1
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Wu X, Cao C, Zhou C, Wu W. Hybrid Density Functional Valence Bond Method with Multistate Treatment. J Chem Theory Comput 2024. [PMID: 38279919 DOI: 10.1021/acs.jctc.3c01170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2024]
Abstract
Recently, a hybrid density functional valence bond (VB) method, λ-DFVB(U), has been proposed and shown to give accuracy that is comparable to that of CASPT2 in calculations of atomization energies, atomic excitation energies, and reaction barriers, while its computational cost is approximately the same as the valence bond self-consistent-field (VBSCF) method. However, the interaction between electronic states is not included in λ-DFVB(U) since the last step of λ-DFVB(U) is not a diagonalization of the Hamiltonian matrix on the electronic state basis. Therefore, λ-DFVB(U) gives the wrong topology of the potential energy surfaces (PESs) near the conical intersection region. In the present paper, we propose a novel hybrid density functional VB method with multistate treatment, named λ-DFVB(MS), in which an effective Hamiltonian matrix is constructed on the basis of the diabatic states obtained by the valence-bond-based compression approach for the diabatization scheme, and the interaction between electronic states can be included through the diagonalization of the effective Hamiltonian matrix. Test calculations show that λ-DFVB(MS) gives the correct topology of the PESs near the conical intersection region. We also show that the VBSCF wave function with selected VB structures can be applied as a reference in λ-DFVB(MS).
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Affiliation(s)
- Xun Wu
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
- Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
| | - Chan Cao
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
- Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
| | - Chen Zhou
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
- Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
| | - Wei Wu
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, China
- Innovation Laboratory for Sciences and Technologies of Energy Materials of Fujian Province (IKKEM), Xiamen 361005, China
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2
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Martinez B JA, Shao X, Jiang K, Pavanello M. Entropy is a good approximation to the electronic (static) correlation energy. J Chem Phys 2023; 159:191102. [PMID: 37965995 DOI: 10.1063/5.0171981] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/11/2023] [Accepted: 10/25/2023] [Indexed: 11/16/2023] Open
Abstract
For an electronic system, given a mean field method and a distribution of orbital occupation numbers that are close to the natural occupations of the correlated system, we provide formal evidence and computational support to the hypothesis that the entropy (or more precisely -σS, where σ is a parameter and S is the entropy) of such a distribution is a good approximation to the correlation energy. Underpinning the formal evidence are mild assumptions: the correlation energy is strictly a functional of the occupation numbers, and the occupation numbers derive from an invertible distribution. Computational support centers around employing different mean field methods and occupation number distributions (Fermi-Dirac, Gaussian, and linear), for which our claims are verified for a series of pilot calculations involving bond breaking and chemical reactions. This work establishes a formal footing for those methods employing entropy as a measure of electronic correlation energy (e.g., i-DMFT [Wang and Baerends, Phys. Rev. Lett. 128, 013001 (2022)] and TAO-DFT [J.-D. Chai, J. Chem. Phys. 136, 154104 (2012)]) and sets the stage for the widespread use of entropy functionals for approximating the (static) electronic correlation.
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Affiliation(s)
| | - Xuecheng Shao
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
| | - Kaili Jiang
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
| | - Michele Pavanello
- Department of Chemistry, Rutgers University, Newark, New Jersey 07102, USA
- Department of Physics, Rutgers University, Newark, New Jersey 07102, USA
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3
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Zheng P, Gan Z, Zhou C, Su P, Wu W. λ-DFVB(U): A hybrid density functional valence bond method based on unpaired electron density. J Chem Phys 2022; 156:204103. [DOI: 10.1063/5.0091592] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this paper, a hybrid density functional valence bond method based on unpaired electron density, called λ-DFVB(U), is presented, which is a combination of the valence bond self-consistent field (VBSCF) method and Kohn–Sham density functional theory. In λ-DFVB(U), the double-counting error of electron correlation is mitigated by a linear decomposition of the electron–electron interaction using a parameter λ, which is a function of an index based on the number of effectively unpaired electrons. In addition, λ-DFVB(U) is based on the approximation that correlation functionals in KS-DFT only cover dynamic correlation and exchange functionals mimic some amount of static correlation. Furthermore, effective spin densities constructed from unpaired density are used to address the symmetry dilemma problem in λ-DFVB(U). The method is applied to test calculations of atomization energies, atomic excitation energies, and reaction barriers. It is shown that the accuracy of λ-DFVB(U) is comparable to that of CASPT2, while its computational cost is approximately the same as VBSCF.
