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## Electrocatalytic Activity of Doped Graphene: Quantum-mechanical Theory View

Based on the quantum-mechanical theory of electron transfer (ET), the parameter was proposed to describe the electrochemical activity of doped graphenes. The parameter is calculated using the density of states (DOS), local density of state (LDOS) values, which are in turn obtained from the density functional theory (DFT) calculations and reorganization energies of redox system. DOS describes the contribution of the electronic structure of the electrode to the ET process, while the LDOS describes the electron density contribution of the atoms at some distance from the surface electrode. Reorganization energy corresponds to the restriction of solvation shell and bonds in redox system due to ET process. The overall contribution of these parameters enables a comprehensive assessment of the activity that is acceptable for semi-quantitative analysis. Calculations have shown that the proposed activity parameter correlates well with the calculated ET rate constants. Theoretical study of the oxygen reduction reaction (ORR) on graphene doped with p-elements in the framework of quantum-mechanical theory showed that ET activity decreases in the series P-Gr > S-Gr > N-Gr > B-Gr > O-Gr > Gr. According to our estimates, the mixed or adiabatic regime of ET is probably observed on doped graphenes for all steps of ORR. Using N- and B-graphenes as an example and activity parameter, the influence of the applied potential and the atomic fraction of the doped element on the ET activity are studied.