1
|
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
|
2
|
Siecińska S, Śmiga S, Grabowski I, Della Sala F, Fabiano E. Boosting the OEP2-sc method with spin-component scaling. Mol Phys 2022. [DOI: 10.1080/00268976.2022.2037771] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Affiliation(s)
- Sylwia Siecińska
- Faculty of Physics, Astronomy and Informatics, Institute of Physics, Nicolaus Copernicus University in Toruń, Toruń, Poland
| | - Szymon Śmiga
- Faculty of Physics, Astronomy and Informatics, Institute of Physics, Nicolaus Copernicus University in Toruń, Toruń, Poland
| | - Ireneusz Grabowski
- Faculty of Physics, Astronomy and Informatics, Institute of Physics, Nicolaus Copernicus University in Toruń, Toruń, Poland
| | - Fabio Della Sala
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Arnesano, Italy
| | - Eduardo Fabiano
- Institute for Microelectronics and Microsystems (CNR-IMM), Campus Unisalento, Lecce, Italy
- Center for Biomolecular Nanotechnologies @UNILE, Istituto Italiano di Tecnologia, Arnesano, Italy
| |
Collapse
|
3
|
Diaz CM, Basurto L, Adhikari S, Yamamoto Y, Ruzsinszky A, Baruah T, Zope RR. Self-interaction-corrected Kohn-Sham effective potentials using the density-consistent effective potential method. J Chem Phys 2021; 155:064109. [PMID: 34391355 DOI: 10.1063/5.0056561] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Density functional theory (DFT) and beyond-DFT methods are often used in combination with photoelectron spectroscopy to obtain physical insights into the electronic structure of molecules and solids. The Kohn-Sham eigenvalues are not electron removal energies except for the highest occupied orbital. The eigenvalues of the highest occupied molecular orbitals often underestimate the electron removal or ionization energies due to the self-interaction (SI) errors in approximate density functionals. In this work, we adapt and implement the density-consistent effective potential method of Kohut, Ryabinkin, and Staroverov [J. Chem. Phys. 140, 18A535 (2014)] to obtain SI-corrected local effective potentials from the SI-corrected Fermi-Löwdin orbitals and density in the Fermi-Löwdin orbital self-interaction correction scheme. The implementation is used to obtain the density of states (photoelectron spectra) and HOMO-LUMO gaps for a set of molecules and polyacenes. Good agreement with experimental values is obtained compared to a range of SI uncorrected density functional approximations.
Collapse
Affiliation(s)
- Carlos M Diaz
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Luis Basurto
- Department of Physics, University of Texas at El Paso, El Paso, Texas 79968, USA
| | - Santosh Adhikari
- 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
| | - Adrienn Ruzsinszky
- Department of Physics, Temple University, Philadelphia, Pennsylvania 19122, 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
| |
Collapse
|
4
|
Trushin E, Görling A. Numerically stable optimized effective potential method with standard Gaussian basis sets. J Chem Phys 2021; 155:054109. [PMID: 34364359 DOI: 10.1063/5.0056431] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
We present a numerically stable optimized effective potential (OEP) method based on Gaussian basis sets. The key point of the approach is a sequence of preprocessing steps of the auxiliary basis set used to represent exchange or correlation potentials, the Kohn-Sham (KS) response function, and the right-hand side of the OEP equation in conjunction with a representation of exchange or correlation potentials via exchange or correlation charge densities whose electrostatic potentials generate the potentials. Due to the preprocessing, standard Gaussian basis sets from basis set libraries can be used in OEP calculations. As examples, we present numerical stable computational setups based on aux-cc-pwCVXZ basis sets with X = T, Q, 5 for the orbitals and aux-cc-pVDZ/mp2fit and aux-cc-pVTZ/mp2fit auxiliary basis sets and use them to calculate KS exchange potentials with the exact exchange-only KS method for various atoms and molecules. The resulting exchange potentials not only are numerically stable and physically reasonable but also show convergence with increasing quality of the orbital basis sets. The effect of incorporating exact conditions that the KS exchange potential has to obey is discussed. Moreover, it is briefly demonstrated that the presented approach not only works for KS exchange potentials but equally well for correlation potentials within the direct random phase approximation. Besides for OEP methods, the introduced preprocessing of auxiliary basis sets should also be beneficial in procedures to calculate back effective KS potentials from given electron densities.
