1
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Cartier NG, Giesbertz KJH. Exploiting the Hessian for a Better Convergence of the SCF-RDMFT Procedure. J Chem Theory Comput 2024; 20:3669-3682. [PMID: 38668734 PMCID: PMC11099978 DOI: 10.1021/acs.jctc.4c00118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/29/2024] [Revised: 04/03/2024] [Accepted: 04/04/2024] [Indexed: 05/15/2024]
Abstract
One-body reduced density matrix functional theory provides an alternative to density functional theory, which is able to treat static correlation while keeping a relatively low computation scaling. Its disadvantageous cost comes mainly from a slow convergence of the self-consistent energy optimization. To improve on that problem, we propose in this work the use of the Hessian of the energy, including the coupling term. We show that using the exact Hessian is very effective at reducing the number of iterations. However, since the exact Hessian is too expensive to use in practice, we propose an approximation based on an inexpensive exact part and BFGS updates.
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Affiliation(s)
- Nicolas G. Cartier
- Department of Chemistry & Pharmaceutical
Sciences and Amsterdam Institute of Molecular and Life Sciences (AIMMS),
Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Klaas J. H. Giesbertz
- Department of Chemistry & Pharmaceutical
Sciences and Amsterdam Institute of Molecular and Life Sciences (AIMMS),
Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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2
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Lew-Yee JFH, Bonfil-Rivera IA, Piris M, M. del Campo J. Excited States by Coupling Piris Natural Orbital Functionals with the Extended Random-Phase Approximation. J Chem Theory Comput 2024; 20:2140-2151. [PMID: 38353418 PMCID: PMC10938499 DOI: 10.1021/acs.jctc.3c01194] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2023] [Revised: 01/30/2024] [Accepted: 01/31/2024] [Indexed: 03/13/2024]
Abstract
In this work, we explore the use of Piris natural orbital functionals (PNOFs) to calculate excited-state energies by coupling their reconstructed second-order reduced density matrix with the extended random-phase approximation (ERPA). We have named the general method PNOF-ERPA, and specific approaches are referred to as PNOF-ERPA0, PNOF-ERPA1, and PNOF-ERPA2, according to the way the excitation operator is built. The implementation has been tested in the first excited states of H2, HeH+, LiH, Li2, and N2 showing good results compared to the configuration interaction (CI) method. As expected, an increase in accuracy is observed on going from ERPA0 to ERPA1 and ERPA2. We also studied the effect of electron correlation included by PNOF5, PNOF7, and the recently proposed global NOF (GNOF) on the predicted excited states. PNOF5 appears to be good and may even provide better results in very small systems, but including more electron correlation becomes important as the system size increases, where GNOF achieves better results. Overall, the extension of PNOF to excited states has been successful, making it a promising method for further applications.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento
de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City C.P.
04510, Mexico
- Donostia
International Physics Center (DIPC), 20018 Donostia, Spain
| | - Iván Alejandro Bonfil-Rivera
- Departamento
de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City C.P.
04510, Mexico
| | - Mario Piris
- Donostia
International Physics Center (DIPC), 20018 Donostia, Spain
- Kimika
Fakultatea, Euskal Herriko Unibertsitatea
(UPV/EHU), 20018 Donostia, Spain
- IKERBASQUE,
Basque Foundation for Science, 48013 Bilbao, Spain
| | - Jorge M. del Campo
- Departamento
de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México City C.P.
04510, Mexico
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3
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Rivero Santamaría A, Piris M. Time evolution of natural orbitals in ab initio molecular dynamics. J Chem Phys 2024; 160:071102. [PMID: 38364005 DOI: 10.1063/5.0188491] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Accepted: 01/28/2024] [Indexed: 02/18/2024] Open
Abstract
This work combines for the first time ab initio molecular dynamics (AIMD) within the Born-Oppenheimer approximation with a global natural orbital functional (GNOF), an approximate functional of the one-particle reduced density matrix. The most prominent feature of GNOF-AIMD is its ability to display the real-time evolution of natural orbitals, providing detailed information on the time-dependent electronic structure of complex systems and processes, including reactive collisions. The quartet ground-state reaction N(4S) + H2(1Σ) → NH(3Σ) + H(2S) is taken as a validation test. Collision energy influences on integral cross sections for different initial rovibrational states of H2 and rotational-state distributions of the NH product are discussed, showing a good agreement with previous high-quality theoretical results.
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Affiliation(s)
| | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain; Euskal Herriko Unibertsitatea (UPV/EHU), PK 1072, 20080 Donostia, Euskadi, Spain; and Basque Foundation for Science (IKERBASQUE), 48009 Bilbao, Euskadi, Spain
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4
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Cioslowski J, Strasburger K. Constraints upon Functionals of the 1-Matrix, Universal Properties of Natural Orbitals, and the Fallacy of the Collins "Conjecture". J Phys Chem Lett 2024; 15:1328-1337. [PMID: 38285733 PMCID: PMC10860149 DOI: 10.1021/acs.jpclett.3c03118] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Revised: 01/02/2024] [Accepted: 01/04/2024] [Indexed: 01/31/2024]
Abstract
Reliability of quantum-chemical calculations based upon the density functional theory and its 1-matrix counterpart hinges upon minimizing the extent of empirical parameterization in the approximate energy expressions of these formalisms while imposing as many rigorous constraints upon them as possible. The recently uncovered universal properties of the natural orbitals facilitate the construction of such constraints for the 1-matrix functionals. The benefits of their employment in the validation of these functionals are vividly demonstrated by a critical review of the three incarnations of the so-called Collins conjecture. Although the incorporation of rigorous definitions of the correlation energy and entropy, and the identification of individual potential energy hypersurfaces as probable domains of its applicability turn the originally published unsubstantiated claim into a proper conjecture, the resulting formalism is found to be merely a conduit for incorporation of static correlation effects in electronic structure calculations that is unlikely to allow attaining chemical accuracy.
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Affiliation(s)
- Jerzy Cioslowski
- Institute
of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
- Max-Planck-Institut
für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany
| | - Krzysztof Strasburger
- Department
of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego
27, 50-370 Wrocław, Poland
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5
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Xu X, Soriano-Agueda L, López X, Ramos-Cordoba E, Matito E. All-Purpose Measure of Electron Correlation for Multireference Diagnostics. J Chem Theory Comput 2024; 20:721-727. [PMID: 38157841 PMCID: PMC10809408 DOI: 10.1021/acs.jctc.3c01073] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Revised: 11/24/2023] [Accepted: 11/27/2023] [Indexed: 01/03/2024]
Abstract
We present an analytical relationship between two natural orbital occupancy-based indices, I N D ¯ and INDmax, and two established electron correlation metrics: the leading term of a configuration interaction expansion, c0, and the D2 diagnostic. Numerical validation revealed that I N D ¯ and INDmax can effectively substitute for c0 and D2, respectively. These indices offer three distinct advantages: (i) they are universally applicable across all electronic structure methods, (ii) their interpretation is more intuitive, and (iii) they can be readily incorporated into the development of hybrid electronic structure methods. Additionally, we draw a distinction between correlation measures and correlation diagnostics, establishing MP2 and CCSD numerical thresholds for INDmax, which are to be used as a multireference diagnostic. Our findings further demonstrate that establishing thresholds for other electronic structure methods can be easily accomplished using small data sets.
