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Schwalbe S, Schulze WT, Trepte K, Lehtola S. Ensemble Generalization of the Perdew-Zunger Self-Interaction Correction: A Way Out of Multiple Minima and Symmetry Breaking. J Chem Theory Comput 2024; 20:7144-7154. [PMID: 39140402 PMCID: PMC11360130 DOI: 10.1021/acs.jctc.4c00694] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/28/2024] [Revised: 07/24/2024] [Accepted: 07/26/2024] [Indexed: 08/15/2024]
Abstract
The Perdew-Zunger (PZ) self-interaction correction (SIC) is an established tool to correct unphysical behavior in density functional approximations. Yet, the PZ-SIC is well-known to sometimes break molecular symmetries. An example of this is the benzene molecule, for which the PZ-SIC predicts a symmetry-broken electron density and molecular geometry, since the method does not describe the two possible Kekulé structures on an even footing, leading to local minima [Lehtola et al. J. Chem. Theory Comput. 2016, 12, 3195]. The PZ-SIC is often implemented with Fermi-Löwdin orbitals (FLOs), yielding the FLO-SIC method, which likewise has issues with symmetry breaking and local minima [Trepte et al. J. Chem. Phys. 2021, 155, 224109]. In this work, we propose a generalization of the PZ-SIC─the ensemble PZ-SIC (E-PZ-SIC) method─which shares the asymptotic computational scaling of the PZ-SIC (albeit with an additional prefactor). The E-PZ-SIC is straightforwardly applicable to various molecules, merely requiring one to average the self-interaction correction over all possible Kekulé structures, in line with chemical intuition. We showcase the implementation of the E-PZ-SIC with FLOs, as the resulting E-FLO-SIC method is easy to realize on top of an existing implementation of the FLO-SIC. We show that the E-FLO-SIC indeed eliminates symmetry breaking, reproducing a symmetric electron density and molecular geometry for benzene. The ensemble approach suggested herein could also be employed within approximate or locally scaled variants of the PZ-SIC and its FLO-SIC versions.
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Affiliation(s)
- Sebastian Schwalbe
- Center
for Advanced Systems Understanding (CASUS), D-02826 Görlitz, Germany
- Helmholtz-Zentrum
Dresden-Rossendorf (HZDR), D-01328 Dresden, Germany
| | - Wanja Timm Schulze
- Institute
for Physical Chemistry, Friedrich Schiller
University, D-07743 Jena, Germany
| | - Kai Trepte
- Taiwan
Semiconductor Manufacturing Company North America, San Jose, California 95134, United States
| | - Susi Lehtola
- Department
of Chemistry, University of Helsinki, P.O. Box 55, FI-00014 Helsinki, Finland
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2
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Oudot B, Doblhoff-Dier K. Reaction barriers at metal surfaces computed using the random phase approximation: Can we beat DFT in the generalized gradient approximation? J Chem Phys 2024; 161:054708. [PMID: 39092949 DOI: 10.1063/5.0220465] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/25/2024] [Accepted: 07/14/2024] [Indexed: 08/04/2024] Open
Abstract
Reaction barriers for molecules dissociating on metal surfaces (as relevant to heterogeneous catalysis) are often difficult to predict accurately with density functional theory (DFT). Although the results obtained for several dissociative chemisorption reactions via DFT in the generalized gradient approximation (GGA), in meta-GGA, and for GGA exchange + van der Waals correlation scatter around the true reaction barrier, there is an entire class of dissociative chemisorption reactions for which GGA-type functionals collectively underestimate the reaction barrier. Little is known why GGA-DFT collectively fails in some cases and not in others, and we do not know whether other methods suffer from the same inconsistency. Here, we present barrier heights for dissociative chemisorption reactions obtained from the random phase approximation in the adiabatic-connection fluctuation-dissipation theorem (ACFDT-RPA) and from hybrid functionals with different amounts of exact exchange. By comparing the results obtained for the dissociative chemisorption reaction of H2 on Al(110) (where GGA-DFT collectively underestimates the barrier) and H2 on Cu(111) (where GGA-DFT scatters around the true barrier), we can gauge whether the inconsistent description of the systems persists for hybrid functionals and ACFDT-RPA. We find hybrid functionals to improve the relative description of the two systems, but to fall short of chemical accuracy. ACFDT-RPA improves the results further and leads to chemically accurate barriers for both systems. Together with an analysis of the density of states and the results from selected GGA, meta-GGA, and GGA exchange + van der Waals correlation functionals, these results allow us to discuss possible origins for the inconsistent behavior of GGA-based functionals for molecule-metal reaction barriers.
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Affiliation(s)
- B Oudot
- Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, Leiden 2300 RA, The Netherlands
| | - K Doblhoff-Dier
- Leiden Institute of Chemistry, Leiden University, P.O. Box 9502, Leiden 2300 RA, The Netherlands
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3
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Peralta JE, Barone V, Melo JI, Alcoba DR, Massaccesi GE, Lain L, Torre A, Oña OB. DOCSIC: A Mean-Field Method for Orbital-by-Orbital Self-Interaction Correction. J Phys Chem A 2024; 128:6026-6032. [PMID: 38985992 DOI: 10.1021/acs.jpca.4c02801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/12/2024]
Abstract
We introduce a new method to remove the one-electron self-interaction error in approximate density functional calculations on an orbital-by-orbital basis, as originally proposed by Perdew and Zunger [Phys. Rev. B 1981, 23, 5048]. This method is motivated by a recent proposal by Pederson et al. [J. Chem. Phys. 2014, 140, 121103] to remove self-interaction that employs orbitals derived from the real-space density matrix, known as FLOSIC (Fermi Löwdin orbitals self-interaction correction). However, instead of Fermi Löwdin orbitals, our scheme utilizes columns of the density matrix to determine localized orbitals, like the localization procedure proposed by Fuemmeler et al. [J. Chem. Theory Comput. 2023, 19, 8572]. The new method, dubbed DOCSIC for density matrix as orbital coefficients self-interaction correction, contrasts with traditional Perdew-Zunger or FLOSIC in that it does not incorporate additional optimization parameters, and, unlike the average density self-interaction correction of Ciofini et al. [Chem. Phys. Lett. 2003, 380, 12], it makes use of localized orbitals. Another advantage of DOCSIC is that it can be implemented as a mean-field formalism. We show details of the self-consistent generalized Kohn-Sham implementation, some illustrative results, and we finally highlight its advantages and limitations.
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Affiliation(s)
- Juan E Peralta
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, United States
| | - Veronica Barone
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, United States
| | - Juan I Melo
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física. Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Diego R Alcoba
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física. Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Gustavo E Massaccesi
- Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- Instituto de Investigaciones Matemáticas "Luis A. Santaló" (IMAS), Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Luis Lain
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Alicia Torre
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Ofelia B Oña
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina
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4
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Maniar R, Withanage KPK, Shahi C, Kaplan AD, Perdew JP, Pederson MR. Symmetry breaking and self-interaction correction in the chromium atom and dimer. J Chem Phys 2024; 160:144301. [PMID: 38587222 DOI: 10.1063/5.0180863] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/12/2023] [Accepted: 03/21/2024] [Indexed: 04/09/2024] Open
Abstract
Density functional approximations to the exchange-correlation energy can often identify strongly correlated systems and estimate their energetics through energy-minimizing symmetry-breaking. In particular, the binding energy curve of the strongly correlated chromium dimer is described qualitatively by the local spin density approximation (LSDA) and almost quantitatively by the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA), where the symmetry breaking is antiferromagnetic for both. Here, we show that a full Perdew-Zunger self-interaction-correction (SIC) to LSDA seems to go too far by creating an unphysical symmetry-broken state, with effectively zero magnetic moment but non-zero spin density on each atom, which lies ∼4 eV below the antiferromagnetic solution. A similar symmetry-breaking, observed in the atom, better corresponds to the 3d↑↑4s↑3d↓↓4s↓ configuration than to the standard 3d↑↑↑↑↑4s↑. For this new solution, the total energy of the dimer at its observed bond length is higher than that of the separated atoms. These results can be regarded as qualitative evidence that the SIC needs to be scaled down in many-electron regions.
