Constraint on the second functional derivative of the exchange-correlation energy

Abstract

Using the density functional adiabatic connection approach for an N-electron system it is shown that

γ is the coupling constant that scales the electron–electron interaction strength. For the non-interacting Kohn–Sham Hamiltonian γ = 0 and for the fully interacting system γ = 1. is the Hartree plus exchange-correlation energy while f⁰(r) and f^γ(r) are the Fukui functions of the non-interacting and interacting systems, respectively. This identity can serve to test the internal self-consistency or quality of approximate functionals. The quality of some popular approximate exchange and correlation functionals are tested for a simple model system.

Keywords:

• density functional
• exchange-correlation
• functional derivative
• local density approximation
• gradient and other approximations

Acknowledgements

The author acknowledges support from the National Research Foundation (NRF).