On the minimization of the energy of a free-electron gas with constrained density function - ENSTA Paris - École nationale supérieure de techniques avancées Paris Accéder directement au contenu
Article Dans Une Revue Nonlinear Analysis: Theory, Methods and Applications Année : 1999

On the minimization of the energy of a free-electron gas with constrained density function

Résumé

One of the aims of density functional theory is to obtain properties of (ground) states of large systems, in particular their energy, by solving a nonlinear equation, involving only the parameters of a single electron. The oldest such theory is the Thomas-Fermi approach. Major developments are due to Hohenberg, Kohn and Sham in the mid-1960s and the present article discusses an approximate nonlinear equation arising within the context of the Kohn-Sham approach [P. Hohenberg and W. Kohn, Phys. Rev. (2) 136 (1964), B864-B871; MR0180312 (31 #4547); W. Kohn and L. J. Sham, Phys. Rev. (2) 140 (1965), A1133-A1138; MR0189732 (32 #7154)]. It is connected to the exchange contribution to the Kohn-Sham functional. The latter arises from taking into account the Fermi-Dirac statistics and complicates the application of a variational procedure significantly. Thus it is often replaced by an approximate term and the authors discuss the existence of a solution for this situation. They make a few physically reasonable assumptions and are then able to demonstrate the existence of a proper solution.
Fichier non déposé

Dates et versions

hal-00982466 , version 1 (23-04-2014)

Identifiants

  • HAL Id : hal-00982466 , version 1

Citer

Olivier Bokanowski, Ian Schindler, Hasnaa Zidani. On the minimization of the energy of a free-electron gas with constrained density function. Nonlinear Analysis: Theory, Methods and Applications, 1999, 35 (8), pp.1073-1090. ⟨hal-00982466⟩
364 Consultations
0 Téléchargements

Partager

Gmail Facebook X LinkedIn More