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Gaikwad PB, Kim TD, Richer M, Lokhande RA, Sánchez-Díaz G, Limacher PA, Ayers PW, Miranda-Quintana RA. Coupled cluster-inspired geminal wavefunctions. J Chem Phys 2024; 160:144108. [PMID: 38597308 DOI: 10.1063/5.0202035] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2024] [Accepted: 03/24/2024] [Indexed: 04/11/2024] Open
Abstract
Electron pairs have an illustrious history in chemistry, from powerful concepts to understanding structural stability and reactive changes to the promise of serving as building blocks of quantitative descriptions of the electronic structure of complex molecules and materials. However, traditionally, two-electron wavefunctions (geminals) have not enjoyed the popularity and widespread use of the more standard single-particle methods. This has changed recently, with a renewed interest in the development of geminal wavefunctions as an alternative to describing strongly correlated phenomena. Hence, there is a need to find geminal methods that are accurate, computationally tractable, and do not demand significant input from the user (particularly via cumbersome and often ill-behaved orbital optimization steps). Here, we propose new families of geminal wavefunctions inspired by the pair coupled cluster doubles ansatz. We present a new hierarchy of two-electron wavefunctions that extends the one-reference orbital idea to other geminals. Moreover, we show how to incorporate single-like excitations in this framework without leaving the quasiparticle picture. We explore the role of imposing seniority restrictions on these wavefunctions and benchmark these new methods on model strongly correlated systems.
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Affiliation(s)
- Pratiksha B Gaikwad
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - Taewon D Kim
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - M Richer
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Rugwed A Lokhande
- Department of Chemistry and Quantum Theory Project, University of Florida, Gainesville, Florida 32603, USA
| | - Gabriela Sánchez-Díaz
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Peter A Limacher
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
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2
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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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3
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Di Sabatino S, Koskelo J, Prodhon J, Berger JA, Caffarel M, Romaniello P. Photoemission Spectra from the Extended Koopman's Theorem, Revisited. Front Chem 2021; 9:746735. [PMID: 34692643 PMCID: PMC8531815 DOI: 10.3389/fchem.2021.746735] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/24/2021] [Accepted: 09/15/2021] [Indexed: 11/13/2022] Open
Abstract
The Extended Koopman's Theorem (EKT) provides a straightforward way to compute charged excitations from any level of theory. In this work we make the link with the many-body effective energy theory (MEET) that we derived to calculate the spectral function, which is directly related to photoemission spectra. In particular, we show that at its lowest level of approximation the MEET removal and addition energies correspond to the so-called diagonal approximation of the EKT. Thanks to this link, the EKT and the MEET can benefit from mutual insight. In particular, one can readily extend the EKT to calculate the full spectral function, and choose a more optimal basis set for the MEET by solving the EKT secular equation. We illustrate these findings with the examples of the Hubbard dimer and bulk silicon.
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Affiliation(s)
- S Di Sabatino
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France.,Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France.,European Theoretical Spectroscopy Facility (ETSF), Toulouse, France
| | - J Koskelo
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France.,European Theoretical Spectroscopy Facility (ETSF), Toulouse, France
| | - J Prodhon
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - J A Berger
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France.,European Theoretical Spectroscopy Facility (ETSF), Toulouse, France
| | - M Caffarel
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - P Romaniello
- Laboratoire de Physique Théorique, Université de Toulouse, CNRS, UPS, Toulouse, France.,European Theoretical Spectroscopy Facility (ETSF), Toulouse, France
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4
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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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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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Cukrowski I, Polestshuk PM. Reliability of interacting quantum atoms (IQA) data computed from post-HF densities: impact of the approximation used. Phys Chem Chem Phys 2017; 19:16375-16386. [DOI: 10.1039/c7cp02216f] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The BBC1 approximation is recommended for IQA calculations; MP2/BBC1 and CCSD/BBC1 produced highly comparable FAMSEC-based interpretations of intramolecular interactions.
