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Fitzhugh HC, Furness JW, Pederson MR, Peralta JE, Sun J. Comparative Density Functional Theory Study of Magnetic Exchange Couplings in Dinuclear Transition-Metal Complexes. J Chem Theory Comput 2023; 19:5760-5772. [PMID: 37582098 PMCID: PMC10500985 DOI: 10.1021/acs.jctc.3c00336] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/24/2023] [Indexed: 08/17/2023]
Abstract
Multicenter transition-metal complexes (MCTMs) with magnetically interacting ions have been proposed as components for information-processing devices and storage units. For any practical application of MCTMs as magnetic units, it is crucial to characterize their magnetic behavior, and in particular, the isotropic magnetic exchange coupling, J, between its magnetic centers. Due to the large size of typical MCTMs, density functional theory is the only practical electronic structure method for evaluating the J coupling. Here, we assess the accuracy of different density functional approximations for predicting the magnetic couplings of eight dinuclear transition-metal complexes, including five dimanganese, two dicopper, and one divanadium with known reliable experimental J couplings spanning from ferromagnetic to strong antiferromagnetic. The density functionals considered include global hybrid functionals which mix semilocal density functional approximations and exact exchange with a fixed admixing parameter, six local hybrid functionals where the admixing parameters are extended to be spatially dependent, the SCAN and r2SCAN meta-generalized gradient approximations (GGAs), and two widely used GGAs. We found that global hybrids tested in this work have a tendency to over-correct the error in magnetic coupling parameters from the Perdew-Burke-Ernzerhof (PBE) GGA as seen for manganese complexes. The performance of local hybrid density functionals shows no improvement in terms of bias and is scattered without a clear trend, suggesting that more efforts are needed for the extension from global to local hybrid density functionals for this particular property. The SCAN and r2SCAN meta-GGAs are found to perform as well as benchmark global hybrids on most tested complexes. We further analyze the charge density redistribution of meta-GGAs as well as global and local hybrid density functionals with respect to that of PBE, in connection to the self-interaction error or delocalization error.
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Affiliation(s)
- Henry C. Fitzhugh
- Department
of Physics and Engineering Physics, Tulane
University, New Orleans, Louisiana 70118, United States
| | - James W. Furness
- Department
of Physics and Engineering Physics, Tulane
University, New Orleans, Louisiana 70118, United States
| | - Mark R. Pederson
- Department
of Physics, The University of Texas at El
Paso, El Paso, Texas 79968, United States
| | - Juan E. Peralta
- Department
of Physics and Science of Advanced Materials, Central Michigan University, Mount Pleasant, Michigan 48859, United States
| | - Jianwei Sun
- Department
of Physics and Engineering Physics, Tulane
University, New Orleans, Louisiana 70118, United States
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2
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Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives. COMPUTATION 2022. [DOI: 10.3390/computation10020030] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals.
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3
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Li M, Kobayashi R, Amos RD, Ford MJ, Reimers JR. Density functionals with asymptotic-potential corrections are required for the simulation of spectroscopic properties of materials. Chem Sci 2022; 13:1492-1503. [PMID: 35222934 PMCID: PMC8809424 DOI: 10.1039/d1sc03738b] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2021] [Accepted: 12/31/2021] [Indexed: 11/21/2022] Open
Abstract
Five effects of correction of the asymptotic potential error in density functionals are identified that significantly improve calculated properties of molecular excited states involving charge-transfer character. Newly developed materials-science computational methods are used to demonstrate how these effects manifest in materials spectroscopy. Connection is made considering chlorophyll-a as a paradigm for molecular spectroscopy, 22 iconic materials as paradigms for 3D materials spectroscopy, and the VN - defect in hexagonal boron nitride as an example of the spectroscopy of defects in 2D materials pertaining to nanophotonics. Defects can equally be thought of as being "molecular" and "materials" in nature and hence bridge the relms of molecular and materials spectroscopies. It is concluded that the density functional HSE06, currently considered as the standard for accurate calculations of materials spectroscopy, should be replaced, in most instances, by the computationally similar but asymptotically corrected CAM-B3LYP functional, with some specific functionals for materials-use only providing further improvements.
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Affiliation(s)
- Musen Li
- International Centre for Quantum and Molecular Structures and Department of Physics, Shanghai University Shanghai 200444 China
| | - Rika Kobayashi
- ANU Supercomputer Facility Leonard Huxley Bldg. 56, Mills Rd Canberra ACT 2601 Australia
| | - Roger D Amos
- ANU Supercomputer Facility Leonard Huxley Bldg. 56, Mills Rd Canberra ACT 2601 Australia
| | - Michael J Ford
- University of Technology Sydney, School of Mathematical and Physical Sciences Ultimo New South Wales 2007 Australia
| | - Jeffrey R Reimers
- International Centre for Quantum and Molecular Structures and Department of Physics, Shanghai University Shanghai 200444 China
- University of Technology Sydney, School of Mathematical and Physical Sciences Ultimo New South Wales 2007 Australia
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4
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Kovács P, Tran F, Hanbury A, Madsen GKH. Similarity Clustering for Representative Sets of Inorganic Solids for Density Functional Testing. J Chem Theory Comput 2022; 18:441-447. [PMID: 34919396 PMCID: PMC8757462 DOI: 10.1021/acs.jctc.1c00536] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2021] [Indexed: 11/30/2022]
Abstract
Benchmarking DFT functionals is complicated since the results highly depend on which properties and materials were used in the process. Unwanted biases can be introduced if a data set contains too many examples of very similar materials. We show that a clustering based on the distribution of density gradient and kinetic energy density is able to identify groups of chemically distinct solids. We then propose a method to create smaller data sets or rebalance existing data sets in a way that no region of the meta-GGA descriptor space is overrepresented, yet the new data set reproduces average errors of the original set as closely as possible. We apply the method to an existing set of 44 inorganic solids and suggest a representative set of seven solids. The representative sets generated with this method can be used to make more general benchmarks or to train new functionals.
