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

Abstract

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient sitecentered, 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 Lmax = (l, m)max, while scattering matrices, which determine spectral properties, are truncated at Ltr = (l, m)tr where phase shifts δ l>l tr are negligible. Historically, Lmax is set equal to Ltr, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax > Ltr with δ l>l tr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically efficient and accurate augmented -KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R 3 process with rank N (ltr + 1) 2 ] and includes higher-L contributions via linear algebra [R 2 process with rank N (lmax + 1) 2 ]. 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 L10 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Ltr.

First-order magnetic phase transition in Pr2In with negligible thermomagnetic hysteresis

“…Spin-polarized, density-functional-theory (DFT) calculations of Pr 2 In were performed employing two codes, namely, the all-electron Korringa-Kohn-Rostoker (KKR) [34,35] Green's function (MECCA) code [36,37], and the full-potential Vienna Ab-initio Simulation Package (VASP) pseudopotential code [38,39]. The electronic (spin-decomposed) DOS was computed using MECCA [36] within the generalized gradient approximation (GGA) exchange-correlation energy functional for solids (PBEsol) [40].…”

Atomistic clustering-ordering and high-strain deformation of an Al0.1CrCoFeNi high-entropy alloy

“…The exchange-correlation functionals used are the von Barth-Hedin 39 local density approximation (LDA) as parameterized by Moruzzi, Janak, and Williams 40 and generalized gradient approximation (GGA) by Perdew-Burke-Ernzerhof revised for solids (PBEsol) 41 . A variational definition 42 of the potential zero (v 0 ) is utilized to yield the kinetic energies and dispersion that approach those of full-potential methods 42 43 . Potentials, charge densities, and total energies are obtained, using a complex-energy Gauss-Legendre semicircular contour with 24 points, and Brillioun-zone integrations use a special k-point method 44 with a 20 × 20 × 20 mesh.…”

Atomic short-range order and incipient long-range order in high-entropy alloys

“…Scalar-relativistic effects are included, but spin orbit is ignored. Because the potential zero v 0 , i.e., muffin-tin zero, can dramatically affect stability prediction for spherical potentials, we use a variational definition [32] that yields kinetic energies that approach those of full-potential methods [32,33].…”