Coherent electron transfer in polyacetylene

Abstract

We examine, using mixed classical-quantum electron-ion dynamics, electron transfer in a donor-acceptor-like molecular junction system based on polyacetylene. We identify two qualitatively-different transfer regimes: hopping and tunnelling. We discuss the criteria for achieving each one and for minimizing inelastic scattering and decoherence arising from the coupling to the ions, and we connect our main results to quantities derived from electron dynamics involving simpler, three-state model systems. We identify the requirements to have near-ballistic transfer. depends on the scattering processes involved. Some of the methods used to describe the scattering include Green's function methods, transfer matrix approaches such as the electron scattering quantum chemistry (ESQC) method [2], or the use of Lippmann-Schwinger scattering operators for mapping the nonequilibrium system onto an equilibrium one [3]. All of these methods are timeindependent, thus enabling the use of the Landauer or, in the case of several leads, the Landauer-Büttiker formula, to evaluate the current. Non-equilibrium Green's function-based approaches or approaches based on the time-dependent Schrödinger equation applied to the key parts of the system [4, 5, 6], enable a direct evaluation of the transmission and the current. The treatment of the electron-ion interaction within semi-empirical formalism assumes the validity of one of two regimes: strongly or weakly-localised electron-ion interaction. The Marcus theory [7] treats electron transfer nonadiabatically with a rate expression involving the initial, donor, and final, acceptor, states and geometries expressed in terms of two key quantities, presumed to be separable owing to the slowness of the intermolecular vibrations compared to the fast electron transfer rate: the difference in energy of the ground-state configurations before and after electron transfer, and the non-adiabatic contribution, called the reorganisation energy, which is defined as the electronic excitation energy from the initial state in its ground-state configuration to the electronic state of the product. As in the Marcus assumption of distinct donors/acceptors, the Holstein model [8] also treats the electron as being highly localised in space.In general, these techniques are most appropriate for non-homogeneous systems or systems containing defects or other strong scattering centres where there is a clear distinction between donor and acceptor and the transfer is accomplished by hopping between these two species. In more homogeneous systems, there tends to be a more delocalised electron-ion interaction, leading to relatively adiabatic electron transfer. Different models for electron transfer have been developed with the goal of describing polaron motion in oligomers. The Holstein model describes "smallpolaron" formation, or localised interaction with a particular molecule (site) and the electron conduction is accomplished by distinct hopping, a non-adiabatic process. The structural perturbation is similarly highly localis...

Short-lived electron transfer in donor-bridge-acceptor systems

“…In such wavepacket approaches though, the transmission function is simply a Fourier-transform of the system (tip-sample or molecule+electrodes). This is to be contrasted with an explicit inclusion of the wavepacket as part of the system [18] where the eigenvalue spectrum can be modified by an incident electron off-resonance, leading to effects such as D-A tunnelling. Time-dependent forms of the transfer-matrix element owing to lattice effects were derived in Ref.…”