Conductance and activation energy for electron transport in series and parallel intramolecular circuits

We investigate electron transport through series and parallel intramolecular circuits in the framework of the multi-level Redfield theory. Based on the assumption of weak monomer-bath couplings, the simulations depict the length and temperature dependence in six types of intramolecular circuits. In the tunneling regime, we find that the intramolecular circuit rule is only valid in the weak monomer coupling limit. In the thermally activated hopping regime, for circuits based on two different molecular units M_a and M_b with distinct activation energies E_act,a > E_act,b, the activation energies of M_a and M_b in series are nearly the same as E_act,a while those in parallel are nearly the same as E_act,b. This study gives a comprehensive description of electron transport through intramolecular circuits from tunneling to thermally activated hopping. We hope that this work can motivate additional studies to design intramolecular circuits based on different types of building blocks, and to explore the corresponding circuit laws and the length and temperature dependence of conductance.