Demonstration of the Gunnarsson-Lundqvist theorem and the multiplicity of potentials for excited states

Authors

Yu-Qi Li, Ningbo University
Xiao-Yin Pan, Ningbo University
Biao Li, Ningbo University
Viraht Sahni, CUNY Graduate Center and CUNY Brooklyn CollegeFollow

Document Type

Article

Publication Date

3-21-2012

Abstract

The Gunnarsson-Lundqvist (GL) theorem of density functional theory states that there is a one-to-one relationship between the density of the lowest nondegenerate excited state of a given symmetry and the external potential. As a consequence, knowledge of this excited state density determines the external potential uniquely. [The GL theorem is the equivalent for such excited states of theHohenberg-Kohn (HK) theorem for nondegenerate ground states.] For other excited states, there is no equivalent of the GL or HK theorem. For these states, there thus exist multiple potentials that generate the excited-state density. We show, by example, the satisfaction that the GL theorem holds and the multiplicity of potentials for excited states.

Comments

This work was originallu published in Physical Review A, available at http://dx.doi.org/10.1103/PhysRevA.85.032517.