To circumvent high energy cutoffs for the plane wave basis without being dependent on pseudo potentials, the GAPW method divides the system into core and interatomic regions, U A and U I , with the former being characterized by heavily fluctuating densities requiring high plane wave cutoffs while the latter represent smoothly decaying densities sufficiently described within a small plane wave basis. To describe the core regions within GAPW, the conventional plane wave and Gaussian orbital basis sets of the underlying GPW method are therefore augmented with adjusted basis sets, that are either mimicking a fluctuating "hard" density using a manifold of atomic orbitals generated from primitive Gaussians with large exponents, {ϕ µ (r)}, or a smoothly decaying "soft" density with, in contrast, diffuse primitive Gaussians with small exponents, { φµ (r)}. Furthermore, corresponding hard and soft localized atom-centered atomic orbitals, {χ µ (r)} and { χµ (r)}, enable to construct related atomic one-center densities within the core regions, ñ1 A (r) and n 1 A (r). A description of any arbitrary total density n(r) in terms of a respective global soft density ñ(r) is then possible if the smooth atomic densities within the core regions, ñ1 A (r), are corrected by their hard counterparts, n 1 A (r),