
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Jinmo Zhao
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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25
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Qiu Y, Henderson TM, Scuseria GE. Projected Hartree-Fock theory as a polynomial of particle-hole excitations and its combination with variational coupled cluster theory. J Chem Phys 2017. [DOI: 10.1063/1.4983065] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Yiheng Qiu
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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26
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Gomez JA, Henderson TM, Scuseria GE. Attenuated coupled cluster: a heuristic polynomial similarity transformation incorporating spin symmetry projection into traditional coupled cluster theory. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1302610] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- John A. Gomez
- Department of Chemistry, Rice University, Houston, TX, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, TX, USA
- Department of Physics and Astronomy, Rice University, Houston, TX, USA
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Perdew JP, Yang W, Burke K, Yang Z, Gross EKU, Scheffler M, Scuseria GE, Henderson TM, Zhang IY, Ruzsinszky A, Peng H, Sun J, Trushin E, Görling A. Understanding band gaps of solids in generalized Kohn-Sham theory. Proc Natl Acad Sci U S A 2017; 114:2801-2806. [PMID: 28265085 PMCID: PMC5358356 DOI: 10.1073/pnas.1621352114] [Citation(s) in RCA: 179] [Impact Index Per Article: 25.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS density-functional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.
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Affiliation(s)
- John P Perdew
- Department of Physics, Temple University, Philadelphia, PA 19122;
- Department of Chemistry, Temple University, Philadelphia, PA 19122
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, NC 27708
| | - Kieron Burke
- Department of Chemistry, University of California, Irvine, CA 92697
- Department of Physics, University of California, Irvine, CA 92697
| | - Zenghui Yang
- Department of Physics, Temple University, Philadelphia, PA 19122
| | | | - Matthias Scheffler
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, CA 93106
- Materials Department, University of California, Santa Barbara, CA 93106
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, Houston, TX 77005
- Department of Physics and Astronomy, Rice University, Houston, TX 77005
| | - Thomas M Henderson
- Department of Chemistry, Rice University, Houston, TX 77005
- Department of Physics and Astronomy, Rice University, Houston, TX 77005
| | - Igor Ying Zhang
- Fritz-Haber-Institut der Max-Planck-Gesellschaft, D-14195 Berlin, Germany
| | | | - Haowei Peng
- Department of Physics, Temple University, Philadelphia, PA 19122
| | - Jianwei Sun
- Department of Physics, The University of Texas at El Paso, El Paso, TX 79968
| | - Egor Trushin
- Department of Chemistry and Pharmacy, Friedrich-Alexander Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - Andreas Görling
- Department of Chemistry and Pharmacy, Friedrich-Alexander Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
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Wahlen-Strothman JM, Henderson TM, Hermes MR, Degroote M, Qiu Y, Zhao J, Dukelsky J, Scuseria GE. Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian. J Chem Phys 2017; 146:054110. [DOI: 10.1063/1.4974989] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
| | - Thomas M. Henderson
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | | | | | - Yiheng Qiu
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Jinmo Zhao
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Jorge Dukelsky
- Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid, Spain
| | - Gustavo E. Scuseria
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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Gomez JA, Henderson TM, Scuseria GE. Recoupling the singlet- and triplet-pairing channels in single-reference coupled cluster theory. J Chem Phys 2016; 145:134103. [DOI: 10.1063/1.4963870] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- John A. Gomez
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
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Taylor DE, Ángyán JG, Galli G, Zhang C, Gygi F, Hirao K, Song JW, Rahul K, Anatole von Lilienfeld O, Podeszwa R, Bulik IW, Henderson TM, Scuseria GE, Toulouse J, Peverati R, Truhlar DG, Szalewicz K. Blind test of density-functional-based methods on intermolecular interaction energies. J Chem Phys 2016; 145:124105. [DOI: 10.1063/1.4961095] [Citation(s) in RCA: 81] [Impact Index Per Article: 10.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- DeCarlos E. Taylor
- U.S. Army Research Laboratory,
Aberdeen Proving Ground, Aberdeen, Maryland 21005-5069, USA
| | - János G. Ángyán
