New practicable forms for exchange and correlation energy functionals of the CDFT

Abstract

We propose the vorticity expansion approximation (VEA) formulas of both the exchange and correlation energy functionals of the current density functional theory (CDFT). Similarly to the strategy of the generalized gradient approximation of the density functional theory, the coefficients of expansions are determined by requiring the VEA formulas to satisfy exact relations that are derived from uniform and nonuniform coordinate scaling of electrons. As compared with formulas of the local density approximation of the CDFT, the resultant VEA formulas satisfy a large number of exact relations. Due to the well-behaved forms, the VEA formulas can be in quite good agreement with the exchange and correlation energies of the homogeneous electron liquid under a uniform magnetic field.