Landscape of an exact energy functional

Aron J. Cohen and Paula Mori-Sánchez
Phys. Rev. A 93, 042511 – Published 26 April 2016
PDFHTMLExport Citation

Abstract

One of the great challenges of electronic structure theory is the quest for the exact functional of density functional theory. Its existence is proven, but it is a complicated multivariable functional that is almost impossible to conceptualize. In this paper the asymmetric two-site Hubbard model is studied, which has a two-dimensional universe of density matrices. The exact functional becomes a simple function of two variables whose three-dimensional energy landscape can be visualized and explored. A walk on this unique landscape, tilted to an angle defined by the one-electron Hamiltonian, gives a valley whose minimum is the exact total energy. This is contrasted with the landscape of some approximate functionals, explaining their failure for electron transfer in the strongly correlated limit. We show concrete examples of pure-state density matrices that are not v representable due to the underlying nonconvex nature of the energy landscape. The exact functional is calculated for all numbers of electrons, including fractional, allowing the derivative discontinuity to be visualized and understood. The fundamental gap for all possible systems is obtained solely from the derivatives of the exact functional.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 17 September 2015

DOI:https://doi.org/10.1103/PhysRevA.93.042511

©2016 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & Optical

Authors & Affiliations

Aron J. Cohen

  • Department of Chemistry, Lensfield Rd, University of Cambridge, Cambridge, CB2 1EW, United Kingdom

Paula Mori-Sánchez

  • Departamento de Química and Instituto de Física de la Materia Condensada (IFIMAC), Universidad Autónoma de Madrid, 28049, Madrid, Spain

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 93, Iss. 4 — April 2016

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×