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Affiliation(s)
- Ignacy Cukrowski
- Department of Chemistry
- Faculty of Natural and Agricultural Sciences
- University of Pretoria
- Pretoria
- South Africa
| | - Pavel M. Polestshuk
- Department of Chemistry
- M. V. Lomonosov Moscow State University
- 119991 Moscow
- Russia
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Theophilou I, Lathiotakis NN, Gidopoulos NI, Rubio A, Helbig N. Orbitals from local RDMFT: Are they Kohn-Sham or natural orbitals? J Chem Phys 2015; 143:054106. [DOI: 10.1063/1.4927784] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Iris Theophilou
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Nektarios N. Lathiotakis
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vass. Constantinou 48, GR-11635 Athens, Greece
- Max-Planck-Institut für Mikrostrukturphysik, Weinberg 2, D-06120 Halle (Saale), Germany
| | - Nikitas I. Gidopoulos
- Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom
| | - Angel Rubio
- Max Planck Institute for the Structure and Dynamics of Matter and Center for Free-Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Dpto. Física de Materiales, Universidad del País Vasco, CFM CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, E-20018 San Sebastián, Spain
| | - Nicole Helbig
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
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8
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Reduced Density Matrix Functional Theory (RDMFT) and Linear Response Time-Dependent RDMFT (TD-RDMFT). DENSITY-FUNCTIONAL METHODS FOR EXCITED STATES 2015; 368:125-83. [DOI: 10.1007/128_2015_624] [Citation(s) in RCA: 46] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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9
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Lathiotakis NN, Helbig N, Rubio A, Gidopoulos NI. Quasi-particle energy spectra in local reduced density matrix functional theory. J Chem Phys 2014; 141:164120. [DOI: 10.1063/1.4899072] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022] Open
Affiliation(s)
- Nektarios N. Lathiotakis
- Theoretical and Physical Chemistry Institute, National Hellenic Research Foundation, Vass. Constantinou 48, GR-11635 Athens, Greece
| | - Nicole Helbig
- Peter-Grünberg Institut and Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich, Germany
| | - Angel Rubio
- Nano-Bio Spectroscopy Group and ETSF Scientific Development Centre, Dpto. Física de Materiales, Universidad del País Vasco, CFM CSIC-UPV/EHU-MPC and DIPC, Av. Tolosa 72, E-20018 San Sebastián, Spain
| | - Nikitas I. Gidopoulos
- Department of Physics, Durham University, South Road, Durham DH1 3LE, United Kingdom
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10
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Bozkaya U. The extended Koopmans' theorem for orbital-optimized methods: Accurate computation of ionization potentials. J Chem Phys 2013; 139:154105. [DOI: 10.1063/1.4825041] [Citation(s) in RCA: 37] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
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11
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Mentel ŁM, Sheng XW, Gritsenko OV, Baerends EJ. On the formulation of a density matrix functional for Van der Waals interaction of like- and opposite-spin electrons in the helium dimer. J Chem Phys 2012. [DOI: 10.1063/1.4767774] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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12
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Lopez X, Ruipérez F, Piris M, Matxain JM, Matito E, Ugalde JM. Performance of PNOF5 Natural Orbital Functional for Radical Formation Reactions: Hydrogen Atom Abstraction and C–C and O–O Homolytic Bond Cleavage in Selected Molecules. J Chem Theory Comput 2012; 8:2646-52. [DOI: 10.1021/ct300414t] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Xabier Lopez
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia International
Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Fernando Ruipérez
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia International
Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Mario Piris
- 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
| | - Jon M. Matxain
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia International
Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Eduard Matito
- Department of Chemistry and Institute
of Computational Chemistry, University of Girona, 17071 Girona, Catalonia, Spain
| | - Jesus M. Ugalde
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU), and Donostia International
Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
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13
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Matxain JM, Piris M, Uranga J, Lopez X, Merino G, Ugalde JM. The Nature of Chemical Bonds from PNOF5 Calculations. Chemphyschem 2012; 13:2297-303. [DOI: 10.1002/cphc.201200205] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2012] [Indexed: 11/07/2022]
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14
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García-Revilla M, Francisco E, Costales A, Martín Pendás A. Performance of the density matrix functional theory in the quantum theory of atoms in molecules. J Phys Chem A 2011; 116:1237-50. [PMID: 21943031 DOI: 10.1021/jp204001n] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
The generalization to arbitrary molecular geometries of the energetic partitioning provided by the atomic virial theorem of the quantum theory of atoms in molecules (QTAIM) leads to an exact and chemically intuitive energy partitioning scheme, the interacting quantum atoms (IQA) approach, that depends on the availability of second-order reduced density matrices (2-RDMs). This work explores the performance of this approach in particular and of the QTAIM in general with approximate 2-RDMs obtained from the density matrix functional theory (DMFT), which rests on the natural expansion (natural orbitals and their corresponding occupation numbers) of the first-order reduced density matrix (1-RDM). A number of these functionals have been implemented in the promolden code and used to perform QTAIM and IQA analyses on several representative molecules and model chemical reactions. Total energies, covalent intra- and interbasin exchange-correlation interactions, as well as localization and delocalization indices have been determined with these functionals from 1-RDMs obtained at different levels of theory. Results are compared to the values computed from the exact 2-RDMs, whenever possible.
