Exchange-Only Theory: Relation Between Exchange Energy, Its Functional Derivative and Eigenvalue Sums in an Inhomogeneous Electron Liquid

Abstract

In earlier work (Phys. Rev. A 55 3465, 1997) one of us (A.N.) has related the exchange-only potential designed to reproduce the Hartree-Fock density to the sum of the Slater potential and a term involving the difference between the eigenvalues of the Hartree-Fock (HF) and Kohn-Sham (KS) wave functions. Here, a consequence of this approximate theory is derived that relates the total exchange energy to its functional derivative and to the difference ΔE_S between the eigenvalue sums of the HF and KS schemes.

Key Words:

• Inhomogeneous electron liquid
• exchange-only theory