Collapse
Affiliation(s)
- Egor Trushin
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany and Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
| | - Andreas Görling
- Lehrstuhl für Theoretische Chemie, Universität Erlangen-Nürnberg, Egerlandstr. 3, D-91058 Erlangen, Germany and Erlangen National High Performance Computing Center (NHR@FAU), Martensstr. 1, D-91058 Erlangen, Germany
| |
Collapse
|
5
|
Stückrath JB, Bischoff FA. Reduction of Hartree-Fock Wavefunctions to Kohn-Sham Effective Potentials Using Multiresolution Analysis. J Chem Theory Comput 2021; 17:1408-1420. [PMID: 33620202 DOI: 10.1021/acs.jctc.0c01103] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a highly accurate numerical implementation for computing the Kohn-Sham effective potentials for molecules based on a Hartree-Fock wavefunction and density, following the RKS approach of Staroverov and co-workers [ J. Chem. Phys. 2014, 140, 18A535]. Potentials and orbitals are represented in a multiresolution wavelet basis, avoiding basis set incompleteness-related issues. Together with the RKS method, the often occurring problems of oscillating potentials are removed. The MRA implementation of the RKS method allows the generation of molecular Kohn-Sham potentials of benchmark quality. Numerical data for atoms up to Kr and a number of molecules are given, with a special emphasis on the role of nodal planes in the calculations, as showcased in HCN and benzene.
Collapse
Affiliation(s)
- Julius B Stückrath
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
| | - Florian A Bischoff
- Institut für Chemie, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany
| |
Collapse
|
6
|
El-Samman AM, Staroverov VN. Asymptotic behavior of the average local ionization energy in finite basis sets. J Chem Phys 2020; 153:134109. [PMID: 33032433 DOI: 10.1063/5.0023459] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The average local ionization energy (ALIE) has important applications in several areas of electronic structure theory. Theoretically, the ALIE should asymptotically approach the first vertical ionization energy (IE) of the system, as implied by the rate of exponential decay of the electron density; for one-determinantal wavefunctions, this IE is the negative of the highest-occupied orbital energy. In practice, finite-basis-set representations of the ALIE exhibit seemingly irregular and sometimes dramatic deviations from the expected asymptotic behavior. We analyze the long-range behavior of the ALIE in finite basis sets and explain the puzzling observations. The findings have implications for practical calculations of the ALIE, the construction of Kohn-Sham potentials from wavefunctions and electron densities, and basis-set development.
Collapse
Affiliation(s)
- Amer M El-Samman
- 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
| |
Collapse
|
7
|
Affiliation(s)
- Susi Lehtola
- Department of Chemistry, University of Helsinki, P.O. Box 55 (A. I. Virtasen aukio 1), FI-00014 Helsinki, Finland
| |
Collapse
|
8
|
Kaur J, Ospadov E, Staroverov VN. What Is the Accuracy Limit of Adiabatic Linear-Response TDDFT Using Exact Exchange-Correlation Potentials and Approximate Kernels? J Chem Theory Comput 2019; 15:4956-4964. [PMID: 31386366 DOI: 10.1021/acs.jctc.9b00618] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Calculation of vertical excitation energies by the adiabatic linear-response time-dependent density-functional theory (TDDFT) requires static Kohn-Sham potentials and exchange-correlation kernels. When these quantities are derived from standard density-functional approximations (DFA), mean absolute errors (MAE) of the method are known to range from 0.2 eV to over 1 eV, depending on the functional and type of excitation. We investigate how the performance of TDDFT varies when increasingly accurate exchange-correlation potentials derived from Hartree-Fock (HF) and post-HF wavefunctions are combined with different approximate kernels. The lowest MAEs obtained in this manner for valence excitations are about 0.15-0.2 eV, which appears to be the practical limit of the accuracy of TDDFT that can be achieved by improving the Kohn-Sham potentials alone. These findings are consistent with previous reports on the benefits of accurate exchange-correlation potentials in TDDFT, but provide new insights and afford more definitive conclusions.
