  The hydrogen molecules $H_2$ and $(H_2)_2$ are analyzed with electronic
correlations taken into account between the $1s$ electrons exactly. The optimal
single-particle Slater orbitals are evaluated in the correlated state of $H_2$
by combining their variational determination with the diagonalization of the
full Hamiltonian in the second-quantization language. All electron--ion
coupling constants are determined explicitly and their relative importance is
discussed. Sizable zero-point motion amplitude and the corresponding energy are
then evaluated by taking into account the anharmonic contributions up to the
ninth order in the relative displacement of the ions from their static
equilibrium value. The applicability of the model to the solid molecular
hydrogen is briefly analyzed by calculating intermolecular microscopic
parameters for $2 \times H_2$ rectangular configurations.
