The energetic ground state of gold clusters with up to 318 atoms consists of complex geometries that have only a limited resemblance to the perfect icosahedra, decahedra, and octahedra that are encountered for some magic numbers. The structure changes in most cases completely by the addition of a single atom. Other low-energy structures are so close in energy that their Boltzmann weight is not negligible at room temperature.

We study the whole Ge-Mn phase diagram with density functional theory (DFT) methods. The 16 known phases are described and trends are analyzed. The compounds are then simulated, allowing a complete evaluation of this method in the projector augmented-wave approach within the collinear spin-polarized framework. Structural parameters, as well as magnetic properties, are compared to experimental values. Stability issues are addressed using a thermodynamic approach based on the grand potential, showing good agreement with experimental data. The impact of semicore electrons and the exchange-correlation functional are also discussed. Finally, it is shown that DFT methods are well suited to study this system, provided that the generalized gradient approximation is used, as opposed to the local density approximation, and correlations between structural errors and Mn concentration are taken into account. In addition, the precision achieved when compared to experiments is 40 meV/atom on energy, ±3% on the lattice parameter, and 0.2μ B /Mn on magnetic moments. Magnetic orders are mostly well reproduced.