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Affiliation(s)
- Peikun Zheng
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Zixi Gan
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Chen Zhou
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Peifeng Su
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
| | - Wei Wu
- State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, Department of Chemistry, and College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China
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4
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Elayan IA, Gupta R, Hollett JW. ΔNO and the complexities of electron correlation in simple hydrogen clusters. J Chem Phys 2022; 156:094102. [DOI: 10.1063/5.0073227] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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5
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Traore D, Giner E, Toulouse J. Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model. J Chem Phys 2022; 156:044113. [DOI: 10.1063/5.0076128] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Diata Traore
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, F-75005 Paris, France
- Institut Universitaire de France, F-75005 Paris, France
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6
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Pernal K, Hapka M. Range‐separated multiconfigurational density functional theory methods. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1566] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
| | - Michał Hapka
- Lodz University of Technology Institute of Physics Lodz Poland
- Faculty of Chemistry University of Warsaw Warsaw Poland
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7
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Casanova D. Restricted active space configuration interaction methods for strong correlation: Recent developments. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1561] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- David Casanova
- Donostia International Physics Center (DIPC) Donostia Spain
- Ikerbasque Basque Foundation for Science Bilbao Spain
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8
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Zheng P, Ji C, Ying F, Su P, Wu W. A Valence-Bond-Based Multiconfigurational Density Functional Theory: The λ-DFVB Method Revisited. Molecules 2021; 26:521. [PMID: 33498268 PMCID: PMC7863953 DOI: 10.3390/molecules26030521] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Revised: 01/17/2021] [Accepted: 01/18/2021] [Indexed: 11/29/2022] Open
Abstract
A recently developed valence-bond-based multireference density functional theory, named λ-DFVB, is revisited in this paper. λ-DFVB remedies the double-counting error of electron correlation by decomposing the electron-electron interactions into the wave function term and density functional term with a variable parameter λ. The λ value is defined as a function of the free valence index in our previous scheme, denoted as λ-DFVB(K) in this paper. Here we revisit the λ-DFVB method and present a new scheme based on natural orbital occupation numbers (NOONs) for parameter λ, named λ-DFVB(IS), to simplify the process of λ-DFVB calculation. In λ-DFVB(IS), the parameter λ is defined as a function of NOONs, which are straightforwardly determined from the many-electron wave function of the molecule. Furthermore, λ-DFVB(IS) does not involve further self-consistent field calculation after performing the valence bond self-consistent field (VBSCF) calculation, and thus, the computational effort in λ-DFVB(IS) is approximately the same as the VBSCF method, greatly reduced from λ-DFVB(K). The performance of λ-DFVB(IS) was investigated on a broader range of molecular properties, including equilibrium bond lengths and dissociation energies, atomization energies, atomic excitation energies, and chemical reaction barriers. The computational results show that λ-DFVB(IS) is more robust without losing accuracy and comparable in accuracy to high-level multireference wave function methods, such as CASPT2.
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Affiliation(s)
| | | | | | - Peifeng Su
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, The State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China; (P.Z.); (C.J.); (F.Y.)
| | - Wei Wu
- Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, The State Key Laboratory of Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, China; (P.Z.); (C.J.); (F.Y.)