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Affiliation(s)
- Xiang Xu
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero
eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Luis Soriano-Agueda
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
| | - Xabier López
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero
eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Eloy Ramos-Cordoba
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Polimero
eta Material Aurreratuak: Fisika, Kimika eta Teknologia, Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, P.K. 1072, 20080 Donostia, Euskadi, Spain
- Ikerbasque
Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
| | - Eduard Matito
- Donostia
International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Ikerbasque
Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
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6
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Ai W, Su NQ, Fang WH. Short-range screened density matrix functional for proper descriptions of thermochemistry, thermochemical kinetics, nonbonded interactions, and singlet diradicals. J Chem Phys 2023; 159:174110. [PMID: 37933778 DOI: 10.1063/5.0169234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2023] [Accepted: 10/09/2023] [Indexed: 11/08/2023] Open
Abstract
Common one-electron reduced density matrix (1-RDM) functionals that depend on Coulomb and exchange-only integrals tend to underestimate dynamic correlation, preventing reduced density matrix functional theory (RDMFT) from achieving comparable accuracy to density functional theory in main-group thermochemistry and thermochemical kinetics. The recently developed ωP22 functional introduces a semi-local density functional to screen the erroneous short-range portion of 1-RDM functionals without double-counting correlation, potentially providing a better treatment of dynamic correlation around equilibrium geometries. Herein, we systematically evaluate the performance of this functional model, which consists of two parameters, on main-group thermochemistry, thermochemical kinetics, nonbonded interactions, and more. Tests on atomization energies, vibrational frequencies, and reaction barriers reveal that the ωP22 functional model can reliably predict properties at equilibrium and slightly away from equilibrium geometries. In particular, it outperforms commonly used density functionals in the prediction of reaction barriers, nonbonded interactions, and singlet diradicals, thus enhancing the predictive power of RDMFT for routine calculations of thermochemistry and thermochemical kinetics around equilibrium geometries. Further development is needed in the future to refine short- and long-range approximations in the functional model in order to achieve an excellent description of properties both near and far from equilibrium geometries.
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Affiliation(s)
- Wenna Ai
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Frontiers Science Center for New Organic Matter, Nankai University, Tianjin 300071, China
| | - Neil Qiang Su
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Frontiers Science Center for New Organic Matter, Nankai University, Tianjin 300071, China
| | - Wei-Hai Fang
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Frontiers Science Center for New Organic Matter, Nankai University, Tianjin 300071, China
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7
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Cioslowski J, Strasburger K. Symmetry Equiincidence of Natural Orbitals. J Phys Chem Lett 2023; 14:9296-9303. [PMID: 37815811 DOI: 10.1021/acs.jpclett.3c01738] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/11/2023]
Abstract
The symmetry equiincidence principle quantifies the apportionment of the natural orbitals (NOs), ordered according to their nonascending occupation numbers, among the irreducible representations (irreps) of the point group pertaining to the underlying on-top two-electron density. This principle, which is rigorously proven for the resolvable Cs, C2v, C3v, C4v, C6v, D2h, D3h, D4h, D6h, and Oh point groups, states that the symmetry incidences, i.e., the asymptotic probabilities with which the NOs belonging to different irreps occur, are proportional to the squares of irreps' dimensions. Since its proof hinges upon a sufficient number of planes of symmetry among the elements of a given point group, it yields only linear combinations of the symmetry incidences for the quasiresolvable groups with too few such planes and fails for the unresolvable C1, Ci, Cn, Dn, S2n, T, O, and I groups whose nontrivial elements comprise only symmetry axes and/or the center of inversion.
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
| | - Krzysztof Strasburger
- Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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8
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Acke G, Van Hende D, De Vriendt X, Bultinck P. Extending Conceptual Density Functional Theory toward First-Order Reduced Density Matrices: An Open Subsystems Viewpoint on the Fukui Matrix. J Chem Theory Comput 2023; 19:5418-5426. [PMID: 37531218 DOI: 10.1021/acs.jctc.3c00080] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/04/2023]
Abstract
As a matrix extension of the Fukui function, a reactivity descriptor grounded within Conceptual Density Functional Theory, the Fukui matrix extends Frontier Molecular Orbital Theory to correlated regimes with its eigendecomposition in Fukui occupations and Fukui naturals. Despite successful applications, the questions remain as to whether replacing a quantity derived from a purely density-based framework by its matrix extension is theoretically well-founded and what chemical information is contained in the corresponding eigendecomposition. In this study, we show that the matrix extension of the Fukui function is only well-defined if one also generalizes the external potential to become nonlocal, leading to the introduction of Conceptual First-Order Reduced Density Matrix Functional Theory. By interpreting the Anderson impurity model from an interacting open subsystem perspective, we show how Fukui occupations and Fukui naturals reflect the influence of an increasing (static) correlation and which characteristic patterns we should expect within a molecular context. This study represents a step in generalizing Conceptual Density Functional Theory beyond its density-based perspective.
