Multiple-scattering approach to band theory. II. Fast band theory

The multiple-scattering equations are used to derive a set of band-theory equations that are called the pivoted-multiple-scattering (PMS) equations. The PMS equations are as legitimate a basis for band-theory calculation as the Korringa-Kohn-Rostoker (KKR) equations that are also derived from the multiple-scattering theory. The primary usefulness of the PMS equations is that an approximate expression can be derived from them that gives all the eigenvalues for one $\overrightarrow{\mathrm{k}}$ with a single-matrix diagonalization. This expression has the form of a quadratic eigenvalue equation. The usefulness and accuracy of this quadratic KKR formalism is demonstrated by a number of numerical studies.