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9
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Jana S, Śmiga S, Constantin LA, Samal P. Generalizing Double-Hybrid Density Functionals: Impact of Higher-Order Perturbation Terms. J Chem Theory Comput 2020; 16:7413-7430. [PMID: 33205659 PMCID: PMC7735712 DOI: 10.1021/acs.jctc.0c00823] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2020] [Indexed: 11/28/2022]
Abstract
Connections between the Görling-Levy (GL) perturbation theory and the parameters of double-hybrid (DH) density functional are established via adiabatic connection formalism. Moreover, we present a more general DH density functional theory, where the higher-order perturbation terms beyond the second-order GL2 one, such as GL3 and GL4, also contribute. It is shown that a class of DH functionals including previously proposed ones can be formed using the present construction. Based on the proposed formalism, we assess the performance of higher-order DH and long-range corrected DH formed on the Perdew-Burke-Ernzerhof (PBE) semilocal functional and second-order GL2 correlation energy. The underlying construction of DH functionals based on the generalized many-body perturbation approaches is physically appealing in terms of the development of the non-local forms using more accurate and sophisticated semilocal functionals.
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Affiliation(s)
- Subrata Jana
- School
of Physical Sciences, National Institute
of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Szymon Śmiga
- Institute
of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
| | - Lucian A. Constantin
- Consiglio
Nazionale delle Ricerche CNR-NANO, Istituto
di Nanoscienze, 41125 Modena, Italy
| | - Prasanjit Samal
- School
of Physical Sciences, National Institute
of Science Education and Research, HBNI, Bhubaneswar 752050, India
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10
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Hapka M, Pastorczak E, Krzemińska A, Pernal K. Long-range-corrected multiconfiguration density functional with the on-top pair density. J Chem Phys 2020; 152:094102. [DOI: 10.1063/1.5138980] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Michał Hapka
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
- Faculty of Chemistry, University of Warsaw, ul. L. Pasteura 1, 02-093 Warsaw, Poland
| | - Ewa Pastorczak
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Agnieszka Krzemińska
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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11
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Jana S, Patra A, Constantin LA, Samal P. Screened range-separated hybrid by balancing the compact and slowly varying density regimes: Satisfaction of local density linear response. J Chem Phys 2020; 152:044111. [PMID: 32007058 DOI: 10.1063/1.5131530] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Due to their quantitative accuracy and ability to solve several difficulties, screened range-separated hybrid exchange-correlation functionals are now a standard approach for ab initio simulation of condensed matter systems. However, the screened range-separated hybrid functionals proposed so far are biased either toward compact or slowly varying densities. In this paper, we propose a screened range-separated hybrid functional, named HSEint, which can well describe these density regimes, achieving good accuracy for both molecular and solid-state systems. The semilocal part of the proposed functional is based on the PBEint generalized gradient approximation [E. Fabiano et al., Phys. Rev. B 82, 113104 (2010)], constructed for hybrid interfaces. To improve the functional performance, we employ exact or nearly exact constraints in the construction of range-separated hybrid functional, such as recovering of the local density linear response and semiclassical atom linear response.
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Affiliation(s)
- Subrata Jana
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Abhilash Patra
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Lucian A Constantin
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Via Barsanti, I-73010 Arnesano, Italy
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
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12
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Hollett JW, Loos PF. Capturing static and dynamic correlation with ΔNO-MP2 and ΔNO-CCSD. J Chem Phys 2020; 152:014101. [PMID: 31914756 DOI: 10.1063/1.5140669] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The ΔNO method for static correlation is combined with second-order Møller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions are adapted from finite-temperature CCSD, which includes orbital occupancies and vacancies, and expanded orbital summations. Correlation is partitioned with the aid of damping factors incorporated into the MP2 and CCSD residual equations. Potential energy curves for a selection of diatomics are in good agreement with extrapolated full configuration interaction results and on par with conventional multireference approaches.