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Affiliation(s)
- Guillaume Acke
- Department of Chemistry - Ghent Quantum Chemistry Group, Ghent University, Krijgslaan 281 (S3), Ghent B-9000, Belgium
| | - Daria Van Hende
- Department of Chemistry - Ghent Quantum Chemistry Group, Ghent University, Krijgslaan 281 (S3), Ghent B-9000, Belgium
| | - Xeno De Vriendt
- Department of Chemistry - Ghent Quantum Chemistry Group, Ghent University, Krijgslaan 281 (S3), Ghent B-9000, Belgium
| | - Patrick Bultinck
- Department of Chemistry - Ghent Quantum Chemistry Group, Ghent University, Krijgslaan 281 (S3), Ghent B-9000, Belgium
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9
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Cioslowski J, Englert BG, Trappe MI, Hue JH. Contactium: A strongly correlated model system. J Chem Phys 2023; 158:2890212. [PMID: 37171198 DOI: 10.1063/5.0150523] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2023] [Accepted: 04/21/2023] [Indexed: 05/13/2023] Open
Abstract
At the limit of an infinite confinement strength ω, the ground state of a system that comprises two fermions or bosons in harmonic confinement interacting through the Fermi-Huang pseudopotential remains strongly correlated. A detailed analysis of the one-particle description of this "contactium" reveals several peculiarities that are not encountered in conventional model systems (such as the two-electron harmonium atom, ballium, and spherium) involving Coulombic interparticle interactions. First of all, none of the natural orbitals (NOs) {ψn(ω;r)} of the contactium is unoccupied, which implies nonzero collective occupancies for all the angular momenta. Second, the NOs and their non-ascendingly ordered occupation numbers {νn} turn out to be related to the eigenfunctions and eigenvalues of a zero-energy Schrödinger equation with an attractive Gaussian potential. This observation enables the derivation of their properties, such as the n-4/3 asymptotic decay of νn at the n→∞ limit (which differs from that of n-8/3 in the Coulombic systems), the independence of the confinement energy vn=⟨ψn(ω;r)|12ω2r2|ψn(ω;r)⟩ of n, and the n-2/3 asymptotic decay of the respective contribution νntn to the kinetic energy. Upon suitable scaling, the weakly occupied NOs of the contactium turn out to be virtually identical to those of the two-electron harmonium atom at the ω → ∞ limit, despite the entirely different interparticle interactions in these systems.
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
| | - Berthold-Georg Englert
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
- MajuLab, CNRS-UCA-SU-NUS-NTU International, Joint Research Unit, Singapore
| | - Martin-Isbjörn Trappe
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
| | - Jun Hao Hue
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
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10
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Cioslowski J, Schilling C, Schilling R. 1-Matrix functional for long-range interaction energy of two hydrogen atoms. J Chem Phys 2023; 158:084106. [PMID: 36859076 DOI: 10.1063/5.0139897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
The leading terms in the large-R asymptotics of the functional of the one-electron reduced density matrix for the ground-state energy of the H2 molecule with the internuclear separation R are derived thanks to the solution of the phase dilemma at the R → ∞ limit. At this limit, the respective natural orbitals (NOs) are given by symmetric and antisymmetric combinations of "half-space" orbitals with the corresponding natural amplitudes having the same amplitudes but opposite signs. Minimization of the resulting explicit functional yields the large-R asymptotics for the occupation numbers of the weakly occupied NOs and the C6 dispersion coefficient. The highly accurate approximates for the radial components of the p-type "half-space" orbitals and the corresponding occupation numbers (that decay like R-6), which are available for the first time thanks to the development of the present formalism, have some unexpected properties.
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
| | - Christian Schilling
- Department of Physics, Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, 80333 München, Germany
| | - Rolf Schilling
- Institute of Physics, Johannes Gutenberg University, Staudinger Weg 9, 55099 Mainz, Germany
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11
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Huan Lew-Yee JF, Piris M, Del Campo JM. Outstanding improvement in removing the delocalization error by global natural orbital functional. J Chem Phys 2023; 158:084110. [PMID: 36859086 DOI: 10.1063/5.0137378] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/11/2023] Open
Abstract
This work assesses the performance of the recently proposed global natural orbital functional (GNOF) against the charge delocalization error. GNOF provides a good balance between static and dynamic electronic correlations leading to accurate total energies while preserving spin, even for systems with a highly multi-configurational character. Several analyses were applied to the functional, namely, (i) how the charge is distributed in super-systems of two fragments, (ii) the stability of ionization potentials while increasing the system size, and (iii) potential energy curves of a neutral and charged diatomic system. GNOF was found to practically eliminate the charge delocalization error in many of the studied systems or greatly improve the results obtained previously with PNOF7.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Mexico City C.P. 04510, Mexico
| | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain; Euskal Herriko Unibertsitatea (UPV/EHU), PK 1072, 20080 Donostia, Euskadi, Spain; and Basque Foundation for Science (IKERBASQUE), 48009 Bilbao, Euskadi, Spain
| | - Jorge M Del Campo
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Mexico City C.P. 04510, Mexico
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12
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Lew-Yee JFH, Del Campo JM, Piris M. Electron Correlation in the Iron(II) Porphyrin by Natural Orbital Functional Approximations. J Chem Theory Comput 2023; 19:211-220. [PMID: 36579972 PMCID: PMC9996833 DOI: 10.1021/acs.jctc.2c01093] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
The relative stability of the singlet, triplet, and quintet spin states of iron(II) porphyrin (FeP) represents a challenging problem for electronic structure methods. While it is currently accepted that the ground state is a triplet, multiconfigurational wave function-based methods predict a quintet, and density functional approximations vary between triplet and quintet states, leading to a prediction that highly depends on the features of the method employed. The recently proposed Global Natural Orbital Functional (GNOF) aims to provide a balanced treatment between static and dynamic correlation, and together with the previous Piris Natural Orbital Functionals (PNOFs), allowed us to explore the importance of each type of correlation in the stability order of the states of FeP with a method that conserves the spin of the system. It is noteworthy that GNOF correlates all electrons in all available orbitals for a given basis set; in the case of the FeP with a double-ζ basis set as used in this work, this means that GNOF can properly correlate 186 electrons in 465 orbitals, significantly increasing the sizes of systems amenable to multiconfigurational treatment. Results show that PNOF5, PNOF7s, and PNOF7 predict the quintet to have a lower energy than the triplet state; however, the addition of dynamic correlation via second-order Møller-Plesset corrections (NOF-MP2) turns the triplet state to be lower than the quintet state, a prediction also reproduced by GNOF that incorporates much more dynamic correlation than its predecessors.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México CityC.P. 04510, México
| | - Jorge M Del Campo
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, México CityC.P. 04510, México
| | - Mario Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080Donostia, Euskadi, Spain.,Donostia International Physics Center (DIPC), 20018Donostia, Euskadi, Spain.,IKERBASQUE, Basque Foundation for Science, 48013Bilbao, Euskadi, Spain
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13
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Mercero JM, Grande-Aztatzi R, Ugalde JM, Piris M. Natural orbital functional theory studies of all-metal aromaticity: The Al 3−anion. ADVANCES IN QUANTUM CHEMISTRY 2023. [DOI: 10.1016/bs.aiq.2023.02.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/28/2023]
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14
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Via-Nadal M, Rodríguez Mayorga MA, Ramos Cordoba E, Matito E. Natural Range Separation of the Coulomb Hole. J Chem Phys 2022; 156:184106. [DOI: 10.1063/5.0085284] [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
A natural range separation of the Coulomb hole into two components, one of them being predominant at long interelectronic separations (hcI ) and the other at short distances (hcII ), is exhaustively analyzed throughout various examples that put forward the most relevant features of this approach and how they can be used to develop efficient ways to capture electron correlation. We show that hcI, which only depends on the first-order reduced density matrix, can be used to identify molecules with a predominant nondynamic correlation regime and differentiate between two types of nondynamic correlation, types A and B. Through the asymptotic properties of the hole components, we explain how hcI can retrieve the long-range part of electron correlation. We perform an exhaustive analysis of the hydrogen molecule in a minimal basis set, dissecting the hole contributions into spin components. We also analyze the simplest molecule presenting a dispersion interaction and how hcII helps identify it. The study of several atoms in different spin states reveals that the Coulomb hole components distinguish correlation regimes that are not apparent from the entire hole. The results of this work hold out the promise to aid in developing new electronic structure methods that efficiently capture electron correlation.
