Two models consisting of 469 atoms each one, for the interaction between the N3 inhibitor and the main protease of SARS-CoV (SARS-CoV Mpro) and SARS-CoV-2 (SARS-CoV-2 Mpro) viruses, were used to reveal by quantum chemistry methods the non-covalent interactions involved in these systems. Through the Density Functional Theory and the Quantum Theory of Atoms in Molecules the main conclusion reached by this study indicates that C-H· · ·O and C-H· · ·H hydrogen bonds are crucial to describe attractive interactions in these complexes. In general, these contacts are overlooked in many studies. However, these non-conventional hydrogen bonds represent more than a half of the energy interaction estimated for non-covalent contacts. These results are quite important for the design of new drugs since these interactions could drive the action mechanisms against these viruses. Hydrogen bonds are crucial to describe correctly the interactions between inhibitors and the main proteases.