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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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2
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Withanage KPK, Jackson KA, Pederson MR. Complex Fermi-Löwdin orbital self-interaction correction. J Chem Phys 2022; 156:231103. [PMID: 35732520 DOI: 10.1063/5.0091212] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
This paper introduces the use of complex Fermi orbital descriptors (FODs) in the Fermi-Löwdin self-interaction-corrected density functional theory (FLOSIC). With complex FODs, the Fermi-Löwdin orbitals (FLOs) that are used to evaluate the SIC correction to the total energy become complex. Complex FLO-SIC (cFLOSIC) calculations based on the local spin density approximation produce total energies that are generally lower than the corresponding energies found with FLOSIC restricted to real orbitals (rFLOSIC). The cFLOSIC results are qualitatively similar to earlier Perdew-Zunger SIC (PZ-SIC) calculations using complex orbitals [J. Chem. Phys. 80, 1972 (1984); Phys. Rev. A 84, 050501(R) (2011); and J. Chem. Phys. 137, 124102 (2012)]. The energy lowering stems from the exchange-correlation part of the self-interaction correction. The Hartree part of the correction is more negative in rFLOSIC. The energy difference between real and complex solutions is greater for more strongly hybridized FLOs in atoms and for FLOs corresponding to double and triple bonds in molecules. The case of N2 is examined in detail to show the differences between the real and complex FLOs. We show that the complex triple-bond orbitals are simple, and physically appealing combinations of π and σg orbitals that have not been discussed before. Consideration of complex FODs, and resulting unitary transformations, underscores the fact that FLO centroids are not necessarily good guesses for FOD positions in a FLOSIC calculation.
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Affiliation(s)
| | - Koblar A Jackson
- Department of Physics, Central Michigan Universiy, Mount Pleasant, Michigan 48859, USA
| | - Mark R Pederson
- Department of Physics, the University of Texas at El Paso, El Paso, Texas 79968, USA
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3
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Withanage KPK, Sharkas K, Johnson JK, Perdew JP, Peralta JE, Jackson KA. Fermi–Löwdin orbital self-interaction correction of adsorption energies on transition metal ions. J Chem Phys 2022; 156:134102. [DOI: 10.1063/5.0078970] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Density functional theory (DFT)-based descriptions of the adsorption of small molecules on transition metal ions are prone to self-interaction errors. Here, we show that such errors lead to a large over-estimation of adsorption energies of small molecules on Cu+, Zn+, Zn2+, and Mn+ in local spin density approximation (LSDA) and Perdew, Burke, Ernzerhof (PBE) generalized gradient approximation calculations compared to reference values computed using the coupled-cluster with single, doubles, and perturbative triple excitations method. These errors are significantly reduced by removing self-interaction using the Perdew–Zunger self-interaction correction (PZ-SIC) in the Fermi–Löwdin Orbital (FLO) SIC framework. In the case of FLO-PBE, typical errors are reduced to less than 0.1 eV. Analysis of the results using DFT energies evaluated on self-interaction-corrected densities [DFT(@FLO)] indicates that the density-driven contributions to the FLO-DFT adsorption energy corrections are roughly the same size in DFT = LSDA and PBE, but the total corrections due to removing self-interaction are larger in LSDA.
