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Title: On the piecewise convex or concave nature of ground state energy as a function of fractional number of electrons for approximate density functionals

Authors:
ORCiD logo [1];  [2]
  1. Department of Chemistry, Duke University, Durham, North Carolina 27708, USA
  2. Department of Chemistry, Duke University, Durham, North Carolina 27708, USA, Key Laboratory of Theoretical Chemistry of Environment, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1361757
Grant/Contract Number:
SC0012575
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 7; Related Information: CHORUS Timestamp: 2018-02-14 11:46:33; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English

Citation Formats

Li, Chen, and Yang, Weitao. On the piecewise convex or concave nature of ground state energy as a function of fractional number of electrons for approximate density functionals. United States: N. p., 2017. Web. doi:10.1063/1.4974988.
Li, Chen, & Yang, Weitao. On the piecewise convex or concave nature of ground state energy as a function of fractional number of electrons for approximate density functionals. United States. doi:10.1063/1.4974988.
Li, Chen, and Yang, Weitao. Tue . "On the piecewise convex or concave nature of ground state energy as a function of fractional number of electrons for approximate density functionals". United States. doi:10.1063/1.4974988.
@article{osti_1361757,
title = {On the piecewise convex or concave nature of ground state energy as a function of fractional number of electrons for approximate density functionals},
author = {Li, Chen and Yang, Weitao},
abstractNote = {},
doi = {10.1063/1.4974988},
journal = {Journal of Chemical Physics},
number = 7,
volume = 146,
place = {United States},
year = {Tue Feb 21 00:00:00 EST 2017},
month = {Tue Feb 21 00:00:00 EST 2017}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1063/1.4974988

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  • 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 andmore » 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.« less
  • Cited by 7
  • The research described in this product was performed in part in the Environmental Molecular Sciences Laboratory, a national scientific user facility sponsored by the Department of Energy's Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. The geometries and binding energies of a recent buckyball tweezers (C60H28) and its supramolecular complexes are investigated using recently developed density functionals (M06-L and M06-2X) that include an accurate treatment of medium-range correlation energy. The pincer part of the tweezers, corannulene, has a strong attractive interaction with C60. However, due to the entropy penalty, the calculated gas-phase free energy ofmore » association of the C60@corannulene supramolecule is positive 3.5 kcal mol-1; and this entropy penalty explains why it is difficult to observe C60@corannulene supramolecule experimentally. By using a p-extended tetrathiafulvalene (TTF), in particular 9,10-bis(1,3-dithiol-2-ylidene)-9,10-dihydroanthracene (TTFAQ or C20H10S4), as the pincer part, we modeled a new buckyball tweezers. The geometries and binding energies of the new buckyball tweezers and its supramolecular complexes are also calculated. Due to fact that the attractive interaction between TTFAQ and C60 is weaker than that between corannulene and C60, the gas-phase binding free energy in the C60@C60H 32S8 supramolecular complex is smaller than that in the C60@C60H28 supramolecule. We also discuss solvent effects.« less
  • We compute the ground-state energy of atoms and quantum dots with a large number N of electrons. Both systems are described by a nonrelativistic Hamiltonian of electrons in a d-dimensional space. The electrons interact via the Coulomb potential. In the case of atoms (d=3), the electrons are attracted by the nucleus via the Coulomb potential. In the case of quantum dots (d=2), the electrons are confined by an external potential, whose shape can be varied. We show that the dominant terms of the ground-state energy are those given by a semiclassical Hartree-exchange energy, whose N{yields}{infinity} limit corresponds to Thomas-Fermi theory.more » This semiclassical Hartree-exchange theory creates oscillations in the ground-state energy as a function of N. These oscillations reflect the dynamics of a classical particle moving in the presence of the Thomas-Fermi potential. The dynamics is regular for atoms and some dots, but in general in the case of dots, the motion contains a chaotic component. We compute the correlation effects. They appear at the order NlnN for atoms, in agreement with available data. For dots, they appear at the order N.« less