The special form of the GAPW energy functional involves several approximations: The accuracy of the local expansion of the density is controlled by the flexibility of the product basis of primitive Gaussians. As already mentioned, the highest exponents of the soft contraction coefficients are hereby defined by a given threshold. Atomic basis sets are constructed choosing the primitives of the orbital basis, with the option to add further primitives. Core compensation charges are built from one primitive with kind-dependent exponent proportional to the square root of the core charge. The exponent of the screening charge n 0 can be defined on input, otherwise it is computed so that the radius of the primitive Gaussian is smaller than 0.8 a.u. (or 1.2 a.u. in the special case of hydrogen) for a chosen threshold. The definition of the atomic radius R at and to what extend the strict conditions on the density are fulfilled in an actual calculation will further determine the accuracy that can be reached.