  The small polaron theory is applied to describe the vibron dynamics in an
adsorbed nanowire with a special emphasis onto finite size effects. It is shown
that the finite size of the nanowire discriminates between side molecules and
core molecules which experience a different dressing mechanism. Moreover, the
inhomogeneous behavior of the polaron hopping constant is established and it is
shown that the core hopping constant depends on the lattice size. However, the
property of a lattice with translational invariance is recovered when the size
of the nanowire is greater than a critical value. Finally, it is pointed out
that these features yield the occurrence of high energy localized states which
both the nature and the number are summarized in a phase diagram in terms of
the relevant parameters of the problem (small polaron binding energy,
temperature, lattice size).
