Direct method for optimized effective potentials in density-functional theory.

The conventional optimized effective potential method is based on a difficult-to-solve integral equation. In the new method, this potential is constructed as a sum of a fixed potential and a linear combination of basis functions. The energy derivatives with respect to the coefficients of the linear combination are obtained. This enables calculations by optimization methods. Accurate atomic and molecular calculations with Gaussian basis sets are presented for exact exchange functionals. This efficient and accurate method for the optimized effective potential should play an important role in the development and application of density functionals.