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Affiliation(s)
| | | | - Eloy Ramos Cordoba
- Theoretical Chemistry Group, Donostia International Physics Center, Spain
| | - Eduard Matito
- Donostia International Physics Center, Donostia International Physics Center, Spain
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15
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Ai W, Fang WH, Su NQ. Functional-Based Description of Electronic Dynamic and Strong Correlation: Old Issues and New Insights. J Phys Chem Lett 2022; 13:1744-1751. [PMID: 35157451 DOI: 10.1021/acs.jpclett.2c00084] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Approximate functionals in Kohn-Sham density functional theory (KS-DFT) and reduced density matrix functional theory (RDMFT) have advantages in dealing with dynamic correlation and strong correlation, respectively; their combination can benefit from complementarity while suffering from the problem of correlation double-counting. Herein, a short-range corrected reduced density matrix (1-RDM) functional is developed to take advantage of the functionals in KS-DFT and RDMFT without double-counting. The resulting functional, denoted as ωP22, outperforms other 1-RDM functionals for the tests of thermochemistry, nonbonded interactions, and bond dissociation energy. In particular, ωP22 shows much less systematic error for systems involving fractional spins, and it can properly predict the energies at both equilibrium and dissociated distances for different single and multiple bonds, which cannot be achieved by commonly used KS-DFT and RDMFT functionals. Therefore, ωP22 is demonstrated effective in balance handling dynamic and strong correlation, and the advances in this work would create new possibilities for the development and application of approximate functionals.
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Affiliation(s)
- Wenna Ai
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education) and Renewable Energy Conversion and Storage Center (RECAST), Nankai University, Tianjin 300071, China
| | - Wei-Hai Fang
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education) and Renewable Energy Conversion and Storage Center (RECAST), Nankai University, Tianjin 300071, China
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
| | - Neil Qiang Su
- Department of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education) and Renewable Energy Conversion and Storage Center (RECAST), Nankai University, Tianjin 300071, China
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16
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Bousiadi S, Gidopoulos N, Lathiotakis N. Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT. Phys Chem Chem Phys 2022; 24:19279-19286. [DOI: 10.1039/d2cp01866g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A density inversion method is presented, to obtain the constrained, optimal, local potential that has a prescribed asymptotic behaviour and reproduces optimally any given ground-state electronic density. This work builds...
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17
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Cioslowski J, Strasburger K. From Fredholm to Schrödinger via Eikonal: A New Formalism for Revealing Unknown Properties of Natural Orbitals. J Chem Theory Comput 2021; 17:6918-6933. [PMID: 34672624 DOI: 10.1021/acs.jctc.1c00709] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Previously unknown properties of the natural orbitals (NOs) pertaining to singlet states (with natural parity, if present) of electronic systems with even numbers of electrons are revealed upon the demonstration that, at the limit of n → ∞, the NO ψn(r⃗) with the nth largest occupation number νn approaches the solution ψ̃n(r⃗) of the zero-energy Schrödinger equation that reads T̂([ρ2(r⃗, r⃗)]-1/8 ψ̃n(r⃗)) - (π2/ṽn)1/4 [ρ2(r⃗, r⃗)]1/4 ([ρ2(r⃗, r⃗)]-1/8 ψ̃n(r⃗)) = 0 (where T̂ is the kinetic energy operator), whereas νn approaches ν̃n. The resulting formalism, in which the "on-top" two-electron density ρ2(r⃗, r⃗) solely controls the asymptotic behavior of both ψn(r⃗) and νn at the limit of the latter becoming infinitesimally small, produces surprisingly accurate values of both quantities even for small n. It opens entirely new vistas in the elucidation of their properties, including single-line derivations of the power laws governing the asymptotic decays of νn and ⟨ψn(r⃗)|T̂|ψn(r⃗)⟩ with n, some of which have been obtained previously with tedious algebra and arcane mathematical arguments. These laws imply a very unfavorable asymptotics of the truncation error in the total energy computed with finite numbers of natural orbitals that severely affects the accuracy of certain quantum-chemical approaches such as the density matrix functional theory. The new formalism is also shown to provide a complete and accurate elucidation of both the observed order (according to decreasing magnitudes of the respective occupation numbers) and the shapes of the natural orbitals pertaining to the 1Σg+ ground state of the H2 molecule. In light of these examples of its versatility, the above Schrödinger equation is expected to have its predictive and interpretive powers harnessed in many facets of the electronic structure theory.
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
| | - Krzysztof Strasburger
- Department of Physical and Quantum Chemistry, Faculty of Chemistry, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27, 50-370 Wrocław, Poland
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18
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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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19
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Lew-Yee JFH, Piris M, M Del Campo J. Resolution of the identity approximation applied to PNOF correlation calculations. J Chem Phys 2021; 154:064102. [PMID: 33588540 DOI: 10.1063/5.0036404] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
In this work, the required algebra to employ the resolution of the identity approximation within the Piris Natural Orbital Functional (PNOF) is developed, leading to an implementation named DoNOF-RI. The arithmetic scaling is reduced from fifth-order to fourth-order, and the memory scaling is reduced from fourth-order to third-order, allowing significant computational time savings. After the DoNOF-RI calculation has fully converged, a restart with four-center electron repulsion integrals can be performed to remove the effect of the auxiliary basis set incompleteness, quickly converging to the exact result. The proposed approach has been tested on cycloalkanes and other molecules of general interest to study the numerical results, as well as the speed-ups achieved by PNOF7-RI when compared with PNOF7.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Mexico City C.P. 04510, Mexico
| | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain; Euskal Herriko Unibertsitatea (UPV/EHU), PK 1072, 20080 Donostia, Euskadi, Spain; and Basque Foundation for Science (IKERBASQUE), 48009 Bilbao, Euskadi, Spain
| | - Jorge M Del Campo
- Departamento de Física y Química Teórica, Facultad de Química, Universidad Nacional Autónoma de México, Mexico City C.P. 04510, Mexico
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20
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Quintero-Monsebaiz R, Perea-Ramírez LI, Piris M, Vela A. Spectroscopic properties of open shell diatomic molecules using Piris natural orbital functionals. Phys Chem Chem Phys 2021; 23:2953-2963. [PMID: 33480904 DOI: 10.1039/d0cp05430e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Spectroscopic properties such as equilibrium distances, vibrational constants, rotational constants, dissociation energies, and excitation energies are calculated for nine heteronuclear diatomic molecules (PH, NF, NH, NO, CS, AlF, ClF, BeO and CF) using an interactive pair model (PNOF7s), that has been generalized for spin multiplet states, and its second order perturbation variant, NOF-MP2, which was also generalized for multiplets. The results obtained are compared with Complete Active Space (CASSCF) and Complete Active Space Perturbation Theory (CASPT2). It is shown that the potential energy curves provided by the PNOF functional for open shell diatomic molecules are in acceptable agreement with those from CASSCF and CASPT2. The spectroscopic constants depending at most on the second derivative of the potential energy are in good agreement with experiment, while those requiring the evaluation of the third and fourth derivatives show larger deviations from experiment and from those predicted by CASPT2. Thus, it is shown that the PNOF functional extension to multiplets is an alternative approach in predicting spectroscopic constants of molecules where static correlation plays an important role, like the open shell heteronuclear diatomic molecules studied in this work.
