Polaron formation for a non-local electron-phonon coupling: A   variational wave-function study
  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. 
C. A. Perroni, E. Piegari, M. Capone, V. Cataudella