Extension of the KohnSham formulation of density functional theory to finite temperature
Abstract
Based on Mermin's extension of the Hohenberg and Kohn theorems to nonzero temperature, the KohnSham formulation of density functional theory (KSDFT) is generalized to finite temperature. Here, we show that present formulations are inconsistent with Mermin's functional containing expressions, in particular describing the Coulomb energy, that defy derivation and are even in violation of rules of logical inference. More; current methodology is in violation of fundamental laws of both quantum and classical mechanics. Based on this feature, we demonstrate the impossibility of extending the KS formalism to finite temperature through the selfconsistent solutions of the singleparticle Schrödinger equation of T>0. Guided by the form of Mermin's functional that depends on the eigenstates of a Hamiltonian, determined at T>0 we base our extension of KSDFT on the determination of the excited states of a noninteracting system at the zero of temperature. The resulting formulation is consistent with that of Mermin constructing the free energy at T>0 in terms of the excited states of a noninteracting Hamiltonian (system) that, within the KS formalism, are described by Slater determinants. To determine the excited states at T=0 use is made of the extension of the Hohenberg and Kohn theorems to excited states presented inmore »
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Physical and Life Sciences
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1438758
 Report Number(s):
 LLNLJRNL707186
Journal ID: ISSN 00223697; TRN: US1900514
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Physics and Chemistry of Solids
 Additional Journal Information:
 Journal Volume: 116; Journal Issue: C; Journal ID: ISSN 00223697
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 97 MATHEMATICS AND COMPUTING; Density functional theory; Temperature DFT; Excited states in DFT; Temperature extension of KohnSham DFT; Excited states in KohnSham theory; Mermin functional
Citation Formats
Gonis, A., and Dane, M. Extension of the KohnSham formulation of density functional theory to finite temperature. United States: N. p., 2017.
Web. doi:10.1016/j.jpcs.2017.12.021.
Gonis, A., & Dane, M. Extension of the KohnSham formulation of density functional theory to finite temperature. United States. doi:10.1016/j.jpcs.2017.12.021.
Gonis, A., and Dane, M. Wed .
"Extension of the KohnSham formulation of density functional theory to finite temperature". United States. doi:10.1016/j.jpcs.2017.12.021. https://www.osti.gov/servlets/purl/1438758.
@article{osti_1438758,
title = {Extension of the KohnSham formulation of density functional theory to finite temperature},
author = {Gonis, A. and Dane, M.},
abstractNote = {Based on Mermin's extension of the Hohenberg and Kohn theorems to nonzero temperature, the KohnSham formulation of density functional theory (KSDFT) is generalized to finite temperature. Here, we show that present formulations are inconsistent with Mermin's functional containing expressions, in particular describing the Coulomb energy, that defy derivation and are even in violation of rules of logical inference. More; current methodology is in violation of fundamental laws of both quantum and classical mechanics. Based on this feature, we demonstrate the impossibility of extending the KS formalism to finite temperature through the selfconsistent solutions of the singleparticle Schrödinger equation of T>0. Guided by the form of Mermin's functional that depends on the eigenstates of a Hamiltonian, determined at T>0 we base our extension of KSDFT on the determination of the excited states of a noninteracting system at the zero of temperature. The resulting formulation is consistent with that of Mermin constructing the free energy at T>0 in terms of the excited states of a noninteracting Hamiltonian (system) that, within the KS formalism, are described by Slater determinants. To determine the excited states at T=0 use is made of the extension of the Hohenberg and Kohn theorems to excited states presented in previous work applied here to a noninteracting collection of replicas of a noninteracting Nparticle system, whose ground state density is taken to match that of K noninteracting replicas of an interacting Nparticle system at T>0. The formalism allows for an ever denser population of the excitation spectrum of a Hamiltonian, within the KS approximation. The form of the auxiliary potential, (KohnSham potential), is formally identical to that in the ground state formalism with the contribution of the Coulomb energy provided by the derivative of the Coulomb energy in all excited states taken into account. Once the excited states are determined, the minimum of the free energy within the KS formalism follows immediately in the form of Mermin's functional, but with the exact excited states in that functional represented by Slater determinants obtained through selfconsistency conditions at the zero of temperature. Lastly, it is emphasized that, in departure from all existing formulations, no selfconsistency conditions are implemented at finite T; as we show, in fact, such formulations are rigorously blocked.},
doi = {10.1016/j.jpcs.2017.12.021},
journal = {Journal of Physics and Chemistry of Solids},
number = C,
volume = 116,
place = {United States},
year = {2017},
month = {12}
}