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Affiliation(s)
- Joshua W Hollett
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques (UMR 5626), Université de Toulouse, CNRS, UPS, Toulouse, France
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13
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Ferté A, Giner E, Toulouse J. Range-separated multideterminant density-functional theory with a short-range correlation functional of the on-top pair density. J Chem Phys 2019; 150:084103. [DOI: 10.1063/1.5082638] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Anthony Ferté
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Emmanuel Giner
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique (LCT), Sorbonne Université and CNRS, F-75005 Paris, France
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14
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Lischka H, Nachtigallová D, Aquino AJA, Szalay PG, Plasser F, Machado FBC, Barbatti M. Multireference Approaches for Excited States of Molecules. Chem Rev 2018; 118:7293-7361. [DOI: 10.1021/acs.chemrev.8b00244] [Citation(s) in RCA: 197] [Impact Index Per Article: 32.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Hans Lischka
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
| | - Dana Nachtigallová
- Institute of Organic Chemistry and Biochemistry v.v.i., The Czech Academy of Sciences, Flemingovo nám. 2, 16610 Prague 6, Czech Republic
- Regional Centre of Advanced Technologies and Materials, Palacký University, 78371 Olomouc, Czech Republic
| | - Adélia J. A. Aquino
- School of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China
- Department of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States
- Institute for Soil Research, University of Natural Resources and Life Sciences Vienna, Peter-Jordan-Strasse 82, A-1190 Vienna, Austria
| | - Péter G. Szalay
- ELTE Eötvös Loránd University, Laboratory of Theoretical Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary
| | - Felix Plasser
- Institute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria
- Department of Chemistry, Loughborough University, Leicestershire LE11 3TU, United Kingdom
| | - Francisco B. C. Machado
- Departamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228-900, São Paulo, Brazil
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15
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Hollett JW, Pegoretti N. On-top density functionals for the short-range dynamic correlation between electrons of opposite and parallel spin. J Chem Phys 2018; 148:164111. [DOI: 10.1063/1.5025171] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joshua W. Hollett
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba, R3B 2G3, Canada
- Department of Chemistry, University of Manitoba, Winnipeg, Manitoba, R3T 2N2, Canada
| | - Nicholas Pegoretti
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba, R3B 2G3, Canada
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16
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Casanova D. Short-range density functional correlation within the restricted active space CI method. J Chem Phys 2018; 148:124118. [DOI: 10.1063/1.5018895] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Affiliation(s)
- David Casanova
- Kimika Fakultatea, Euskal Herria Unibersitatea (UPV/EHU), Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Euskadi, Spain
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17
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Sharma P, Truhlar DG, Gagliardi L. Active Space Dependence in Multiconfiguration Pair-Density Functional Theory. J Chem Theory Comput 2018; 14:660-669. [DOI: 10.1021/acs.jctc.7b01052] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Prachi Sharma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, Minneapolis, Minnesota 55455-0431, United States
| | - Donald G. Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, Minneapolis, Minnesota 55455-0431, United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute, Minneapolis, Minnesota 55455-0431, United States
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18
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Rebolini E, Teale AM, Helgaker T, Savin A, Toulouse J. Excitation energies from Görling–Levy perturbation theory along the range-separated adiabatic connection. Mol Phys 2018. [DOI: 10.1080/00268976.2017.1422811] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
| | - Andrew M. Teale
- School of Chemistry, University of Nottingham, Nottingham, United Kingdom
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
- Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway
| | - Trygve Helgaker
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
- Centre for Advanced Study at the Norwegian Academy of Science and Letters, Oslo, Norway
| | - Andreas Savin
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, Paris, France
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, CNRS, Sorbonne Universités, Paris, France
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19
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Gagliardi L, Truhlar DG, Li Manni G, Carlson RK, Hoyer CE, Bao JL. Multiconfiguration Pair-Density Functional Theory: A New Way To Treat Strongly Correlated Systems. Acc Chem Res 2017; 50:66-73. [PMID: 28001359 DOI: 10.1021/acs.accounts.6b00471] [Citation(s) in RCA: 193] [Impact Index Per Article: 27.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
