INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 13 (2001) 3073–3081 www.iop.org/Journals/cm PII: S0953-8984(01)19124-1 Angular momentum convergence of Korringa–Kohn–Rostoker Green’s function methods Nassrin Y Moghadam 1 , G M Stocks 1 , X-G Zhang 1 , D M C Nicholson 1 , W A Shelton 1 , Yang Wang 2 and J S Faulkner 3 1 Oak Ridge National Laboratory, Oak Ridge, TN 37831-6114, USA 2 Pittsburgh Supercomputing Center, 4400 5th Avenue, Pittsburgh, PA 15213, USA 3 Florida Atlantic University, Boca Raton, FL 33431, USA Received 17 November 2000, in final form 19 February 2001 Abstract The convergence of multiple-scattering-theory-based electronic structure methods (e.g. the Korringa–Kohn–Rostoker (KKR) band theory method), is determined by l max , the maximum value of the angular momentum quantum number l . It has been generally assumed that l max = 3 or 4 is sufficient to ensure a converged ground state and other properties. Using the locally self-consistent multiple-scattering method, which facilitates the use of very high values of l max , it is shown that the convergence of KKR Green’s function methods is much slower than previously supposed, even when spherical approximations to the crystal potential are used. Calculations for Cu using 3  l max  16 indicate that the total energy is converged to within ∼0.04 mRyd at l max = 12. For both face-centred cubic and body-centred cubic structures, the largest error in the total energy occurs at l max = 4; l max = 8 gives total energies, bulk moduli, and lattice constants that are converged to accuracies of 0.1 mRyd, 0.1 Mbar, and 0.002 Bohr respectively. 1. Introduction Multiple-scattering theory (MST) was first applied to electronic structure calculations by Korringa [1] in a theory now known as the Korringa–Kohn–Rostoker (KKR) band theory method [1, 2]. Recast in terms of Green’s function (GF) techniques, MST now underpins electronic structure methods for a wide variety of systems (e.g. ordered metals, substitutional alloys, surfaces, interfaces, and multi-layers) and physical properties (e.g. transport), as well as computer codes used for the interpretation of spectroscopies (e.g. LEED, EELS, photo- emission, and soft-x-ray) [3]. MST–GF techniques also underpin recently developed order-N methods for treating large systems [4–6] and a new full-potential version of the KKR band- structure method [7, 8] that yields results of an accuracy comparable to that of the all-electron FLAPW method. In MST–GF calculations the primary convergence parameter is the cut-off l max used in angular momentum expansions of the Green’s function, scattering t -matrix, and wave © 2001 US Government Printed in the UK 3073