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Affiliation(s)
- Raúl Quintero-Monsebaiz
- Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Av Instituto Politécnico Nacional 2508, San Pedro Zacatenco, Gustavo A. Madero, 07360 Ciudad de México, Mexico.
| | - Luis Ignacio Perea-Ramírez
- Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Av Instituto Politécnico Nacional 2508, San Pedro Zacatenco, Gustavo A. Madero, 07360 Ciudad de México, Mexico.
| | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain and Euskal Herriko Unibertsitatea (UPV/EHU), PK 1072, 20080 Donostia, Euskadi, Spain and Basque Foundation for Science (IKERBASQUE), Plaza Euskadi 5, 48009 Bilbao, Euskadi, Spain.
| | - Alberto Vela
- Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Av Instituto Politécnico Nacional 2508, San Pedro Zacatenco, Gustavo A. Madero, 07360 Ciudad de México, Mexico.
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21
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Cioslowski J. Off-diagonal derivative discontinuities in the reduced density matrices of electronic systems. J Chem Phys 2020; 153:154108. [PMID: 33092376 DOI: 10.1063/5.0023955] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Abstract
An explicit expression relating the magnitude of the fifth-order off-diagonal cusp in the real part of the one-electron reduced density matrix to the "on-top" two-electron density is derived in a rigorous manner from the behavior of the underlying electronic wavefunction at the electron-electron coalescence. The implications of the presence of this cusp upon electronic structure calculations of quantum chemistry and solid-state physics, including the limits imposed upon their accuracy, are elucidated. In particular, the power-law decay of the occupation numbers of the natural orbitals is demonstrated for 1S states of systems composed of arbitrary even numbers of electrons. The practical importance of analogous off-diagonal cusps in many-electron reduced density matrices is briefly discussed.
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
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22
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Mitxelena I, Piris M. An efficient method for strongly correlated electrons in one dimension. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:17LT01. [PMID: 31952058 DOI: 10.1088/1361-648x/ab6d11] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
The one-particle reduced density matrix functional theory in its natural orbital functional (NOF) version is used to study strongly correlated electrons. We show the ability of the Piris NOF 7 (PNOF7) to describe non-dynamic correlation effects in one-dimensional (1D) systems. An extensive study of 1D systems that includes Hydrogen (H) chains and the 1D Hubbard model with periodic boundary conditions is provided. Different filling situations and large sizes with up to 122 electrons are considered. Compared to quasi-exact results, PNOF7 is accurate in different correlation regimes for the 1D Hubbard model even away from the half-filling, and maintains its accuracy when the system size increases. The symmetric and asymmetric dissociations of the linear H chain composed of 50 atoms are described to remark the importance of long-range interactions in presence of strong correlation effects. Our results compare remarkably well with those obtained at the density-matrix renormalization group level of theory.
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Affiliation(s)
- Ion Mitxelena
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
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23
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Maulén B, Echeverri A, Gómez T, Fuentealba P, Cárdenas C. Electron Localization Function in Excited States: The Case of the Ultrafast Proton Transfer of the Salicylidene Methylamine. J Chem Theory Comput 2019; 15:5532-5542. [DOI: 10.1021/acs.jctc.9b00691] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Boris Maulén
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
| | - Andrea Echeverri
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
| | - Tatiana Gómez
- Instituto de Ciencias Químicas Aplicadas, Theoretical and Computational Chemistry Center, Facultad de Ingeniería, Universidad Autónoma de Chile, Av. El Llano Subercaseaux 2801, San Miguel, Santiago, Chile
| | - Patricio Fuentealba
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
- Centro para el Desarrollo de la Nanociencia y la Nanotecnología (CEDENNA), Avda. Ecuador 3493, Santiago 9170124, Chile
| | - Carlos Cárdenas
- Departamento de Física, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile
- Centro para el Desarrollo de la Nanociencia y la Nanotecnología (CEDENNA), Avda. Ecuador 3493, Santiago 9170124, Chile
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24
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Benavides-Riveros CL, Marques MAL. On the time evolution of fermionic occupation numbers. J Chem Phys 2019; 151:044112. [DOI: 10.1063/1.5109009] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Miguel A. L. Marques
- Institut für Physik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle (Saale), Germany
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25
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Lopez X, Piris M. Performance of the NOF-MP2 method in hydrogen abstraction reactions. Theor Chem Acc 2019. [DOI: 10.1007/s00214-019-2475-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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26
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Baerends EJ. On derivatives of the energy with respect to total electron number and orbital occupation numbers. A critique of Janak's theorem. Mol Phys 2019. [DOI: 10.1080/00268976.2019.1612955] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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27
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Cioslowski J, Pra Tnicki F. Natural amplitudes of the ground state of the helium atom: Benchmark calculations and their relevance to the issue of unoccupied natural orbitals in the H 2 molecule. J Chem Phys 2019; 150:074111. [PMID: 30795659 DOI: 10.1063/1.5065791] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Employment of exact numerical quadratures in the evaluation of matrix elements involving highly accurate wavefunctions of helium (and its isoelectronic congeners) generated with the help of the regularized Krylov sequences of Nakatsuji results in an efficient algorithm for the calculation of natural orbitals and the corresponding natural amplitudes {λnl}. The results of such calculations are presented for the total of 600 natural orbitals pertaining to the ground state of the helium atom. The benchmark-quality values of {λnl} computed for 1 ≤ n ≤ 100 and 0 ≤ l ≤ 5 reveal gross inaccuracies in the previously published data. In particular, the dependence of λnl on n is found to follow very closely a simple power-scaling law λnl≈-Al (n+Bl)-4 with Al that, contrary to previous claims, varies only weakly with l. Even more importantly, the numerical trends observed in the present calculations strongly suggest that in the case of the ground state of the helium atom, the only positive-valued natural amplitude is that pertaining to the strongly occupied orbital, i.e., λ10. The relevance of this finding to the existence of unoccupied natural orbitals pertaining to the ground state wavefunction of the H2 molecule is discussed.
