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Zhang et al. J Mater Inf 2024;4:1 https://dx.doi.org/10.20517/jmi.2023.34 Page 3 of 14

catalysts were then proposed. Finally, in-depth electronic structure analyses revealed the activity origins of
the catalysts to provide a theoretical guide for the rational design of related catalytic materials.

COMPUTATIONAL METHODS
DFT calculations considering spin polarization were carried out by using the Vienna ab initio simulation
[41]
[42]
package (VASP) . The Perdew-Burke-Ernzerhof (PBE) functional and the projector augmented wave
(PAW) method are used. The dispersion interactions during adsorption were considered by using the
popular Grimme’s DFT-D3 correction method . The convergence thresholds are 10 eV and 0.02 eV/Å for
-5
[43]
the energy and force, respectively, and the cutoff energy for the plane wave basis set is 500 eV. A vacuum
space of 15 Å was applied along the z-direction to avoid the interactions between slabs. A 2 × 2 × 1
Monkhorst-Pack k-point mesh was used because the cell is as large as 17.22 Å × 17.22 Å × 15.04 Å. All these
parameters have been carefully tested in our recent work . All the results were visualized with the aid of
[44]
[45]
the VESTA software .
To evaluate the structural stability of metal atoms in the N-doped graphene, the formation energy (taking
low-coordinated ones as an example) was calculated as:

or

where E MN3-gra and E N3-gra are the calculated energies of SACs and corresponding N-doped graphene without
the metal atom, respectively. Similarly, E MMN5-gra and E N5-gra are the homonuclear DAC and corresponding
metal-free structures, respectively. E denotes the calculated energy of a metal atom in its stable bulk
M
structure. Therefore, a more stable metal site has a more negative E value.
f
The adsorption Gibbs free energies were calculated as:

where the adsorption energies of the first and second H atoms are calculated as ΔE = E - E - 1/2E and
*H1
H2
*
*H1
ΔE = E - E - 1/2E , respectively. E and ΔE are the energies of the systems with one and two
H2
*H1
*H2
*H2
*H1
*H2
adsorbed H atoms, respectively. E is the energy of the catalyst. E is the energy of a free H molecule. ΔZPE
H2
2
*
is the change in zero-point energy upon adsorption, while ΔS represents the change in entropy. They were
obtained from the vibrational frequency calculations and standard thermodynamic data, as done in the
recent literature . T is the temperature (298.15 K). We assume pH = 0 and applied potential U = 0 V vs.
[46]
Standard hydrogen electrodes (SHE) in the calculations. The computational hydrogen electrode (CHE)
model was used to calculate the Gibbs free energy change, namely assuming the free energy of an isolated
[47]
H molecule is twice that of a proton-electron pair. For simplicity, the hydrogen coverage was not
2
considered, and it is assumed to have a negligible effect as it does on other catalyst surfaces .
[46]