  In this Chapter we reexamine the concept of $\textit{covalency}$ and
$\textit{ionicity}$ on example of the simplest molecules. First, starting from
the exact expression for the two-particle wave function in the case of $H_2$
molecule within the Heitler-London model, we demonstrate an unphysical behavior
of the covalency at large interatomic distance which, within standard
definition, reaches the maximal value in the limit of separated atoms. Second,
we correct this deficiency by introducing the concept of $\textit{atomicity}$,
with the help of which, we define the $\textit{true}$ (intrinsic)
$\textit{covalency}$, as well as retain the precise concept of
$\textit{ionicity}$. We connect the introduced atomicity to the onset of
Mott-Hubbard localization, adopted here from the well established notion in the
condensed matter. The evolution from the molecular to atomic states develops
rapidly with interatomic distance beyond the localization threshold. This brief
overview is intented as pedagogical in nature, nonetheless is analyzed
quantitatively for the case of $H_2$ molecule. At the end, we outline a
similar-type of model for the related case of the hydrogen bond on example of
adenine-tymine pair. Methodologically, the approach is based on combining the
first- (wave mechanics) and second-quantization into a single scheme of formal
description.