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Affiliation(s)
- Rohan Maniar
- Department of Physics and Engineering Physics, Tulane University, 6400 Freret St., New Orleans, Louisiana 70118, USA
| | - Kushantha P K Withanage
- Department of Physics, The University of Texas at El Paso, 500 West University Ave., El Paso, Texas 79968, USA
| | - Chandra Shahi
- Department of Physics and Engineering Physics, Tulane University, 6400 Freret St., New Orleans, Louisiana 70118, USA
| | - Aaron D Kaplan
- Materials Project, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., B33-141B, Berkeley, California 94720, USA
| | - John P Perdew
- Department of Physics and Engineering Physics, Tulane University, 6400 Freret St., New Orleans, Louisiana 70118, USA
| | - Mark R Pederson
- Department of Physics, The University of Texas at El Paso, 500 West University Ave., El Paso, Texas 79968, USA
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5
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Zhang Y, Ke D, Wu J, Zhang C, Hou L, Lin B, Chen Z, Perdew JP, Sun J. Challenges for density functional theory in simulating metal-metal singlet bonding: A case study of dimerized VO2. J Chem Phys 2024; 160:134101. [PMID: 38557836 DOI: 10.1063/5.0180315] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2023] [Accepted: 03/03/2024] [Indexed: 04/04/2024] Open
Abstract
VO2 is renowned for its electric transition from an insulating monoclinic (M1) phase, characterized by V-V dimerized structures, to a metallic rutile (R) phase above 340 K. This transition is accompanied by a magnetic change: the M1 phase exhibits a non-magnetic spin-singlet state, while the R phase exhibits a state with local magnetic moments. Simultaneous simulation of the structural, electric, and magnetic properties of this compound is of fundamental importance, but the M1 phase alone has posed a significant challenge to the density functional theory (DFT). In this study, we show none of the commonly used DFT functionals, including those combined with on-site Hubbard U to treat 3d electrons better, can accurately predict the V-V dimer length. The spin-restricted method tends to overestimate the strength of the V-V bonds, resulting in a small V-V bond length. Conversely, the spin-symmetry-breaking method exhibits the opposite trends. Each of these two bond-calculation methods underscores one of the two contentious mechanisms, i.e., Peierls lattice distortion or Mott localization due to electron-electron repulsion, involved in the metal-insulator transition in VO2. To elucidate the challenges encountered in DFT, we also employ an effective Hamiltonian that integrates one-dimensional magnetic sites, thereby revealing the inherent difficulties linked with the DFT computations.
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Affiliation(s)
- Yubo Zhang
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Da Ke
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Junxiong Wu
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Chutong Zhang
- Minjiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou, China
| | - Lin Hou
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Baichen Lin
- School of Materials Science and Engineering, Nanyang Technological University, Singapore 639798, Republic of Singapore
- Institute of Materials Research and Engineering (IMRE), Agency for Science, Technology and Research (A*STAR), Singapore 138634, Republic of Singapore
| | - Zuhuang Chen
- School of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
- Flexible Printed Electronics Technology Center, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
| | - John P Perdew
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
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6
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Singh Y, Peralta JE, Jackson KA. The rise and fall of stretched bond errors: Extending the analysis of Perdew-Zunger self-interaction corrections of reaction barrier heights beyond the LSDA. J Chem Phys 2024; 160:124105. [PMID: 38526103 DOI: 10.1063/5.0179261] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2023] [Accepted: 03/07/2024] [Indexed: 03/26/2024] Open
Abstract
Incorporating self-interaction corrections (SIC) significantly improves chemical reaction barrier height predictions made using density functional theory methods. We present a detailed orbital-by-orbital analysis of these corrections for three semi-local density functional approximations (DFAs) situated on the three lowest rungs of Jacob's ladder of approximations. The analysis is based on Fermi-Löwdin Orbital Self-Interaction Correction (FLOSIC) calculations performed at several steps along the reaction pathway from the reactants (R) to the transition state (TS) to the products (P) for four representative reactions selected from the BH76 benchmark set. For all three functionals, the major contribution to self-interaction corrections of the barrier heights can be traced to stretched bond orbitals that develop near the TS configuration. The magnitude of the ratio of the self-exchange-correlation energy to the self-Hartree energy (XC/H) for a given orbital is introduced as an indicator of one-electron self-interaction error. XC/H = 1.0 implies that an orbital's self-exchange-correlation energy exactly cancels its self-Hartree energy and that the orbital, therefore, makes no contribution to the SIC in the FLOSIC scheme. For the practical DFAs studied here, XC/H spans a range of values. The largest values are obtained for stretched or strongly lobed orbitals. We show that significant differences in XC/H for corresponding orbitals in the R, TS, and P configurations can be used to identify the major contributors to the SIC of barrier heights and reaction energies. Based on such comparisons, we suggest that barrier height predictions made using the strongly constrained and appropriately normed meta-generalized gradient approximation may have attained the best accuracy possible for a semi-local functional using the Perdew-Zunger SIC approach.
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Affiliation(s)
- Yashpal Singh
- Department of Physics, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Juan E Peralta
- Department of Physics and Science of Advanced Materials PhD Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Koblar A Jackson
- Department of Physics and Science of Advanced Materials PhD Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
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7
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Zope RR, Yamamoto Y, Baruah T. How well do one-electron self-interaction-correction methods perform for systems with fractional electrons? J Chem Phys 2024; 160:084102. [PMID: 38385511 DOI: 10.1063/5.0182773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2023] [Accepted: 01/28/2024] [Indexed: 02/23/2024] Open
Abstract
Recently developed locally scaled self-interaction correction (LSIC) is a one-electron SIC method that, when used with a ratio of kinetic energy densities (zσ) as iso-orbital indicator, performs remarkably well for both thermochemical properties as well as for barrier heights overcoming the paradoxical behavior of the well-known Perdew-Zunger self-interaction correction (PZSIC) method. In this work, we examine how well the LSIC method performs for the delocalization error. Our results show that both LSIC and PZSIC methods correctly describe the dissociation of H2+ and He2+ but LSIC is overall more accurate than the PZSIC method. Likewise, in the case of the vertical ionization energy of an ensemble of isolated He atoms, the LSIC and PZSIC methods do not exhibit delocalization errors. For the fractional charges, both LSIC and PZSIC significantly reduce the deviation from linearity in the energy vs number of electrons curve, with PZSIC performing superior for C, Ne, and Ar atoms while for Kr they perform similarly. The LSIC performs well at the endpoints (integer occupations) while substantially reducing the deviation. The dissociation of LiF shows both LSIC and PZSIC dissociate into neutral Li and F but only LSIC exhibits charge transfer from Li+ to F- at the expected distance from the experimental data and accurate ab initio data. Overall, both the PZSIC and LSIC methods reduce the delocalization errors substantially.
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Affiliation(s)
- Rajendra R Zope
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Yoh Yamamoto
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA
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8
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Perdew JP. My life in science: Lessons for yours? J Chem Phys 2024; 160:010402. [PMID: 38180261 DOI: 10.1063/5.0179606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2023] [Accepted: 10/26/2023] [Indexed: 01/06/2024] Open
Abstract
Because of an acquired obsession to understand as much as possible in a limited but important area of science and because of optimism, luck, and help from others, my life in science turned out to be much better than I or others could have expected or planned. This is the story of how that happened, and also the story of the groundstate density functional theory of electronic structure, told from a personal perspective.
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Affiliation(s)
- John P Perdew
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, USA
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9
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Nguyen DB, Jackson KA, Peralta JE. Bond length alternation of π-conjugated polymers predicted by the Fermi-Löwdin orbital self-interaction correction method. J Chem Phys 2024; 160:014101. [PMID: 38165094 DOI: 10.1063/5.0178251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2023] [Accepted: 12/07/2023] [Indexed: 01/03/2024] Open
Abstract
π-conjugated polymers have been used in a wide range of practical applications, partly due to their unique properties that originate in the delocalization of electrons through the polymer backbone. The level of delocalization can be characterized by the induced bond length alternation (BLA), with shorter BLA connected with strong delocalization and vice versa. The accurate description of this structural parameter can be considered a benchmark for testing the capability of different electronic structure methods for self-interaction error (SIE) removal and electron correlation inclusion. Density functional theory (DFT), in its local or semi-local flavors, suffers from SIE and, thus, underestimates the BLA compared to self-interaction-free methods. In this work, we utilize the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method for one-electron self-interaction removal to characterize the BLA of five oligomers with increasing length extrapolated to the polymeric limit. We compare the self-interaction-free BLA to several DFT approximations, Møller-Plesset second-order perturbation theory (MP2), and the BLA obtained with the domain based local pair natural orbital CCSD(T) [DLPNO-CCSD(T)] approximation. Our findings show that FLOSIC corrects for the small BLA given by (semi-)local DFT approximations, but it tends to overcorrect with respect to CAM-B3LYP, MP2, and DLPNO-CCSD(T).