Collapse
Affiliation(s)
- Jaspreet Kaur
- Department of Chemistry , The University of Western Ontario , London , Ontario N6A 5B7 , Canada
| | - Egor Ospadov
- 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
| |
Collapse
|
9
|
Unified construction of Fermi, Pauli and exchange-correlation potentials. ADVANCES IN QUANTUM CHEMISTRY 2019. [DOI: 10.1016/bs.aiq.2019.04.002] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 03/12/2023]
|
10
|
Visualizing atomic sizes and molecular shapes with the classical turning surface of the Kohn-Sham potential. Proc Natl Acad Sci U S A 2018; 115:E11578-E11585. [PMID: 30463943 DOI: 10.1073/pnas.1814300115] [Citation(s) in RCA: 23] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The Kohn-Sham potential [Formula: see text] is the effective multiplicative operator in a noninteracting Schrödinger equation that reproduces the ground-state density of a real (interacting) system. The sizes and shapes of atoms, molecules, and solids can be defined in terms of Kohn-Sham potentials in a nonarbitrary way that accords with chemical intuition and can be implemented efficiently, permitting a natural pictorial representation for chemistry and condensed-matter physics. Let [Formula: see text] be the maximum occupied orbital energy of the noninteracting electrons. Then the equation [Formula: see text] defines the surface at which classical electrons with energy [Formula: see text] would be turned back and thus determines the surface of any electronic object. Atomic and ionic radii defined in this manner agree well with empirical estimates, show regular chemical trends, and allow one to identify the type of chemical bonding between two given atoms by comparing the actual internuclear distance to the sum of atomic radii. The molecular surfaces can be fused (for a covalent bond), seamed (ionic bond), necked (hydrogen bond), or divided (van der Waals bond). This contribution extends the pioneering work of Z.-Z. Yang et al. [Yang ZZ, Davidson ER (1997) Int J Quantum Chem 62:47-53; Zhao DX, et al. (2018) Mol Phys 116:969-977] by our consideration of the Kohn-Sham potential, protomolecules, doubly negative atomic ions, a bond-type parameter, seamed and necked molecular surfaces, and a more extensive table of atomic and ionic radii that are fully consistent with expected periodic trends.
Collapse
|
11
|
Potential Functional Embedding Theory with an Improved Kohn–Sham Inversion Algorithm. J Chem Theory Comput 2018; 14:5680-5689. [DOI: 10.1021/acs.jctc.8b00717] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
|
12
|
Uniform electron gas limit of an exact expression for the Kohn–Sham exchange-correlation potential. Theor Chem Acc 2018. [DOI: 10.1007/s00214-018-2303-3] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
|
13
|
Affiliation(s)
- Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario, Canada
| |
Collapse
|
14
|
Ryabinkin IG, Ospadov E, Staroverov VN. Exact exchange-correlation potentials of singlet two-electron systems. J Chem Phys 2017; 147:164117. [DOI: 10.1063/1.5003825] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ilya G. Ryabinkin
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4,
Canada
| | - Egor Ospadov
- 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
| |
Collapse
|
15
|
Kim J, Hong K, Hwang SY, Ryu S, Choi S, Kim WY. Effects of the locality of a potential derived from hybrid density functionals on Kohn-Sham orbitals and excited states. Phys Chem Chem Phys 2017; 19:10177-10186. [PMID: 28374031 DOI: 10.1039/c7cp00704c] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Density functional theory (DFT) has been an essential tool for electronic structure calculations in various fields. In particular, its hybrid method including the Hartree-Fock (HF) exchange term remarkably improves the reliability of DFT for chemical applications and computational material design. There are two different types of exchange-correlation potential that can be derived from hybrid functionals. The conventional approach adopts a non-multiplicative potential including the non-local HF exchange operator. Herein, we propose to use a local multiplicative potential as an alternative for accurate excited state calculations. We show that such a local potential can be derived from existing global hybrid functionals using the optimized effective potential method. As a proof-of-concept, we chose PBE0 and investigated its performance for the Caricato benchmark set. Unlike the conventional one, the local potential produced orbital energy gaps with no strong dependence on the mixing ratio as a good approximation for optical excitations. Furthermore, its time-dependent DFT resulted in a surprisingly small mean absolute error even with a local density approximation kernel, surpassing all reported values with various popular functionals. In particular, most excitations were dictated by single orbital transitions due to physically meaningful virtual orbitals, which is beneficial to clear interpretations in the molecular orbital picture.
