LOCAL DENSITY CALCULATIONS FOR LARGE SYSTEMS USING MULTIPLE SCATTERING THEORY

The accuracy of energy differences calculated from first principles within the local density approximation (LDA) has been demonstrated for a large number of systems. Armed with these energy differences researchers are addressing questions of phase stability and structural relaxation. However, these techniques are very computationally intensive and are therefore not being used for the simulation of large complex systems. Many of the methods for solving the Kohn-Sham equations of the LDA rely on basis set methods for solution of the Schrodinger equation. An alternative approach is multiple scattering theory (MST). We feel that the locally exact solutions of the Schrodinger equation which are at the heart of the multiple scattering method give the method an efficiency which cannot be ignored in the search for methods with which to attack large systems. Furthermore, the analytic properties of the Green function which is determined directly in MST result in computational shortcuts.

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A Multiple Scattering Theory Approach to Solving the Time-Dependent Schrödinger Equation with an Asymmetric Rectangular Potential

Reports on Mathematical Physics ◽

10.1016/s0034-4877(16)30020-9 ◽

2016 ◽

Vol 77 (2) ◽

pp. 211-238

Author(s):

Victor F. Los ◽

Nicholas V. Los

Keyword(s):

Schrödinger Equation ◽

Multiple Scattering ◽

Scattering Theory ◽

Schrodinger Equation ◽

Time Dependent ◽

Theory Approach ◽

Multiple Scattering Theory

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Classical Appucations of Multiple Scattering Theory, an Overview

MRS Proceedings ◽

10.1557/proc-253-99 ◽

1991 ◽

Vol 253 ◽

Author(s):

Richard L Weaver

Keyword(s):

Wave Equation ◽

Schrödinger Equation ◽

Multiple Scattering ◽

Scattering Theory ◽

Schrodinger Equation ◽

Heterogeneous Medium ◽

Linear Partial Differential Equation ◽

Multiple Scattering Theory ◽

Symmetry Classes ◽

Classical Waves

It appears that the most salient of the issues that a brief overview might address in this symposium concerns the relationship - the differences, the parallels, and the similarities - between research in classical wave applications of multiple scattering theory and that research whose chief focus is electronic. Each desires the solution to a linear partial differential equation, usually a wave equation such as the Schrodinger equation or Maxwell's equations, in a heterogeneous medium, and each seeks to derive bulk properties from knowledge of the properties of the constituents. As with the Schrodinger equation, Korringa-Kohn-Rostoker like equations are often used for classical waves, and expansions in spherical harmonics and outgoing and regular solutions of the wave equation in the bare medium used to represent the equations. There remain, however, substantial differences in their respective formulations and methodologies. These appear to be traceable, at least in part, to differences in the questions that are asked about the field in the heterogeneous medium, to differences in the prior information available in regard to the microstructure, and to different symmetry classes of the microphysics. It is perhaps these differences which can account for the otherwise rather surprising absence of interaction between researchers in classical applications and those in electronic structure.

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