Influence of the electron-phonon interactions on the transport properties at the molecular scale

In the present work we investigate the influence of molecular vibrations on the tunneling of electrons, through a molecule sandwiched between two metal contacts. The study is confined to the elastic scattering only, but beyond the harmonic approximation. The problem is tackled both from a classical and a quantum-mechanical point of 14 view. The classical approach consists in the computation of the time-dependent current fluctuations calculated at each step of a, molecular dynamics (MD) simulation. On the other hand, the vibrational modes are treated quantum-mechanically and the tunneling current is computed as an ensemble average over the distribution of the atomic configurations obtained by a suitable approximation of the density matrix for the normal mode oscillators. We show that the lattice fluctuations modify the electron transmission. At low temperatures the quantum-mechanical treatment is necessary in order to correctly include the zero-point fluctuations. However, for temperatures higher than few hundreds Kelvin the simple harmonic approximation which leads to the phonon modes breaks because the oscillation amplitudes of the lowest energy modes become large.