Collapse
Affiliation(s)
- Jaewook Kim
- Department of Chemistry, KAIST, 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Republic of Korea.
| | | | | | | | | | | |
Collapse
|
16
|
Ospadov E, Ryabinkin IG, Staroverov VN. Improved method for generating exchange-correlation potentials from electronic wave functions. J Chem Phys 2017; 146:084103. [DOI: 10.1063/1.4975990] [Citation(s) in RCA: 33] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Egor Ospadov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Ilya G. Ryabinkin
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| |
Collapse
|
17
|
Hollins TW, Clark SJ, Refson K, Gidopoulos NI. A local Fock-exchange potential in Kohn-Sham equations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2017; 29:04LT01. [PMID: 27897132 DOI: 10.1088/1361-648x/29/4/04lt01] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
We derive and employ a local potential to represent the Fock exchange operator in electronic single-particle equations. This local Fock-exchange (LFX) potential is very similar to the exact exchange (EXX) potential in density functional theory (DFT). The practical software implementation of the two potentials (LFX and EXX) yields robust and accurate results for a variety of systems (semiconductors, transition metal oxides) where Hartree-Fock and popular approximations of DFT typically fail. This includes examples traditionally considered qualitatively inaccessible to calculations that omit correlation.
Collapse
Affiliation(s)
- T W Hollins
- Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK
| | | | | | | |
Collapse
|
18
|
Cuevas-Saavedra R, Staroverov VN. Exact expressions for the Kohn–Sham exchange-correlation potential in terms of wave-function-based quantities. Mol Phys 2016. [DOI: 10.1080/00268976.2015.1131861] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario, Canada
| |
Collapse
|
19
|
Kohut SV, Polgar AM, Staroverov VN. Origin of the step structure of molecular exchange–correlation potentials. Phys Chem Chem Phys 2016; 18:20938-44. [DOI: 10.1039/c6cp00878j] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The step structure of exact exchange–correlation potentials is linked to the properties of the average local electron energy (ALEE).
Collapse
|
20
|
Cuevas-Saavedra R, Ayers PW, Staroverov VN. Kohn–Sham exchange-correlation potentials from second-order reduced density matrices. J Chem Phys 2015; 143:244116. [DOI: 10.1063/1.4937943] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| |
Collapse
|
21
|
Tran F, Blaha P, Schwarz K. How close are the Slater and Becke-Roussel potentials in solids? J Chem Theory Comput 2015; 11:4717-26. [PMID: 26500460 PMCID: PMC4606396 DOI: 10.1021/acs.jctc.5b00675] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2015] [Indexed: 11/30/2022]
Abstract
The Becke–Roussel (BR) potential [Phys. Rev. A 1989, 39, 3761] was proposed as an approximation to the Slater potential, which is the Coulomb potential generated by the exact exchange hole. In the present work, a detailed comparison between the Slater and BR potentials in solids is presented. It is shown that the two potentials usually lead to very similar results for the electronic structure; however, in a few cases, e.g., Si, Ge, or strongly correlated systems like NiO, the fundamental band gap or magnetic properties can differ markedly. Such differences should not be neglected when the computationally expensive Slater potential is replaced by the cheap semilocal BR potential in approximations to the exact-exchange Kohn–Sham potential, such as the one proposed by Becke and Johnson [J. Chem. Phys. 2006, 124, 221101].