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Affiliation(s)
- Kushantha P. K. Withanage
- Department of Physics and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, Michigan 48859, USA
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Kamal Sharkas
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - J. Karl Johnson
- Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - John P. Perdew
- Department of Physics and Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Juan E. Peralta
- Department of Physics and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Koblar A. Jackson
- Department of Physics and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, Michigan 48859, USA
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4
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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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5
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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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6
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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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7
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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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8
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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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9
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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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10
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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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11
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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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12
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Johnson AI, Withanage KPK, Sharkas K, Yamamoto Y, Baruah T, Zope RR, Peralta JE, Jackson KA. The effect of self-interaction error on electrostatic dipoles calculated using density functional theory. J Chem Phys 2019; 151:174106. [PMID: 31703485 DOI: 10.1063/1.5125205] [Citation(s) in RCA: 25] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Spurious electron self-interaction in density functional approximations (DFAs) can lead to inaccurate predictions of charge transfer in heteronuclear molecules that manifest as errors in calculated electrostatic dipoles. Here, we show the magnitude of these errors on dipoles computed for a diverse set of 47 molecules taken from the recent benchmark study of Hait and Head-Gordon [J. Chem. Theory Comput. 14, 1969 (2018)]. We compare the results of Perdew-Wang local spin density approximation (PW92), Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA), and strongly constrained and appropriately normed (SCAN) meta-GGA dipole calculations, along with those of their respective self-interaction-corrected (SIC) counterparts, to reference values from accurate wave function-based methods. The SIC calculations were carried out using the Fermi-Löwdin orbital (FLO-SIC) approach. We find that correcting for self-interaction generally increases the degree of charge transfer, thereby increasing the size of calculated dipole moments. The FLO-SIC-PW92 and FLO-SIC-PBE dipoles are in better agreement with reference values than their uncorrected DFA counterparts, particularly for strongly ionic molecules where significant improvement is seen. Applying FLO-SIC to SCAN does not improve dipole values overall. We also show that removing self-interaction improves the description of the dipole for stretched-bond geometries and recovers the physically correct separated atom limit of zero dipole. Finally, we find that the best agreement between the FLO-SIC-DFA and reference dipoles occurs when the molecular geometries are optimized using the FLO-SIC-DFA.
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Affiliation(s)
- Alexander I Johnson
- Physics Department, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Kushantha P K Withanage
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Kamal Sharkas
- Physics Department, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Yoh Yamamoto
- 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
| | - Rajendra R Zope
- Physics Department, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Juan E Peralta
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
| | - Koblar A Jackson
- Physics Department and Science of Advanced Materials Program, Central Michigan University, Mt. Pleasant, Michigan 48859, USA
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Jackson KA, Peralta JE, Joshi RP, Withanage KP, Trepte K, Sharkas K, Johnson AI. Towards efficient density functional theory calculations without self-interaction: The Fermi-Löwdin orbital self-interaction correction. ACTA ACUST UNITED AC 2019. [DOI: 10.1088/1742-6596/1290/1/012002] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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14
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Jackson KA, Withanage KPK, Peralta JE. Comment on "Additional Insights Between Fermi-Löwdin Orbital SIC and the Localization Equation Constraints in SIC-DFT". J Phys Chem A 2019; 123:4322-4323. [PMID: 31009221 DOI: 10.1021/acs.jpca.9b02516] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Koblar A Jackson
- Department of Physics and Science of Advanced Materials Program , Central Michigan University , Mount Pleasant , Michigan 48859 , United States
| | - Kushantha P K Withanage
- Department of Physics and Science of Advanced Materials Program , Central Michigan University , Mount Pleasant , Michigan 48859 , United States
| | - Juan E Peralta
- Department of Physics and Science of Advanced Materials Program , Central Michigan University , Mount Pleasant , Michigan 48859 , United States
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15
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Bajaj A, Liu F, Kulik HJ. Non-empirical, low-cost recovery of exact conditions with model-Hamiltonian inspired expressions in jmDFT. J Chem Phys 2019; 150:154115. [PMID: 31005112 DOI: 10.1063/1.5091563] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023] Open
Abstract
Density functional theory (DFT) is widely applied to both molecules and materials, but well known energetic delocalization and static correlation errors in practical exchange-correlation approximations limit quantitative accuracy. Common methods that correct energetic delocalization errors, such as the Hubbard U correction in DFT+U or Hartree-Fock exchange in global hybrids, do so at the cost of worsening static correlation errors. We recently introduced an alternate approach [Bajaj et al., J. Chem. Phys. 147, 191101 (2017)] known as judiciously modified DFT (jmDFT), wherein the deviation from exact behavior of semilocal functionals over both fractional spin and charge, i.e., the so-called flat plane, was used to motivate functional forms of second order analytic corrections. In this work, we introduce fully nonempirical expressions for all four coefficients in a DFT+U+J-inspired form of jmDFT, where all coefficients are obtained only from energies and eigenvalues of the integer-electron systems. We show good agreement for U and J coefficients obtained nonempirically as compared with the results of numerical fitting in a jmDFT U+J/J' correction. Incorporating the fully nonempirical jmDFT correction reduces and even eliminates the fractional spin error at the same time as eliminating the energetic delocalization error. We show that this approach extends beyond s-electron systems to higher angular momentum cases including p- and d-electrons. Finally, we diagnose some shortcomings of the current jmDFT approach that limit its ability to improve upon DFT results for cases such as weakly bound anions due to poor underlying semilocal functional behavior.
