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Page 2 of 14 Zhang et al. J Mater Inf 2024;4:1 https://dx.doi.org/10.20517/jmi.2023.34

INTRODUCTION
The massive consumption of fossil resources and the increasingly serious environmental problems prompt
people to search for suitable alternative energy sources and develop efficient energy conversion
technologies. However, the lack of cheap and high-efficiency catalysts largely restricts the overall efficiency
of energy conversion devices and is the main bottleneck for realizing the transformation of energy supply
forms. As important chemical reactions, hydrogen evolution reactions (HER) and oxygen evolution
[1-4]
reactions (OER) form the whole reaction of water electrolysis to produce hydrogen (H) . The generated
[5-7]
hydrogen can then be used in fuel cells as a carrier of clean energy due to its high mass energy density .
Unfortunately, the current utilization of hydrogen energy is still in its infancy due to the lack of cheap and
efficient HER catalysts. As an optimal HER catalyst, platinum (Pt) requires only negligible overpotentials in
acidic solutions to achieve high reaction rates [8-11] . However, the scarcity limits its large-scale application.
Although many HER catalysts such as transition-metal phosphides [12-14] , carbides [15-17] and sulfides [18,19] have
been developed, the excellent performance as that of Pt/C is still hard to achieve.

In recent years, single-atom catalysts (SACs), exemplified by the metal atoms anchored on nitrogen (N)-
doped graphenes (M-N-C), exhibit excellent catalytic activities in many important electrocatalytic
processes [20-22] . The unique structure of SACs achieves nearly 100% atomic utilization and excellent catalytic
performance [23-25] . Thus, they become promising catalyst materials for HER [26-32] . For example, Lu et al.
prepared a Ru and N co-doped carbon material (RuC N ) as an efficient HER catalyst . When the
[33]
x
y
-2
overpotential is only -12 mV, the current density can reach 10 mA·cm , and the catalytic performance is
significantly better than that of commercial Pt-based catalysts. Its excellent catalytic activity is mainly
attributed to the embedded Ru atoms in the carbon matrix. First-principles calculations indicate that
RuC N has a lower hydrogen binding energy and a lower dissociation kinetics energy barrier than the Ru
x
y
nanoparticles.
Compared with SACs, dual-atom catalysts (DACs) not only maintain the high atomic utilization and good
selectivity and stability but also have higher metal loading and more complex and flexible active sites. The
possible synergistic effect, orbital coupling, and electron redistribution between adjacent metal centers and
their functionality complementarity provide more opportunities for better catalytic performance [34-36] . Thus,
they have attracted more interest than SACs. For example, Zheng et al. constructed a series of N-doped
porous graphene (NPG)-based diatomic catalysts MM’-NPG and studied their HER activity . Due to the
[37]
dual active centers and controllable electronic structure, FeV-NPG and NiV-NPG could replace the noble
metal HER catalysts under alkaline conditions. Zhou et al. synthesized the Rh-Fe dual atoms-embedded N-
doped carbon hollow spheres, which exhibit a low overpotential of 36 mV for HER due to the electron
redistribution promoted by Fe on the active Rh site . Zhao et al. reported that the presence of C -Pt-Ru-N
[38]
1
2
structures in Pt Ru /NMHCS-A (activated N-doped mesoporous hollow carbon spheres) can greatly
1
1
accelerate the H generation with a rather low overpotential of 22 mV to achieve a current density of
2
10 mA·cm -2[39] . However, the formation of atomic-scale metal sites without obvious aggregation remains as a
large challenge for DACs. On the other hand, the coordination environment of the catalyst active center
also greatly affects the H adsorption and desorption. By carefully adjusting the coordination environment of
the active center, the performance of the catalyst can be further improved .
[40]
To obtain potential HER catalysts, we herein constructed a series of single-/dual-metal atom-incorporated
N-doped graphenes with different coordination environments and systematically investigated their HER
activities by density functional theory (DFT) calculations. The potential active centers of various catalysts
and the adsorption structures of the key *H intermediate were investigated in detail. The HER activity of
each catalyst was evaluated by calculating the free energy of H adsorption, and some very promising HER