Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

Giarrusso, Sara; Gori‐Giorgi, Paola

doi:10.1021/acs.jpca.9b10538

Cited by 11 publications

(13 citation statements)

References 67 publications

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“…It is negative everywhere in a position space and hence it yields a stabilizing contribution to the energy density. The static response potential,

v_{x}^{resp} ((), r)

> 0, measures sensitivity of the exchange correlation to the electron density variations and only makes a destabilizing second‐order contribution to the energy density; therefore, it is neglected in this study 52,69–71 …”

Section: Methodsmentioning

confidence: 99%

Keto‐enol tautomerism from the electron delocalization perspective

et al. 2022

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The equilibrium between keto and enol forms in acetylacetone and its derivatives is studied using electron delocalization indices and delocalization tensor density. We demonstrate how electron delocalization governs the equilibrium between keto and enol forms. The less stable enols have more distinct double and single bond character in the C C C fragment, while electron delocalization in this fragment is more pronounced in more stable enols. Looking for the origin of such behavior, we considered the one-electron potentials entering the Euler equation for the electron density. We found that electron delocalization is mainly governed by the static exchange potential, which depends on the three-dimensional atomic structure. It, however, does not distinguish differences in electron delocalization in more and less stable enols, the effect arising from the kinetic exchange contribution, which reflects spin-dependent effects in the electron motion. The local depletion of kinetic exchange in the conjugated fragment yields the enhanced electron delocalization along the C C C bonds in more stable enols. Thus, a combination of considered descriptors allowed us to reveal the influence of electron delocalization on the equilibrium between keto and enol forms and showed the significant features of this phenomenon.

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“…It is negative everywhere in a position space and hence it yields a stabilizing contribution to the energy density. The static response potential,

v_{x}^{resp} ((), r)

Section: Methodsmentioning

confidence: 99%

Keto‐enol tautomerism from the electron delocalization perspective

et al. 2022

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“…Here, v x, hole (r) < 0 is the potential resulting from the exchange-hole charge density, while v x, resp (r) > 0 describes the response of exchange screening to small density variations, when preserving the number of electrons. The last term is $10 times less than v x, hole in absolute value and it is not expressed via electron density (Nagy & March, 1992;Gritsenko et al, 1996Gritsenko et al, , 2016Fuentealba, 1997;Nagy, 2010;Kohut et al, 2016;Giarrusso & Gori-Giorgi, 2020;Kreisler, 2020). We also found that the local density approximation (LDA), gradient expansion approximations, generalized gradient approximation (Parr & Yang, 1989) and empirical approximations to v x, resp give unrealistic exchange potentials and do not provide the expected formation of electron shells.…”

Section: Methodsmentioning

confidence: 81%

“…Unfortunately, a reliable local-density approximation for potential v P (r) is unknown (Levy & Go ¨rling, 1994;Finzel, 2016;Nagy, 2018;Giarrusso & Gori-Giorgi, 2020). Moreover, the gradient expansion of T P violates the exact condition v P (r) !…”

Section: Methodsmentioning

confidence: 99%

Developing orbital-free quantum crystallography: the local potentials and associated partial charge densities

Tsirelson¹,

Сташ²

2021

Acta Crystallogr B Struct Sci Cryst Eng Mater

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This work extends the orbital-free density functional theory to the field of quantum crystallography. The total electronic energy is decomposed into electrostatic, exchange, Weizsacker and Pauli components on the basis of physically grounded arguments. Then, the one-electron Euler equation is re-written through corresponding potentials, which have clear physical and chemical meaning. Partial electron densities related with these potentials by the Poisson equation are also defined. All these functions were analyzed from viewpoint of their physical content and limits of applicability. Then, they were expressed in terms of experimental electron density and its derivatives using the orbital-free density functional theory approximations, and applied to the study of chemical bonding in a heteromolecular crystal of ammonium hydrooxalate oxalic acid dihydrate. It is demonstrated that this approach allows the electron density to be decomposed into physically meaningful components associated with electrostatics, exchange, and spin-independent wave properties of electrons or with their combinations in a crystal. Therefore, the bonding information about a crystal that was previously unavailable for X-ray diffraction analysis can be now obtained.

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“…[30]) and that the different kinetic energy densities of the interacting and the KS system fully account for the differences between v G and v PG . Hence, v G has been called the "kinetic potential" in the literature [31,43].…”

Section: The Geometric Potentialmentioning

confidence: 99%

“…The separation of a wavefunction into a marginal and a conditional part was first considered for the electron-nuclear problem [29] and has subsequently been transferred to the many-electron problem [27], which lead to first studies of the properties of and the connections between v, v KS , and v P , for atoms [30][31][32][33] and diatomics [30,[34][35][36], and to further studies of the conditional wavefunction in the DFT literature [37][38][39][40][41][42][43][44]. Recently, the formalism of the wavefunction separation has been further developed for the electron-nuclear problem and been termed the exact factorization [45][46][47].…”

Section: Introductionmentioning

confidence: 99%

On the Geometric Potential and the Relationship between the Exact Electron Factorization and Density Functional Theory

Kocák¹,

Kraisler²,

Schild³

2021

Preprint

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There are different ways to obtain an exact one-electron theory for a many-electron system, and the exact electron factorization (EEF) is one of them. In the EEF, the Schrödinger equation for one electron in the environment of other electrons is constructed. The environment provides the potentials that appear in this equation: A scalar potential v H representing the energy of the environment and another scalar potential v G as well as a vector potential that have geometric meaning. By replacing the interacting many-electron system with the non-interacting Kohn-Sham (KS) system, we show how the EEF is related to density functional theory (DFT) and we interpret the Hartree-exchangecorrelation potential as well as the Pauli potential in terms of the EEF. In particular, we show that from the EEF viewpoint, the Pauli potential does not represent the difference between a fermionic and a bosonic non-interacting system, but that it corresponds to v G and partly to v H for the (fermionic) KS system. We then study the meaning of v G in detail: Its geometric origin as a metric measuring the change of the environment is presented. Additionally, its behavior for a simple model of a homoand heteronucler diatomic is investigated and interpreted with the help of a two-state model. In this way, we provide a physical interpretation for the one-electron potentials that appear in the EEF and in DFT.

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Exchange-Correlation Energy Densities and Response Potentials: Connection between Two Definitions and Analytical Model for the Strong-Coupling Limit of a Stretched Bond

Cited by 11 publications

References 67 publications

Keto‐enol tautomerism from the electron delocalization perspective

Keto‐enol tautomerism from the electron delocalization perspective

Developing orbital-free quantum crystallography: the local potentials and associated partial charge densities

On the Geometric Potential and the Relationship between the Exact Electron Factorization and Density Functional Theory

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