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Electron transfer through a single barrier inside a molecule: from strong to weak coupling

In all theoretical treatments of electron transport through single molecules between two metal electrodes, a clear distinction has to be made between a coherent transport regime with a strong coupling throughout the junction and a Coulomb blockade regime in which the molecule is only weakly coupled to both leads. The former case where the tunnelling barrier is considered to be delocalized across the system can be well described with common mean-field techniques based on density functional theory (DFT), while the latter case with its two distinct barriers localized at the interfaces usually requires a multideterminant description. There is a third scenario with just one barrier localized inside the molecule which we investigate here using a variety of quantum-chemical methods by studying partial charge shifts in biphenyl radical ions induced by an electric field at different angles to modulate the coupling and thereby the barrier within the $π$-system. We find steps rounded off at the edges in the charge versus field curves for weak and intermediate coupling, whose accurate description requires a correct treatment of both exchange and dynamical correlation effects is essential. We establish that DFT standard functionals fail to reproduce this feature, while a long range corrected hybrid functional fares much better, which makes it a reasonable choice for a proper DFT-based transport description of such single barrier systems