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Affiliation(s)
- Marco García-Revilla
- Departamento de Química Física y Analítica, Facultad de Química, Universidad de Oviedo, 33006 Oviedo, Spain.
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Helbig N, Theodorakopoulos G, Lathiotakis NN. Fractional spin in reduced density-matrix functional theory. J Chem Phys 2011; 135:054109. [DOI: 10.1063/1.3615955] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
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16
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Piris M, Lopez X, Ruipérez F, Matxain JM, Ugalde JM. A natural orbital functional for multiconfigurational states. J Chem Phys 2011; 134:164102. [DOI: 10.1063/1.3582792] [Citation(s) in RCA: 106] [Impact Index Per Article: 8.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Matxain JM, Piris M, Ruipérez F, Lopez X, Ugalde JM. Homolytic molecular dissociation in natural orbital functional theory. Phys Chem Chem Phys 2011; 13:20129-35. [DOI: 10.1039/c1cp21696a] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Piris M, Matxain JM, Lopez X, Ugalde JM. Communication: The role of the positivity N-representability conditions in natural orbital functional theory. J Chem Phys 2010; 133:111101. [DOI: 10.1063/1.3481578] [Citation(s) in RCA: 58] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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20
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Giesbertz KJH, Baerends EJ. Aufbau derived from a unified treatment of occupation numbers in Hartree–Fock, Kohn–Sham, and natural orbital theories with the Karush–Kuhn–Tucker conditions for the inequality constraints ni≤1 and ni≥0. J Chem Phys 2010; 132:194108. [DOI: 10.1063/1.3426319] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Lathiotakis NN, Sharma S, Helbig N, Dewhurst JK, Marques MAL, Eich F, Baldsiefen T, Zacarias A, Gross EKU. Discontinuities of the Chemical Potential in Reduced Density Matrix Functional Theory. ACTA ACUST UNITED AC 2010. [DOI: 10.1524/zpch.2010.6118] [Citation(s) in RCA: 34] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
Abstract
Abstract
Using the discontinuity of the chemical potential as a function of excess charge, the fundamental gaps for finite systems and the band gaps of extended solids are determined within reduced density matrix functional theory. We also present the necessary and sufficient conditions for the one-body reduced density matrix of a system with fractional charge to be ensemble N-representable. The performance of most modern day reduced density matrix functionals is assessed for the gaps and the correlation energy of finite systems. Our results show that for finite systems the PNOF, BBC3, and power functionals yield very accurate correlation energies while for a correct description of the fundamental gap the removal of self-interaction terms is essential. For extended solids we find that the power functional captures the correct band gap behavior for conventional semiconductors as well as strongly correlated Mott insulators, where a gap is obtained in absence of any magnetic ordering.
