We analyze two-particle binding factors for the case of the H2 molecule with the help of our original exact diagonalization ab initio approach. Explicitly, we redefine the many-particle covalency and ionicity factors as a function of interatomic distance. Insufficiency of those basic characteristics is stressed, and the concept of atomicity is introduced and corresponds to the Mott and Hubbard criteria concerning the electron localization in many-particle systems. This additional characteristic introduces atomic ingredients into the essentially molecular states and thus eliminates a spurious behavior of the standard covalency factor with the increasing interatomic distance, and also provides a physical reinterpretation of the chemical bond’s nature.