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Affiliation(s)
- Akash Bajaj
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Fang Liu
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - Heather J Kulik
- Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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16
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Trepte K, Schwalbe S, Hahn T, Kortus J, Kao DY, Yamamoto Y, Baruah T, Zope RR, Withanage KPK, Peralta JE, Jackson KA. Analytic atomic gradients in the fermi-löwdin orbital self-interaction correction. J Comput Chem 2018; 40:820-825. [DOI: 10.1002/jcc.25767] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2018] [Revised: 10/18/2018] [Accepted: 11/23/2018] [Indexed: 11/08/2022]
Affiliation(s)
- Kai Trepte
- Department of Physics; Central Michigan University; Mount Pleasant Michigan, 48859
| | - Sebastian Schwalbe
- TU Freiberg, Institute of Theoretical Physics; Leipziger Street 23, D-09599, Freiberg Germany
| | - Torsten Hahn
- TU Freiberg, Institute of Theoretical Physics; Leipziger Street 23, D-09599, Freiberg Germany
| | - Jens Kortus
- TU Freiberg, Institute of Theoretical Physics; Leipziger Street 23, D-09599, Freiberg Germany
| | - Der-You Kao
- NASA Postdoctoral Program Fellow; NASA Goddard Space Flight Center; Greenbelt Maryland, 20771
| | - Yoh Yamamoto
- Department of Physics; The University of Texas at El Paso; El Paso Texas, 79968
| | - Tunna Baruah
- Department of Physics; The University of Texas at El Paso; El Paso Texas, 79968
| | - Rajendra R. Zope
- Department of Physics; The University of Texas at El Paso; El Paso Texas, 79968
| | - Kushantha P. K. Withanage
- Department of Physics, Science of Advanced Materials Program; Central Michigan University; Mount Pleasant Michigan, 48859
| | - Juan E. Peralta
- Department of Physics, Science of Advanced Materials Program; Central Michigan University; Mount Pleasant Michigan, 48859
| | - Koblar A. Jackson
- Department of Physics, Science of Advanced Materials Program; Central Michigan University; Mount Pleasant Michigan, 48859
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17
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Sharkas K, Li L, Trepte K, Withanage KPK, Joshi RP, Zope RR, Baruah T, Johnson JK, Jackson KA, Peralta JE. Shrinking Self-Interaction Errors with the Fermi-Löwdin Orbital Self-Interaction-Corrected Density Functional Approximation. J Phys Chem A 2018; 122:9307-9315. [PMID: 30412407 DOI: 10.1021/acs.jpca.8b09940] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The self-interaction error (SIE) is one of the major drawbacks of practical exchange-correlation functionals for Kohn-Sham density functional theory. Despite this, the use of methods that explicitly remove SIE from approximate density functionals is scarce in the literature due to their relatively high computational cost and lack of consistent improvement over standard modern functionals. In this article we assess the performance of a novel approach recently proposed by Pederson, Ruzsinszky, and Perdew [ J. Chem. Phys. 2014, 140, 121103] for performing self-interaction free calculations in density functional theory based on Fermi orbitals. To this end, we employ test sets consisting of reaction energies that are considered particularly sensitive to SIE. We found that the parameter-free Fermi-Löwdin orbital self-interaction correction method combined with the standard local spin density approximation (LSDA) and Perdew-Burke-Ernzerhof (PBE) functionals gives a much better estimate of reaction energies compared to their parent LSDA and PBE functionals for most of the reactions in these two sets. They also perform on par with the global PBE0 and range-separated LC-ωPBE hybrids, which partially eliminate the SIE by including Hartree-Fock exchange. This shows the potential of the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method for practical density functional calculations without SIE.