The electronic energy of a system provides the Born-Oppenheimer potential energy for internuclear motion and thus determines molecular structure and spectra, bond energies, conformational energies, reaction barrier heights, and vibrational frequencies. The development of more efficient and more accurate ways to calculate the electronic energy of systems with inherently multiconfigurational electronic structure is essential for many applications, including transition metal and actinide chemistry, systems with partially broken bonds, many transition states, and most electronically excited states. Inherently multiconfigurational systems are called strongly correlated systems or multireference systems, where the latter name refers to the need for using more than one ("multiple") configuration state function to provide a good zero-order reference wave function. This Account describes multiconfiguration pair-density functional theory (MC-PDFT), which was developed as a way to combine the advantages of wave function theory (WFT) and density functional theory (DFT) to provide a better treatment of strongly correlated systems. First we review background material: the widely used Kohn-Sham DFT (which uses only a single Slater determinant as reference wave function), multiconfiguration WFT methods that treat inherently multiconfigurational systems based on an active space, and previous attempts to combine multiconfiguration WFT with DFT. Then we review the formulation of MC-PDFT. It is a generalization of Kohn-Sham DFT in that the electron kinetic energy and classical electrostatic energy are calculated from a reference wave function, while the rest of the energy is obtained from a density functional. However, there are two main differences with respent to Kohn-Sham DFT: (i) The reference wave function is multiconfigurational rather than being a single Slater determinant. (ii) The density functional is a function of the total density and the on-top pair density rather than being a function of the spin-up and spin-down densities. In work carried out so far, the multiconfigurational wave function is a multiconfiguration self-consistent-field wave function. The new formulation has the advantage that the reference wave function has the correct spatial and spin symmetry and can describe bond dissociation (of both single and multiple bonds) and electronic excitations in a formally and physically correct way. We then review the formulation of density functionals in terms of the on-top pair density. Finally we review successful applications of the theory to bond energies and bond dissociation potential energy curves of main-group and transition metal bonds, to barrier heights (including pericyclic reactions), to proton affinities, to the hydrogen bond energy of water dimer, to ground- and excited-state charge transfer, to valence and Rydberg excitations of molecules, and to singlet-triplet splittings of radicals. We find that that MC-PDFT can give accurate results not only with complete-active-space multiconfiguration wave functions but also with generalized-active-space multiconfiguration wave functions, which are practical for larger numbers of active electrons and active orbitals than are complete-active-space wave functions. The separated-pair approximation, which is a special case of generalized active space self-consistent-field theory, is especially promising. MC-PDFT, because it requires much less computer time and storage than pure WFT methods, has the potential to open larger and more complex strongly correlated systems to accurate simulation.
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Affiliation(s)
- Laura Gagliardi
- Department of Chemistry,
Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Donald G. Truhlar
- Department of Chemistry,
Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Giovanni Li Manni
- Department of Chemistry,
Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Rebecca K. Carlson
- Department of Chemistry,
Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Chad E. Hoyer
- Department of Chemistry,
Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Junwei Lucas Bao
- Department of Chemistry,
Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
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20
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Zhou C, Zhang Y, Gong X, Ying F, Su P, Wu W. Hamiltonian Matrix Correction Based Density Functional Valence Bond Method. J Chem Theory Comput 2017; 13:627-634. [PMID: 27992721 DOI: 10.1021/acs.jctc.6b01144] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
In this work, a valence bond type multireference density functional theory (MRDFT) method, called the Hamiltonian matrix correction based density functional valence bond method (hc-DFVB), is presented. In hc-DFVB, the static electronic correlation is considered by the valence bond self-consistent field (VBSCF) strategy, while the dynamic correlation energy is taken into account by Kohn-Sham density functional theory (KS-DFT). Different from our previous version of DFVB (J. Chem. Theory Comput. 2012, 8, 1608), hc-DFVB corrects the dynamic correlation energy with a Hamiltonian correction matrix, improving the functional adaptability and computational accuracy. The method was tested for various physical and chemical properties, including spectroscopic constants, bond dissociation energies, reaction barriers, and singlet-triplet gaps. The accuracy of hc-DFVB matches that of KS-DFT and high level molecular orbital (MO) methods quite well. Furthermore, hc-DFVB keeps the advantages of VB methods, which are able to provide clear interpretations and chemical insights with compact wave functions.