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Lathiotakis NN, Gidopoulos NI, Helbig N. Size consistency of explicit functionals of the natural orbitals in reduced density matrix functional theory. J Chem Phys 2010; 132:084105. [DOI: 10.1063/1.3324699] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Piris M, Matxain JM, Lopez X, Ugalde JM. Communications: Accurate description of atoms and molecules by natural orbital functional theory. J Chem Phys 2010; 132:031103. [DOI: 10.1063/1.3298694] [Citation(s) in RCA: 63] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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Piris M, Ugalde JM. Iterative diagonalization for orbital optimization in natural orbital functional theory. J Comput Chem 2009; 30:2078-86. [DOI: 10.1002/jcc.21225] [Citation(s) in RCA: 65] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
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25
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Vanfleteren D, Van Neck D, Ayers PW, Morrison RC, Bultinck P. Exact ionization potentials from wavefunction asymptotics: The extended Koopmans’ theorem, revisited. J Chem Phys 2009; 130:194104. [DOI: 10.1063/1.3130044] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023] Open
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26
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Giesbertz KJH, Pernal K, Gritsenko OV, Baerends EJ. Excitation energies with time-dependent density matrix functional theory: Singlet two-electron systems. J Chem Phys 2009; 130:114104. [DOI: 10.1063/1.3079821] [Citation(s) in RCA: 50] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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27
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Lathiotakis NN, Helbig N, Zacarias A, Gross EKU. A functional of the one-body-reduced density matrix derived from the homogeneous electron gas: Performance for finite systems. J Chem Phys 2009; 130:064109. [DOI: 10.1063/1.3073053] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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28
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Rohr DR, Pernal K, Gritsenko OV, Baerends EJ. A density matrix functional with occupation number driven treatment of dynamical and nondynamical correlation. J Chem Phys 2008; 129:164105. [DOI: 10.1063/1.2998201] [Citation(s) in RCA: 89] [Impact Index Per Article: 5.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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29
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Giesbertz KJH, Baerends EJ, Gritsenko OV. Charge transfer, double and bond-breaking excitations with time-dependent density matrix functional theory. PHYSICAL REVIEW LETTERS 2008; 101:033004. [PMID: 18764252 DOI: 10.1103/physrevlett.101.033004] [Citation(s) in RCA: 44] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2008] [Indexed: 05/26/2023]
Abstract
Time-dependent density functional theory (TDDFT) in its current adiabatic implementations exhibits three remarkable failures: (a) completely wrong behavior of the excited state surface along a bond-breaking coordinate; (b) lack of doubly excited configurations; (c) much too low charge transfer excitation energies. These TDDFT failure cases are all strikingly exhibited by prototype two-electron systems such as dissociating H2 and HeH+. We find for these systems with time-dependent density matrix functional theory that: (a) Within previously formulated simple adiabatic approximations, the bonding-to-antibonding excited state surface as well as charge transfer excitations are described without problems, but not the double excitations; (b) An adiabatic approximation is formulated in which also the double excitations are fully accounted for.
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Affiliation(s)
- K J H Giesbertz
- Afdeling Theoretische Chemie, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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30
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Piris M, Matxain JM, Ugalde JM. Piris natural orbital functional study of the dissociation of the radical helium dimer. J Chem Phys 2008; 129:014108. [DOI: 10.1063/1.2950094] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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31
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Lathiotakis NN, Marques MAL. Benchmark calculations for reduced density-matrix functional theory. J Chem Phys 2008; 128:184103. [DOI: 10.1063/1.2899328] [Citation(s) in RCA: 66] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Pernal K, Giesbertz K, Gritsenko O, Baerends EJ. Adiabatic approximation of time-dependent density matrix functional response theory. J Chem Phys 2007; 127:214101. [DOI: 10.1063/1.2800016] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023] Open
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Piris M, Lopez X, Ugalde JM. Dispersion interactions within the Piris natural orbital functional theory: The helium dimer. J Chem Phys 2007; 126:214103. [PMID: 17567186 DOI: 10.1063/1.2743019] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The authors have investigated the description of the dispersion interaction within the Piris natural orbital functional (PNOF) theory. The PNOF arises from an explicit antisymmetric approach for the two-particle cumulant in terms of two symmetric matrices, Delta and Lambda. The functional forms of these matrices are obtained from the generalization of the two-particle system expressions, except for the off-diagonal elements of Delta. The mean value theorem and the partial sum rule obtained for the off-diagonal elements of Delta provide a prescription for deriving practical functionals. In particular, the previous employed approximation {Jpp/2} for the mean values {Jp*} affords several molecular properties but it is incapable to account for dispersion effects. In this work, the authors analyze a new approach for Jp* obtained by factorization of the matrix Delta within the bounds on its off-diagonal elements imposed by the positivity conditions of the two-particle reduced density matrix. Additional terms for the matrix elements of Lambda proportional to the square root of the holes are again introduced to describe properly the occupation numbers of the lowest occupied levels. The authors have found that the cross products between weakly occupied orbitals must be removed from the functional form of Lambda to obtain a correct long-range asymptotic behavior. The PNOF is used to predict the binding energy as well as the equilibrium distance of the helium dimer. The results are compared with the full configuration-interaction calculations and the corresponding experimental data.
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Affiliation(s)
- M Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea, Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
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Leiva P, Piris M. Calculation of vertical ionization potentials with the Piris natural orbital functional. ACTA ACUST UNITED AC 2006. [DOI: 10.1016/j.theochem.2006.05.001] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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