We are now in position to analyze numerically the proposed algorithms, starting from the convergence rate for the iterative solution of Eq.( ) which is schematically summarized below. In this and in the following section, argon clusters are taken as test systems as this only involves free-atom parameters and decouples the MBD model from the Hirshfeld partitioning, thus allowing to easily work with increasingly large system sizes without facing the DFT computational bottleneck.