scholarly journals Multiple Scattering Theory with Space Filling Potentials

1991 ◽  
Vol 253 ◽  
Author(s):  
W. H. Butler
Keyword(s):  
Multiple Scattering ◽  
Scattering Theory ◽  
Space Filling ◽  
Multiple Scattering Theory ◽  
Full Cell ◽  
Current State

ABSTRACTA brief account of the current state or our understanding of full cell multiple scattering theory is given. The development of this understanding is also briefly outlined.

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

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.

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 Multiple Scattering Theory for Space Filling Potentials

1990 ◽  
Vol 193 ◽  
Author(s):  
W. H. Butler ◽  
R. G. Brown ◽  
R. K. Nesbet
Keyword(s):  
Wave Equation ◽  
Multiple Scattering ◽  
Scattering Theory ◽  
Efficient Technique ◽  
Two Dimensional ◽  
Space Filling ◽  
Simple Modification ◽  
Multiple Scattering Theory ◽  
Partial Waves ◽  
Special Case

ABSTRACTMultiple scattering theory (MST) provides an efficient technique for solving the wave equation for the special case of muffin-tin potentials. Here MST is extended to treat space filling non- muffin tin potentials and its validity, accuracy and efficiency are tested by application of the two dimensional empty lattice test. For this test it is found that the traditional formulation of MST does not converge as the number of partial waves is increased. A simple modification of MST, however, allows this problem to be solved exactly and efficiently.

Relativistic-multiple-scattering theory for space-filling potentials

1992 ◽  
Vol 46 (15) ◽  
pp. 9352-9358 ◽  
Author(s):  
Xindong Wang ◽  
X.-G. Zhang ◽  
W. H. Butler ◽  
G. M. Stocks ◽  
B. N. Harmon
Keyword(s):  
Multiple Scattering ◽  
Scattering Theory ◽  
Space Filling ◽  
Multiple Scattering Theory

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.

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