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Title: Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number

Abstract

Properties of exact density functionals provide useful constraints for the development of new approximate functionals. This paper focuses on convex sums of ground-level densities. It is observed that the electronic kinetic energy of a convex sum of degenerate ground-level densities is equal to the convex sum of the kinetic energies of the individual degenerate densities. (The same type of relationship holds also for the electron-electron repulsion energy.) This extends a known property of the Levy-Valone Ensemble Constrained-Search and the Lieb Legendre-Transform refomulations of the Hohenberg-Kohn functional to the individual components of the functional. Moreover, we observe that the kinetic and electron-repulsion results also apply to densities with fractional electron number (even if there are no degeneracies), and we close with an analogous point-wise property involving the external potential. Examples where different degenerate states have different kinetic energy and electron-nuclear attraction energy are given; consequently, individual components of the ground state electronic energy can change abruptly when the molecular geometry changes. These discontinuities are predicted to be ubiquitous at conical intersections, complicating the development of universally applicable density-functional approximations.

Authors:
 [1]; ;
  1. Department of Chemistry, Duke University, Durham, North Carolina 27708 (United States)
Publication Date:
OSTI Identifier:
22253028
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 140; Journal Issue: 18; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; DENSITY; DENSITY FUNCTIONAL METHOD; ELECTRONS; GROUND LEVEL; GROUND STATES; KINETIC ENERGY

Citation Formats

Levy, Mel, Department of Physics, North Carolina A and T State University, Greensboro, North Carolina 27411, Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, Anderson, James S. M., Zadeh, Farnaz Heidar, and Ayers, Paul W., E-mail: ayers@mcmaster.ca, E-mail: mlevy@tulane.edu. Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number. United States: N. p., 2014. Web. doi:10.1063/1.4871734.
Levy, Mel, Department of Physics, North Carolina A and T State University, Greensboro, North Carolina 27411, Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, Anderson, James S. M., Zadeh, Farnaz Heidar, & Ayers, Paul W., E-mail: ayers@mcmaster.ca, E-mail: mlevy@tulane.edu. Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number. United States. https://doi.org/10.1063/1.4871734
Levy, Mel, Department of Physics, North Carolina A and T State University, Greensboro, North Carolina 27411, Department of Chemistry, Tulane University, New Orleans, Louisiana 70118, Anderson, James S. M., Zadeh, Farnaz Heidar, and Ayers, Paul W., E-mail: ayers@mcmaster.ca, E-mail: mlevy@tulane.edu. 2014. "Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number". United States. https://doi.org/10.1063/1.4871734.
@article{osti_22253028,
title = {Kinetic and electron-electron energies for convex sums of ground state densities with degeneracies and fractional electron number},
author = {Levy, Mel and Department of Physics, North Carolina A and T State University, Greensboro, North Carolina 27411 and Department of Chemistry, Tulane University, New Orleans, Louisiana 70118 and Anderson, James S. M. and Zadeh, Farnaz Heidar and Ayers, Paul W., E-mail: ayers@mcmaster.ca, E-mail: mlevy@tulane.edu},
abstractNote = {Properties of exact density functionals provide useful constraints for the development of new approximate functionals. This paper focuses on convex sums of ground-level densities. It is observed that the electronic kinetic energy of a convex sum of degenerate ground-level densities is equal to the convex sum of the kinetic energies of the individual degenerate densities. (The same type of relationship holds also for the electron-electron repulsion energy.) This extends a known property of the Levy-Valone Ensemble Constrained-Search and the Lieb Legendre-Transform refomulations of the Hohenberg-Kohn functional to the individual components of the functional. Moreover, we observe that the kinetic and electron-repulsion results also apply to densities with fractional electron number (even if there are no degeneracies), and we close with an analogous point-wise property involving the external potential. Examples where different degenerate states have different kinetic energy and electron-nuclear attraction energy are given; consequently, individual components of the ground state electronic energy can change abruptly when the molecular geometry changes. These discontinuities are predicted to be ubiquitous at conical intersections, complicating the development of universally applicable density-functional approximations.},
doi = {10.1063/1.4871734},
url = {https://www.osti.gov/biblio/22253028}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 18,
volume = 140,
place = {United States},
year = {Wed May 14 00:00:00 EDT 2014},
month = {Wed May 14 00:00:00 EDT 2014}
}