General aspects of the relativistic FPLO method

We start our discussion of the relativistic FPLO method (RFPLO) with the Kohn-Sham-Dirac equation for the crystal 

The Kohn-Sham-Dirac equation (28) has to be solved self consistently, since the crystal potential and the XC-field depend via the (magnetization) density on its solutions. For a local orbital method it is advantageous to use a strictly local language for all relevant quantities, so that computationally expensive transformations between different numerical representations are avoided during the self consistency cycle. In the (R)FPLO method, the density n(r) and the magnetization density m(r) = m r)z are represented as lattice sums 

As starting point for the self consistency cycle we use a density n(r) and a magnetization density m r) represented as lattice sum (29). These initial densities may be either obtained from an atomic or a scalar-relativistic band 

The eigenvectors of the lattice periodic Hamiltonian of the Kohn-Sham-Dirac equation (28) are Bloch states fen) with crystal momentum k and band index n. They are expressed by the ansatz 

This equation includes a spherical and orbital dependent potential 

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