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Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
| | - Filip Pra Tnicki
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
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28
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Rodríguez-Mayorga M, Ramos-Cordoba E, Lopez X, Solà M, Ugalde JM, Matito E. The Coulomb Hole of the Ne Atom. ChemistryOpen 2019; 8:411-417. [PMID: 30976484 PMCID: PMC6442706 DOI: 10.1002/open.201800235] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/30/2018] [Revised: 12/20/2018] [Indexed: 11/10/2022] Open
Abstract
We analyze the Coulomb hole of Ne from highly-accurate CISD wave functions obtained from optimized even-tempered basis sets. Using a two-fold extrapolation procedure we obtain highly accurate results that recover 97 % of the correlation energy. We confirm the existence of a shoulder in the short-range region of the Coulomb hole of the Ne atom, which is due to an internal reorganization of the K-shell caused by electron correlation of the core electrons. The feature is very sensitive to the quality of the basis set in the core region and it is not exclusive to Ne, being also present in most of second-row atoms, thus confirming that it is due to K-shell correlation effects.
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Affiliation(s)
- Mauricio Rodríguez-Mayorga
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com.,Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química University of Girona C/ Maria Aurèlia Capmany, 69 17003 Girona Catalonia Spain
| | - Eloy Ramos-Cordoba
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com
| | - Xabier Lopez
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com
| | - Miquel Solà
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química University of Girona C/ Maria Aurèlia Capmany, 69 17003 Girona Catalonia Spain
| | - Jesus M Ugalde
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com
| | - Eduard Matito
- Kimika Fakultatea Euskal Herriko Unibertsitatea (UPV/EHU) Donostia International Physics Center (DIPC) P.K. 1072 20080 Donostia, Euskadi Spain E-mail: eloy.raco_at_gmail.com.,IKERBASQUE, Basque Foundation for Science 48011 Bilbao, Euskadi Spain
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29
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Romero AH. Influence of heteroelement on dipole and quadrupole moments of a series of three-membered rings containing a second, third, fourth, or fifth-row atom: a theoretical investigation. Struct Chem 2019. [DOI: 10.1007/s11224-018-1190-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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30
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Mitxelena I, Piris M, Ugalde JM. Advances in approximate natural orbital functional theory. ADVANCES IN QUANTUM CHEMISTRY 2019. [DOI: 10.1016/bs.aiq.2019.04.001] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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31
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Schulz CE, Dutta AK, Izsák R, Pantazis DA. Systematic High-Accuracy Prediction of Electron Affinities for Biological Quinones. J Comput Chem 2018; 39:2439-2451. [PMID: 30281169 DOI: 10.1002/jcc.25570] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2018] [Revised: 08/06/2018] [Accepted: 08/07/2018] [Indexed: 11/07/2022]
Abstract
Quinones play vital roles as electron carriers in fundamental biological processes; therefore, the ability to accurately predict their electron affinities is crucial for understanding their properties and function. The increasing availability of cost-effective implementations of correlated wave function methods for both closed-shell and open-shell systems offers an alternative to density functional theory approaches that have traditionally dominated the field despite their shortcomings. Here, we define a benchmark set of quinones with experimentally available electron affinities and evaluate a range of electronic structure methods, setting a target accuracy of 0.1 eV. Among wave function methods, we test various implementations of coupled cluster (CC) theory, including local pair natural orbital (LPNO) approaches to canonical and parameterized CCSD, the domain-based DLPNO approximation, and the equations-of-motion approach for electron affinities, EA-EOM-CCSD. In addition, several variants of canonical, spin-component-scaled, orbital-optimized, and explicitly correlated (F12) Møller-Plesset perturbation theory are benchmarked. Achieving systematically the target level of accuracy is challenging and a composite scheme that combines canonical CCSD(T) with large basis set LPNO-based extrapolation of correlation energy proves to be the most accurate approach. Methods that offer comparable performance are the parameterized LPNO-pCCSD, the DLPNO-CCSD(T0 ), and the orbital optimized OO-SCS-MP2. Among DFT methods, viable practical alternatives are only the M06 and the double hybrids, but the latter should be employed with caution because of significant basis set sensitivity. A highly accurate yet cost-effective DLPNO-based coupled cluster approach is used to investigate the methoxy conformation effect on the electron affinities of ubiquinones found in photosynthetic bacterial reaction centers. © 2018 Wiley Periodicals, Inc.
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Affiliation(s)
- Christine E Schulz
- Fakultät für Chemie und Biochemie, Ruhr-Universität Bochum, 44780, Bochum, Germany
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, 45470, Mülheim an der Ruhr, Germany
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470, Mülheim an der Ruhr, Germany
| | - Achintya Kumar Dutta
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, 45470, Mülheim an der Ruhr, Germany
- Department of Chemistry, Indian Institute of Technology Bombay, Mumbai 400076, India
| | - Róbert Izsák
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, 45470, Mülheim an der Ruhr, Germany
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470, Mülheim an der Ruhr, Germany
| | - Dimitrios A Pantazis
- Max-Planck-Institut für Chemische Energiekonversion, Stiftstr. 34-36, 45470, Mülheim an der Ruhr, Germany
- Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470, Mülheim an der Ruhr, Germany
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32
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Baerends EJ. Density functional approximations for orbital energies and total energies of molecules and solids. J Chem Phys 2018; 149:054105. [PMID: 30089375 DOI: 10.1063/1.5026951] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The relation of Kohn-Sham (KS) orbital energies to ionization energies and electron affinities is different in molecules and solids. In molecules, the local density approximation (LDA) and generalized gradient approximations (GGA) approximate the exact ionization energy (I) and affinity (A) rather well with self-consistently calculated (total energy based) ILDFA and ALDFA, respectively. The highest occupied molecular orbital (HOMO) energy and lowest unoccupied molecular orbital (LUMO) energy, however, differ significantly (by typically 4-6 eV) from these quantities, ϵHLDFA(mol)>-I(mol)≈-ILDFA(mol), ϵLLDFA(mol)<-A(mol)≈-ALDFA(mol). In solids, these relations are very different, due to two effects. The (almost) infinite extent of a solid makes the difference of orbital energies and (L)DFA calculated ionization energy and affinity disappear: in the solid state limit, ϵH(L)DFA(solid)=-I(L)DFA(solid) and ϵL(L)DFA(solid)=-A(L)DFA(solid). Slater's relation ∂E/∂ni = ϵi for local density functional approximations (LDFAs) [and Hartree-Fock (HF) and hybrids] is useful to prove these relations. The equality of LDFA orbital energies and LDFA calculated -ILDFA and -ALDFA in solids does not mean that they are good approximations to the exact quantities. The LDFA total energies of the ions with a delocalized charge are too low, hence ILDFA(solid) < I and ALDFA(solid) > A, due to the local-approximation error, also denoted delocalization error, of LDFAs in extended systems. These errors combine to make the LDFA orbital energy band gap considerably smaller than the exact fundamental gap, ϵLLDFA(solid)-ϵHLDFA(solid)=ILDFA(solid)-ALDFA(solid)<I-A (the LDFA band gap problem). These results for density functional approximations are compared to exact KS and to HF and hybrids. For the exact KS HOMO energy, one has ϵHKS=-I. The exact KS LUMO energy does not approximate the experimental -A (neither in molecules nor in solids), but is considerably below, which is the main reason for the exact KS HOMO-LUMO energy gap being considerably below the fundamental gap I - A (the exact KS band gap problem).
