1
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Moore CC, Staroverov VN. Discontinuities of Kinetic Energy Densities within Finite and Complete Basis Sets. J Phys Chem A 2024; 128:6019-6025. [PMID: 38985544 DOI: 10.1021/acs.jpca.4c02712] [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
Although electron densities are always continuous, other ingredients of density-functional approximations can be sharply discontinuous at isolated points. In particular, the positive-definite, Weizsäcker, and Pauli kinetic energy densities expressed in terms of Slater-type orbitals all have discontinuities at the positions of the atomic nuclei in molecules. The first two of those quantities are similarly discontinuous even in the basis-set limit. These striking features are not as widely recognized as they deserve to be. We show in detail how discontinuities of kinetic energy densities arise from asymmetric electron-nucleus cusps of molecular wave functions and point out instances of their significance in electronic structure theory.
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Affiliation(s)
- Conrad C Moore
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Viktor N Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
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2
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Giarrusso S, Gori-Giorgi P, Agostini F. Electronic Vector Potential from the Exact Factorization of a Complex Wavefunction. Chemphyschem 2024:e202400127. [PMID: 38837609 DOI: 10.1002/cphc.202400127] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2024] [Revised: 06/01/2024] [Accepted: 06/03/2024] [Indexed: 06/07/2024]
Abstract
We generalize the definitions of local scalar potentials namedυ kin ${\upsilon _{{\rm{kin}}} }$ andυ N - 1 ${\upsilon _{N - 1} }$ , which are relevant to properly describe phenomena such as molecular dissociation with density-functional theory, to the case in which the electronic wavefunction corresponds to a complex current-carrying state. In such a case, an extra term in the form of a vector potential appears which cannot be gauged away. Both scalar and vector potentials are introduced via the exact factorization formalism which allows us to express the given Schrödinger equation as two coupled equations, one for the marginal and one for the conditional amplitude. The electronic vector potential is directly related to the paramagnetic current density carried by the total wavefunction and to the diamagnetic current density in the equation for the marginal amplitude. An explicit example of this vector potential in a triplet state of two non-interacting electrons is showcased together with its associated circulation, giving rise to a non-vanishing geometric phase. Some connections with the exact factorization for the full molecular wavefunction beyond the Born-Oppenheimer approximation are also discussed.
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Affiliation(s)
- Sara Giarrusso
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France
| | - Paola Gori-Giorgi
- Department of Chemistry & Pharmaceutical Sciences and Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081HV, Amsterdam, The Netherlands
- Microsoft Research AI4Science, Evert van de Beekstraat 354, 1118CZ, Schiphol, The Netherlands
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France
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3
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Gautam S, Ghosh S, Gupta DC. Understanding the computational insights of spin-polarised density functional theory into the newly half-metallic f electron-based actinide perovskites SrMO 3 (M = Pa, Np, Cm, Bk). Sci Rep 2023; 13:16882. [PMID: 37803067 PMCID: PMC10558508 DOI: 10.1038/s41598-023-43624-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2023] [Accepted: 09/26/2023] [Indexed: 10/08/2023] Open
Abstract
Here, we investigated the structural, mechanical, electronic, magnetic, thermodynamic and thermoelectric properties of Strontium based simple perovskites SrMO3 (M = Pa, Np, Cm, Bk) by using density functional theory. First and foremost, the ground state stability of these perovskites was initially evaluated by optimizing their total ground state energies in distinct ferromagnetic and non-magnetic configurations. The structural stability in terms of their ground state energies defines that these alloys stabilize in ferromagnetic rather than competing non-magnetic phase. From the understandings of mechanical parameters these alloys are characterized to be ductile in nature. After that, two approximation schemes namely Generalized Gradient approximation and Tran-Blaha modified Becke-Johnson potential have been used to find their intimate electronic structures which displays the half-metallic nature of these alloys. Further, we have verified temperature and pressure effect on these alloys. Finally, the transport properties have been evaluated within the selected temperature range of 150-900 K. In view of this, the different transport parameters along with half-metallic nature advocate their possible applications in thermoelectric and spintronics devices.