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Affiliation(s)
- Chen Zhou
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University , Xiamen, Fujian 361005, China
| | - Yang Zhang
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University , Xiamen, Fujian 361005, China
| | - Xiping Gong
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University , Xiamen, Fujian 361005, China
| | - Fuming Ying
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University , Xiamen, Fujian 361005, China
| | - Peifeng Su
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University , Xiamen, Fujian 361005, China
| | - Wei Wu
- The State Key Laboratory of Physical Chemistry of Solid Surfaces, iChEM, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry and College of Chemistry and Chemical Engineering, Xiamen University , Xiamen, Fujian 361005, China
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21
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Yu HS, Li SL, Truhlar DG. Perspective: Kohn-Sham density functional theory descending a staircase. J Chem Phys 2016; 145:130901. [DOI: 10.1063/1.4963168] [Citation(s) in RCA: 204] [Impact Index Per Article: 25.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Haoyu S. Yu
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
| | - Shaohong L. Li
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
| | - Donald G. Truhlar
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, Minneapolis, Minnesota 55455-0431, USA
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22
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Hedegård ED, Reiher M. Polarizable Embedding Density Matrix Renormalization Group. J Chem Theory Comput 2016; 12:4242-53. [PMID: 27537835 DOI: 10.1021/acs.jctc.6b00476] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
The polarizable embedding (PE) approach is a flexible embedding model where a preselected region out of a larger system is described quantum mechanically, while the interaction with the surrounding environment is modeled through an effective operator. This effective operator represents the environment by atom-centered multipoles and polarizabilities derived from quantum mechanical calculations on (fragments of) the environment. Thereby, the polarization of the environment is explicitly accounted for. Here, we present the coupling of the PE approach with the density matrix renormalization group (DMRG). This PE-DMRG method is particularly suitable for embedded subsystems that feature a dense manifold of frontier orbitals which requires large active spaces. Recovering such static electron-correlation effects in multiconfigurational electronic structure problems, while accounting for both electrostatics and polarization of a surrounding environment, allows us to describe strongly correlated electronic structures in complex molecular environments. We investigate various embedding potentials for the well-studied first excited state of water with active spaces that correspond to a full configuration-interaction treatment. Moreover, we study the environment effect on the first excited state of a retinylidene Schiff base within a channelrhodopsin protein. For this system, we also investigate the effect of dynamical correlation included through short-range density functional theory.
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Affiliation(s)
- Erik D Hedegård
- Laboratorium für Physikalische Chemie, ETH Zürich , Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland
| | - Markus Reiher
- Laboratorium für Physikalische Chemie, ETH Zürich , Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland
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23
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Hollett JW, Hosseini H, Menzies C. A cumulant functional for static and dynamic correlation. J Chem Phys 2016; 145:084106. [DOI: 10.1063/1.4961243] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joshua W. Hollett
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada
- Department of Chemistry, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
| | - Hessam Hosseini
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada
| | - Cameron Menzies
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada
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24
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Hubert M, Hedegård ED, Jensen HJA. Investigation of Multiconfigurational Short-Range Density Functional Theory for Electronic Excitations in Organic Molecules. J Chem Theory Comput 2016; 12:2203-13. [DOI: 10.1021/acs.jctc.5b01141] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mickaël Hubert
- Department
of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
| | - Erik D. Hedegård
- Laboratorium
für Physikalische Chemie, ETH Zürich, Vladimir-Prelog-Weg 2, CH-8093 Zürich, Switzerland
| | - Hans Jørgen Aa. Jensen
- Department
of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
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25