Collapse
Affiliation(s)
- 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
| | - Karlheinz Schwarz
- Institute of Materials Chemistry, Vienna University of Technology, Getreidemarkt 9/165-TC, A-1060 Vienna, Austria
| |
Collapse
|
22
|
Ryabinkin IG, Kohut SV, Staroverov VN. Reduction of Electronic Wave Functions to Kohn-Sham Effective Potentials. PHYSICAL REVIEW LETTERS 2015; 115:083001. [PMID: 26340185 DOI: 10.1103/physrevlett.115.083001] [Citation(s) in RCA: 43] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2015] [Indexed: 06/05/2023]
Abstract
A method for calculating the Kohn-Sham exchange-correlation potential v(XC)(r) from a given electronic wave function is devised and implemented. It requires on input one- and two-electron reduced density matrices and involves construction of the generalized Fock matrix. The method is free from numerical limitations and basis-set artifacts of conventional schemes for constructing v(XC)(r) in which the potential is recovered from a given electron density, and is simpler than various many-body techniques. The chief significance of this development is that it allows one to directly probe the functional derivative of the true exchange-correlation energy functional and to rigorously test and improve various density-functional approximations.
Collapse
Affiliation(s)
- Ilya G Ryabinkin
- Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4, Canada
| | - Sviataslau V Kohut
- 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
| |
Collapse
|
23
|
Vyboishchikov SF. Modeling exact exchange potential in spherically confined atoms. J Comput Chem 2015; 36:2037-43. [DOI: 10.1002/jcc.24040] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2015] [Revised: 07/08/2015] [Accepted: 07/10/2015] [Indexed: 01/08/2023]
Affiliation(s)
- Sergei F. Vyboishchikov
- Departament de Química; Institut de Química Computacional i Catàlisi, Universitat de Girona; 17071 Girona Spain
| |
Collapse
|
24
|
Gaiduk AP, Ryabinkin IG, Staroverov VN. Modified Slater exchange potential with correct uniform electron gas limit. CAN J CHEM 2015. [DOI: 10.1139/cjc-2014-0250] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023]
Abstract
Bulat and Levy recently deduced an expansion for the exact-exchange potential whose leading term is Slater’s averaged exchange-charge potential modified through the inclusion of orbital eigenvalues. When used as a stand-alone approximation to the exact-exchange potential, this leading term is much more accurate than Slater’s original. We give an alternative derivation of this term and show that, unlike the Slater potential, it correctly reduces to the Dirac exchange potential (i.e., the local density approximation) for a uniform electron gas, provided that the zero-energy reference of orbital eigenvalues is chosen as the Fermi level of the system. The orbital-energy-modified Slater potential should also recover the Dirac exchange potential for neutral atoms in the limit of infinite nuclear charge, but in practice converges to this limit very slowly on account of extreme sensitivity to the choice of zero-energy reference around the Fermi level.
Collapse
Affiliation(s)
- Alex P. Gaiduk
- Department of Chemistry, The University of Western Ontario, London, ON N6A 5B7, Canada
| | - Ilya G. Ryabinkin
- Department of Chemistry, The University of Western Ontario, London, ON N6A 5B7, Canada
| | - Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, ON N6A 5B7, Canada
| |
Collapse
|
25
|
Ryabinkin IG, Staroverov VN. Average local ionization energy generalized to correlated wavefunctions. J Chem Phys 2014; 141:084107. [DOI: 10.1063/1.4893424] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
|