Cusp relation for the Pauli potential

This work describes a new approach for approximate obtaining the positively defined electronic kinetic energy density (KED) from electron density. KED is presented as a sum of the Weizs€ acker KED, which is calculated in terms of electron density exactly, and unknown Pauli KED. The latter is presented via local Pauli potential and Gritsenko-van Leeuwen-Baerends kinetic response potential, to which the second-order gradient expansion is applied. The resulting expression for KED contains only one empirical parameter. The approach allowed to correctly reproduce all the features of KED, and electron localization descriptors as electron localization function and phasespace defined Fisher information density for main types of bonds in molecules and molecular crystals. It is also demonstrated that the method is immediately applicable to derivation of mentioned bonding descriptors from experimental electron density. Herewith the method is significantly free from the drawback of Kirzhnits approximation, which is now commonly accepted for evaluation of the electronic kinetic energy characteristics from precise X-ray diffraction experiment.

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“…Here

υ_{P} (r)

is the Pauli potential corresponding to the Pauli KED,

t_{P} true(boldr true)

;

ε_{M}

is the energy of the highest occupied orbital, which, in fact coincides with the electronic chemical potential

μ_{s}

. Eq.…”

Section: Methodsmentioning

confidence: 99%

Improving approximate determination of the noninteracting electronic kinetic energy density from electron density

Astakhov

Сташ

Tsirelson

2015

Int J of Quantum Chemistry

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“…A general expression for v θ [n](r) in terms of the density is not known, but several approximations to it have been suggested (see [17,21,24,[31][32][33][34][35][36] and references therein) and applied to selected atoms [22,37,38] and molecules [21,23,31]. Furthermore, there exists an exact expression for v θ [n](r) in terms of the KS orbitals and energy levels [17].…”

Section: Introductionmentioning

confidence: 99%

“…Several analytical properties of the Pauli potential have been discovered during the years. The positivity of the potential [15,31], its coordinate scaling [17], the cusp in the vicinity of the nucleus [38], conditions on the gradient expansion [17], as well as properties for spherically symmetric systems [39,40] and particularly for two-and three-level atoms and ions [41] have been discussed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Discontinuous behavior of the Pauli potential in density functional theory as a function of the electron number

Kraisler

Schild

2020

Phys. Rev. Research

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“…A general expression for v θ [n](r) in terms of the density is not known, but several approximations to it have been suggested (see [15,19,22,[29][30][31][32][33][34] and references therein) and applied to selected atoms [20,35,36] and molecules [19,21,29]. Furthermore, there exists an exact expression for v θ [n](r) in terms of the KS orbitals and energy levels [15].…”

Section: Introductionmentioning

confidence: 99%

“…Several analytical properties of the Pauli potential have been discovered during the years. The positivity of the potential [13,29], its coordinate scaling [15], the cusp in the vicinity of the nucleus [36], conditions on the gradient expansion [15], as well as properties for sphericallysymmetric systems [37,38] and particularly for two-and three-level atoms and ions [39] have been discussed in the literature.…”

Section: Introductionmentioning

confidence: 99%

Discontinuous Behavior of the Pauli Potential in Density Functional Theory as a Function of the Electron Number

Kraisler¹,

Schild²

2019

Preprint

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<div>The Pauli potential is an essential quantity in orbital-free density-functional theory (DFT) and in the exact electron factorization (EEF) method for many-electron systems. Knowledge of the Pauli potential allows the description of a system relying on the density alone, without the need to calculate the orbitals.</div><div>In this work we explore the behavior of the exact Pauli potential in finite systems as a function of the number of electrons, employing the ensemble approach in DFT. Assuming the system is in contact with an electron reservoir, we allow the number of electrons to vary continuously and to obtain fractional as well as integer values. We derive an expression for the Pauli potential for a spin-polarized system with a fractional number of electrons and find that when the electron number surpasses an integer, the Pauli potential jumps by a spatially uniform constant, similarly to the Kohn-Sham potential. The magnitude of the jump equals the Kohn-Sham gap. We illustrate our analytical findings by calculating the exact and approximate Pauli potentials for Li and Na atoms with fractional numbers of electrons.</div>

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Cusp relation for the Pauli potential

Cited by 16 publications

References 53 publications

Improving approximate determination of the noninteracting electronic kinetic energy density from electron density

Improving approximate determination of the noninteracting electronic kinetic energy density from electron density

Discontinuous behavior of the Pauli potential in density functional theory as a function of the electron number

Discontinuous Behavior of the Pauli Potential in Density Functional Theory as a Function of the Electron Number

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