- CNRS, CRM2, UMR 7036,
Vandœuvre-lès-Nancy F-54506, France and Université de Lorraine, CRM2, UMR 7036, Vandœuvre-lès-Nancy F-54506,
France
| | - Giulia Galli
- Institute for Molecular Engineering, University of Chicago, Chicago, Illinois 60637,
USA
| | - Cui Zhang
- Department of Chemistry, University of California Davis, Davis, California 95616,
USA
| | - Francois Gygi
- Department of Computer Science,
University of California, Davis, California 95616, USA
| | - Kimihiko Hirao
- Computational Chemistry Unit, RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 6500047,
Japan
| | - Jong Won Song
- Computational Chemistry Unit, RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 6500047,
Japan
| | - Kar Rahul
- Computational Chemistry Unit, RIKEN Advanced Institute for Computational Science, Kobe, Hyogo 6500047,
Japan
| | - O. Anatole von Lilienfeld
- General Chemistry (ALGC), Free University Brussels (VUB), Pleinlaan 2, 1050 Brussel,
Belgium and Institute of Physical Chemistry and National Center
for Computational Design and Discovery of Novel Materials (MARVEL), Department of
Chemistry, University of Basel, 4056 Basel,
Switzerland
| | - Rafał Podeszwa
- Institute of Chemistry, University of Silesia, Szkolna 9, 40-006 Katowice, Poland
| | | | | | | | - Julien Toulouse
- Laboratoire de Chimie Théorique, Sorbonne Universités,
Université Pierre et Marie Curie, CNRS, F-75005 Paris,
France
| | - Roberto Peverati
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455,
USA
- Department of Chemistry, Florida Institute of Technology, Melbourne, Florida 32901,
USA
| | - Donald G. Truhlar
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455,
USA
| | - Krzysztof Szalewicz
- Department of Physics and Astronomy,
University of Delaware, Newark, Delaware 19716,
USA
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Qiu Y, Henderson TM, Scuseria GE. Communication: Projected Hartree Fock theory as a polynomial similarity transformation theory of single excitations. J Chem Phys 2016. [DOI: 10.1063/1.4963082] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Yiheng Qiu
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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Abstract
Restricted single-reference coupled cluster theory truncated to single and double excitations accurately describes weakly correlated systems, but often breaks down in the presence of static or strong correlation. Good coupled cluster energies in the presence of degeneracies can be obtained by using a symmetry-broken reference, such as unrestricted Hartree-Fock, but at the cost of good quantum numbers. A large body of work has shown that modifying the coupled cluster ansatz allows for the treatment of strong correlation within a single-reference, symmetry-adapted framework. The recently introduced singlet-paired coupled cluster doubles (CCD0) method is one such model, which recovers correct behavior for strong correlation without requiring symmetry breaking in the reference. Here, we extend singlet-paired coupled cluster for application to open shells via restricted open-shell singlet-paired coupled cluster singles and doubles (ROCCSD0). The ROCCSD0 approach retains the benefits of standard coupled cluster theory and recovers correct behavior for strongly correlated, open-shell systems using a spin-preserving ROHF reference.
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Affiliation(s)
- John A Gomez
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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Shepherd JJ, Henderson TM, Scuseria GE. 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. J Chem Phys 2016; 144:094112. [DOI: 10.1063/1.4942770] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Affiliation(s)
- James J. Shepherd
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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Abstract
While hybrid functionals are largely responsible for the utility of modern Kohn-Sham density functional theory, they are not without their weaknesses. In the solid state, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally demanding and can introduce unphysical effects. Both problems can be remedied by a screened hybrid which uses exact exchange only at short-range. Many molecular properties, in contrast, benefit from the inclusion of long-range exact exchange. Recently, the authors reconciled these two seemingly contradictory requirements by introducing the HISS functional [ J. Chem. Phys. 2007 , 127 , 221103 ], which uses exact exchange only in the middle range. In this paper, we expand upon our previous work, benchmarking the performance of the HISS functional for several simple properties and applying it to the dissociation of homonuclear diatomic cations and to the polarizability of linear H2 chains to determine the importance of middle-range exact exchange for these systems, which are expected to be sensitive to the asymptotic exchange potential.