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Affiliation(s)
- Evert Jan Baerends
- Section Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands
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33
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Ghosh S, Verma P, Cramer CJ, Gagliardi L, Truhlar DG. Combining Wave Function Methods with Density Functional Theory for Excited States. Chem Rev 2018; 118:7249-7292. [PMID: 30044618 DOI: 10.1021/acs.chemrev.8b00193] [Citation(s) in RCA: 128] [Impact Index Per Article: 21.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
We review state-of-the-art electronic structure methods based both on wave function theory (WFT) and density functional theory (DFT). Strengths and limitations of both the wave function and density functional based approaches are discussed, and modern attempts to combine these two methods are presented. The challenges in modeling excited-state chemistry using both single-reference and multireference methods are described. Topics covered include background, combining density functional theory with single-configuration wave function theory, generalized Kohn-Sham (KS) theory, global hybrids, range-separated hybrids, local hybrids, using KS orbitals in many-body theory (including calculations of the self-energy and the GW approximation), Bethe-Salpeter equation, algorithms to accelerate GW calculations, combining DFT with multiconfigurational WFT, orbital-dependent correlation functionals based on multiconfigurational WFT, building multiconfigurational wave functions from KS configurations, adding correlation functionals to multiconfiguration self-consistent-field (MCSCF) energies, combining DFT with configuration-interaction singles by means of time-dependent DFT, using range separation to combine DFT with MCSCF, embedding multiconfigurational WFT in DFT, and multiconfiguration pair-density functional theory.
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Affiliation(s)
- Soumen Ghosh
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Pragya Verma
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Christopher J Cramer
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Laura Gagliardi
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
| | - Donald G Truhlar
- Department of Chemistry, Chemical Theory Center, and Minnesota Supercomputing Institute , University of Minnesota , 207 Pleasant Street SE , Minneapolis , Minnesota 55455-0431 , United States
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van Meer R, Gritsenko OV, Baerends EJ. A non-JKL density matrix functional for intergeminal correlation between closed-shell geminals from analysis of natural orbital configuration interaction expansions. J Chem Phys 2018; 148:104102. [DOI: 10.1063/1.5018671] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- R. van Meer
- Computational Molecular Science Research Team, RIKEN Advanced Institute for Computational Science, Kobe, Japan
- Section Theoretical Chemistry, VU University, Amsterdam, The Netherlands
| | - O. V. Gritsenko
- Section Theoretical Chemistry, VU University, Amsterdam, The Netherlands
| | - E. J. Baerends
- Section Theoretical Chemistry, VU University, Amsterdam, The Netherlands
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35
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Rodríguez-Mayorga M, Via-Nadal M, Solà M, Ugalde JM, Lopez X, Matito E. Electron-Pair Distribution in Chemical Bond Formation. J Phys Chem A 2018; 122:1916-1923. [PMID: 29381071 DOI: 10.1021/acs.jpca.7b12556] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The chemical formation process has been studied from relaxation holes, Δh(u), resulting from the difference between the radial intracule density and the nonrelaxed counterpart, which is obtained from atomic radial intracule densities and the pair density constructed from the overlap of the atomic densities. Δh(u) plots show that the internal reorganization of electron pairs prior to bond formation and the covalent bond formation from electrons in separate atoms are completely recognizable processes from the shape of the relaxation hole, Δh(u). The magnitude of Δh(u), the shape of Δh(u) ∀ u < Req, and the distance between the minimum and the maximum in Δh(u) provide further information about the nature of the chemical bond formed. A computational affordable approach to calculate the radial intracule density from approximate pair densities has been also suggested, paving the way to study electron-pair distributions in larger systems.
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Affiliation(s)
- M Rodríguez-Mayorga
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain.,Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona , C/ Maria Aurèlia Capmany, 69, 17003 Girona, Catalonia, Spain
| | - M Via-Nadal
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain
| | - M Solà
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona , C/ Maria Aurèlia Capmany, 69, 17003 Girona, Catalonia, Spain
| | - J M Ugalde
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain
| | - X Lopez
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain
| | - E Matito
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072 , 20080 Donostia, Euskadi, Spain.,IKERBASQUE, Basque Foundation for Science , 48013 Bilbao, Euskadi, Spain
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36
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Rodríguez-Mayorga M, Ramos-Cordoba E, Via-Nadal M, Piris M, Matito E. Comprehensive benchmarking of density matrix functional approximations. Phys Chem Chem Phys 2018; 19:24029-24041. [PMID: 28832052 DOI: 10.1039/c7cp03349d] [Citation(s) in RCA: 20] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The energy usually serves as a yardstick in assessing the performance of approximate methods in computational chemistry. After all, these methods are mostly used for the calculation of the electronic energy of chemical systems. However, computational methods should be also aimed at reproducing other properties, such strategy leading to more robust approximations with a wider range of applicability. In this study, we suggest a battery of ten tests with the aim to analyze density matrix functional approximations (DMFAs), including several properties that the exact functional should satisfy. The tests are performed on a model system with varying electron correlation, carrying a very small computational effort. Our results not only put forward a complete and exhaustive benchmark test for DMFAs, currently lacking, but also reveal serious deficiencies of existing approximations that lead to important clues in the construction of more robust DMFAs.