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Affiliation(s)
- Duyen B Nguyen
- Department of Physics and Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Koblar A Jackson
- Department of Physics and Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Juan E Peralta
- Department of Physics and Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
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10
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Reimann M, Kirsch C, Sebastiani D, Kaupp M. Rydberg electron stabilizes the charge localized state of the diamine cation. Nat Commun 2024; 15:293. [PMID: 38177143 PMCID: PMC10767003 DOI: 10.1038/s41467-023-44526-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/04/2023] [Accepted: 12/18/2023] [Indexed: 01/06/2024] Open
Abstract
A previous controversial discussion regarding the interpretation of Rydberg spectra of gaseous dimethylpiperazine (DMP) as showing the co-existence of a localized and delocalized mixed-valent DMP+ radical cation is revisited. Here we show by high-level quantum-chemical calculations that an apparent barrier separating localized and delocalized DMP+ minima in previous multi-reference configuration-interaction (MRCI) calculations and in some other previous computations were due to unphysical curve crossings of the reference wave functions. These discontinuities on the surface are removed in state-averaged MRCI calculations and with some other, orthogonal high-level approaches, which do not provide a barrier and thus no localized minimum. We then proceed to show that in the actually observed Rydberg state of neutral DMP the 3s-type Rydberg electron binds more strongly to a localized positive charge distribution, generating a localized DMP* Rydberg-state minimum, which is absent for the DMP+ cation. This work presents a case where interactions of a Rydberg electron with the underlying cationic core alter molecular structure in a fundamental way.
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Affiliation(s)
- Marc Reimann
- Theoretische Chemie/Quantenchemie, Institut für Chemie, Sekr. C7, Technische Universität Berlin, 10623, Berlin, Germany
| | - Christoph Kirsch
- Institut für Chemie, Martin-Luther-University Halle-Wittenberg, 06120, Halle (Saale), Germany
| | - Daniel Sebastiani
- Institut für Chemie, Martin-Luther-University Halle-Wittenberg, 06120, Halle (Saale), Germany
| | - Martin Kaupp
- Theoretische Chemie/Quantenchemie, Institut für Chemie, Sekr. C7, Technische Universität Berlin, 10623, Berlin, Germany.
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11
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Pederson MR, Withanage KPK, Hooshmand Z, Johnson AI, Baruah T, Yamamoto Y, Zope RR, Kao DY, Shukla PB, Johnson JK, Peralta JE, Jackson KA. Use of FLOSIC for understanding anion-solvent interactions. J Chem Phys 2023; 159:154112. [PMID: 37861122 DOI: 10.1063/5.0172300] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2023] [Accepted: 09/20/2023] [Indexed: 10/21/2023] Open
Abstract
An Achille's heel of lower-rung density-functional approximations is that the highest-occupied-molecular-orbital energy levels of anions, known to be stable or metastable in nature, are often found to be positive in the worst case or above the lowest-unoccupied-molecular-orbital levels on neighboring complexes that are not expected to accept charge. A trianionic example, [Cr(C2O4)3]3-, is of interest for constraining models linking Cr isotope ratios in rock samples to oxygen levels in Earth's atmosphere over geological timescales. Here we describe how crowd sourcing can be used to carry out self-consistent Fermi-Löwdin-Orbital-Self-Interaction corrected calculations (FLOSIC) on this trianion in solution. The calculations give a physically correct description of the electronic structure of the trianion and water. In contrast, uncorrected local density approximation (LDA) calculations result in approximately half of the anion charge being transferred to the water bath due to the effects of self-interaction error. Use of group-theory and the intrinsic sparsity of the theory enables calculations roughly 125 times faster than our initial implementation in the large N limit reached here. By integrating charge density densities and Coulomb potentials over regions of space and analyzing core-level shifts of the Cr and O atoms as a function of position and functional, we unambiguously show that FLOSIC, relative to LDA, reverses incorrect solute-solvent charge transfer in the trianion-water complex. In comparison to other functionals investigated herein, including Hartree-Fock and the local density approximation, the FLOSIC Cr 1s eigenvalues provide the best agreement with experimental core ionization energies.
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Affiliation(s)
- Mark R Pederson
- Physics Department, University of Texas at El Paso, El Paso, Texas 79968, USA
| | | | - Zahra Hooshmand
- Physics Department, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Alex I Johnson
- Physics Department, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Physics Department, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Yoh Yamamoto
- Physics Department, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R Zope
- Physics Department, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Der-You Kao
- NASA Postdoctoral Program, NASA Goddard Space Flight Center, Greenbelt, Maryland 20771, USA
| | - Priyanka B Shukla
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - J Karl Johnson
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Juan E Peralta
- Physics Department, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Koblar A Jackson
- Physics Department, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
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12
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Bosko IP, Staroverov VN. Derivation and reinterpretation of the Fermi-Amaldi functional. J Chem Phys 2023; 159:131101. [PMID: 37800642 DOI: 10.1063/5.0166358] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2023] [Accepted: 09/13/2023] [Indexed: 10/07/2023] Open
Abstract
The Fermi-Amaldi correction to the electrostatic self-repulsion of the particle density is usually regarded as a semi-classical exchange functional that happens to be exact only for one- and closed-shell two-electron systems. We show that this functional can be derived quantum-mechanically and is exact for any number of fermions or bosons of arbitrary spin as long as the particles occupy the same spatial orbital. The Fermi-Amaldi functional is also size-consistent for such systems, provided that the factor N in its expression is understood as an orbital occupation number rather than the total number of particles. These properties of the Fermi-Amaldi functional are ultimately related to the fact that it is a special case of the self-exchange energy formula. Implications of our findings are discussed.
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Affiliation(s)
- Ivan P Bosko
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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13
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Shukla PB, Mishra P, Baruah T, Zope RR, Jackson KA, Johnson JK. How Do Self-Interaction Errors Associated with Stretched Bonds Affect Barrier Height Predictions? J Phys Chem A 2023; 127:1750-1759. [PMID: 36787213 PMCID: PMC10032567 DOI: 10.1021/acs.jpca.2c07894] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/15/2023]
Abstract
Density functional theory (DFT) suffers from self-interaction errors (SIEs) that generally result in the underestimation of chemical reaction barrier heights. This is commonly attributed to the tendency of density functional approximations to overstabilize delocalized densities that typically occur in the stretched bonds of transition state structures. The Perdew-Zunger self-interaction correction (PZSIC) and locally scaled self-interaction correction (LSIC) improve the prediction of barrier heights of chemical reactions, with LSIC giving better accuracy than PZSIC on average. These methods employ an orbital-by-orbital correction scheme to remove the one-electron SIE. In the context of barrier heights, this allows an analysis of how the self-interaction correction (SIC) for each orbital contributes to the calculated barriers using Fermi-Löwdin orbitals (FLOs). We hypothesize that the SIC contribution to the reaction barrier comes mainly from a limited number of orbitals that are directly involved in bond-breaking and bond-making in the reaction transition state. We call these participant orbitals (POs), in contrast to spectator orbitals (SOs) which are not directly involved in changes to the bonding. Our hypothesis is that ΔETotalSIC ≈ ΔEPOSIC, where ΔETotalSIC is the difference in the SIC corrections for the reactants or products and the transition state. We test this hypothesis for the reaction barriers of the BH76 benchmark set of reactions. We find that the stretched-bond orbitals indeed make the largest individual SIC contributions to the barriers. These contributions increase the barrier heights relative to LSDA, which underpredicts the barrier. However, the full stretched-bond hypothesis does not hold in all cases for either PZSIC or LSIC. There are many cases where the total SIC contribution from the SOs is significant and cannot be ignored. The size of the SIC contribution to the barrier height is a key indicator. A large SIC correction is correlated to a large LSDA error in the barrier, showing that PZSIC properly gives larger corrections when corrections are needed most. A comparison of the performance of PZSIC and LSIC shows that the two methods have similar accuracy for reactions with large LSDA errors, but LSIC is clearly better for reactions with small errors. We trace this to an improved description of reaction energies in LSIC.
