  We discuss electronic properties and their evolution for the linear chain of
$H_2$ molecules in the presence of a uniform external force $f$ acting along
the chain. The system is described by an extended Hubbard model within a fully
microscopic approach. Explicitly, the microscopic parameters describing the
intra- and inter-site Coulomb interactions are determined together with the
hopping integrals by optimizing the system ground state energy and the
single-particle wave functions in the correlated state. The many-body wave
function is taken in the Jastrow form and the Variational Monte-Carlo (VMC)
method is used in combination with an ab initio approach to determine the
energy. Both the effective Bohr radii of the renormalized single-particle wave
functions and the many-body wave function parameters are determined for each
$f$. Hence, the evolution of the system can be analyzed in detail as a function
of the equilibrium intermolecular distance, which in turn is determined for
each $f$ value. The transition to the atomic state, including the Peierls
distortion stability, can thus be studied in a systematic manner, particularly
near the threshold of the dissociation of the molecular into atomic chain. The
computational reliability of VMC approach is also estimated.