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Affiliation(s)
- Mauricio Rodríguez-Mayorga
- Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain.
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37
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Rodriguez-Mayorga M, Ramos-Cordoba E, Feixas F, Matito E. Electron correlation effects in third-order densities. Phys Chem Chem Phys 2018; 19:4522-4529. [PMID: 28121319 DOI: 10.1039/c6cp07616e] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The electronic energy of a system of fermions can be obtained from the second-order reduced density matrix through the contracted Schrödinger equation or its anti-Hermitian counterpart. Both energy expressions depend on the third-order reduced density matrix (3-RDM) which is usually approximated from lower-order densities. The accuracy of these methods depends critically on the set of N-representability conditions enforced in the calculation and the quality of the approximate 3-RDM. There are no benchmark studies including most 3-RDM approximations and, thus far, no assessment of the deterioration of the approximations with correlation effects has been performed. In this paper we introduce a series of tests to assess the performance of 3-RDM approximations in a model system with varying electron correlation effects, the three-electron harmonium atom. The results of this work put forward several limitations of the currently most used 3-RDM approximations for systems with important electron correlation effects.
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Affiliation(s)
- Mauricio Rodriguez-Mayorga
- Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain. and Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona, 17071 Girona, Catalonia, Spain
| | - Eloy Ramos-Cordoba
- Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain. and Department of Chemistry, University of California Berkeley, 94720, Berkeley, CA, USA
| | - Ferran Feixas
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona, 17071 Girona, Catalonia, Spain
| | - Eduard Matito
- Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain. and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
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Ramos-Cordoba E, Salvador P, Matito E. Separation of dynamic and nondynamic correlation. Phys Chem Chem Phys 2018; 18:24015-23. [PMID: 27523386 DOI: 10.1039/c6cp03072f] [Citation(s) in RCA: 64] [Impact Index Per Article: 10.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The account of electron correlation and its efficient separation into dynamic and nondynamic parts plays a key role in the development of computational methods. In this paper we suggest a physically-sound matrix formulation to split electron correlation into dynamic and nondynamic parts using the two-particle cumulant matrix and a measure of the deviation from idempotency of the first-order density matrix. These matrices are applied to a two-electron model, giving rise to a simplified electron correlation index that (i) depends only on natural orbitals and their occupancies, (ii) can be straightforwardly decomposed into orbital contributions and (iii) splits into dynamic and nondynamic correlation parts that (iv) admit a local version. These expressions are shown to account for dynamic and nondynamic correlation in a variety of systems containing different electron correlation regimes, thus providing the first separation of dynamic and nondynamic correlation using solely natural orbital occupancies.
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Affiliation(s)
- Eloy Ramos-Cordoba
- Faculty of Chemistry, University of the Basque Country UPV/EHU, and Donostia International Physics Center (DIPC)., P.K. 1072, 20080 Donostia, Euskadi, Spain. and Department of Chemistry, University of California Berkeley, Berkeley, California 94720, USA
| | - Pedro Salvador
- Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química, University of Girona, 17071 Girona, Catalonia, Spain
| | - Eduard Matito
- Faculty of Chemistry, University of the Basque Country UPV/EHU, and Donostia International Physics Center (DIPC)., P.K. 1072, 20080 Donostia, Euskadi, Spain. and IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
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Mitxelena I, Piris M, Rodríguez-Mayorga M. On the performance of natural orbital functional approximations in the Hubbard model. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:425602. [PMID: 28722686 DOI: 10.1088/1361-648x/aa80ca] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Strongly correlated materials are now under intense development, and natural orbital functional (NOF) methods seem to be able to capture the physics of these systems. We present a benchmark based on the Hubbard model for a class of commonly used NOF approximations (also known as reduced density matrix functional approximations). Our findings highlight the importance of imposing ensemble N-representability conditions in order to obtain consistent results in systems with either weak or strong electronic correlation, such as the Hubbard system with a varying two-particle interaction parameter. Based on the accuracy of the results obtained using PNOF7, which retrieves a large amount of the total strong nondynamic correlation, the Hubbard model points out that N-representability gives solid foundations for NOF development.
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Affiliation(s)
- I Mitxelena
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain. Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), 20018 Donostia, Euskadi, Spain
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Piris M, Pernal K. Comment on “Generalization of the Kohn-Sham system that can represent arbitrary one-electron density matrices”. PHYSICAL REVIEW A 2017; 96:046501. [DOI: 10.1103/physreva.96.046501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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Ramos-Cordoba E, Matito E. Local Descriptors of Dynamic and Nondynamic Correlation. J Chem Theory Comput 2017; 13:2705-2711. [DOI: 10.1021/acs.jctc.7b00293] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Eloy Ramos-Cordoba
- Kimika
Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi Spain
| | - Eduard Matito
- Kimika
Fakultatea, Euskal Herriko Unibertsitatea, UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi Spain
- IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain
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42
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Mitxelena I, Piris M. Analytic gradients for natural orbital functional theory. J Chem Phys 2017; 146:014102. [PMID: 28063441 DOI: 10.1063/1.4973271] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The analytic energy gradients with respect to nuclear motion are derived for the natural orbital functional (NOF) theory. The resulting equations do not require resorting to linear-response theory, so the computation of NOF energy gradients is analogous to gradient calculations at the Hartree-Fock level of theory. The structures of 15 spin-compensated systems, composed of first- and second-row atoms, are optimized employing the conjugate gradient algorithm. As functionals, two orbital-pairing approaches were used, namely, the fifth and sixth Piris NOFs (PNOF5 and PNOF6). For the latter, the obtained equilibrium geometries are compared with coupled cluster singles and doubles calculations and accurate empirical data.
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Affiliation(s)
- Ion Mitxelena
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080 Donostia, Spain
| | - Mario Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080 Donostia, Spain
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Mitxelena I, Piris M. Molecular electric moments calculated by using natural orbital functional theory. J Chem Phys 2016; 144:204108. [PMID: 27250280 DOI: 10.1063/1.4951685] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The molecular electric dipole, quadrupole, and octupole moments of a selected set of 21 spin-compensated molecules are determined employing the extended version of the Piris natural orbital functional 6 (PNOF6), using the triple-ζ Gaussian basis set with polarization functions developed by Sadlej, at the experimental geometries. The performance of the PNOF6 is established by carrying out a statistical analysis of the mean absolute errors with respect to the experiment. The calculated PNOF6 electric moments agree satisfactorily with the corresponding experimental data and are in good agreement with the values obtained by accurate ab initio methods, namely, the coupled-cluster single and doubles and multi-reference single and double excitation configuration interaction methods.
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Affiliation(s)
- Ion Mitxelena
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080 Donostia, Spain
| | - Mario Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080 Donostia, Spain
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