Role of thermal vibrations in molecular wire conduction

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 view. The classical approach consists in the computation of the time-dependent current fluctuations along the 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. However, the answers obtained with the two methods are different. At low temperatures, the quantum-mechanical treatment is necessary in order to correctly include the zero-point fluctuations. For temperatures higher than a few hundred kelvin the simple harmonic approximation which leads to the phonon modes breaks down because the oscillation amplitudes of the lowest-energy modes become very large. In this regime beyond the harmonic approximation, higher-order terms should be considered leading to phonon-phonon interactions and classical MD simulations prove to be simpler and give better results.