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Li Manni G, Carlson RK, Luo S, Ma D, Olsen J, Truhlar DG, Gagliardi L. Multiconfiguration Pair-Density Functional Theory. J Chem Theory Comput 2015; 10:3669-80. [PMID: 26588512 DOI: 10.1021/ct500483t] [Citation(s) in RCA: 299] [Impact Index Per Article: 33.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a new theoretical framework, called Multiconfiguration Pair-Density Functional Theory (MC-PDFT), which combines multiconfigurational wave functions with a generalization of density functional theory (DFT). A multiconfigurational self-consistent-field (MCSCF) wave function with correct spin and space symmetry is used to compute the total electronic density, its gradient, the on-top pair density, and the kinetic and Coulomb contributions to the total electronic energy. We then use a functional of the total density, its gradient, and the on-top pair density to calculate the remaining part of the energy, which we call the on-top-density-functional energy in contrast to the exchange-correlation energy of Kohn-Sham DFT. Because the on-top pair density is an element of the two-particle density matrix, this goes beyond the Hohenberg-Kohn theorem that refers only to the one-particle density. To illustrate the theory, we obtain first approximations to the required new type of density functionals by translating conventional density functionals of the spin densities using a simple prescription, and we perform post-SCF density functional calculations using the total density, density gradient, and on-top pair density from the MCSCF calculations. Double counting of dynamic correlation or exchange does not occur because the MCSCF energy is not used. The theory is illustrated by applications to the bond energies and potential energy curves of H2, N2, F2, CaO, Cr2, and NiCl and the electronic excitation energies of Be, C, N, N(+), O, O(+), Sc(+), Mn, Co, Mo, Ru, N2, HCHO, C4H6, c-C5H6, and pyrazine. The method presented has a computational cost and scaling similar to MCSCF, but a quantitative accuracy, even with the present first approximations to the new types of density functionals, that is comparable to much more expensive multireference perturbation theory methods.
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Affiliation(s)
- Giovanni Li Manni
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Rebecca K Carlson
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Sijie Luo
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Dongxia Ma
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Jeppe Olsen
- Department of Chemistry, Aarhus University , Langelandsgade 140, DK-8000, Aarhus C, Denmark
| | - Donald G Truhlar
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
| | - Laura Gagliardi
- Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota , Minneapolis, Minnesota 55455, United States
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26
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Garza AJ, Bulik IW, Alencar AGS, Sun J, Perdew JP, Scuseria GE. Combinations of coupled cluster, density functionals, and the random phase approximation for describing static and dynamic correlation, and van der Waals interactions. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1123315] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
| | | | | | - Jianwei Sun
- Department of Physics, Temple University, Philadelphia, PA, USA
| | - John P. Perdew
- Department of Physics, Temple University, Philadelphia, PA, USA
- Department of Chemistry, Temple University, Philadelphia, PA, 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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27
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Senjean B, Hedegård ED, Alam MM, Knecht S, Fromager E. Combining linear interpolation with extrapolation methods in range-separated ensemble density functional theory. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1119902] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- Bruno Senjean
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
| | - Erik D. Hedegård
- Laboratory of Physical Chemistry, ETH Zürich, Zürich, Switzerland
| | - Md. Mehboob Alam
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
| | - Stefan Knecht
- Laboratory of Physical Chemistry, ETH Zürich, Zürich, Switzerland
| | - Emmanuel Fromager
- Laboratoire de Chimie Quantique, Institut de Chimie, CNRS/Université de Strasbourg, Strasbourg, France
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28
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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] [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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29
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Rebolini E, Toulouse J, Teale AM, Helgaker T, Savin A. Excited states from range-separated density-functional perturbation theory. Mol Phys 2015. [DOI: 10.1080/00268976.2015.1011248] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- Elisa Rebolini
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, Paris, France
- CNRS, UMR 7616, Laboratoire de Chimie Théorique, Paris, France
- Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, Oslo, Norway
| | - Julien Toulouse
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, Paris, France
- CNRS, UMR 7616, Laboratoire de Chimie Théorique, Paris, France
| | - Andrew M. Teale
