Angular momentum convergence of Korringa-Kohn-Rostoker Green's function methods

Abstract

The convergence of multiple-scattering-theory-based electronic structure methods (e.g. the Korringa-Kohn-Rostoker (KKR) band theory method), is determined by lmax, the maximum value of the angular momentum quantum number l. It has been generally assumed that lmax = 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 lmax, 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⩽lmax⩽16 indicate that the total energy is converged to within ~0.04 mRyd at lmax = 12. For both face-centred cubic and body-centred cubic structures, the largest error in the total energy occurs at lmax = 4; lmax = 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.

Structural phase transitions and fundamental band gaps ofMgxZn1−xOalloys from first principles

“…One might speculate that earlier implementations of multiple-scattering theory failed to optimize these structural parameters in any open structure due to the slow angular momentum convergence of the Green function (see Section III; the convergence is significantly improved by using Lloyd's formula). 73 In summary, the agreement of our results for the ordered alloys with those of other theoretical investigations and experiments indicates that the present approach is as reliable and accurate as any other state-of-the-art methods.…”

Structural phase transitions and fundamental band gaps of Mg(x)Zn(1-x)O alloys from first principles

“…Moreover, due to the negative pressure these phases cannot be realized experimentally, hence ruling out a clar- any open structure due to the slow angular momentum convergence of the Green function (see Section III; the convergence is significantly improved by using Lloyd's formula). 73 In summary, the agreement of our results for the ordered alloys with those of other theoretical investigations and experiments indicates that the present approach is as reliable and accurate as any other state-of-the-art methods.…”

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

“…Moghadam et al 34 carried out a test of l convergence for fcc Cu in a real-space KKR, linear-scaling multiplescattering (LSMS) method. The difference between the total energy (E F ) for l max = 3 and l max = 8 is 7 mRy (6 mRy).…”

“…As such, a faster convergence in the l-space can be achieved by an improved basis set, but with a concomitant increase in R 3 process. Moghadam et al 34 carried out a test of l convergence for fcc Cu in a real-space KKR, linear-scaling multiplescattering (LSMS) method. The difference between the total energy (E F ) for l max = 3 and l max = 8 is 7 mRy (6 mRy).…”