Efficient exact exchange approximations in density-functional theory.

Two approaches to approximate the Slater potential component of local exact exchange of density-functional theory are investigated. The first approach employs density fitting of the electrostatic potential integrals over two occupied orbitals and the other approach approximates the "exact" Slater potential with the potential derived from the Becke-Roussel [Phys. Rev. A. 39, 3761 (1989)] model of the exchange hole. In both cases significant time savings can be achieved for larger systems compared to the calculation of the numerical Slater potential. It is then analyzed how well the orbitals obtained from the various total exchange potentials reproduce Hartree-Fock energies and molecular properties. A large range of atoms and small molecules has been utilized, including the three DNA bases adenine, thymine, and cytosine.