Multiple scattering theory linearized methods

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. 

The calculation of the diffracted intensities usually proceeds in two steps. The first step is the construction of the crystal potential and the calculation of the scattering amplitudes from a single atom, and the second step is the calculation of scattering processes within a single atomic layer and the calculation of scattering between different atomic layers. In the second step the multiple scattering processes are based on the condition that the scattered wave from one atom is an incident wave on all other atoms. This leads to a set of linear equations that is solved by matrix inversion. The formulation of the theory is based on the KKR (Korringa-Kohn-Rostocker) method used for band structure calculations. 

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