Locally self-consistent Green’s function approach to the electronic structure problem

The locally self-consistent Green’s function (LSGF) method is an order-$N$ method for calculation of the electronic structure of systems with an arbitrary distribution of atoms of different kinds on an underlying crystal lattice. For each atom Dyson’s equation is used to solve the electronic multiple scattering problem in a local interaction zone (LIZ) embedded in an effective medium judiciously chosen to minimize the size of the LIZ. The excellent real-space convergence of the LSGF calculations and the reliability of its results are demonstrated for a broad spectrum of metallic alloys with different degree of order. The relation of the convergence of our method to fundamental properties of the system, that is, the effective cluster interactions, is discussed.