  An analytical variational method is applied to the molecular Holstein
Hamiltonian in which the dispersive features of the dimension dependent phonon
spectrum are taken into account by a force constant approach. The crossover
between a large and a small size polaron is monitored, in one, two and three
dimensions and for different values of the adiabatic parameter, through the
behavior of the effective mass as a function of the electron-phonon coupling.
By increasing the strength of the inter-molecular forces the crossover becomes
smoother and occurs at higher {\it e-ph} couplings. These effects are more
evident in three dimensions. We show that our Modified Lang-Firsov method
starts to capture the occurence of a polaron self-trapping transition when the
electron energies become of order of the phonon energies. The self-trapping
event persists in the fully adiabatic regime. At the crossover we estimate
polaron effective masses of order $\sim 5 - 40$ times the bare band mass
according to dimensionality and value of the adiabatic parameter. Modified
Lang-Firsov polaron masses are substantially reduced in two and three
dimensions. There is no self-trapping in the antiadiabatic regime.
