1
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Obeng A, Autschbach J. How Much Electron Donation Is There In Transition Metal Complexes? A Computational Study. J Chem Theory Comput 2024; 20:4965-4976. [PMID: 38857528 DOI: 10.1021/acs.jctc.4c00404] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2024]
Abstract
The "dative" covalent interactions between metals and ligands in coordination compounds, i.e., metal-to-ligand and ligand-to-metal donation, are manifestations of electron delocalization and subject to errors in approximate calculations. This work addresses the extent of dative bonding/donation in a series of closed-shell transition metal complexes. Several Kohn-Sham density functionals, representing different "rungs" of approximations, along with post-Hartree-Fock methods are assessed in comparison to CCSD(T). Two widely used nonhybrid and global hybrid density functionals (B3LYP, PBE0) tend to produce notably too strong donation. Global hybrids with elevated fractions of exact exchange (40 to 50%) and the range-separated exchange functional CAM-B3LYP tend to perform better for the description of the donation. The performance of a double-hybrid functional is found to be quite satisfactory, correcting errors seen in MP2 calculations. A fast approximate coupled-cluster model (DLPNO-CCSD) also gives a reasonable description of the donation, with a tendency to underestimate its extent.
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Affiliation(s)
- Augustine Obeng
- Department of Chemistry, University at Buffalo State University of New York Buffalo, New York 14260-3000, United States
| | - Jochen Autschbach
- Department of Chemistry, University at Buffalo State University of New York Buffalo, New York 14260-3000, United States
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2
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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: 6] [Impact Index Per Article: 6.0] [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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3
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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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4
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Lew-Yee JFH, M. del Campo J. Charge delocalization error in Piris Natural Orbital Functionals. J Chem Phys 2022; 157:104113. [DOI: 10.1063/5.0102310] [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
Piris Natural Orbital Functionals (PNOF) have been recognized as a low-scaling alternative to study strong correlated systems. In this work, we address the performance of the fifth functional (PNOF5) and the seventh functional (PNOF7) to deal with another common problem, the charge delocalization error. The effects of this problem can be observed in charged systems of repeated well-separated fragments, where the energy should be the sum of the charged and neutral fragments, regardless of how the charge is distributed. In practice, an energetic overstabilization of fractional charged fragments leads to a preference for having the charge delocalized throughout the system. To establish the performance of PNOF functionals regarding charge delocalization error, charged chains of helium atoms and the W4-17-MR set molecules were used as base fragments and their energy, charge distribution and correlation regime were studied. It was found that PNOF5 prefers localized charge distributions, while PNOF7 improves the treatment of interpair static correlation and tends to the correct energetic limit for several cases, although a preference for delocalized charge distributions may arise in highly strong correlation regimes. Overall, it is concluded that PNOF functionals can simultaneously deal with static correlation and charge delocalization errors, resulting in a promising choice to study charge-related problems.
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Affiliation(s)
- Juan Felipe Huan Lew-Yee
- Departamento de Física y Química Teórica, Universidad Nacional Autónoma de México Facultad de Química, Mexico
| | - Jorge M. del Campo
- Departamento de Física y Química Teórica, Universidad Nacional Autónoma de México, Mexico
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5
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Mitxelena I, Piris M. Benchmarking GNOF against FCI in challenging systems in one, two, and three dimensions. J Chem Phys 2022; 156:214102. [DOI: 10.1063/5.0092611] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
This work assesses the reliability of the recently proposed [M. Piris, Phys. Rev. Lett. 127, 233001 (2021)] global natural orbital functional (GNOF) in the treatment of the strong electron correlation regime. First, we use an H10 benchmark set of four hydrogen model systems of different dimensionalities and distinctive electronic structures: a 1D chain, a 2D ring, a 2D sheet, and a 3D close-packed pyramid. Second, we study two paradigmatic models for strongly correlated Mott insulators, namely, a 1D H50 chain and a 4 × 4 × 4 3D H cube. We show that GNOF, without hybridization to other electronic structure methods and free of tuned parameters, succeeds in treating weak and strong correlation in a more balanced way than the functionals that have preceded it.
