FPLO, relativistic

Fig. 1. Total energy of fee thorium in dependenee of the lattiee eonstant, ealeulated with the relativistie FPLO method (RFPLO) using the Perdew-Wang 92 version of LDA [25]. The position of the minimum is indieated by the dashed line. Further, the experimental lattice constant is given by a box, where the width shows the scatter of the experimental data. Calculated equilibrium lattice constants with other relativistic band structure codes are denoted by arrows. Figure taken from Ref. [26].

In the remainder of this section we discuss the practical implementation of the relativistic FPLO-method, a full potential local orbital scheme using a minimum basis approach, which has this just mentioned level of accuracy and at present is presumably the best compromise between high accuracy and efficiency. 

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

The calculation of the matrix elements (38) and (39) is for small elementary cells the most time-consuming part of the (R)FPLO approach. For the overlap matrix S, one- and two-center integrals have to be provided while the Hamiltonian matrix requires the calculation of one-, two- and three-center integrals. As both the orbital and potential functions involved are well localized, only a limited number of multi-center integrals have to be calculated. The one- and two-center-integrals are further simplified by the application of angular momentum rules to one- and two-dimensional integrations, respectively. There are however two points which make the calculation of these matrix elements (in principle) much more involved for the relativistic approach. At first, the... 

The expression for the overlap densities (88) has the same structure as in the non-relativistic FPLO approach. Hence, a redistribution between the two lattice sites involved can be obtained with the same technique using a partition of unity as discussed in Ref [1]. 

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