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Affiliation(s)
- Péter Kovács
- Institute
of Materials Chemistry, Technical University
of Vienna, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
| | - Fabien Tran
- Institute
of Materials Chemistry, Technical University
of Vienna, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
| | - Allan Hanbury
- Institute
for Information Systems Engineering, Technical
University of Vienna, Favoritenstrasse 9-11/194, A-1040 Vienna, Austria
| | - Georg K. H. Madsen
- Institute
of Materials Chemistry, Technical University
of Vienna, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
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5
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Francisco HI, Carmona-Espíndola J, Gázquez JL. Analysis of the kinetic energy functional in the generalized gradient approximation. J Chem Phys 2021; 154:084107. [PMID: 33639771 DOI: 10.1063/5.0040973] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new density functional for the total kinetic energy in the generalized gradient approximation is developed through an enhancement factor that leads to the correct behavior in the limits when the reduced density gradient tends to 0 and to infinity and by making use of the conjoint conjecture for the interpolation between these two limits, through the incorporation, in the intermediate region of constraints that are associated with the exchange energy functional. The resulting functional leads to a reasonable description of the kinetic energies of atoms and molecules when it is used in combination with Hartree-Fock densities. Additionally, in order to improve the behavior of the kinetic energy density, a new enhancement factor for the Pauli kinetic energy is proposed by incorporating the correct behavior into the limits when the reduced density gradient tends to 0 and to infinity, together with the positivity condition, and imposing through the interpolation function that the sum of its integral over the whole space and the Weiszacker energy must be equal to the value obtained with the enhancement factor developed for the total kinetic energy.
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Affiliation(s)
- Héctor I Francisco
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, Ciudad de México 09340, Mexico
| | - Javier Carmona-Espíndola
- Departamento de Química, CONACYT-Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| | - José L Gázquez
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, México, Ciudad de México 09340, Mexico
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Patra A, Jana S, Myneni H, Samal P. Laplacian free and asymptotic corrected semilocal exchange potential applied to the band gap of solids. Phys Chem Chem Phys 2019; 21:19639-19650. [PMID: 31468039 DOI: 10.1039/c9cp03356d] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
It is well known that the modified semilocal exchange potentials explicitly designed for the study of solid-state band gaps are very successful in describing these properties. These exchange potentials are in principle designed either from a spherically averaged exchange hole or by satisfying the exact asymptotic conditions. In this present attempt, we use the recently developed novel technique of density matrix expansion to construct the model exchange hole potential. The proposed exchange hole potential is free from the Laplacian of density and generalized through the coordinate transformation. An improvement in the exchange energies of atoms using this potential is shown. The salient feature of the proposed semilocal potential is that it can be used within generalized Kohn-Sham formalism because of its Laplacian free representation. This modified potential is used in the framework of TBMBJ [Phys. Rev. Lett., 2009, 102, 226401] to calculate the band gaps of materials. The comparison and assessment of the newly constructed Laplacian free, asymptotically corrected semilocal potential to address the band gap problem show good agreement with the experimental band gaps and diversify the studies done in the same direction.
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Affiliation(s)
- Abhilash Patra
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India.
| | - Subrata Jana
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India.
| | - Hemanadhan Myneni
- Department of Physics, Temple University, Philadelphia, PA 19122-1801, USA
| | - Prasanjit Samal
- School of Physical Sciences, National Institute of Science Education and Research, HBNI, Bhubaneswar 752050, India.
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Witt WC, Jiang K, Carter EA. Upper bound to the gradient-based kinetic energy density of noninteracting electrons in an external potential. J Chem Phys 2019. [DOI: 10.1063/1.5108896] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- William C. Witt
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - Kaili Jiang
- Department of Mechanical and Aerospace Engineering, Princeton University, Princeton, New Jersey 08544-5263, USA
| | - Emily A. Carter
- School of Engineering and Applied Science, Princeton University, Princeton, New Jersey 08544-5263, USA
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Kovács P, Tran F, Blaha P, Madsen GKH. Comparative study of the PBE and SCAN functionals: The particular case of alkali metals. J Chem Phys 2019; 150:164119. [DOI: 10.1063/1.5092748] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Péter Kovács
- Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
| | - Fabien Tran
- Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
| | - Peter Blaha
- Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
| | - Georg K. H. Madsen
- Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
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