We find that both the fast and slow ETs are possible for the studied redox reactions. The barrierless ET reactions occur when molecules are strongly bound to graphene. Our results are validated by the existing experiments, where strong adsorption of active molecules to electrodes has been confirmed for DMDQ +2/+1 , and Me-Vi +2/+1 reactions. In this class, the reactant and product states minima collapse into a deep single-minimum on the free energy surface (See Fig. ). In another class, the slow ETs have an energy barrier of less than 0.81 eV, except for dBR5 -1/-2 . The electron is displaced along a double-minimum surface (See Fig. ). For the reduction, the electron transfer between electrode and the redox species takes place when the Ferm.i level of the electrode becomes higher than the Fermi level of the electrons in the redox species Due to this, the Fermi level and the electronic structure of the electrode affects the performance of an electrochemical system (since the electrochemical reactions are driven by potentials at the electrode surface). Additionally, it is expected that the ET will occur at a constant potential in the flow batteries. But our CDFT-AIMD simulations using 7×4 graphene shows dramatic changes in the Fermi-level due to finite-size model systems: for charge states of -2, -1, and 0, the levels are positioned at -0.79, -2.84, and -3.79 eV, respectively.