Approximate relativistic optimized potential method

Approximate semianalytical solutions of the integral equation for the relativistic optimized potential are constructed by extending a method recently proposed by Krieger, Li, and Iafrate [Phys. Lett. A 146, 256 (1990)] to the relativistic regime. The quality of the approximation is tested in the longitudinal x-only limit where fully numerical solutions of the relativistic optimized effective potential integral equation are available for spherical atoms. The results obtained turn out to be in excellent agreement with the exact x-only values. The proposed method provides significant improvement over the conventional relativistic local density approximation and generalized gradient approximation schemes.