Why Asymmetric Molecular Coupling to Electrodes Cannot Be at Work in Real Molecular Rectifiers

Every now and then one can hear in the molecular electronics community that asymmetric couplings ($\Gamma_{s} \neq \Gamma_{t}$) of the dominant level (molecular orbital) to electrodes ($s$ and $t$) which typically have shapes different of each other may be responsible for current rectification observed in experiments. Using a general single level model going beyond the Lorentzian transmission limit, in this work we present a rigorous demonstration that this is not the case. In particular, we deduce an analytical for the bias ($V$) driven shift of the level energy $\delta \varepsilon_{0}(V)$ showing that $\delta \varepsilon_{0}(V)/V$ scales as $\Gamma_t/W_t - \Gamma_s/W_s$, which is merely a tiny quantity because the electrode bandwidths $W_{s,t}$ are much larger than $\Gamma_{s,t}$. This result invalidates a previous, never-deduced formula in use in some previous publications that neither could be justified theoretically nor is supported by experiment. To the latter aim, we present new experimental evidence adding to that already inferred in earlier analysis.