Recursion, non-orthogonal basis vectors, and the computation of electronic properties

The authors present a more general and systematic formulation of the recursion method, from which one can simply compute any matrix element of the Green function as a continued fraction. The generalisations are important if one uses non-orthogonal basis functions, such as overlapping atomic orbitals. They investigate the significance of these generalisations for computation of densities of states and of the electrical conductivity of disordered metals. The corrections are unimportant for liquid Mn, but they are very important for liquid Co.