A theory of molecular transistor based on the two-center electrochemical bridged tunneling contact

► The tunneling contact based on the two-center redox molecule operates as transistor. ► A theory takes into account both Coulomb blockade and Debye screening effects. ► We obtain new expressions for the tunnel current in the non-adiabatic limit. ► We reveal the regions where both strong rectification and amplification take place. ► The transistor-like current/voltage characteristics are calculated.