Vorticity expansion approximation of the exchange-correlation energy functional in current density functional theory

We propose the vorticity expansion approximation VEA formulas of the exchange and correlation energy functionals of the current density functional theory CDFT . They have a form of the second-order expansion with respect to the vorticity. Expansion coefficients are determined by requiring them to satisfy exact relations that have been derived from scaling properties of exchange and correlation energy functionals. Resultant VEA formulas satisfy a larger number of exact relations than those of the local-density approximation of the CDFT. 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.