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Affiliation(s)
- Ion Mitxelena
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Euskal Herriko Unibertsitatea (UPV/EHU), PK 1072, 20080 Donostia, Euskadi, Spain
| | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
- Euskal Herriko Unibertsitatea (UPV/EHU), PK 1072, 20080 Donostia, Euskadi, Spain
- Basque Foundation for Science (IKERBASQUE), 48009 Bilbao, Euskadi, Spain
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Lemke Y, Kussmann J, Ochsenfeld C. Efficient Integral-Direct Methods for Self-Consistent Reduced Density Matrix Functional Theory Calculations on Central and Graphics Processing Units. J Chem Theory Comput 2022; 18:4229-4244. [DOI: 10.1021/acs.jctc.2c00231] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Y. Lemke
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 5−13, D-81377 Munich, Germany
| | - J. Kussmann
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 5−13, D-81377 Munich, Germany
| | - C. Ochsenfeld
- Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 5−13, D-81377 Munich, Germany
- Max Planck Institute for Solid State Research, Heisenbergstr. 1, D-70569 Stuttgart, Germany
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7
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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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8
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Rodríguez-Mayorga M, Mitxelena I, Bruneval F, Piris M. Coupling Natural Orbital Functional Theory and Many-Body Perturbation Theory by Using Nondynamically Correlated Canonical Orbitals. J Chem Theory Comput 2021; 17:7562-7574. [PMID: 34806362 DOI: 10.1021/acs.jctc.1c00858] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We develop a new family of electronic structure methods for capturing at the same time the dynamic and nondynamic correlation effects. We combine the natural orbital functional theory (NOFT) and many-body perturbation theory (MBPT) through a canonicalization procedure applied to the natural orbitals to gain access to any MBPT approximation. We study three different scenarios: corrections based on second-order Møller-Plesset (MP2), random-phase approximation (RPA), and coupled-cluster singles doubles (CCSD). Several chemical problems involving different types of electron correlation in singlet and multiplet spin states have been considered. Our numerical tests reveal that RPA-based and CCSD-based corrections provide similar relative errors in molecular dissociation energies (De) to the results obtained using a MP2 correction. With respect to the MP2 case, the CCSD-based correction improves the prediction, while the RPA-based correction reduces the computational cost.
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Affiliation(s)
- Mauricio Rodríguez-Mayorga
- Université Paris-Saclay, CEA, Service de Recherches de Métallurgie Physique, 91191 Gif Sur Yvette, France.,Department of Theoretical Chemistry, VU University Amsterdam, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Ion Mitxelena
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
| | - Fabien Bruneval
- Université Paris-Saclay, CEA, Service de Recherches de Métallurgie Physique, 91191 Gif Sur Yvette, France
| | - Mario Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain.,IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Euskadi, Spain
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9
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Piris M. Global Natural Orbital Functional: Towards the Complete Description of the Electron Correlation. PHYSICAL REVIEW LETTERS 2021; 127:233001. [PMID: 34936779 DOI: 10.1103/physrevlett.127.233001] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2021] [Accepted: 10/26/2021] [Indexed: 06/14/2023]
Abstract
The current work presents a natural orbital functional (NOF) for electronic systems with any spin value independent of the external potential being considered, that is, a global NOF (GNOF). It is based on a new two-index reconstruction of the two-particle reduced density matrix for spin multiplets. The emergent functional describes the complete intrapair electron correlation, and the correlation between orbitals that make up both the pairs and the individual electrons. The interorbital correlation is composed of static and dynamic terms. The concept of dynamic part of the occupation numbers is introduced. To evaluate the accuracy achieved with the GNOF, calculation of a variety of properties is presented. They include the total energies and energy differences between the ground state and the lowest-lying excited state with different spin of atoms from H to Ne, ionization potentials of the first-row transition-metal atoms (Sc-Zn), and the total energies of a selected set of 55 molecular systems in different spin states. The GNOF is also applied to the homolytic dissociation of selected diatomic molecules in different spin states and to the rotation barrier of ethylene, both paradigmatic cases of systems with significant multiconfigurational character. The values obtained agree with those reported at high level of theory and experimental data.
