1
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Kanungo B, Hatch J, Zimmerman PM, Gavini V. Exact and Model Exchange-Correlation Potentials for Open-Shell Systems. J Phys Chem Lett 2023; 14:10039-10045. [PMID: 37910134 DOI: 10.1021/acs.jpclett.3c01713] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2023]
Abstract
The conventional approaches to the inverse density functional theory problem typically assume nondegeneracy of the Kohn-Sham (KS) eigenvalues, greatly hindering their use in open-shell systems. We present a generalization of the inverse density functional theory problem that can seamlessly admit degenerate KS eigenvalues. Additionally, we allow for fractional occupancy of the Kohn-Sham orbitals to also handle noninteracting ensemble-v-representable densities, as opposed to just noninteracting pure-v-representable densities. We present the exact exchange-correlation (XC) potentials for six open-shell systems─four atoms (Li, C, N, and O) and two molecules (CN and CH2)─using accurate ground-state densities from configuration interaction calculations. We compare these exact XC potentials with model XC potentials obtained using nonlocal (B3LYP, SCAN0) and local/semilocal (SCAN, PBE, PW92) XC functionals. Although the relative errors in the densities obtained from these DFT functionals are of O (10-3 to 10-2), the relative errors in the model XC potentials remain substantially large─O (10-1 to 100).
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Affiliation(s)
- Bikash Kanungo
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Jeffrey Hatch
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Paul M Zimmerman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Vikram Gavini
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
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2
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Oueis Y, Sizov GN, Staroverov VN. Local Potentials Reconstructed within Linearly Independent Product Basis Sets of Increasing Size. J Phys Chem A 2023; 127:2664-2669. [PMID: 36898043 PMCID: PMC10042162 DOI: 10.1021/acs.jpca.3c00119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2023] [Revised: 02/24/2023] [Indexed: 03/12/2023]
Abstract
Given a matrix representation of a local potential v(r) within a one-electron basis set of functions that form linearly independent products (LIP), it is possible to construct a well-defined local potential v ~ ( r ) that is equivalent to v(r) within that basis set and has the form of an expansion in basis function products. Recently, we showed that for exchange-correlation potentials vXC(r) defined on the infinite-dimensional Hilbert space, the potentials v ~ XC ( r ) reconstructed from matrices of vXC(r) within minimal LIP basis sets of occupied Kohn-Sham orbitals bear only qualitative resemblance to the originals. Here, we show that if the LIP basis set is enlarged by including low-lying virtual Kohn-Sham orbitals, the agreement between v ~ XC ( r ) and vXC(r) improves to the extent that the basis function products are appropriate as a basis for vXC(r). These findings validate the LIP technology as a rigorous potential reconstruction method.
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Affiliation(s)
- Yan Oueis
- Department of Chemistry, The
University of Western Ontario, London, Ontario N6A 5B7, Canada
| | - Georgii N. Sizov
- 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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3
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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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4
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Oueis Y, Staroverov VN. Reconstruction of Exchange-Correlation Potentials from Their Matrix Representations. J Chem Theory Comput 2022; 18:6092-6098. [PMID: 36094818 DOI: 10.1021/acs.jctc.2c00655] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Within a basis set of one-electron functions that form linearly independent products (LIPs), it is always possible to construct a unique local (multiplicative) real-space potential that is precisely equivalent to an arbitrary given operator. Although standard basis sets of quantum chemistry rarely form LIPs in a numerical sense, occupied and low-lying virtual canonical Kohn-Sham orbitals often do so, at least for small atoms and molecules. Using these principles, we construct atomic and molecular exchange-correlation potentials from their matrix representations in LIP basis sets of occupied canonical Kohn-Sham orbitals. The reconstructions are found to imitate the original potentials in a consistent but exaggerated way. Since the original and reconstructed potentials produce the same ground-state electron density and energy within the associated LIP basis set, the procedure may be regarded as a rigorous solution to the Kohn-Sham inversion problem within the subspace spanned by the occupied Kohn-Sham orbitals.
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Affiliation(s)
- Yan Oueis
- 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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5
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Bousiadi S, Gidopoulos N, Lathiotakis N. Density inversion method for local basis sets without potential auxiliary functions: inverting densities from RDMFT. Phys Chem Chem Phys 2022; 24:19279-19286. [DOI: 10.1039/d2cp01866g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A density inversion method is presented, to obtain the constrained, optimal, local potential that has a prescribed asymptotic behaviour and reproduces optimally any given ground-state electronic density. This work builds...
