General considerations and philosophy

The current version of the code implements a screened KKR method. The traditional KKR method used free space as a reference system and the Green's function of the true system was found through a Dyson equation. However the free space structure constants do not converge easily and an Ewald procedure is necessary for 3D, while Kambe sums are needed for 2D geometries. This makes the method complicated and time consuming. The screened KKR avoids these problems by introducing a fictitious reference system of an infinite array of repulsive MT potentials typically 4 Rydberg high. Since the structure constants decay exponentially only a cluster of repulsive MT potentials around each cite is needed. This is often called the Tight Binding-cluster (TB-cluster). Important is that this reference system is strictly Muffin-Tin (no overlap) but this has no limitation on the true system which can be ASA or FP.

The introduction of the TB-structure constants has at least two big advantages. First it leads to a banded matrix in the Dyson equation which can be inverted O(N) for N cites. The second big advantage is that the structure constant part of the KKR calculation is simplified and is unique in 3D, 2D, and even 1D or a real space formulation where a free cluster is considered with no periodicity.

The current SKKR implementation can treat 3D periodic lattices or super-cells and multi-layers, and 2D structures where no periodicity is required in the third direction, like finite slabs or semi-infinite systems using the "decimation method".

Another advantage of the Green's function formalism is the ability to describe non periodic systems like impurities in bulk or surfaces or interfaces etc. This is done with the impurity programs which are also included in this manual. But we will cover the calculation of "host Green function" briefly later.