Optimized effective potential method in current-spin-density-functional theory

Current-spin-density-functional theory (CSDFT) provides a framework to describe interacting many-electron systems in a magnetic field which couples to both spin and orbital degrees of freedom. Unlike in the usual (spin-)density-functional theory, approximations to the exchange-correlation energy based on the model of the uniform electron gas face problems in practical applications. In this work, explicitly orbital-dependent functionals are used and a generalization of the optimized effective potential method to the CSDFT framework is presented. A simplifying approximation to the resulting integral equations for the exchange-correlation potentials is suggested. A detailed analysis of these equations is carried out for the case of open-shell atoms and numerical results are given using the exact-exchange energy functional. For zero external magnetic field, a small systematic lowering of the total energy for current-carrying states is observed due to the inclusion of the current in the Kohn-Sham scheme. For states without current, CSDFT results coincide with those of spin-density-functional theory.