  We analyze two-particle binding factors of H2, LiH, and HeH+ molecules/ions
with the help of our original exact diagonalization ab intio (EDABI) approach.
The interelectronic correlations are taken into account rigorously within the
second quantization scheme for restricted basis of renormalized single-particle
wave functions, i.e., with their size readjusted in the correlated state. This
allows us to determine the many-particle covalency and ionicity factors in a
natural and intuitive manner in terms of the microscopic single-particle and
interaction parameters, also determined within our method. We discuss the
limitations of those basic characteristics and introduce the concept of
atomicity, corresponding to the Mott and Hubbard criterion concerning
localization threshold in many-particle systems. This addition introduces an
atomic ingredient into the electron states and thus removes a spurious behavior
of covalency with the increasing interatomic distance, as well as provides a
more complete physical interpretation of bonding.
