Convergence Tests

All DFT results presented in this work have been obtained within the FP-(L)APW+lo method (cf. Chapter 3) as implemented in the WIEN2k code. Besides the error introduced by the only approximate exchange-correlation functional the accuracy of the results does also depend on several other computational parameters, which have to be carefully tested for every new investigated problem. Within the (L)APW+lo method the most important parameters that have to be considered are the muffin-tin radii, RMT, the planewave cutoff for the expansion of the wave function in the interstitial, Ewf max, and the k-point mesh for the sampling of the Brillouin zone. The remaining parameters have usually a much smaller influence on the computational time as well as on the accuracy and are therefore always set to rather conservative values.

The muffin-tin radii have to be carefully chosen at the beginning of each new project. Since the muffin-tin spheres are not allowed to overlap, the smallest possible nearest neighbor distance has to be estimated to obtain an upper limit for RMT. With respect to this upper limit the muffin-tin radii should always be chosen as large as possible to minimize the interstitial region, which reduces the number of required planewaves and thus the computational cost. Since in the (L)APW+lo method the core states are only treated within the muffin-tin spheres, the muffin-tin radius has to be large enough to include the spatial extension of the core states. Thus, heavier atoms usually require a larger RMT than lighter atoms. Absolute energies of the same system obtained with different muffin-tin radii are not comparable.

The planewave cutoff for the expansion of the wave function in the interstitial, Ewf max, determines the number of basis functions. With increasing Ewf max the basis set can be systematically improved by an increasing number of planewaves. Since it is not possible to include an infinite number of basis functions, the expansion has to be truncated by a suitable choice of Ewf max. The size of the required basis set depends on the aspired accuracy, as well as on the muffin-tin radii and the investigated system. Usually it is much more efficient to test the basis set with respect to the investigated physical quantity instead of the total energy of the system.

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