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Affiliation(s)
- Mario Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), P.K. 1072, 20080 Donostia, Spain Donostia International Physics Center (DIPC), 20018 Donostia, Spain and IKERBASQUE, Basque Foundation for Science, 48013 Bilbao, Spain
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10
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Chemical reactivity studies by the natural orbital functional second-order Møller–Plesset (NOF-MP2) method: water dehydrogenation by the scandium cation. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02775-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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11
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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: 10] [Impact Index Per Article: 3.3] [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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12
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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: 7] [Impact Index Per Article: 2.3] [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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13
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Gibney D, Boyn JN, Mazziotti DA. Toward a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming. J Phys Chem Lett 2021; 12:385-391. [PMID: 33356286 DOI: 10.1021/acs.jpclett.0c03371] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Kohn-Sham density functional theory (DFT) has long struggled with the accurate description of strongly correlated and open shell systems, and improvements have been minor even in the newest hybrid functionals. In this Letter we treat the static correlation in DFT when frontier orbitals are degenerate by the means of using a semidefinite programming (SDP) approach to minimize the system energy as a function of the N-representable, non-idempotent 1-electron reduced density matrix. While showing greatly improved singlet-triplet gaps for local density approximation and generalized gradient approximation (GGA) functionals, the SDP procedure reveals flaws in modern meta and hybrid GGA functionals, which show no major improvements when provided with an accurate electron density.
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Affiliation(s)
- Daniel Gibney
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - Jan-Niklas Boyn
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
| | - David A Mazziotti
- The James Franck Institute and The Department of Chemistry, The University of Chicago, Chicago, Illinois 60637, United States
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14
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Mitxelena I, Piris M. Analytic gradients for spin multiplets in natural orbital functional theory. J Chem Phys 2020; 153:044101. [PMID: 32752719 DOI: 10.1063/5.0012897] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Analytic energy gradients with respect to nuclear motion are derived for non-singlet compounds in the natural orbital functional theory. We exploit the formulation for multiplets in order to obtain a simple formula valid for any many-electron system in its ground mixed state with a total spin S and all possible spin projection Sz values. We demonstrate that the analytic gradients can be obtained without resorting to linear response theory or involving iterative procedures. A single evaluation is required, so integral derivatives can be computed on-the-fly along the calculation, thus improving the effectiveness of screening by the Schwarz inequality. The results for small- and medium-sized molecules with many spin multiplicities are shown. Our results are compared with the experimental data and accurate theoretical equilibrium geometries.
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Affiliation(s)
- Ion Mitxelena
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
| | - Mario Piris
- Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
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15
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Mitxelena I, Piris M. An efficient method for strongly correlated electrons in two-dimensions. J Chem Phys 2020; 152:064108. [PMID: 32061239 DOI: 10.1063/1.5140985] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This work deals with the problem of strongly correlated electrons in two-dimensions. We give a reduced density matrix (RDM) based tool through which the ground-state energy is given as a functional of the natural orbitals and their occupation numbers. Specifically, the Piris Natural Orbital Functional 7 (PNOF7) is used for studying the 2D Hubbard model and hydrogen square lattices. The singlet ground-state is studied, as well as the doublet mixed quantum state obtained by extracting an electron from the system. Our method satisfies two-index necessary N-representability conditions of the two-particle RDM (2RDM) and guarantees the conservation of the total spin. We show the ability of PNOF7 to describe strong correlation effects in two-dimensional (2D) systems by comparing our results with the exact diagonalization, density matrix renormalization group (DMRG), and auxiliary-field quantum Monte Carlo calculations. PNOF7 overcomes variational 2RDM methods with two- and three-index positivity N-representability conditions, reducing computational cost to mean-field scaling. Consistent results are obtained for small and large systems up to 144 electrons, weak and strong correlation regimes, and many filling situations. Unlike other methods, there is no dependence on dimensionality in the results obtained with PNOF7 and no particular difficulties have been observed to converge PNOF7 away from half-filling. Smooth double occupancy of sites is obtained, regardless of the filling. Symmetric dissociation of 2D hydrogen lattices shows that long-range nondynamic correlation dramatically affects electron detachment energies. PNOF7 compares well with DMRG along the dissociation curve.
