Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density

Paola Gori-Giorgi, Evert Jan Baerends

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

It is known that the asymptotic decay (|r|→∞) of the electron density n(r) outside a molecule is informative about its first ionization potential I0. It has recently become clear that the special circumstance that the Kohn–Sham (KS) highest-occupied molecular orbital (HOMO) has a nodal plane that extends to infinity may give rise to different cases for the asymptotic behavior of the exact density and of the exact KS potential [P. Gori-Giorgi et al., Mol. Phys. 114, 1086 (2016)]. Here we investigate the consequences of such a HOMO nodal plane for the effective potential in the Schrödinger-like equation for the square root of the density, showing that for atoms and molecules it will usually diverge asymptotically on the plane, either exponentially or polynomially, depending on the coupling between Dyson orbitals. We also analyze the issue in the external harmonic potential, reporting an example of an exact analytic density for a fully interacting system that exhibits a different asymptotic behavior on the nodal plane.

Original languageEnglish
Article number160
Pages (from-to)1-10
Number of pages10
JournalEuropean Physical Journal B
Volume91
Issue number7
Early online date11 Jul 2018
DOIs
Publication statusPublished - Jul 2018

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Molecular orbitals
Carrier concentration
Molecules
Ionization potential
molecular orbitals
ionization potentials
Atoms
infinity
molecules
harmonics
orbitals
decay
atoms

Cite this

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abstract = "It is known that the asymptotic decay (|r|→∞) of the electron density n(r) outside a molecule is informative about its first ionization potential I0. It has recently become clear that the special circumstance that the Kohn–Sham (KS) highest-occupied molecular orbital (HOMO) has a nodal plane that extends to infinity may give rise to different cases for the asymptotic behavior of the exact density and of the exact KS potential [P. Gori-Giorgi et al., Mol. Phys. 114, 1086 (2016)]. Here we investigate the consequences of such a HOMO nodal plane for the effective potential in the Schr{\"o}dinger-like equation for the square root of the density, showing that for atoms and molecules it will usually diverge asymptotically on the plane, either exponentially or polynomially, depending on the coupling between Dyson orbitals. We also analyze the issue in the external harmonic potential, reporting an example of an exact analytic density for a fully interacting system that exhibits a different asymptotic behavior on the nodal plane.",
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Asymptotic nodal planes in the electron density and the potential in the effective equation for the square root of the density. / Gori-Giorgi, Paola; Baerends, Evert Jan.

In: European Physical Journal B, Vol. 91, No. 7, 160, 07.2018, p. 1-10.

Research output: Contribution to JournalArticleAcademicpeer-review

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