1
|
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. [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.
Collapse
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
| |
Collapse
|
2
|
Janesko BG. Multiconfigurational Correlation at DFT + U Cost: On-Site Electron-Electron Interactions Yield a Block-Localized Configuration Interaction Hamiltonian. J Phys Chem A 2024; 128:5077-5087. [PMID: 38878060 DOI: 10.1021/acs.jpca.4c02326] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2024]
Abstract
This work presents a first-principles wavefunction-in-DFT approach based on the Hubbard density functional theory (DFT) + U method. This approach begins with the standard DFT reference system of noninteracting electrons and introduces an electron-electron interaction projected onto DFT+U-type atomic states. The reference system's configuration interaction Hamiltonian is block-localized to these states and can be expressed in terms of state occupation numbers, state self-energies (which correspond to unscreened Hubbard U values), and the promotion energies of doubly excited Slater determinants. Simple approximations for the promotion energies provide multiconfigurational correlation energies without requiring explicit orbital localization/transform. Numerical results for fractionally occupied chromium atom, bonded chromium dimer, dissociating covalent bonds, and large active spaces show that the approach provides beyond-zero-sum accuracy at computational cost comparable to standard DFT+U.
Collapse
Affiliation(s)
- Benjamin G Janesko
- Department of Chemistry & Biochemistry, Texas Christian University, Fort Worth, Texas 76129, United States
| |
Collapse
|
3
|
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: 0] [Impact Index Per Article: 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.
Collapse
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
| |
Collapse
|
4
|
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.
Collapse
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
| |
Collapse
|
5
|
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
| |
Collapse
|
6
|
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: 0] [Impact Index Per Article: 0] [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.
Collapse
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
| |
Collapse
|
7
|
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: 2] [Impact Index Per Article: 1.0] [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.
Collapse
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
| |
Collapse
|
8
|
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: 6] [Impact Index Per Article: 2.0] [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.
Collapse
Affiliation(s)
- Sharmin Akter
- Computational Science Program, The University of Texas at El Paso, El Paso, Texas 79968, USA.
| | | | | | | | | | | | | |
Collapse
|