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6
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Kanungo B, Zimmerman PM, Gavini V. A Comparison of Exact and Model Exchange-Correlation Potentials for Molecules. J Phys Chem Lett 2021; 12:12012-12019. [PMID: 34898217 DOI: 10.1021/acs.jpclett.1c03670] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Accurate exchange-correlation (XC) potentials for three-dimensional systems─via solution of the inverse density functional theory (DFT) problem─are now available to test the quality of DFT approximations. Herein, the exact XC potential for seven molecules─dihydrogen at four different bond-lengths, lithium hydride, water, and ortho-benzyne─are computed from full configuration interaction reference densities. These are compared to model XC potentials from nonlocal (B3LYP, HSE06, SCAN0, and M08-HX) and semilocal/local (SCAN, PBE, and PW92) XC functionals. Whereas for most systems, relative errors in the ground-state densities are O(10-3-10-2), the model XC potentials have much higher errors of O(10-1-100). Among the model XC functionals, SCAN0 offers the best agreement with the exact XC potential, underlining the significance of satisfying exact conditions as well as including nonlocal effects in XC functionals. This work indicates that tests against the exact XC potential will provide a promising new direction for building more accurate XC functionals for DFT.
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Affiliation(s)
- Bikash Kanungo
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Paul M Zimmerman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Vikram Gavini
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
- Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, United States
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7
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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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8
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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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9
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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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10
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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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11
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Kanungo B, Zimmerman PM, Gavini V. Exact exchange-correlation potentials from ground-state electron densities. Nat Commun 2019; 10:4497. [PMID: 31582755 PMCID: PMC6776552 DOI: 10.1038/s41467-019-12467-0] [Citation(s) in RCA: 29] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2019] [Accepted: 09/05/2019] [Indexed: 11/09/2022] Open
Abstract
The quest for accurate exchange-correlation functionals has long remained a grand challenge in density functional theory (DFT), as it describes the many-electron quantum mechanical behavior through a computationally tractable quantity-the electron density-without resorting to multi-electron wave functions. The inverse DFT problem of mapping the ground-state density to its exchange-correlation potential is instrumental in aiding functional development in DFT. However, the lack of an accurate and systematically convergent approach has left the problem unresolved, heretofore. This work presents a numerically robust and accurate scheme to evaluate the exact exchange-correlation potentials from correlated ab-initio densities. We cast the inverse DFT problem as a constrained optimization problem and employ a finite-element basis-a systematically convergent and complete basis-to discretize the problem. We demonstrate the accuracy and efficacy of our approach for both weakly and strongly correlated molecular systems, including up to 58 electrons, showing relevance to realistic polyatomic molecules.
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Affiliation(s)
- Bikash Kanungo
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, 48109, USA
| | - Paul M Zimmerman
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan, 48109, USA
| | - Vikram Gavini
- Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan, 48109, USA. .,Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan, 48109, USA.
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12
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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.
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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
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13
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Mostafanejad M, Haney J, DePrince AE. Kinetic-energy-based error quantification in Kohn–Sham density functional theory. Phys Chem Chem Phys 2019; 21:26492-26501. [DOI: 10.1039/c9cp04595c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present a basis-independent metric to assess the quality of the electron density obtained from Kohn–Sham (KS) density functional theory (DFT).
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Affiliation(s)
| | - Jessica Haney
- Department of Chemistry and Biochemistry
- Florida State University
- Tallahassee
- USA
| | - A. Eugene DePrince
- Department of Chemistry and Biochemistry
- Florida State University
- Tallahassee
- USA
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14
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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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15
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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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16
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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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17
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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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18
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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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19
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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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20
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Affiliation(s)
- Viktor N. Staroverov
- Department of Chemistry, The University of Western Ontario, London, Ontario, Canada
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21
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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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22
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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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23
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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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24
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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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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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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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Abstract
The energy change per electron in a chemical or physical transformation, ΔE/n, may be expressed as Δχ̅ + Δ(VNN + ω)/n, where Δχ̅ is the average electron binding energy, a generalized electronegativity, ΔVNN is the change in nuclear repulsions, and Δω is the change in multielectron interactions in the process considered. The last term can be obtained by the difference from experimental or theoretical estimates of the first terms. Previously obtained consequences of this energy partitioning are extended here to a different analysis of bonding in a great variety of diatomics, including more or less polar ones. Arguments are presented for associating the average change in electron binding energy with covalence, and the change in multielectron interactions with electron transfer, either to, out, or within a molecule. A new descriptor Q, essentially the scaled difference between the Δχ̅ and Δ(VNN + ω)/n terms, when plotted versus the bond energy, separates nicely a wide variety of bonding types, covalent, covalent but more correlated, polar and increasingly ionic, metallogenic, electrostatic, charge-shift bonds, and dispersion interactions. Also, Q itself shows a set of interesting relations with the correlation energy of a bond.
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Affiliation(s)
- Martin Rahm
- Chemistry and Chemical Biology, Baker Laboratory, Cornell University , Ithaca, New York 14853, United States
| | - Roald Hoffmann
- Chemistry and Chemical Biology, Baker Laboratory, Cornell University , Ithaca, New York 14853, United States
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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
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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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