Integer Discontinuity of Density Functional Theory

Abstract

Density functional approximations to the exchange-correlation energy of Kohn-Sham theory, such as the local density approximation and generalized gradient approximations, lack the well-known integer discontinuity, a feature that is critical to describe molecular dissociation correctly. Moreover, standard approximations to the exchange-correlation energy also fail to yield the correct linear dependence of the ground-state energy on the number of electrons when this is a non-integer number obtained from the grand canonical ensemble statistics. We present a formal framework to restore the integer discontinuity of any density functional approximation. Our formalism derives from a formula for the exact energy functional and a new constrained search functional that recovers the linear dependence of the energy on the number of electrons.

5 pages, 2 figures

References in corpus (4)

• Localization and delocalization errors in density functional theory and implications for band-gap prediction
• Piecewise Linearity of Approximate Density Functionals Revisited: Implications for Frontier Orbital Energies
• Density functional theory in one-dimension for contact-interacting fermions
• Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions

Cited by in corpus (6)

• The derivative discontinuity of the exchange-correlation functional
• How is the derivative discontinuity related to steps in the exact Kohn-Sham potential?
• Elimination of the asymptotic fractional dissociation problem in Kohn-Sham density functional theory using the ensemble-generalization approach
• Nonequilibrium Anderson model made simple with density functional theory
• Effect of ensemble generalization on the highest-occupied Kohn-Sham eigenvalue
• Comparison of local density functionals based on electron gas and finite systems