respectively, where α 0 is the readjusted inverse orbital size, here at R = R M ott . The first of them implies that for R = R M ott the kinetic (hopping) energy is equal to the correlation energy, i.e., for R < R M ott the ratio is greater than unity, whereas for R > R M ott it is smaller than unity and reduces quite rapidly to zero with increasing R beyond R M ott . In other words, the kinetic energy dominates in the former case and enhances hopping electrons to resonate strongly between the sites, whereas the electrons become gradually frozen as R increases beyond R M ott . On the other hand, the Mott criterion expresses the onset of localization in terms of the renormalized single-particle wave function size at the localization threshold. Namely, the threshold is reached when the diameter of the orbital in the correlated state (2α -1 0 ) is equal to the interorbital distance (R = R M ott ). Semiclassically, it means that the collective character is estab- lished when the orbitals start overlapping. To visualize this formal reasoning we have plotted in Fig. the left parts of both (11) as a function of R, as well as have marked by red points their values at R M ott . The blue shaded area may be called the Mottness regime. Inset shows the corresponding dependence of the renormalized size of the Slater orbital in the correlated state, with the dotted vertical line marking the equilibrium bond length R bond ≃ 1.43a 0 . Note that the orbital size for R > R M ott approaches rapidly to the free-atom values a 0 . The explicit connection of the above onset to the true covalency (γ cov ), ionicity (γ ion ), and atomicity (γ at ) is visualized in Fig. , where the R dependence of those quantities is drawn. Remarkably, at the distance R M ott the true covalency and atomicity acquire the same value, so the point R M ott is a crossover point from true-covalency dominated to atomicity (Mottness) regime. Furthermore, γ cov is predominant for R < R M ott , whereas γ at is for R > R M ott , as it should. Additionally, the covalency and ionicity (atom double occupancy) coincide as R → 0, whereas then γ at → 0. Both γ cov and γ ion disappear in the atomic limit (R >> R M ott ), where γ at → 1.