Figure 5 . (a) Charge density difference of the represented N2 captured Mn2@site1and V2@site4 systems, the yellow and green area stand for the charge depletion and accumulation, the isosurface value is 0.05 Å3; the dark magenta and red ball represent the Mn and V atoms. (b) the values of charges transfer between the adsorbed N2 molecule and the substrate for the Mn2@site1, Co2@site2, Ru2site1, W2@site2, Os2@site3, V2@site4, and Cr2@site4; (c)-(j) pDOS and COHP of N-N bond for the selected N2 adsorbed TM2@sitex (x = 1, 2, 3, 4) systems, including Mn1@site1, Co2@site1, Ru2@site2, W2@site2, Os2@site3, V2@site4, and Cr2@site4, respectively.
Generally, several moieties, such as the adsorbed spices, active dual TM sites, neighboring atoms bonded to the TM site, and the substrate without TM and TM-bonded atoms, are common in most eNRR studies. But in our systems, the TM sites are divided into the fundamental moiety of intermediate spices (moiety 1) and the substrate without TM and TM-bonded atoms (moiety 6). Four new moieties are implemented in our systems, including moiety 2, moiety 3, moiety 4, and moiety 5. As depicted in Figure 6(a) , to ensure the various roles of TM1 and TM2 and the adjacent atoms affected by each TM atom. For the Mn2@site1 system, all the intermediate species gain electrons from the substrate except for the last species (*NH3). Meanwhile, both TM atoms lose electrons after adsorbing the N2 molecule except for the TM2 atom in *N2 intermediate, leading to electrons transfer into the adsorbed spices, similar to most studies in the eNRR field. However, we note that moiety 4 and moiety 5 gain electrons, where the extra electrons may come from the substrate or the TM atoms, but considering the substrate gains electrons in 3 to 7 protonation process, moiety 4 and moiety 5 gain electrons from the TM atoms in 3 to 7 protonation steps reasonably. In contrast, the 1 to 3 steps remain uncertain. Besides, it is notable that each TM atom and its adjacent atoms show differential charge transfer for the whole hydrogenate steps, mainly from the fully heteronuclear of two homonuclear TM atoms. For a similar end-on configuration Co2@site2 system, the charge distribution changes significantly; moiety 1 obtains electrons for the first six proton steps and loses electrons for the last step. For Moiety 4 and 5, slight charge transformation in moiety 4 while huge electron transferred into moiety 5, demonstrate each TM atom act in various roles. Meanwhile, all moiety 2, moiety 3, and moiety 6 as donors donate electrons to moiety 1, moiety 4, and moiety 5, causing the TM atom to act as the electron donor and carriers among the eNRR process for the Co2@site2 system. Charge transformation between various moieties becomes more complex for the side-on configuration N2 adsorbed systems. Taking V2@site4 and Cr2@site4 as examples, both moiety 2 and moiety 3 lose electrons for the whole interaction. Meanwhile, moiety 6 loses electron less than TM1 and TM2 slightly. In contrast, moiety 4 and moiety 5 obtain most of the electrons compared with moiety 1, suggesting that TM-bonded atoms obtain electrons from both TM atoms and moiety 6, while the electron transfer into moiety1 only originates from the TM atoms. Therefore, both TM atoms act as two roles during the electrocatalytic process; that is, both the TM atoms lose electron and donated them to the adjacent atoms (either adsorbed species or TM-bonded atom in the substrate), which is inversed to most of the eNRR studies, where the TM atoms act as charge carrier among most studies. The primary origin may be due to the additional TM atom participating in the eNRR process and offering more electrons. Those may explain why heteronuclear DAC is more effective than homonuclear DAC for the eNRR.