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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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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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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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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: 19] [Impact Index Per Article: 6.3] [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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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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Piris M. Dynamic electron-correlation energy in the natural-orbital-functional second-order-Møller-Plesset method from the orbital-invariant perturbation theory. PHYSICAL REVIEW A 2018; 98:022504. [DOI: 10.1103/physreva.98.022504] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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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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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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Hollett JW, Hosseini H, Menzies C. A cumulant functional for static and dynamic correlation. J Chem Phys 2016; 145:084106. [DOI: 10.1063/1.4961243] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Joshua W. Hollett
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada
- Department of Chemistry, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada
| | - Hessam Hosseini
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada
| | - Cameron Menzies
- Department of Chemistry, University of Winnipeg, Winnipeg, Manitoba R3B 2G3, Canada
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Chatterjee K, Pastorczak E, Jawulski K, Pernal K. A minimalistic approach to static and dynamic electron correlations: Amending generalized valence bond method with extended random phase approximation correlation correction. J Chem Phys 2016; 144:244111. [PMID: 27369501 DOI: 10.1063/1.4954694] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A perfect-pairing generalized valence bond (GVB) approximation is known to be one of the simplest approximations, which allows one to capture the essence of static correlation in molecular systems. In spite of its attractive feature of being relatively computationally efficient, this approximation misses a large portion of dynamic correlation and does not offer sufficient accuracy to be generally useful for studying electronic structure of molecules. We propose to correct the GVB model and alleviate some of its deficiencies by amending it with the correlation energy correction derived from the recently formulated extended random phase approximation (ERPA). On the examples of systems of diverse electronic structures, we show that the resulting ERPA-GVB method greatly improves upon the GVB model. ERPA-GVB recovers most of the electron correlation and it yields energy barrier heights of excellent accuracy. Thanks to a balanced treatment of static and dynamic correlation, ERPA-GVB stays reliable when one moves from systems dominated by dynamic electron correlation to those for which the static correlation comes into play.
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Affiliation(s)
- Koushik Chatterjee
- Institute of Applied Radiation Chemistry, Lodz University of Technology, ul. Wroblewskiego 15, 93-590 Lodz, Poland
| | - Ewa Pastorczak
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
| | - Konrad Jawulski
- Institute of Applied Radiation Chemistry, Lodz University of Technology, ul. Wroblewskiego 15, 93-590 Lodz, Poland
| | - Katarzyna Pernal
- Institute of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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Ramos-Cordoba E, Lopez X, Piris M, Matito E. H4: A challenging system for natural orbital functional approximations. J Chem Phys 2016; 143:164112. [PMID: 26520503 DOI: 10.1063/1.4934799] [Citation(s) in RCA: 20] [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 correct description of nondynamic correlation by electronic structure methods not belonging to the multireference family is a challenging issue. The transition of D(2h) to D(4h) symmetry in H4 molecule is among the most simple archetypal examples to illustrate the consequences of missing nondynamic correlation effects. The resurgence of interest in density matrix functional methods has brought several new methods including the family of Piris Natural Orbital Functionals (PNOF). In this work, we compare PNOF5 and PNOF6, which include nondynamic electron correlation effects to some extent, with other standard ab initio methods in the H4 D(4h)/D(2h) potential energy surface (PES). Thus far, the wrongful behavior of single-reference methods at the D(2h)-D(4h) transition of H4 has been attributed to wrong account of nondynamic correlation effects, whereas in geminal-based approaches, it has been assigned to a wrong coupling of spins and the localized nature of the orbitals. We will show that actually interpair nondynamic correlation is the key to a cusp-free qualitatively correct description of H4 PES. By introducing interpair nondynamic correlation, PNOF6 is shown to avoid cusps and provide the correct smooth PES features at distances close to the equilibrium, total and local spin properties along with the correct electron delocalization, as reflected by natural orbitals and multicenter delocalization indices.
