A simple approach towards non-local potentials: theory and applications

The many-body problem of finding a correlation potential in an electron gas is solved as a two-electron problem. The resulting correlation potential for a constant density compares well with other local-density potentials for a wide range of different densities. The formalism is extended for non-constant electron densities and spin-polarisation. For nonlocal exchange we use a simple rescaling of the Kohn-Sham potential, in which non-locality up to a certain cut-off radius is included. It is argued that the obtained formalism is applicable for relatively high densities in which the exchange-correlation hole is small in comparison with the size of a lobe of an atomic wavefunction. Applications for V. Cu. Nb. Pd, Ni, Fe, and Ce usingself-consistent linear-muffin-tin-orbital (LMTO) band calculations give in general improved Fermi Surface (FS) properties in all metals. In Li, having low electronic density, the FS does not change significantly from the local-density result. The formalism, with its advantages and shortcomings compared to other methods and calculated results, is discussed.