Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

The Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of N scatterers. Wave functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L sub(max) = (l, m) sub(max), while scattering matrices, which determine spectral properties, are truncated at L sub(tr) = (l, m) sub(tr) where phase shifts delta l>ltr are negligible. Historically, L sub(max) is set equal to L sub(tr), which is correct for large enough L sub(max) but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L sub(max) > L sub(tr) with delta l>ltr set to zero [X.-G. Zhang and W. H. Butler, Phys. Rev. B 46, 7433 (1992) (http://dx.doi.org/10.1103/PhysRevB.46.7433)]. We present a numerically efficient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [[scriptR] super(3) process with rank N(l sub(tr) + 1) super(2)] and includes higher-L contributions via linear algebra [[scriptR] super(2) process with rank N(l sub(max) + 1) super(2)]. The augmented-KKR approach yields properly normalized wave functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe, and L1 sub(0) CoPt and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L sub(max) for a given L sub(tr).