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Affiliation(s)
- Priyanka B Shukla
- Department of Chemical & Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States
| | - Prakash Mishra
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Tunna Baruah
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, United States
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Rajendra R Zope
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, United States
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Koblar A Jackson
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, Michigan 48859, United States
| | - J Karl Johnson
- Department of Chemical & Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States
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14
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Ruan S, Jackson KA, Ruzsinszky A. Spin-crossover complexes: Self-interaction correction vs density correction. J Chem Phys 2023; 158:064303. [PMID: 36792493 DOI: 10.1063/5.0128950] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
Complexes containing a transition metal atom with a 3d4-3d7 electron configuration typically have two low-lying, high-spin (HS) and low-spin (LS) states. The adiabatic energy difference between these states, known as the spin-crossover energy, is small enough to pose a challenge even for electronic structure methods that are well known for their accuracy and reliability. In this work, we analyze the quality of electronic structure approximations for spin-crossover energies of iron complexes with four different ligands by comparing energies from self-consistent and post-self-consistent calculations for methods based on the random phase approximation and the Fermi-Löwdin self-interaction correction. Considering that Hartree-Fock densities were found by Song et al., J. Chem. Theory Comput. 14, 2304 (2018), to eliminate the density error to a large extent, and that the Hartree-Fock method and the Perdew-Zunger-type self-interaction correction share some physics, we compare the densities obtained with these methods to learn their resemblance. We find that evaluating non-empirical exchange-correlation energy functionals on the corresponding self-interaction-corrected densities can mitigate the strong density errors and improves the accuracy of the adiabatic energy differences between HS and LS states.
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Affiliation(s)
- Shiqi Ruan
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Koblar A Jackson
- Physics Department and Science of Advanced Materials Ph. D. Program, Central Michigan University, Mount Pleasant, Michigan 48858, USA
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
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15
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Yamamoto Y, Baruah T, Chang PH, Romero S, Zope RR. Self-consistent implementation of locally scaled self-interaction-correction method. J Chem Phys 2023; 158:064114. [PMID: 36792502 DOI: 10.1063/5.0130436] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023] Open
Abstract
Recently proposed local self-interaction correction (LSIC) method [Zope et al., J. Chem. Phys. 151, 214108 (2019)] is a one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities. The LSIC method is exact for the one-electron densities, also recovers the uniform electron gas limit of the uncorrected density functional approximation, and reduces to the well-known Perdew-Zunger SIC (PZSIC) method as a special case. This article presents the self-consistent implementation of the LSIC method using the ratio of Weizsäcker and Kohn-Sham kinetic energy densities as an iso-orbital indicator. The atomic forces as well as the forces on the Fermi-Löwdin orbitals are also implemented for the LSIC energy functional. Results show that LSIC with the simplest local spin density functional predicts atomization energies of the AE6 dataset better than some of the most widely used generalized-gradient-approximation (GGA) functional [e.g., Perdew-Burke-Ernzerhof (PBE)] and barrier heights of the BH6 database better than some of the most widely used hybrid functionals (e.g., PBE0 and B3LYP). The LSIC method [a mean absolute error (MAE) of 0.008 Å] predicts bond lengths of a small set of molecules better than the PZSIC-LSDA (MAE 0.042 Å) and LSDA (0.011 Å). This work shows that accurate results can be obtained from the simplest density functional by removing the self-interaction-errors using an appropriately designed SIC method.
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Affiliation(s)
- Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Po-Hao Chang
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Selim Romero
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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16
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Romero S, Baruah T, Zope RR. Spin-state gaps and self-interaction-corrected density functional approximations: Octahedral Fe(II) complexes as case study. J Chem Phys 2023; 158:054305. [PMID: 36754787 DOI: 10.1063/5.0133999] [Citation(s) in RCA: 5] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
Accurate prediction of a spin-state energy difference is crucial for understanding the spin crossover phenomena and is very challenging for density functional approximations, especially for local and semi-local approximations due to delocalization errors. Here, we investigate the effect of the self-interaction error removal from the local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof generalized gradient approximation on the spin-state gaps of Fe(II) complexes with various ligands using recently developed locally scaled self-interaction correction (LSIC) by Zope et al. [J. Chem. Phys. 151, 214108 (2019)]. The LSIC method is exact for one-electron density, recovers the uniform electron gas limit of the underlying functional, and approaches the well-known Perdew-Zunger self-interaction correction (PZSIC) as a particular case when the scaling factor is set to unity. Our results, when compared with reference diffusion Monte Carlo results, show that the PZSIC method significantly overestimates spin-state gaps favoring low spin states for all ligands and does not improve upon density functional approximations. The perturbative LSIC-LSDA using PZSIC densities significantly improves the gaps with a mean absolute error of 0.51 eV but slightly overcorrects for the stronger CO ligands. The quasi-self-consistent LSIC-LSDA, such as coupled-cluster single double and perturbative triple [CCSD(T)], gives a correct sign of spin-state gaps for all ligands with a mean absolute error of 0.56 eV, comparable to that of CCSD(T) (0.49 eV).
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Affiliation(s)
- Selim Romero
- Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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17
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Melo JI, Pederson MR, Peralta JE. Density Matrix Implementation of the Fermi-Löwdin Orbital Self-Interaction Correction Method. J Phys Chem A 2023; 127:527-534. [PMID: 36598275 DOI: 10.1021/acs.jpca.2c07646] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
The Fermi-Löwdin orbital self-interaction correction (FLOSIC) method effectively provides a transformation from canonical orbitals to localized Fermi-Löwdin orbitals which are used to remove the self-interaction error in the Perdew-Zunger (PZ) framework. This transformation is solely determined by a set of points in space, called Fermi-Löwdin descriptors (FODs), and the occupied canonical orbitals or the density matrix. In this work, we provide a detailed workflow for the implementation of the FLOSIC method for removal of self-interaction error in DFT calculations in an orbital-by-orbital basis that takes advantage of the unitary invariant nature of the FLOSIC method. In this way, it is possible to cast the self-consistent energy minimization at fixed FODs in the same manner than standard Kohn-Sham with one additional term in the Kohn-Sham Hamiltonian that introduces the PZ self-interaction correction. Each energy minimization iteration is divided in two substeps, one for the density matrix and one for the FODs. Expressions for the effective Kohn-Sham matrix and FOD gradients are provided such that its implementation is suitable for most electronic structure codes. We analyze the convergence characteristics of the algorithm and present applications for the evaluation of NMR shielding constants and real-time time-dependent DFT simulations based on the Liouville-von Neumann equation to calculate excitation energies.
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Affiliation(s)
- Juan I Melo
- Facultad de Ciencias Exactas y Naturales, Departamento de Física, Universidad de Buenos Aires, Buenos Aires1428, Argentina.,CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Buenos Aires1428, Argentina
| | - Mark R Pederson
- Department of Physics, the University of Texas at El Paso, El Paso, Texas79968, United States
| | - Juan E Peralta
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan48859, United States
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18
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Kaplan AD, Shahi C, Bhetwal P, Sah RK, Perdew JP. Understanding Density-Driven Errors for Reaction Barrier Heights. J Chem Theory Comput 2023; 19:532-543. [PMID: 36599075 DOI: 10.1021/acs.jctc.2c00953] [Citation(s) in RCA: 12] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Abstract
Delocalization errors, such as charge-transfer and some self-interaction errors, plague computationally efficient and otherwise accurate density functional approximations (DFAs). Evaluating a semilocal DFA non-self-consistently on the Hartree-Fock (HF) density is often recommended as a computationally inexpensive remedy for delocalization errors. For sophisticated meta-GGAs like SCAN, this approach can achieve remarkable accuracy. This HF-DFT (also known as DFA@HF) is often presumed to work, when it significantly improves over the DFA, because the HF density is more accurate than the self-consistent DFA density in those cases. By applying the metrics of density-corrected density functional theory (DFT), we show that HF-DFT works for barrier heights by making a localizing charge-transfer error or density overcorrection, thereby producing a somewhat reliable cancellation of density- and functional-driven errors for the energy. A quantitative analysis of the charge-transfer errors in a few randomly selected transition states confirms this trend. We do not have the exact functional and electron densities that would be needed to evaluate the exact density- and functional-driven errors for the large BH76 database of barrier heights. Instead, we have identified and employed three fully nonlocal proxy functionals (SCAN 50% global hybrid, range-separated hybrid LC-ωPBE, and SCAN-FLOSIC) and their self-consistent proxy densities. These functionals are chosen because they yield reasonably accurate self-consistent barrier heights and because their self-consistent total energies are nearly piecewise linear in fractional electron number─two important points of similarity to the exact functional. We argue that density-driven errors of the energy in a self-consistent density functional calculation are second order in the density error and that large density-driven errors arise primarily from incorrect electron transfers over length scales larger than the diameter of an atom.
