  We introduce a variational wave-function to study the polaron formation when
the electronic transfer integral depends on the relative displacement between
nearest-neighbor sites giving rise to a non-local electron-phonon coupling with
optical phonon modes. We analyze the ground state properties such as the
energy, the electron-lattice correlation function, the phonon number and the
spectral weight. Variational results are found in good agreement with analytic
weak-coupling perturbative calculations and exact numerical diagonalization of
small clusters. We determine the polaronic phase diagram and we find that the
tendency towards strong localization is hindered from the pathological sign
change of the effective next-nearest-neighbor hopping.
