Multiple-scattering Green-function method for space-filling cell potentials

Journal Article · Sat Jul 15 00:00:00 EDT 1989 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.40.947· OSTI ID:5627365

Gonis, A; Zhang, X; Nicholson, D M

It is shown that the equations of multiple-scattering theory (MST) originally derived for scattering off collections of muffin-tin (MT) potentials, i.e., potential cells bounded by non overlapping spheres, remain valid in the case of arbitrarily shaped, non overlapping, and particularly space-filling potential cells. Specifically, it is shown that in the angular momentum representation the total scattering (transition) matrix, the Greenfunction, the Bloch function for a translationally invariant material, and the Lloyd formula for the change in the integrated density of states have forms that are invariant with respect to the partition of a given potential into non overlapping cells, and with respect to the choice of the cell centers. Ananalytic proof is provided for the vanishing of near-field corrections (NFC's)long conjectured to arise when the spheres bounding individual cells over lap one another or adjacent potentials. Thus, the well-known MST expressions, originally derived for the case of MT potentials, for obtaining the solution of the Schroedinger equation and hence determining the band structure and the charge density of materials, ordered or disordered, are rigorously valid in the completely general case of arbitrarily shaped cells. The differences between this work and previous attempts to generalize MST to non-MT space-filling potentials are discussed. It is pointed out that in calculations involving non-MT potential cells, particular attention must be paid to the question of convergence of expansions in angular momentum eigenstates. This convergence is tested numerically in terms of cluster calculations and through the calculation of the electronic structure of elemental bcc Nb and fcc Zr and Rh.

• Research Organization: Division of Chemistry and Materials Science (L-280), Lawrence Livermore National Laboratory, Livermore, California 94551 (US); Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60201; Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5627365
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Vol. 40:2
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
36 MATERIALS SCIENCE
NIOBIUM
ELECTRONIC STRUCTURE
RHODIUM
ZIRCONIUM
BCC LATTICES
GREEN FUNCTION
MUFFIN-TIN POTENTIAL
MULTIPLE SCATTERING
POTENTIAL SCATTERING
CRYSTAL LATTICES
CRYSTAL STRUCTURE
CUBIC LATTICES
ELASTIC SCATTERING
ELEMENTS
FUNCTIONS
METALS
PLATINUM METALS
POTENTIALS
SCATTERING
TRANSITION ELEMENTS
656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)
360104 - Metals & Alloys- Physical Properties