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Affiliation(s)
- Aaron D Kaplan
- Department of Physics, Temple University, Philadelphia, Pennsylvania19122, United States
| | - Chandra Shahi
- Department of Physics, Temple University, Philadelphia, Pennsylvania19122, United States
| | - Pradeep Bhetwal
- Department of Physics, Temple University, Philadelphia, Pennsylvania19122, United States
| | - Raj K Sah
- Department of Physics, Temple University, Philadelphia, Pennsylvania19122, United States
| | - John P Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania19122, United States
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania19122, United States
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19
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Albavera-Mata A, Trickey SB, Hennig RG. Mean Value Ensemble Hubbard- U Correction for Spin-Crossover Molecules. J Phys Chem Lett 2022; 13:12049-12054. [PMID: 36542415 DOI: 10.1021/acs.jpclett.2c03388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/17/2023]
Abstract
High-throughput searches for spin-crossover molecules require Hubbard-U corrections to common density functional exchange-correlation (XC) approximations. However, the Ueff values obtained from linear response or based on previous studies overcorrect the spin-crossover energies. We demonstrate that employing a linearly mixed ensemble average spin state as the reference configuration for the linear response calculation of Ueff resolves this issue. Validation on a commonly used set of spin-crossover complexes shows that these ensemble Ueff values consistently are smaller than those calculated directly on a pure spin state, irrespective of whether that be low- or high-spin. Adiabatic crossover energies using this methodology for a generalized gradient approximation XC functional are closer to the expected target energy range than with conventional Ueff values. Based on the observation that the Ueff correction is similar for different complexes that share transition metals with the same oxidation state, we devise a set of recommended averaged Ueff values for high-throughput calculations.
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Affiliation(s)
- Angel Albavera-Mata
- Center for Molecular Magnetic Quantum Materials, Quantum Theory Project, University of Florida, Gainesville, Florida32611, United States
- Department of Materials Science and Engineering, University of Florida, Gainesville, Florida32611, United States
| | - S B Trickey
- Center for Molecular Magnetic Quantum Materials, Quantum Theory Project, University of Florida, Gainesville, Florida32611, United States
- Department of Physics and Department of Chemistry, University of Florida, Gainesville, Florida32611, United States
| | - Richard G Hennig
- Center for Molecular Magnetic Quantum Materials, Quantum Theory Project, University of Florida, Gainesville, Florida32611, United States
- Department of Materials Science and Engineering, University of Florida, Gainesville, Florida32611, United States
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20
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Janesko BG. Unification of Perdew-Zunger self-interaction correction, DFT+U, and Rung 3.5 density functionals. J Chem Phys 2022; 157:151101. [PMID: 36272781 DOI: 10.1063/5.0109338] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
This Communication presents a unified derivation of three different approximations used in density functional theory (DFT): the Perdew-Zunger self-interaction correction (PZSIC), the Hubbard correction DFT+U, and the Rung 3.5 density functionals. All three approximations can be derived by introducing electron self-interaction into the Kohn-Sham (KS) reference system of noninteracting electrons. The derivation uses the Adiabatic Projection formalism: one projects the electron-electron interaction operator onto certain states, introduces the projected operator into the reference system, and defines a density functional for the remainder. Projecting onto individual localized KS orbitals recovers our previous derivation of the PZSIC [B. G. Janesko, J. Phys. Chem. Lett. 13, 5698-5702 (2022)]. Projecting onto localized atom-centered orbitals recovers a variant of DFT+U. Projecting onto localized states at each point in space recovers Rung 3.5 approaches. New results include an "atomic state PZSIC" that does not require localizing the KS orbitals, a demonstration that typical Hubbard U parameters reproduce a scaled-down PZSIC, and a Rung 3.5 variant of DFT+U that does not require choosing atom-dependent states.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry and Biochemistry, Texas Christian University, 2800 S. University Dr., Fort Worth, Texas 76109, USA
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21
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Bryenton KR, Adeleke AA, Dale SG, Johnson ER. Delocalization error: The greatest outstanding challenge in density‐functional theory. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2022. [DOI: 10.1002/wcms.1631] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Affiliation(s)
- Kyle R. Bryenton
- Department of Physics and Atmospheric Science Dalhousie University Halifax Nova Scotia Canada
| | | | - Stephen G. Dale
- Queensland Micro‐ and Nanotechnology Centre Griffith University Nathan Queensland Australia
| | - Erin R. Johnson
- Department of Physics and Atmospheric Science Dalhousie University Halifax Nova Scotia Canada
- Department of Chemistry Dalhousie University Halifax Nova Scotia Canada
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22
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Janesko BG. Systematically Improvable Generalization of Self-Interaction Corrected Density Functional Theory. J Phys Chem Lett 2022; 13:5698-5702. [PMID: 35709503 DOI: 10.1021/acs.jpclett.2c01359] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Perdew-Zunger self-interaction correction (PZSIC) reintroduces an exact constraint to approximate density functional theory (DFT). However, PZSIC can paradoxically degrade performance, and standard DFT approximations (with or without PZSIC) are not systematically improvable. We use the adiabatic projection formalism (Janesko, B. G. J. Chem. Phys. 2022, 156, 014111, https://doi.org/10.1063/5.0076144) to derive PZSIC in terms of a reference system experiencing only electron self-interaction. Generalization to a "self-and-some-others" interaction introduces correlation into the reference system, systematically bridging from PZSIC to exact wave function theory without the double counting of correlation. Minimal active spaces accurately treat nearly one electron, near-equilibrium, and strongly correlated model systems at modest computational expense.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, 2800 S. University Drive, Fort Worth, Texas 76129, United States
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23
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Mishra P, Yamamoto Y, Chang PH, Nguyen DB, Peralta JE, Baruah T, Zope RR. Study of Self-Interaction Errors in Density Functional Calculations of Magnetic Exchange Coupling Constants Using Three Self-Interaction Correction Methods. J Phys Chem A 2022; 126:1923-1935. [PMID: 35302373 DOI: 10.1021/acs.jpca.1c10354] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We examine the role of self-interaction error (SIE) removal on the evaluation of magnetic exchange coupling constants. In particular, we analyze the effect of scaling down the self-interaction correction (SIC) for three nonempirical density functional approximations (DFAs) namely, the local spin density approximation, the Perdew-Burke-Ernzerhof generalized gradient approximation, and the recent SCAN family of meta-GGA functionals. To this end, we employ three one-electron SIC methods: Perdew-Zunger SIC [Perdew, J. P.; Zunger, A. Phys. Rev. B, 1981, 23, 5048.], the orbitalwise scaled SIC method [Vydrov, O. A. et al. J. Chem. Phys. 2006, 124, 094108.], and the recent local scaling method [Zope, R. R. et al. J. Chem. Phys. 2019, 151, 214108.]. We compute the magnetic exchange coupling constants using the spin projection and nonprojection approaches for sets of molecules composed of dinuclear and polynuclear H···He models, organic radical molecules, and chlorocuprate and compare these results against accurate theories and experiment. Our results show that for the systems that mainly consist of single-electron regions, PZSIC performs well, but for more complex organic systems and the chlorocuprates, an overcorrecting tendency of PZSIC combined with the DFAs utilized in this work is more pronounced, and in such cases, LSIC with kinetic energy density ratio performs better than PZSIC. Analysis of the results in terms of SIC corrections to the density and to the total energy shows that both density and energy correction are required to obtain an improved prediction of magnetic exchange couplings.
