Korringa-Kohn-Rostocker

Augmented Plane Waves (APW). This method is a detailed application of the muffin-tin potential, as is the Korringa-Kohn-Rostocker Method (KKR) [30],... 

Fig. 17. Band dispersion (along the FX and FY directions) of Xe adsorbed on a hydrogen modified Pt(l 10)-(lx2) surface (Xe coverage 6 = 0.45 ML). The symbols correspond to experimental data derived from ARUPS spectra with different photon energies (26 and 30 eV) and different directions of light incidence (normal and 45° off-normal). The soUd hnes are the results of a fiiUy relativistic Korringa-Kohn-Rostocker (KKR) calculation for freestanding Xe chains [99W].

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. 

S. bei der Kellen, A. J. Freeman. Self-consistent relativistic full-potential Korringa-Kohn-Rostocker total-energy method and applications. Phys. Rev. B, 54(16) (1996) 11187-11198. 

Various methods for the calculation of band structures have been devised. The augmented plane wave (APW) method (23,24) and the Green s function (GF) method of Korringa, Kohn, and Rostocker (KKR) (25-28) were used for most of the early calculations of the band structures of transition metal compounds. A common approximation in both methods is the use of the so-called muffin tin potential. In this approximation it is assumed that the crystal potential is spherically symmetric within nonoverlapping spheres around the atomic sites and constant in the region between the atomic spheres. 

The first method for solving the MST problem in angular momentum representation was made by Korringa [43] and Kohn and Rostocker [44] separately. The method came to be called the KKR method for electronic structure calculations and used the Green s function technique from Chapter 3 to solve the electronic structure problem. The separation into potential- and structure dependent parts made the method conceptually clean and also speeded up calculations, since the structural dependent part could be calculated once and for all for each structure. Furthermore, the Green s function technique made the method very suitable for the treatment of disordered alloys, since the Coherent Potential Approximation [45] could easily be implemented. 

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