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Affiliation(s)
- Ion Mitxelena
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
| | - Mario Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) and Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
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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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Cioslowski J. One-Electron Reduced Density Matrix Functional Theory of Spin-Polarized Systems. J Chem Theory Comput 2020; 16:1578-1585. [DOI: 10.1021/acs.jctc.9b01155] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Jerzy Cioslowski
- Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland
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18
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19
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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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20
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Araújo JP, Alves MD, da Silva RS, Ballester MY. A comparative study of analytic representations of potential energy curves for O2, N2, and SO in their ground electronic states. J Mol Model 2019; 25:198. [DOI: 10.1007/s00894-019-4079-3] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/16/2019] [Accepted: 05/28/2019] [Indexed: 11/24/2022]
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21
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Quintero-Monsebaiz R, Mitxelena I, Rodríguez-Mayorga M, Vela A, Piris M. Natural orbital functional for spin-polarized periodic systems. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2019; 31:165501. [PMID: 30673638 DOI: 10.1088/1361-648x/ab0170] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Natural orbital functional theory is considered for systems with one or more unpaired electrons. An extension of the Piris natural orbital functional (PNOF) based on electron pairing approach is presented, specifically, we extend the independent pair model, PNOF5, and the interactive pair model PNOF7 to describe spin-uncompensated systems. An explicit form for the two-electron cumulant of high-spin cases is only taken into account, so that singly occupied orbitals with the same spin are solely considered. The rest of the electron pairs with opposite spins remain paired. The reconstructed two-particle reduced density matrix fulfills certain N-representability necessary conditions, as well as guarantees the conservation of the total spin. The theory is applied to model systems with strong non-dynamic (static) electron correlation, namely, the one-dimensional Hubbard model with periodic boundary conditions and hydrogen rings. For the latter, PNOF7 compares well with exact diagonalization results so the model presented here is able to provide a correct description of the strong-correlation effects.
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Affiliation(s)
- Raul Quintero-Monsebaiz
- Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, D. F. 07360, Mexico. Donostia International Physics Center (DIPC), 20018 Donostia, Euskadi, Spain
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22
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Schilling C, Schilling R. Diverging Exchange Force and Form of the Exact Density Matrix Functional. PHYSICAL REVIEW LETTERS 2019; 122:013001. [PMID: 31012728 DOI: 10.1103/physrevlett.122.013001] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2018] [Indexed: 06/09/2023]
Abstract
For translationally invariant one-band lattice models, we exploit the ab initio knowledge of the natural orbitals to simplify reduced density matrix functional theory (RDMFT). Striking underlying features are discovered. First, within each symmetry sector, the interaction functional F depends only on the natural occupation numbers n. The respective sets P_{N}^{1} and E_{N}^{1} of pure and ensemble N-representable one-matrices coincide. Second, and most importantly, the exact functional is strongly shaped by the geometry of the polytope E_{N}^{1}≡P_{N}^{1}, described by linear constraints D^{(j)}(n)≥0. For smaller systems, it follows as F[n]=[under ∑]i,i^{'}V[over ¯]_{i,i^{'}}sqrt[D^{(i)}(n)D^{(i^{'})}(n)]. This generalizes to systems of arbitrary size by replacing each D^{(i)} by a linear combination of {D^{(j)}(n)} and adding a nonanalytical term involving the interaction V[over ^]. Third, the gradient dF/dn is shown to diverge on the boundary ∂E_{N}^{1}, suggesting that the fermionic exchange symmetry manifests itself within RDMFT in the form of an "exchange force." All findings hold for systems with a nonfixed particle number as well and V[over ^] can be any p-particle interaction. As an illustration, we derive the exact functional for the Hubbard square.
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Affiliation(s)
- Christian Schilling
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Rolf Schilling
- Institut für Physik, Johannes Gutenberg-Universität, D-55099 Mainz, Germany
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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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