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Affiliation(s)
- Prakash Mishra
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Po-Hao Chang
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Duyen B Nguyen
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, United States
| | - Juan E Peralta
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, United States
| | - Tunna Baruah
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, United States.,Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, United States
| | - Rajendra R Zope
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, United States.,Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, United States
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24
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Mishra P, Yamamoto Y, Johnson JK, Jackson KA, Zope RR, Baruah T. Study of self-interaction-errors in barrier heights using locally scaled and Perdew-Zunger self-interaction methods. J Chem Phys 2022; 156:014306. [PMID: 34998352 DOI: 10.1063/5.0070893] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
We study the effect of self-interaction errors on the barrier heights of chemical reactions. For this purpose, we use the well-known Perdew-Zunger self-interaction-correction (PZSIC) [J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981)] as well as two variations of the recently developed, locally scaled self-interaction correction (LSIC) [Zope et al., J. Chem. Phys. 151, 214108 (2019)] to study the barrier heights of the BH76 benchmark dataset. Our results show that both PZSIC and especially the LSIC methods improve the barrier heights relative to the local density approximation (LDA). The version of LSIC that uses the iso-orbital indicator z as a scaling factor gives a more consistent improvement than an alternative version that uses an orbital-dependent factor w based on the ratio of orbital densities to the total electron density. We show that LDA energies evaluated using the self-consistent and self-interaction-free PZSIC densities can be used to assess density-driven errors. The LDA reaction barrier errors for the BH76 set are found to contain significant density-driven errors for all types of reactions contained in the set, but the corrections due to adding SIC to the functional are much larger than those stemming from the density for the hydrogen transfer reactions and of roughly equal size for the non-hydrogen transfer reactions.
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Affiliation(s)
- Prakash Mishra
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - J Karl Johnson
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Koblar A Jackson
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Rajendra R Zope
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, USA
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25
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Nguyen DB, Pederson MR, Perdew JP, Jackson KA, Peralta JE. Initial Fermi orbital descriptors for FLOSIC calculations: The quick-FOD method. Chem Phys Lett 2021. [DOI: 10.1016/j.cplett.2021.138952] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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26
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Jana S, Myneni H, Śmiga S, Constantin LA, Samal P. Benchmark test of a dispersion corrected revised Tao-Mo semilocal functional for thermochemistry, kinetics, and noncovalent interactions of molecules and solids. J Chem Phys 2021; 155:114102. [PMID: 34551544 DOI: 10.1063/5.0060538] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
In the density functional theory, dispersion corrected semilocal approximations are often used to benchmark weekly interacting finite and extended systems. Here, the focus is on providing a broad overview of the performance of D3 dispersion corrected revised Tao-Mo (revTM) semilocal functionals [A. Patra et al., J. Chem. Phys. 153, 084 117 (2020)] for thermochemistry and kinetics of molecules, molecular crystals, ice polymorphs, metal-organic systems, atom/molecular adsorption on solids, water interacting with nano-materials, binding energies of layered materials, and properties of weekly and strongly bonded solids. We show that the most suitable "optimized power" function for the revTM functional needs a modification to make it suitable for properties related to the diverse nature of finite and extended systems. The present work is an extension of the previously proposed revTM+D3 method with the motivation to design and benchmark the dispersion corrected cost-effective method based on this semilocal approximation. We show that the revised revTM+D3 functional provides various general purpose molecular and solid properties with the closest to experimental findings than its predecessor. The present assessment and benchmarking can be practically useful for performing cost-effective method based simulations of various molecular and solid-state properties.
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Affiliation(s)
- Subrata Jana
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752 050, India
| | - Hemanadhan Myneni
- Science Institute and Faculty of Physical Sciences, University of Iceland, VR-III, 107 Reykjavík, Iceland
| | - Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
| | - Lucian A Constantin
- Istituto di Nanoscienze, Consiglio Nazionale delle Ricerche CNR-NANO, 41125 Modena, Italy
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752 050, India
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27
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Akter S, Vargas JA, Sharkas K, Peralta JE, Jackson KA, Baruah T, Zope RR. How well do self-interaction corrections repair the overestimation of static polarizabilities in density functional calculations? Phys Chem Chem Phys 2021; 23:18678-18685. [PMID: 34612405 DOI: 10.1039/d0cp06512a] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We examine the effect of removing self-interaction error (SIE) on the calculation of molecular polarizabilities in the local spin density (LSDA) and generalized gradient approximations (GGA). To this end, we utilize a database of 132 molecules taken from a recent benchmark study [Hait and Head-Gordon, Phys. Chem. Chem. Phys., 2018, 20, 19800] to assess the influence of SIE on polarizabilities by comparing results with accurate reference data. Our results confirm that the general overestimation of molecular polarizabilities by these density functional approximations can be attributed to SIE. However, removing SIE using the Perdew-Zunger self-interaction-correction (PZ-SIC) method, implemented using the Fermi-Löwdin Orbital SIC approach, leads to an underestimation of molecular polarizabilities, showing that PZ-SIC overcorrects when combined with LSDA or GGA. Application of a recently proposed locally scaled SIC [Zope, et al., J. Chem. Phys., 2019, 151, 214108] is found to provide more accurate polarizabilities. We attribute this to the ability of the local scaling scheme to selectively correct for SIE in the regions of space where the correction is needed most.
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Affiliation(s)
- Sharmin Akter
- Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA.
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28
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Sengupta T, Bista D, Khanna SN. Developing Efficient Suzuki Cross-Coupling Catalysts by Doping Palladium Clusters with Silver. ACS Catal 2021. [DOI: 10.1021/acscatal.1c02083] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023]
Affiliation(s)
- Turbasu Sengupta
- Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284-2000, United States
| | - Dinesh Bista
- Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284-2000, United States
| | - Shiv N. Khanna
- Department of Physics, Virginia Commonwealth University, Richmond, Virginia 23284-2000, United States
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29
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Pietezak DF, Vieira D. N-dependent self-interaction corrections: Are they still appealing? Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02828-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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30
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Ramos C, Muehlbrad J, Janesko BG. Density functionals with full nonlocal exchange, nonlocal rung-3.5 correlation, and D3 dispersion: Combined accuracy for general main-group thermochemistry, kinetics, and noncovalent interactions. J Comput Chem 2021; 42:1974-1981. [PMID: 34387364 DOI: 10.1002/jcc.26728] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/04/2021] [Accepted: 07/25/2021] [Indexed: 11/11/2022]
Abstract
We introduce the HF-R35-D3(BJ) functional combining full nonlocal exact (Hartree-Fock-like, HF) exchange, inexpensive rung-3.5 correlation constructed from nonlocal one-electron operators, and nonlocal D3 dispersion corrections. HF-R35-D3(BJ) is among the first full-exact-exchange functionals offering competitive accuracy for general main-group thermochemistry, kinetics, and noncovalent interactions. HF-R35-D3(BJ) gives weighted mean absolute deviation WTMAD-2 8.5 kcal/mol across the entire GMTKN55 dataset, outperforming most dispersion-corrected semilocal functionals and approaching the accuracy of dispersion-corrected global hybrids. This requires six fitted parameters, three each in the nonlocal correlation and dispersion corrections. Full nonlocal exchange appears to help give accurate binding energies and reasonable energy orderings for water hexamers. These results motivate continued exploration of inexpensive nonlocal correlation corrections to nonlocal exchange.
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Affiliation(s)
- Chloe Ramos
- Department of Chemistry & Biochemistry, Texas Christian University, Fort Worth, Texas, USA
| | - Jeremiah Muehlbrad
- Department of Chemistry & Biochemistry, Texas Christian University, Fort Worth, Texas, USA
| | - Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, Fort Worth, Texas, USA
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31
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Janesko BG. Replacing hybrid density functional theory: motivation and recent advances. Chem Soc Rev 2021; 50:8470-8495. [PMID: 34060549 DOI: 10.1039/d0cs01074j] [Citation(s) in RCA: 59] [Impact Index Per Article: 19.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
Density functional theory (DFT) is the most widely-used electronic structure approximation across chemistry, physics, and materials science. Every year, thousands of papers report hybrid DFT simulations of chemical structures, mechanisms, and spectra. Unfortunately, hybrid DFT's accuracy is ultimately limited by tradeoffs between over-delocalization and under-binding. This review summarizes these tradeoffs, and introduces six modern attempts to go beyond them while maintaining hybrid DFT's relatively low computational cost: DFT+U, self-interaction corrections, localized orbital scaling corrections, local hybrid functionals, real-space nondynamical correlation, and our rung-3.5 approach. The review concludes with practical suggestions for DFT users to identify and mitigate these tradeoffs' impact on their simulations.