- School of Chemistry, University of Nottingham, Nottingham, United Kingdom
| | - Trygve Helgaker
- Department of Chemistry, Centre for Theoretical and Computational Chemistry, University of Oslo, Oslo, Norway
| | - Andreas Savin
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, Paris, France
- CNRS, UMR 7616, Laboratoire de Chimie Théorique, Paris, France
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30
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Fromager E. On the exact formulation of multi-configuration density-functional theory: electron density versus orbitals occupation. Mol Phys 2015. [DOI: 10.1080/00268976.2014.993342] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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31
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Rebolini E, Toulouse J, Teale AM, Helgaker T, Savin A. Excitation energies along a range-separated adiabatic connection. J Chem Phys 2014; 141:044123. [PMID: 25084897 DOI: 10.1063/1.4890652] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
We present a study of the variation of total energies and excitation energies along a range-separated adiabatic connection. This connection links the non-interacting Kohn-Sham electronic system to the physical interacting system by progressively switching on the electron-electron interactions whilst simultaneously adjusting a one-electron effective potential so as to keep the ground-state density constant. The interactions are introduced in a range-dependent manner, first introducing predominantly long-range, and then all-range, interactions as the physical system is approached, as opposed to the conventional adiabatic connection where the interactions are introduced by globally scaling the standard Coulomb interaction. Reference data are reported for the He and Be atoms and the H2 molecule, obtained by calculating the short-range effective potential at the full configuration-interaction level using Lieb's Legendre-transform approach. As the strength of the electron-electron interactions increases, the excitation energies, calculated for the partially interacting systems along the adiabatic connection, offer increasingly accurate approximations to the exact excitation energies. Importantly, the excitation energies calculated at an intermediate point of the adiabatic connection are much better approximations to the exact excitation energies than are the corresponding Kohn-Sham excitation energies. This is particularly evident in situations involving strong static correlation effects and states with multiple excitation character, such as the dissociating H2 molecule. These results highlight the utility of long-range interacting reference systems as a starting point for the calculation of excitation energies and are of interest for developing and analyzing practical approximate range-separated density-functional methodologies.
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Affiliation(s)
- Elisa Rebolini
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
| | - Julien Toulouse
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
| | - Andrew M Teale
- School of Chemistry, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - Trygve Helgaker
- Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway
| | - Andreas Savin
- Sorbonne Universités, UPMC Univ Paris 06, UMR 7616, Laboratoire de Chimie Théorique, F-75005 Paris, France
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32
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Risthaus T, Steinmetz M, Grimme S. Implementation of nuclear gradients of range-separated hybrid density functionals and benchmarking on rotational constants for organic molecules. J Comput Chem 2014; 35:1509-16. [DOI: 10.1002/jcc.23649] [Citation(s) in RCA: 45] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2014] [Revised: 05/16/2014] [Accepted: 05/21/2014] [Indexed: 01/16/2023]
Affiliation(s)
- Tobias Risthaus
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Universität Bonn; Beringstr. 4 D-53115 Bonn Germany
- International NRW Graduate School of Chemistry; Wilhelm-Klemm-Str. 10 D-48149 Münster Germany
| | - Marc Steinmetz
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Universität Bonn; Beringstr. 4 D-53115 Bonn Germany
| | - Stefan Grimme
- Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie, Universität Bonn; Beringstr. 4 D-53115 Bonn Germany
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33
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Mori-Sánchez P, Cohen AJ. The derivative discontinuity of the exchange–correlation functional. Phys Chem Chem Phys 2014; 16:14378-87. [DOI: 10.1039/c4cp01170h] [Citation(s) in RCA: 57] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
Abstract
Manifestations of the derivative discontinuity of the energy in density functional theory are demonstrated in simple systems in chemistry and physics.
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Affiliation(s)
- Paula Mori-Sánchez
- Departamento de Química and Instituto de Física de la Materia Condensada (IFIMAC)
- Universidad Autónoma de Madrid
- Madrid, Spain
| | - Aron J. Cohen
- Department of Chemistry
- University of Cambridge
- Cambridge, UK
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