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Affiliation(s)
- Sakshi Gautam
- Condensed Matter Theory Group, School of Studies in Physics, Jiwaji University Gwalior, Gwalior, MP, 474001, India.
| | - Sukriti Ghosh
- Condensed Matter Theory Group, School of Studies in Physics, Jiwaji University Gwalior, Gwalior, MP, 474001, India
| | - Dinesh C Gupta
- Condensed Matter Theory Group, School of Studies in Physics, Jiwaji University Gwalior, Gwalior, MP, 474001, India
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4
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Kato T, Saito S. Kohn–Sham
potentials by an inverse
Kohn–Sham
equation and accuracy assessment by virial theorem. J CHIN CHEM SOC-TAIP 2022. [DOI: 10.1002/jccs.202200355] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Tsuyoshi Kato
- Department of Chemistry School of Science, The University of Tokyo Tokyo Japan
| | - Shinji Saito
- Department of Theoretical and Computational Molecular Science Institute for Molecular Science Okazaki Japan
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5
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First principles study on copper and iridium co-doped SrTiO3 for shifting the optical absorption into visible region. SN APPLIED SCIENCES 2020. [DOI: 10.1007/s42452-020-03851-3] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022] Open
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6
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El-Samman AM, Ospadov E, Staroverov VN. First Ionization Energy as the Asymptotic Limit of the Average Local Electron Energy. J Chem Theory Comput 2020; 16:6886-6893. [PMID: 33073573 DOI: 10.1021/acs.jctc.0c00806] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The first vertical ionization energy of an atom or molecule is encoded in the rate of exponential decay of the exact natural orbitals. For natural orbitals represented in terms of Gaussian basis functions, this property does not hold even approximately. We show that it is nevertheless possible to deduce the first ionization energy from the long-range behavior of Gaussian-basis-set wave functions by evaluating the asymptotic limit of a quantity called the average local electron energy (ALEE), provided that the most diffuse functions of the basis set have a suitable shape and location. The ALEE method exposes subtle qualitative differences between seemingly analogous Gaussian basis sets and complements the extended Koopmans theorem by being robust in situations where the one-electron reduced density matrix is ill-conditioned.
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Affiliation(s)
- Amer M El-Samman
- 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
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7
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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.
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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
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8
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Nam S, Song S, Sim E, Burke K. Measuring Density-Driven Errors Using Kohn-Sham Inversion. J Chem Theory Comput 2020; 16:5014-5023. [PMID: 32667787 DOI: 10.1021/acs.jctc.0c00391] [Citation(s) in RCA: 22] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Kohn-Sham (KS) inversion, that is, the finding of the exact KS potential for a given density, is difficult in localized basis sets. We study the precision and reliability of several inversion schemes, finding estimates of density-driven errors at a useful level of accuracy. In typical cases of substantial density-driven errors, Hartree-Fock density functional theory (HF-DFT) is almost as accurate as DFT evaluated on CCSD(T) densities. A simple approximation in practical HF-DFT also makes errors much smaller than the density-driven errors being calculated. Two paradigm examples, stretched NaCl and the HO·Cl- radical, illustrate just how accurate HF-DFT is.
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Affiliation(s)
- Seungsoo Nam
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Suhwan Song
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Eunji Sim
- Department of Chemistry, Yonsei University, 50 Yonsei-ro Seodaemun-gu, Seoul 03722, Korea
| | - Kieron Burke
- Departments of Chemistry and of Physics, University of California, Irvine, California 92697, United States
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9
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Giarrusso S, Gori-Giorgi P. Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond. J Phys Chem A 2020; 124:2473-2482. [PMID: 32118422 PMCID: PMC7104238 DOI: 10.1021/acs.jpca.9b10538] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
![]()
We
analyze in depth two widely used definitions (from the theory
of conditional probability amplitudes and from the adiabatic connection
formalism) of the exchange-correlation energy density and of the response
potential of Kohn–Sham density functional theory. We introduce
a local form of the coupling-constant-dependent Hohenberg–Kohn functional, showing that
the difference between the two definitions is due to a corresponding
local first-order term in the coupling constant, which disappears
globally (when integrated over all space), but not locally. We also
design an analytic representation for the response potential in the
strong-coupling limit of density functional theory for a model single
stretched bond.
