Relativistic Multiple Scattering Theory for Space Filling Potentials

1991 ◽  
Vol 253 ◽  
Author(s):  
Xindong Wang ◽  
X. -G. Zhang ◽  
W. H. Butler ◽  
B. N. Harmon ◽  
G. M. Stocks
Keyword(s):  
Wave Function ◽  
Dirac Equation ◽  
Multiple Scattering ◽  
Scattering Theory ◽  
Secular Equation ◽  
Basis Functions ◽  
Full Potential ◽  
Space Filling ◽  
Multiple Scattering Theory ◽  
The Relationship

ABSTRACTWe derive a relativistic full potential multiple scattering theory (MST) in direct analog to the non-relativistic full potential MST[1, 2]. The secular equation is derived fromi the Lippmann-Schwinger equation by expanding the wave function in terms of cell basis functions which are locally exact solutions of the Dirac equation. The relationship between this theory and currently widely used relativistic munffin-tin MST is also discussed.

scholarly journals Korringa-Kohn-Rostoker Electronic Structure Method for Space-Filling Cell Potentials

1991 ◽  
Vol 253 ◽  
Author(s):  
A. Gonis ◽  
W. H. Butler ◽  
X.-G. Zhang
Keyword(s):  
Wave Function ◽  
Electronic Structure ◽  
Multiple Scattering ◽  
Scattering Theory ◽  
Arbitrary Shape ◽  
Convergence Rates ◽  
Space Filling ◽  
Multiple Scattering Theory ◽  
Variational Formalism ◽  
Overlapping Spheres

ABSTRACTThe 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 noa-overlapping spheres (Muffin-tin (MT) potentials), is generalized to the case of space-filling potential cells of arbitrary shape through the use of a variational formalism. This generalized version of MST retains the separability of structure and potential characteristic of the application of MST to MT potentials. However, in contrast to the MT case, different forms of MST exhibit different convergence rates for the energy and the wave function. Numerical results are presented which illustrate the differing convergence rates of the variational and nonvariatonal forms of MST for space-filling potentials.

The Wave Function in Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
W. H. Butler ◽  
X. -G. Zhang
Keyword(s):  
Exact Solution ◽  
Wave Function ◽  
Green Function ◽  
Multiple Scattering ◽  
Density Of States ◽  
Scattering Theory ◽  
Secular Equation ◽  
Multiple Scattering Theory ◽  
Full Cell ◽  
The Green Function

ABSTRACTThe wave function in Multiple Scattering Theory (MST) is a locally exact solution to the Schrödinger equation for any ℓ truncation (ℓmax), except at the the muffin-tin boundaries (or cell boundaries in a full cell calculation) where it and its derivative generally have discontinuities. These discontinuities vanish only in the limit ℓmax → ∞. Furthermore, the MST wave function as usually calculated is not correctly normalized which means the density of states calculated from the Green function does not agree with that calculated from the Lloyd formula. Here we obtain an alternative wave function from the usual MST secular equation which is smooth and continuous everywhere and which is correctly normalized.

Multiple-scattering theory for space-filling cell potentials

1992 ◽  
Vol 45 (20) ◽  
pp. 11527-11541 ◽  
Author(s):  
W. H. Butler ◽  
A. Gonis ◽  
X.-G. Zhang
Keyword(s):  
Multiple Scattering ◽  
Scattering Theory ◽  
Space Filling ◽  
Multiple Scattering Theory

Basis functions for arbitrary cells in multiple-scattering theory

1993 ◽  
Vol 48 (4) ◽  
pp. 2118-2130 ◽  
Author(s):  
W. H. Butler ◽  
A. Gonis ◽  
X.-G. Zhang
Keyword(s):  
Multiple Scattering ◽  
Scattering Theory ◽  
Basis Functions ◽  
Multiple Scattering Theory

scholarly journals Fully-relativistic full-potential multiple scattering theory: A pathology-free scheme

2018 ◽  
Vol 224 ◽  
pp. 265-272 ◽  
Author(s):  
Xianglin Liu ◽  
Yang Wang ◽  
Markus Eisenbach ◽  
G. Malcolm Stocks
Keyword(s):  
Multiple Scattering ◽  
Scattering Theory ◽  
Full Potential ◽  
Multiple Scattering Theory

The Green Function Cellular Method and Its Relation to Multiple Scattering Theory

1991 ◽  
Vol 253 ◽  
Author(s):  
W. H. Butler ◽  
X.-G Zhang ◽  
A. Gonis
Keyword(s):  
Multiple Scattering ◽  
Scattering Theory ◽  
Nearest Neighbor ◽  
Tight Binding ◽  
Full Potential ◽  
Multiple Scattering Theory ◽  
Secular Matrix ◽  
The Green Function ◽  
Cellular Method ◽  
Structure Calculations

ABSTRACTWe investigate techniques for solving the wave equation which are based on the idea of obtaining exact local solutions within each potential cell, which are then joined to form a global solution. We derive full potential multiple scattering theory (MST) from the Lippmann-Schwinger equation and show that it as well as a closely related cellular method are techniques of this type. This cellular method appears to have all of the advantages of MST and the added advantage of having a secular matrix with only nearest neighbor interactions. Since this cellular method is easily linearized one can rigorously reduce electronic structure calculations to the problem of solving a nearest neighbor tight-binding problem.

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