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Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, 2800 S. University Dr, Fort Worth, TX 76129, USA.
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32
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Akter S, Yamamoto Y, Zope RR, Baruah T. Static dipole polarizabilities of polyacenes using self-interaction-corrected density functional approximations. J Chem Phys 2021; 154:114305. [DOI: 10.1063/5.0041265] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sharmin Akter
- Computational Science Program, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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33
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Wagle K, Santra B, Bhattarai P, Shahi C, Pederson MR, Jackson KA, Perdew JP. Self-interaction correction in water–ion clusters. J Chem Phys 2021; 154:094302. [DOI: 10.1063/5.0041620] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kamal Wagle
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Biswajit Santra
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Puskar Bhattarai
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Chandra Shahi
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Mark R. Pederson
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Koblar A. Jackson
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - John P. Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
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34
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Bhattarai P, Santra B, Wagle K, Yamamoto Y, Zope RR, Ruzsinszky A, Jackson KA, Perdew JP. Exploring and enhancing the accuracy of interior-scaled Perdew–Zunger self-interaction correction. J Chem Phys 2021; 154:094105. [DOI: 10.1063/5.0041646] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Puskar Bhattarai
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Biswajit Santra
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Kamal Wagle
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Koblar A. Jackson
- Department of Physics and Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - John P. Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
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35
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Diaz CM, Suryanarayana P, Xu Q, Baruah T, Pask JE, Zope RR. Implementation of Perdew–Zunger self-interaction correction in real space using Fermi–Löwdin orbitals. J Chem Phys 2021; 154:084112. [DOI: 10.1063/5.0031341] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Carlos M. Diaz
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Phanish Suryanarayana
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Qimen Xu
- College of Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - John E. Pask
- Physics Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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36
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Santra G, Martin JML. What Types of Chemical Problems Benefit from Density-Corrected DFT? A Probe Using an Extensive and Chemically Diverse Test Suite. J Chem Theory Comput 2021; 17:1368-1379. [PMID: 33625863 PMCID: PMC8028055 DOI: 10.1021/acs.jctc.0c01055] [Citation(s) in RCA: 42] [Impact Index Per Article: 14.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
![]()
For the large and
chemically diverse GMTKN55 benchmark suite, we
have studied the performance of density-corrected density functional
theory (HF-DFT), compared to self-consistent DFT, for several pure
and hybrid GGA and meta-GGA exchange–correlation (XC) functionals
(PBE, BLYP, TPSS, and SCAN) as a function of the percentage of HF
exchange in the hybrid. The D4 empirical dispersion correction has
been added throughout. For subsets dominated by dynamical correlation,
HF-DFT is highly beneficial, particularly at low HF exchange percentages.
This is especially true for noncovalent interactions where the electrostatic
component is dominant, such as hydrogen and halogen bonds: for π-stacking,
HF-DFT is detrimental. For subsets with significant nondynamical correlation
(i.e., where a Hartree–Fock determinant is not a good zero-order
wavefunction), HF-DFT may do more harm than good. While the self-consistent
series show optima at or near 37.5% (i.e., 3/8) for all four XC functionals—consistent
with Grimme’s proposal of the PBE38 functional—HF-BnLYP-D4, HF-PBEn-D4, and HF-TPSSn-D4 all exhibit minima nearer 25% (i.e., 1/4) as the use
of HF orbitals greatly mitigates the error at 25% for barrier heights.
Intriguingly, for HF-SCANn-D4, the minimum is near
10%, but the weighted mean absolute error (WTMAD2) for GMTKN55 is
only barely lower than that for HF-SCAN-D4 (i.e., where the post-HF
step is a pure meta-GGA). The latter becomes an attractive option,
only slightly more costly than pure Hartree–Fock, and devoid
of adjustable parameters other than the three in the dispersion correction.
Moreover, its WTMAD2 is only surpassed by the highly empirical M06-2X
and by the combinatorially optimized empirical range-separated hybrids
ωB97X-V and ωB97M-V.
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Affiliation(s)
- Golokesh Santra
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, 7610001 Reḥovot, Israel
| | - Jan M L Martin
- Department of Molecular Chemistry and Materials Science, Weizmann Institute of Science, 7610001 Reḥovot, Israel
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37
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Withanage KPK, Bhattarai P, Peralta JE, Zope RR, Baruah T, Perdew JP, Jackson KA. Density-related properties from self-interaction corrected density functional theory calculations. J Chem Phys 2021; 154:024102. [DOI: 10.1063/5.0034545] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kushantha P. K. Withanage
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Puskar Bhattarai
- Physics Department, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Juan E. Peralta
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Rajendra R. Zope
- Physics Department and Computational Science Program, University of Texas, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Physics Department and Computational Science Program, University of Texas, El Paso, Texas 79968, USA
| | - John P. Perdew
- Physics Department and Chemistry Department, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Koblar A. Jackson
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
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38
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Romero S, Yamamoto Y, Baruah T, Zope RR. Local self-interaction correction method with a simple scaling factor. Phys Chem Chem Phys 2021; 23:2406-2418. [DOI: 10.1039/d0cp06282k] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The local self-interaction correction method with a simple scaling factor performs better than the Perdew-Zunger self-interaction correction method and also provides a good description of the binding energies of weakly bonded water clusters.
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Affiliation(s)
- Selim Romero
- Department of Physics
- University of Texas at El Paso
- El Paso
- USA
- Computational Science Program
| | - Yoh Yamamoto
- Department of Physics
- University of Texas at El Paso
- El Paso
- USA
| | - Tunna Baruah
- Department of Physics
- University of Texas at El Paso
- El Paso
- USA
- Computational Science Program
| | - Rajendra R. Zope
- Department of Physics
- University of Texas at El Paso
- El Paso
- USA
- Computational Science Program
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39
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Jana S, Patra A, Śmiga S, Constantin LA, Samal P. Insights from the density functional performance of water and water–solid interactions: SCAN in relation to other meta-GGAs. J Chem Phys 2020; 153:214116. [DOI: 10.1063/5.0028821] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022] Open
Affiliation(s)
- Subrata Jana
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Abhilash Patra
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
| | - Szymon Śmiga
- Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University, Grudziadzka 5, 87-100 Toruń, Poland
| | - Lucian A. Constantin
- Istituto di Nanoscienze, Consiglio Nazionale delle Ricerche CNR-NANO, 41125 Modena, Italy
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India
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40
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Adhikari S, Santra B, Ruan S, Bhattarai P, Nepal NK, Jackson KA, Ruzsinszky A. The Fermi–Löwdin self-interaction correction for ionization energies of organic molecules. J Chem Phys 2020; 153:184303. [DOI: 10.1063/5.0024776] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Santosh Adhikari
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Biswajit Santra
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Shiqi Ruan
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Puskar Bhattarai
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Niraj K. Nepal
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Koblar A. Jackson
- Department of Physics and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
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41
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Akter S, Yamamoto Y, Diaz CM, Jackson KA, Zope RR, Baruah T. Study of self-interaction errors in density functional predictions of dipole polarizabilities and ionization energies of water clusters using Perdew–Zunger and locally scaled self-interaction corrected methods. J Chem Phys 2020; 153:164304. [DOI: 10.1063/5.0025601] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/08/2023] Open
Affiliation(s)
- Sharmin Akter
- Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Carlos M. Diaz
- Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Koblar A. Jackson
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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42
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Furness JW, Kaplan AD, Ning J, Perdew JP, Sun J. Accurate and Numerically Efficient r 2SCAN Meta-Generalized Gradient Approximation. J Phys Chem Lett 2020; 11:8208-8215. [PMID: 32876454 DOI: 10.1021/acs.jpclett.0c02405] [Citation(s) in RCA: 251] [Impact Index Per Article: 62.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The recently proposed rSCAN functional [ J. Chem. Phys. 2019 150, 161101] is a regularized form of the SCAN functional [ Phys. Rev. Lett. 2015 115, 036402] that improves SCAN's numerical performance at the expense of breaking constraints known from the exact exchange-correlation functional. We construct a new meta-generalized gradient approximation by restoring exact constraint adherence to rSCAN. The resulting functional maintains rSCAN's numerical performance while restoring the transferable accuracy of SCAN.
