Multiple-scattering theory with a truncated basis set (original) (raw)
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Use of general potentials in multiple-scattering theory
Physical Review A, 1986
A mathematically transparent derivation of the multiple-scattering equations valid for a general non-muffin-tin potential, as applied to clusters of atoms with and without a surrounding outer sphere, is presented. These equations are shown to be a natural generahzation of the analogous equations vahd for muffin-tin potentials. An expression for the photoabsorption and electron scattering cross section in the framework of the multiple-scattering theory valid for a general potential is derived for what may be the first time, providing the nummary generalization for the similar expression valid in the muffin-tin case. A connection with the Green-function approach to the problem is also established via a generalized optical theorem.
Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism
Physical Review B, 2014
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; however, a more proper procedure retains 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 secular equations by matrix inversion [R 3 process with rank N (ltr +1) 2 ] and includes higher-order L contributions via linear algebra [R 2 process with rank N (lmax + 1) 2 ]. Augmented-KKR yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. For fcc Cu, bcc Fe and L10 CoPt, we present the formalism and numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Ltr.
Physical Review B, 2012
We investigate one of the most common analytic continuation techniques in condensed matter physics, namely the Padé approximant. Aspects concerning its implementation in the exact muffin-tin orbitals (EMTO) method are scrutinized with special regard towards making it stable and free of artificial defects. The electronic structure calculations are performed for solid hydrogen, and the performance of the analytical continuation is assessed by monitoring the density of states constructed directly and via the Padé approximation. We discuss the difference between the k-integrated and k-resolved analytical continuations, as well as describing the use of random numbers and pole residues to analyze the approximant. It is found that the analytic properties of the approximant can be controlled by appropriate modifications, making it a robust and reliable tool for electronic structure calculations. At the end, we propose a route to perform analytical continuation for the EMTO + dynamical mean field theory (DMFT) method.
Full-potential multiple scattering theory with space-filling cells for bound and continuum states
Journal of Physics: Condensed Matter, 2010
We present a rigorous derivation of a real space Full-Potential Multiple-Scattering-Theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space-partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wave function. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach, provides a straightforward extension of MST in the Muffin-Tin (MT) approximation, with only one truncation parameter given by the classical relation l max = kR b , where k is the electron wave vector (either in the excited or ground state of the system under consideration) and R b the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l max → ∞ limit. Consequently, this feature provides a firm ground to the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.
Multiple-scattering theory for space-filling cell potentials
Physical Review B, 1992
The multiple-scattering theory (MST) method of Korringa, and of Kohn and Rostoker for determining the electronic structure of solids, originally developed in connection with potentials bounded by nonoverlapping spheres (muffin-tin potentials), is generalized to the case of space-filling potential cells of arbitrary shape. Both variational and nonvariational formalisms are used in effecting this generalization. In contrast to the case of muNn-tin potentials, different forms of MST exhibit different convergence rates for the energy and the wave function. Numerical results are presented that illustrate the differing convergence rates of the variational and nonvariational forms of MST for space-filling potentials. The generalized MST described here should be useful quite generally for constructing global solutions to linear partial differential equations from sets of locally exact solutions.
Muffin-tin orbitals and the total energy of atomic clusters
Physical Review B, 1977
The Hohenberg-Kohn-Sham (HKS) density-functional equations are solved for clusters of atoms using the linear muAin-tin orbital method (LMTO) of Andersen. The approach is numerically efficient and the selfconsistency condition applies to the full potential. Binding energies, equilibrium separations, vibration frequencies, and dipole moments calculated for a series of first-row diatomic molecules agree well with experiment, indicating that the HKS scheme gives a quantitative description of the energy and electron&ensity changes associated with chemical bonding. The ability of the LMTO method to treat non-muffin-tin potential terms and its energy-independent partial-wave basis make it ideally suited for application to larger systems.
Accuracy and convergence properties of multiple-scattering theory in three dimensions
Physical Review B, 1991
We present a numerical and analytical study of the accuracy and convergence properties of multiple-scattering theory (MST) in three dimensions. The convergence with respect to the number of angular momentum states, X ", of the solutions to the three-dimensional MST equations for two muon-tin potentials is studied analytically and by means of numerical calculations. The rate of convergence appears to be a universal quantity which depends, in the limit of E "~oo, only on the separation between the scatterers relative to their radii. No evidence of error in the energy, the wave function, or the derivative of the wave function in the limit E "-+ oo is found. In numerical tests which use square-well potentials and truncated Coulomb potentials it is found that the accuracy of the calculated wave functions and their derivatives is limited by the precision with which real numbers can be represented on the digital computers available to the authors (approximately one part in 10) rather than by postulated errors inherent in MST. Analytic formulas, valid in the limit of large E ", for the residual errors in the solutions of the MST equations indicate that these errors vanish in the limit E "~oo. These results are inconsistent with the claim of Badralexe and Freeman [Phys. Rev. B 37, 10469 (1988); 41, 10226 (1990)] that multiple-scattering theory does not yield exact solutions to the wave equation for muKn-tin potentials.
Four-Component Electronic Structure Methods for Atoms
Progress in Theoretical Chemistry and Physics, 2003
Four-component methods for high-accuracy atomic calculations are reviewed. The projected (or no-virtual-pair) Dirac-Coulomb-Breit Hamiltonian serves as the starting point and defines the physical framework. One-electron four-component Dirac-Fock-Breit functions, similar in spirit to Hartree-Fock orbitals in the nonrelativistic formulation, are calculated first, followed by treatment of electron correlation. Correlation methods include multiconfiguration Dirac-Fock and many-body perturbation theory or its all-order limit, the coupled cluster approach. The Fock-space CC and its extension to the intermediate Hamiltonian approach are described. Applications address mostly transition energies in various atoms. Very large basis sets, going up to I = 8, are used. High I orbitals are particularly important for transitions involving / electrons. The Breit term is required for fine-structure splittings and for / transitions. Representative applications are described, including the gold atom, with relativistic effects of 3-4 eV on transition energies; eka-gold (Elll), where relativity changes the ground state from 6d 10 7s to 6d*7s 2 ; Pr 3+ , where the many / 2 levels are reproduced with great precision; Rf (E104), where opposite effects of relativity and correlation lead finally to a 7s 2 6d 2 ground state, ~0.3 eV below the 7a 2 6d7p predicted by MCDF; eka-lead (El 14), a potential member of the "island of stability" forecast by nuclear physics, predicted to have ionization potentials higher than all other group-14 atoms except carbon; and eka-radon (E118), which has a unique property for a rare gas, positive electron affinity. Heavy anions are described, showing instances of multiple stable excited states. Finally, applications to properties other than energy are discussed.
Cluster coherent-potential approximation in the tight-binding linear-muffin-tin-orbital formalism
Physical Review B, 1993
We present a method for the determination of the electronic structure of random alloys within the self-consistent cluster coherent-potential approximation in the tight-binding linear-muffin-tin-orbital method. This formalism combines the simplicity of the tight-binding linear-muffin-tin-orbital scheme with the cluster coherent-potential approximation to determine the effective medium self-consistently. This approximation is analytic and guarantees non-negative and single-valued density of states at all energies. We have derived an expression for the configuration-averaged Green s function from which one can determine various electronic properties of the alloys, in particular, the charge densities, which are needed for charge self-consistent calculations. We have applied this formalism to an s-band model and found that cluster e6'ects could cause significant changes in the density of states.