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Affiliation(s)
- Thomas M Henderson
- Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005-1892, and Laboratoire de Chimie Théorique, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris, France
| | - Artur F Izmaylov
- Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005-1892, and Laboratoire de Chimie Théorique, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris, France
| | - Gustavo E Scuseria
- Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005-1892, and Laboratoire de Chimie Théorique, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris, France
| | - Andreas Savin
- Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005-1892, and Laboratoire de Chimie Théorique, CNRS, Université Pierre et Marie Curie, 4 Place Jussieu, F-75252 Paris, France
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35
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Garza AJ, Bulik IW, Henderson TM, Scuseria GE. Range separated hybrids of pair coupled cluster doubles and density functionals. Phys Chem Chem Phys 2015; 17:22412-22. [PMID: 26249820 DOI: 10.1039/c5cp02773j] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Pair coupled cluster doubles (pCCD) is a size-consistent, size-extensive, low-cost simplification of CCD that has been shown to be able to describe static correlation without breaking symmetry. We combine pCCD with Kohn-Sham functionals of the density and the local pair density in order to incorporate dynamic correlation in pCCD while maintaining its low cost. Double counting is eliminated by splitting the (interelectron) Coulomb operator into complementary short- and long-range parts, and evaluating the two-body energy with pCCD in the long-range and with density functionals in the short-range. This simultaneously suppresses self-interaction in the Hartree-exchange term of the functionals. Generalizations including a fraction of wavefunction two-body energy in the short-range are also derived and studied. The improvement of our pCCD+DFT hybrids over pCCD is demonstrated in calculations on benchmarks where both types of correlation are important.
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Affiliation(s)
- Alejandro J Garza
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA.
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Affiliation(s)
- Ireneusz W. Bulik
- Department
of Chemistry, Rice University, Houston, Texas 77005-1892, United States
| | - Thomas M. Henderson
- Department
of Chemistry, Rice University, Houston, Texas 77005-1892, United States
- Department
of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, United States
| | - Gustavo E. Scuseria
- Department
of Chemistry, Rice University, Houston, Texas 77005-1892, United States
- Department
of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, United States
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Affiliation(s)
- Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Ireneusz W. Bulik
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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38
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Garza AJ, Bulik IW, Henderson TM, Scuseria GE. Synergy between pair coupled cluster doubles and pair density functional theory. J Chem Phys 2015; 142:044109. [DOI: 10.1063/1.4906607] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023] Open
Affiliation(s)
- Alejandro J. Garza
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
| | - Ireneusz W. Bulik
- Department of Chemistry, Rice University, Houston, Texas 77251-1892, USA
| | - Thomas M. Henderson
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77251-1892, USA
- Chemistry Department, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
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Affiliation(s)
- Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Ireneusz W. Bulik
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Tamar Stein
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77005-1892, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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40
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Affiliation(s)
- Tamar Stein
- Department of Chemistry, Rice University, Houston, Texas 77251, USA
| | - Thomas M. Henderson
- Department of Chemistry, Rice University, Houston, Texas 77251, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251, USA
| | - Gustavo E. Scuseria
- Department of Chemistry, Rice University, Houston, Texas 77251, USA
- Department of Physics and Astronomy, Rice University, Houston, Texas 77251, USA
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Abstract
We introduce a range-separation approximation to coupled cluster doubles (CCD) theory that successfully overcomes limitations of regular CCD when applied to the uniform electron gas. We combine the short-range ladder channel with the long-range ring channel in the presence of a Bruckner renormalized one-body interaction and obtain ground-state energies with an accuracy of 0.001 a.u./electron across a wide range of density regimes. Our scheme is particularly useful in the low-density and strongly correlated regimes, where regular CCD has serious drawbacks. Moreover, we cure the infamous overcorrelation of approaches based on ring diagrams (i.e., the particle-hole random phase approximation). Our energies are further shown to have appropriate basis set and thermodynamic limit convergence, and overall this scheme promises energetic properties for realistic periodic and extended systems which existing methods do not possess.