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Affiliation(s)
- James W Furness
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
| | - Aaron D Kaplan
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Jinliang Ning
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
| | - John P Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, United States
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States
| | - Jianwei Sun
- Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana 70118, United States
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43
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Li L, Trepte K, Jackson KA, Johnson JK. Application of Self-Interaction Corrected Density Functional Theory to Early, Middle, and Late Transition States. J Phys Chem A 2020; 124:8223-8234. [DOI: 10.1021/acs.jpca.0c06485] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Lin Li
- Department of Chemical and Petroleum Engineering University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States
| | - Kai Trepte
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, United States
| | - Koblar A. Jackson
- Department of Physics and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, Michigan 48859, United States
| | - J. Karl Johnson
- Department of Chemical and Petroleum Engineering University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States
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44
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Schwalbe S, Fiedler L, Kraus J, Kortus J, Trepte K, Lehtola S. PyFLOSIC: Python-based Fermi–Löwdin orbital self-interaction correction. J Chem Phys 2020; 153:084104. [DOI: 10.1063/5.0012519] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Sebastian Schwalbe
- Institute of Theoretical Physics, TU Bergakademie Freiberg, Leipziger Str. 23, D-09599 Freiberg, Germany
| | - Lenz Fiedler
- Institute of Theoretical Physics, TU Bergakademie Freiberg, Leipziger Str. 23, D-09599 Freiberg, Germany
| | - Jakob Kraus
- Institute of Theoretical Physics, TU Bergakademie Freiberg, Leipziger Str. 23, D-09599 Freiberg, Germany
| | - Jens Kortus
- Institute of Theoretical Physics, TU Bergakademie Freiberg, Leipziger Str. 23, D-09599 Freiberg, Germany
| | - Kai Trepte
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Susi Lehtola
- Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen Aukio 1), FI-00014 University of Helsinki, Finland
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45
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Yamamoto Y, Salcedo A, Diaz CM, Alam MS, Baruah T, Zope RR. Assessing the effect of regularization on the molecular properties predicted by SCAN and self-interaction corrected SCAN meta-GGA. Phys Chem Chem Phys 2020; 22:18060-18070. [PMID: 32760934 DOI: 10.1039/d0cp02717k] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Recent regularization of the SCAN meta-GGA functional (rSCAN) has simplified the numerical complexities of the SCAN functional, alleviating SCAN's stringent demand on the numerical integration grids to some extent. The regularization of rSCAN, however, results in the breaking of some constraints such as the uniform electron gas limit, the slowly varying density limit, and coordinate scaling of the iso-orbital indicator. Here, we assess the effects of regularization on the electronic, structural, vibrational, and magnetic properties of molecules by comparing the SCAN and rSCAN predictions. The properties studied include atomic energies, atomization energies, ionization potentials, electron affinities, barrier heights, infrared intensities, dissociation and reaction energies, spin moments of molecular magnets, and isomer ordering of water clusters. Our results show that rSCAN requires less dense numerical grids and gives very similar results to those of SCAN for all properties examined with the exception of atomization energies, which are worsened in rSCAN. We also examine the performance of self-interaction-corrected (SIC) rSCAN with respect to SIC-SCAN using the Perdew-Zunger (PZ) SIC method. The PZSIC method uses orbital densities to compute one-electron self-interaction errors and places an even more stringent demand on numerical grids. Our results show that SIC-rSCAN gives marginally better performance than SIC-SCAN for almost all properties studied in this work with numerical grids that are on average half or less as dense as that needed for SIC-SCAN.
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Affiliation(s)
- Yoh Yamamoto
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA.
| | - Alan Salcedo
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA.
| | - Carlos M Diaz
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA. and Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Md Shamsul Alam
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA. and Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA. and Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R Zope
- Department of Physics, The University of Texas at El Paso, El Paso, Texas 79968, USA. and Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA
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46
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Kaplan AD, Santra B, Bhattarai P, Wagle K, Chowdhury STUR, Bhetwal P, Yu J, Tang H, Burke K, Levy M, Perdew JP. Simple hydrogenic estimates for the exchange and correlation energies of atoms and atomic ions, with implications for density functional theory. J Chem Phys 2020; 153:074114. [PMID: 32828077 DOI: 10.1063/5.0017805] [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
Exact density functionals for the exchange and correlation energies are approximated in practical calculations for the ground-state electronic structure of a many-electron system. An important exact constraint for the construction of approximations is to recover the correct non-relativistic large-Z expansions for the corresponding energies of neutral atoms with atomic number Z and electron number N = Z, which are correct to the leading order (-0.221Z5/3 and -0.021Z ln Z, respectively) even in the lowest-rung or local density approximation. We find that hydrogenic densities lead to Ex(N, Z) ≈ -0.354N2/3Z (as known before only for Z ≫ N ≫ 1) and Ec ≈ -0.02N ln N. These asymptotic estimates are most correct for atomic ions with large N and Z ≫ N, but we find that they are qualitatively and semi-quantitatively correct even for small N and N ≈ Z. The large-N asymptotic behavior of the energy is pre-figured in small-N atoms and atomic ions, supporting the argument that widely predictive approximate density functionals should be designed to recover the correct asymptotics. It is shown that the exact Kohn-Sham correlation energy, when calculated from the pure ground-state wavefunction, should have no contribution proportional to Z in the Z → ∞ limit for any fixed N.
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Affiliation(s)
- Aaron D Kaplan
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Biswajit Santra
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Puskar Bhattarai
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Kamal Wagle
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | | | - Pradeep Bhetwal
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Jie Yu
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Hong Tang
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Kieron Burke
- Departments of Chemistry and Physics, University of California, Irvine, California 92697, USA
| | - Mel Levy
- Department of Chemistry and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118, USA
| | - John P Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
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47
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Bhattarai P, Wagle K, Shahi C, Yamamoto Y, Romero S, Santra B, Zope RR, Peralta JE, Jackson KA, Perdew JP. A step in the direction of resolving the paradox of Perdew–Zunger self-interaction correction. II. Gauge consistency of the energy density at three levels of approximation. J Chem Phys 2020; 152:214109. [DOI: 10.1063/5.0010375] [Citation(s) in RCA: 16] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2023] Open
Affiliation(s)
- Puskar Bhattarai
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Kamal Wagle
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Chandra Shahi
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
- Department of Physics and Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Selim Romero
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Biswajit Santra
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Juan E. Peralta
- Department of Physics and Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Koblar A. Jackson
- Department of Physics and Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - John P. Perdew
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, USA
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
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48
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Self-interaction error overbinds water clusters but cancels in structural energy differences. Proc Natl Acad Sci U S A 2020; 117:11283-11288. [PMID: 32393631 DOI: 10.1073/pnas.1921258117] [Citation(s) in RCA: 49] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Abstract
We gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi-Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction-corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/[Formula: see text] from about 42 meV/[Formula: see text] for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction-corrected SCAN. These results indicate that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.
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49
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Yamamoto Y, Romero S, Baruah T, Zope RR. Improvements in the orbitalwise scaling down of Perdew–Zunger self-interaction correction in many-electron regions. J Chem Phys 2020; 152:174112. [DOI: 10.1063/5.0004738] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yoh Yamamoto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Selim Romero
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Rajendra R. Zope
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
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50
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Vargas J, Ufondu P, Baruah T, Yamamoto Y, Jackson KA, Zope RR. Importance of self-interaction-error removal in density functional calculations on water cluster anions. Phys Chem Chem Phys 2020; 22:3789-3799. [DOI: 10.1039/c9cp06106a] [Citation(s) in RCA: 23] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Removing self-interaction errors in density functional approximations results in significantly improved vertical detachment energies of water anions and is essential for obtaining orbital energies consistent with electron binding energies.
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Affiliation(s)
- Jorge Vargas
- Department of Physics
- The University of Texas at El Paso
- El Paso
- USA
| | - Peter Ufondu
- Department of Physics
- The University of Texas at El Paso
- El Paso
- USA
| | - Tunna Baruah
- Department of Physics
- The University of Texas at El Paso
- El Paso
- USA
- Computational Science Program
| | - Yoh Yamamoto
- Department of Physics
- The University of Texas at El Paso
- El Paso
- USA
| | - Koblar A. Jackson
- Physics Department and Science of Advanced Materials Program
- Central Michigan University
- USA
| | - Rajendra R. Zope
- Department of Physics
- The University of Texas at El Paso
- El Paso
- USA
- Computational Science Program
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