Backing structural investigations, quantum mechanical calculations based on energy criteria are needed to derive quantities describing accurately the targeted function, such as hardness from elastic properties. Complementary search of dynamic stability is needed as well as the fingerprint of the electronic behavior as metal, insulator, or semi-conductor. Most adopted theoretical framework is the quantum mechanics Density Functional Theory (DFT) devised in two papers: in 1964 for the theoretical framework by Hohenberg and Kohn and followed in 1965 by Kohn and Sham who established the Kohn-Sham equations for solving the wave equation practically in calculation codes built around the DFT (cf. next section).