Multiple-scattering theory

Before we get into the specifics of how to solve the single particle Kohn-Sham equation, it is helpful to do a small excursion into Multiple Scattering Theory (MST), the reason being that this is what is employed in the methods I have been using for the papers connected to the thesis. 

Multiple Scattering Theory was first formulated by Lord Rayleigh [17] in a paper published in 1892 dealing with the propagation of heat or electricity through an inhomogeneous media. However, for most people the application to optics known as Huygens principle [36], is probably better known. It states that  

Each point on a moving wavefront acts as an independent source of wavelets. The surface of tangency to these wavelets determine the position of the wavefront at later times. 

This chapter is divided into three sections In the first one I give a small, intuitive introduction to Multiple Scattering Theory, whereupon I expand a little 

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It should be noted that a comprehensive ELNES study is possible only by comparing experimentally observed structures with those calculated [2.210-2.212]. This is an extra field of investigation and different procedures based on molecular orbital approaches [2.214—2.216], multiple-scattering theory [2.217, 2.218], or band structure calculations [2.219, 2.220] can be used to compute the densities of electronic states in the valence and conduction bands. 

To improve the latter a number of 0 N) methods have been recently proposed but practically all of them exploit Hamiltonian formalism. However, in Refs. 4,5 the locally self-consistent multiple scattering (LSMS) method based on the real space multiple scattering theory has been outlined, and in Ref. 6 its central idea in the form of the local interaction zone (LIZ) was incorporated into the Green s function technique, leading to the locally self-consistent Green s function method (LSGF). 

In summary, a fully relativistic theoretical description of photo emission for magnetic solids has been presented that is based on multiple scattering theory. For the VB-XPS case a very simple expression for the photo current intensity is found that can... 

Brouder, C., Alouani, M and Bennemann, K. H., 1996, Multiple-scattering theory of x-ray magnetic circular dlchroism Implementation and results for iron K-edge , Phys. Rev. B 54 7334. 

Ebert, H., and Battocletti, M., 1996, Spin and orbital polarized relativistic multiple scattering theory - with applications to Fe, Co, Ni and Fe cCoi- c , Solid State Commun. 98 785. 

SPIN AND ORBITAL POLARIZED RELATIVISTIC MULTIPLE SCATTERING THEORY... 

MULTIPLE SCATTERING THEORY APPLIED TO XMCD SPECTRA IN MOLECULE-BASED MAGNETS. 

Ch. Brouder, and M. Hikam. Multiple scattering theory of magnetic x-ray circular dichroism. Phys. Rev. 

C.R. Natoli, M. Benfatto, and S. Doniach. Use of general potentials in multiple-scattering theory. Phys. 

All ab initio applications of multiple scattering theory in dilute substitutional alloys rely on the one-to-one correspondence configuration. This holds both for the calculation of transition probabilities [7], represented by Eq. (7), and the electronic structure [8], represented by the Green s function equation [9]... 

Defect configurations in dilute alloys, studied up to now in the framework of multiple scattering theory, are such that a one-to-one correspondence exists between the atoms in the alloy and the reference system, the latter system regularly being the unperturbed host system. This one-to-one correspondence does not apply to the defect studied in substitutional electromigration, in which a host atom or an impurity can move to a neighbouring vacancy. 

The result of this work can be considered as another illustration of the powerful flexibility of multiple scattering theory with respect to the choice of a reference system [31. ... 

Butler, W.H., and Nesbet, R.K., 1990, Validity, accuracy, and efficiency of multiple-scattering theory for space-filling scatterers, Phys. Rev. B 42 1518. 

Kirtley J, Soven P (1979) Multiple-scattering theory of intensities in inelastic-electron-tunneling spectroscopy. Phys Rev B 19 1812-1817... 

This part introduces variational principles relevant to the quantum mechanics of bound stationary states. Chapter 4 covers well-known variational theory that underlies modern computational methodology for electronic states of atoms and molecules. Extension to condensed matter is deferred until Part III, since continuum theory is part of the formal basis of the multiple scattering theory that has been developed for applications in this subfield. Chapter 5 develops the variational theory that underlies independent-electron models, now widely used to transcend the practical limitations of direct variational methods for large systems. This is extended in Chapter 6 to time-dependent variational theory in the context of independent-electron models, including linear-response theory and its relationship to excitation energies. 

Butler, W.H. and Zhang, X.-G. (1991). Accuracy and convergence properties of multiple-scattering theory in three dimensions, Phys. Rev. B 44, 969-983. 

Nesbet, R.K. (1992). Variational principles for full-potential multiple scattering theory, Mat. Res. Symp. Proc. 253, 153-158. 

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