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Affiliation(s)
| | - Lin Li
- Department of Chemical and Petroleum Engineering , University of Pittsburgh , Pittsburgh , Pennsylvania 15261 , United States
| | | | | | | | - Rajendra R Zope
- Department of Physics , University of Texas El Paso , El Paso , Texas 79968 , United States
| | - Tunna Baruah
- Department of Physics , University of Texas El Paso , El Paso , Texas 79968 , United States
| | - J Karl Johnson
- Department of Chemical and Petroleum Engineering , University of Pittsburgh , Pittsburgh , Pennsylvania 15261 , United States
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18
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Aquino FW, Wong BM. Additional Insights between Fermi-Löwdin Orbital SIC and the Localization Equation Constraints in SIC-DFT. J Phys Chem Lett 2018; 9:6456-6462. [PMID: 30365317 DOI: 10.1021/acs.jpclett.8b02786] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
This letter highlights additional mathematical relationships between the Fermi-Löwdin orbital self-interaction correction (FLO-SIC) formalism and the localization equation constraints in SIC-DFT. We demonstrate this relationship analytically by highlighting symmetries in the mathematical expression for the gradient of EPZ-SIC, which has not been previously shown in the scientific literature. To complement our analytical derivation, we also present additional numerical tests that allow us to investigate a possible accelerated-convergence technique that could be used when solving the iterative FLO-SIC equations. Taken together, our results highlight the importance of satisfying the localization equation constraints for obtaining accurate DFT energies, which we demonstrate are nearly satisfied in the FLO-SIC formalism.
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Affiliation(s)
- Fredy W Aquino
- Department of Chemical & Environmental Engineering, Materials Science & Engineering Program, and Department of Physics & Astronomy , University of California-Riverside , Riverside , California 92521 , United States
| | - Bryan M Wong
- Department of Chemical & Environmental Engineering, Materials Science & Engineering Program, and Department of Physics & Astronomy , University of California-Riverside , Riverside , California 92521 , United States
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19
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Joshi RP, Trepte K, Withanage KPK, Sharkas K, Yamamoto Y, Basurto L, Zope RR, Baruah T, Jackson KA, Peralta JE. Fermi-Löwdin orbital self-interaction correction to magnetic exchange couplings. J Chem Phys 2018; 149:164101. [PMID: 30384709 DOI: 10.1063/1.5050809] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
We analyze the effect of removing self-interaction error on magnetic exchange couplings using the Fermi-Löwdin orbital self-interaction correction (FLOSIC) method in the framework of density functional theory (DFT). We compare magnetic exchange couplings obtained from self-interaction-free FLOSIC calculations with the local spin density approximation (LSDA) with several widely used DFT realizations and wave function based methods. To this end, we employ the linear H-He-H model system, six organic radical molecules, and [Cu2Cl6]2- as representatives of different types of magnetic interactions. We show that the simple self-interaction-free version of LSDA improves calculated couplings with respect to LSDA in all cases, even though the nature of the exchange interaction varies across the test set, and in most cases, it yields results comparable to modern hybrids and range-separated approximate functionals.
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Affiliation(s)
- Rajendra P Joshi
- Department of Physics, Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Kai Trepte
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Kushantha P K Withanage
- Department of Physics, Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Kamal Sharkas
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Yoh Yamamoto
- Department of Physics, University of Texas El Paso, El Paso, Texas 79968, USA
| | - Luis Basurto
- Department of Physics, University of Texas El Paso, El Paso, Texas 79968, USA
| | - Rajendra R Zope
- Department of Physics, University of Texas El Paso, El Paso, Texas 79968, USA
| | - Tunna Baruah
- Department of Physics, University of Texas El Paso, El Paso, Texas 79968, USA
| | - Koblar A Jackson
- Department of Physics, Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
| | - Juan E Peralta
- Department of Physics, Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, USA
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