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Affiliation(s)
- Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, Amsterdam, 1081HV, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, Amsterdam, 1081HV, The Netherlands
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10
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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]
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11
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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.
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12
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Kooi DP, Gori-Giorgi P. Local and global interpolations along the adiabatic connection of DFT: a study at different correlation regimes. Theor Chem Acc 2018; 137:166. [PMID: 30464722 PMCID: PMC6223841 DOI: 10.1007/s00214-018-2354-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2018] [Accepted: 09/21/2018] [Indexed: 11/16/2022]
Abstract
Interpolating the exchange-correlation energy along the density-fixed adiabatic connection of density functional theory is a promising way to build approximations that are not biased toward the weakly correlated regime. These interpolations can be performed at the global (integrated over all spaces) or at the local level, using energy densities. Many features of the relevant energy densities as well as several different ways to construct these interpolations, including comparisons between global and local variants, are investigated here for the analytically solvable Hooke's atom series, which allows for an exploration of different correlation regimes. We also analyze different ways to define the correlation kinetic energy density, focusing on the peak in the kinetic correlation potential.
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Affiliation(s)
- Derk P. Kooi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Faculty of Science, Vrije Universiteit, De Boelelaan 1083, 1081 HV Amsterdam, The Netherlands
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13
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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]
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14
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Giarrusso S, Vuckovic S, Gori-Giorgi P. Response Potential in the Strong-Interaction Limit of Density Functional Theory: Analysis and Comparison with the Coupling-Constant Average. J Chem Theory Comput 2018; 14:4151-4167. [PMID: 29906106 PMCID: PMC6096453 DOI: 10.1021/acs.jctc.8b00386] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Using the formalism of the conditional amplitude, we study the response part of the exchange-correlation potential in the strong-coupling limit of density functional theory, analyzing its peculiar features and comparing it with the response potential averaged over the coupling constant for small atoms and for the hydrogen molecule. We also use a simple one-dimensional model of a stretched heteronuclear molecule to derive exact properties of the response potential in the strong-coupling limit. The simplicity of the model allows us to unveil relevant features also of the exact Kohn-Sham potential and its different components, namely the appearance of a second peak in the correlation kinetic potential on the side of the most electronegative atom.
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Affiliation(s)
- Sara Giarrusso
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
| | - Stefan Vuckovic
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
| | - Paola Gori-Giorgi
- Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW , Vrije Universiteit , De Boelelaan 1083 , 1081HV Amsterdam , The Netherlands
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15
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Ospadov E, Staroverov VN. Construction of Fermi Potentials from Electronic Wave Functions. J Chem Theory Comput 2018; 14:4246-4253. [DOI: 10.1021/acs.jctc.8b00490] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- 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
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16
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Affiliation(s)
- Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario, Canada
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17
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Kaplan IG. Symmetry properties of the electron density and following from it limits on the KS-DFT applications. Mol Phys 2017. [DOI: 10.1080/00268976.2017.1393573] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
Affiliation(s)
- Ilya G. Kaplan
- Instituto De Investigaciones en Materiales, Universidad Nacional Autónomo de México, Ciudad de México, México
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18
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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
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19
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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
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20
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Kohut SV, Cuevas-Saavedra R, Staroverov VN. Generalized average local ionization energy and its representations in terms of Dyson and energy orbitals. J Chem Phys 2016; 145:074113. [DOI: 10.1063/1.4961071] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Ryabinkin IG, Kohut SV, Cuevas-Saavedra R, Ayers PW, Staroverov VN. Response to "Comment on 'Kohn-Sham exchange-correlation potentials from second-order reduced density matrices'" [J. Chem. Phys. 145, 037101 (2016)]. J Chem Phys 2016; 145:037102. [PMID: 27448911 DOI: 10.1063/1.4958623] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.9] [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
| | - Sviataslau V Kohut
- Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada
| | | | - 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
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22
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Baerends EJ, Gritsenko O. Comment on “Kohn-Sham exchange-correlation potentials from second-order reduced density matrices” [J. Chem. Phys. 143, 244116 (2015)]. J Chem Phys 2016; 145:037101. [DOI: 10.1063/1.4958622] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
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23
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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).
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24
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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
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