  This study details the conditions under which strong-coupling perturbation
theory can be applied to the molecular crystal model, a fundamental theoretical
tool for analysis of the polaron properties. I show that lattice dimensionality
and intermolecular forces play a key role in imposing constraints on the
applicability of the perturbative approach. The polaron effective mass has been
computed in different regimes ranging from the fully antiadiabatic to the fully
adiabatic. The polaron masses become essentially dimension independent for
sufficiently strong intermolecular coupling strengths and converge to much
lower values than those tradition-ally obtained in small-polaron theory. I find
evidence for a self-trapping transition in a moderately adiabatic regime at an
electron-phonon coupling value of .3. Our results point to a substantial
independence of the self-trapping event on dimensionality.
