FROM ELECTRON TO SMALL POLARON - AN EXACT CLUSTER SOLUTION

We perform the exact diagonalization of two, four, and six vibrating m olecules strongly coupled with one electron to show that a small polar on describes both adiabatic and nonadiabatic regimes. Electron spectra am derived and compared with the adiabatic Holstein approximation and with the Lang-Firsov canonical transformation in a wide range of the adiabatic parameter and the coupling strength. We show that the self-c onsistent Migdal approximation is violated at an intermediate value of the coupling constant lambda congruent-to 1 and the adiabatic or nona diabatic small polaron is the ground state for the intermediate and st rong coupling lambda > 1. The phonon frequencies are calculated for a wide range of the coupling, including the intermediate region.