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Affiliation(s)
- James J Shepherd
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Thomas M Henderson
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
| | - Gustavo E Scuseria
- Department of Chemistry and Department of Physics and Astronomy, Rice University, Houston, Texas 77005-1892, USA
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Cui Y, Bulik IW, Jiménez-Hoyos CA, Henderson TM, Scuseria GE. Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration. J Chem Phys 2013; 139:154107. [DOI: 10.1063/1.4824905] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023] Open
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45
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Scuseria GE, Henderson TM, Bulik IW. Particle-particle and quasiparticle random phase approximations: Connections to coupled cluster theory. J Chem Phys 2013; 139:104113. [DOI: 10.1063/1.4820557] [Citation(s) in RCA: 63] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
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46
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Wen XD, Martin RL, Henderson TM, Scuseria GE. Density Functional Theory Studies of the Electronic Structure of Solid State Actinide Oxides. Chem Rev 2012; 113:1063-96. [DOI: 10.1021/cr300374y] [Citation(s) in RCA: 163] [Impact Index Per Article: 13.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xiao-Dong Wen
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico
87545, United States
| | - Richard L. Martin
- Theoretical
Division, Los Alamos National Laboratory, Los Alamos, New Mexico
87545, United States
| | - Thomas M. Henderson
- Department
of Chemistry and
Department of Physics and Astronomy, Rice University, Houston, Texas 77251, United States
| | - Gustavo E. Scuseria
- Department
of Chemistry and
Department of Physics and Astronomy, Rice University, Houston, Texas 77251, United States
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Lucero MJ, Henderson TM, Scuseria GE. Improved semiconductor lattice parameters and band gaps from a middle-range screened hybrid exchange functional. J Phys Condens Matter 2012; 24:145504. [PMID: 22417942 DOI: 10.1088/0953-8984/24/14/145504] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
We show that the middle-range exchange-correlation hybrid of Henderson, Izmaylov, Scuseria and Savin (HISS) performs extremely well for elemental and binary semiconductors with narrow or visible spectrum band gaps, as well as some wider gap or more ionic systems used in devices. The lattice parameters are superior to those predicted by the screened hybrid functional of Heyd, Scuseria and Ernzerhof (HSE), and provide a significant improvement over the geometries predicted by typical semilocal functionals, yielding results competitive with PBEsol, which was specially tuned for solids. HISS also yields band gaps superior to those produced by functionals developed specifically for the solid state. Timings indicate that HISS is more computationally efficient than HSE, implying that the high quality lattice constants coupled with improved optical band gap predictions render HISS a useful adjunct to HSE in the modeling of geometry-sensitive semiconductors.
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Affiliation(s)
- M J Lucero
- Department of Chemistry, Rice University, Houston, TX 77005-1892, USA
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Scuseria GE, Jiménez-Hoyos CA, Henderson TM, Samanta K, Ellis JK. Projected quasiparticle theory for molecular electronic structure. J Chem Phys 2011; 135:124108. [DOI: 10.1063/1.3643338] [Citation(s) in RCA: 133] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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50
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Irelan RM, Henderson TM, Scuseria GE. Long-range-corrected hybrids using a range-separated Perdew-Burke-Ernzerhof functional and random phase approximation correlation. J Chem Phys 2011; 135:094105. [DOI: 10.1063/1.3630951] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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