One-body spin-density matrix expansion and exchange energy in spin-current density functional theory

Abstract

Density functional theory (DFT) is an approach describing the properties of an interacting many-fermion system. The DFT is applied in various elds of physics at the quantum level such as the calculation of electronic structure and band structures in solid-state physics, and also applied in quantum chemistry for molecules. In the primitive version of DFT, the local particle density 0(~r) constitutes the basic variable to describe the properties of the systemof N interact- ing particles. Including the spin and spin-orbit coupling the corresponding density-functional is called spin-current DFT and requires additional basic set of variables n 0;􀀀!j ;􀀀! ;􀀀!J o , namely the particle density 0, the current density 􀀀!j , the spin-vector density 􀀀! and the spin-currents density 􀀀!J . In this work we are interested in approximate functional of exchange energy Ex within the spin-current-DFT. For that we perform an appropriate short range expansion of the one-body spin-density matrix up to second order in relative distance. Using this expansion we were able to derive an analytical exchange energy functional. This novel result is then used toexamine some particular situations known in the literature. In particular we nd an improved exchange functional in the so-called gradient expansion approximation (GEA). We also show that our general functional reduce for spin-orbit coupled systems to an exchange functional used very recently