Before the discussion and analysis of the newly proposed algorithms, we validated the implementation of the standard model which will then represents our target reference. This was done by selecting, from the S66 57 dataset, 9 structures for which dispersion plays a major role in inter-molecular interaction energies. For these selected dimers the implemented model generates MBD energies being in agreement (average deviation of 0.4 kcal/mol, Supporting Information) with the ones computed with the MBD correction implementation included in the Q-Chem package. We note however, that the Hirshfeld partitioning can give as output slightly different parameters according to the software implementation employed thus leading to potentially small discrepancies.