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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
| | - Xabier Lopez
- Faculty of Chemistry, University of the Basque Country UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Mario Piris
- Faculty of Chemistry, University of the Basque Country UPV/EHU, and Donostia International Physics Center (DIPC), P.K. 1072, 20080 Donostia, Euskadi, 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
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Filatov M, Martínez TJ, Kim KS. Using the GVB Ansatz to develop ensemble DFT method for describing multiple strongly correlated electron pairs. Phys Chem Chem Phys 2016; 18:21040-50. [PMID: 26947515 DOI: 10.1039/c6cp00236f] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Ensemble density functional theory (DFT) furnishes a rigorous theoretical framework for describing the non-dynamic electron correlation arising from (near) degeneracy of several electronic configurations. Ensemble DFT naturally leads to fractional occupation numbers (FONs) for several Kohn-Sham (KS) orbitals, which thereby become variational parameters of the methodology. The currently available implementation of ensemble DFT in the form of the spin-restricted ensemble-referenced KS (REKS) method was originally designed for systems with only two fractionally occupied KS orbitals, which was sufficient to accurately describe dissociation of a single chemical bond or the singlet ground state of biradicaloid species. To extend applicability of the method to systems with several dissociating bonds or to polyradical species, more fractionally occupied orbitals must be included in the ensemble description. Here we investigate a possibility of developing the extended REKS methodology with the help of the generalized valence bond (GVB) wavefunction theory. The use of GVB enables one to derive a simple and physically transparent energy expression depending explicitly on the FONs of several KS orbitals. In this way, a version of the REKS method with four electrons in four fractionally occupied orbitals is derived and its accuracy in the calculation of various types of strongly correlated molecules is investigated. We propose a possible scheme to ameliorate the partial size-inconsistency that results from perfect spin-pairing. We conjecture that perfect pairing natural orbital (NO) functionals of reduced density matrix functional theory (RDMFT) should also display partial size-inconsistency.
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Affiliation(s)
- Michael Filatov
- Department of Chemistry, School of Natural Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Korea.
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Piris M, Lopez X, Ugalde JM. The Bond Order of C2 from a Strictly N-Representable Natural Orbital Energy Functional Perspective. Chemistry 2016; 22:4109-15. [PMID: 26822104 DOI: 10.1002/chem.201504491] [Citation(s) in RCA: 35] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2015] [Indexed: 11/08/2022]
Abstract
The bond order of the ground electronic state of the carbon dimer has been analyzed in the light of natural orbital functional theory calculations carried out with an approximate, albeit strictly N-representable, energy functional. Three distinct solutions have been found from the Euler equations of the minimization of the energy functional with respect to the natural orbitals and their occupation numbers, which expand upon increasing values of the internuclear coordinate. In the close vicinity of the minimum energy region, two of the solutions compete around a discontinuity point. The former, corresponding to the absolute minimum energy, features two valence natural orbitals of each of the following symmetries, σ, σ*, π and π*, and has three bonding interactions and one antibonding interaction, which is very suggestive of a bond order large than two but smaller than three. The latter, features one σ-σ* linked pair of natural orbitals and three degenerate pseudo-bonding like orbitals, paired each with one triply degenerate pseudo-antibonding orbital, which points to a bond order larger than three. When correlation effects, other than Hartree-Fock for example, between the paired natural orbitals are accounted for, this second solution vanishes yielding a smooth continuous dissociation curve. Comparison of the vibrational energies and electron ionization energies, calculated on this curve, with their corresponding experimental marks, lend further support to a bond order for C2 intermediate between acetylene and ethylene.
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Affiliation(s)
- 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, 48013, Bilbao, Euskadi, Spain.
| | - Xabier Lopez
- Kimika Fakultatea, Euskal Herriko Unibertsitatea (UPV/EHU) and, Donostia International Physics Center (DIPC), P.K. 1072, 20080, Donostia, Euskadi, 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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Lopez X, Piris M. PNOF5 calculations based on the “thermodynamic fragment energy method”: C n H2n+2 (n = 1, 10) and (FH) n (n = 1, 8) as test cases. Theor Chem Acc 2015. [DOI: 10.1007/s00214-015-1756-x] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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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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Ramos-Cordoba E, Salvador P, Piris M, Matito E. Two new constraints for the cumulant matrix. J Chem Phys 2014; 141:234101. [DOI: 10.1063/1.4903449] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Eloy Ramos-Cordoba
- Institut de Química Computacional i Catàlisi (IQCC) and Department de Química, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia, Spain
| | - Pedro Salvador
- Institut de Química Computacional i Catàlisi (IQCC) and Department de Química, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia, Spain
| | - Mario Piris
- Kimika Fakultatea, Euskal Herriko Unibertsitatea UPV/EHU, and Donostia International Physics Center (DIPC). P.K. 1072, 20080 Donostia, Euskadi, Spain
| | - Eduard Matito
- Institut de Química Computacional i Catàlisi (IQCC) and Department de Química, Universitat de Girona, Campus de Montilivi, 17071 Girona, Catalonia, Spain
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Pernal K. Intergeminal Correction to the Antisymmetrized Product of Strongly Orthogonal Geminals Derived from the Extended Random Phase Approximation. J Chem Theory Comput 2014; 10:4332-41. [DOI: 10.1021/ct500478t] [Citation(s) in RCA: 59] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Katarzyna Pernal
- Institute
of Physics, Lodz University of Technology, ul. Wolczanska 219, 90-924 Lodz, Poland
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Piris M, Matxain JM, Lopez X. The intrapair electron correlation in natural orbital functional theory. J Chem Phys 2013; 139:234109. [DOI: 10.1063/1.4844075] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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