Regulation mechanisms of electron-delocalized single transition metal-doped ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$ MXene hydrogen evolution reaction catalysts

Two-dimensional (2D) Mo-based MXenes $\left({\mathrm{Mo}}_{n+1}{C}_n{T}_x\right)$ are recognized to have significant potential as hydrogen evolution reaction (HER) activity electrocatalysts. However, appropriate descriptors are absent to predict the H-adsorption Gibbs energy $\left(\mathrm{\Delta }{G}_{\mathrm{H}}\right)$ due to the unique delocalized electronic properties of the Mo atom. In this paper, we used first-principles calculations and machine learning to study the HER activity of ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$ with single transition metal-doped (${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$-STM), and elucidate the mechanisms by which single transition metals (STMs) regulate the hydrogen evolution reaction. Our results revealed that $\mathrm{\Delta }{G}_{\mathrm{H}}$ has a “W” shape as a function of the doped atom changing in one period. The electronic structure analysis indicates that the electronic delocalized Mo has a longer range affecting not only the nearest atoms, but the second-nearest neighbor (STM-Mo) bonding effect controls the periodic distribution of $\mathrm{\Delta }{G}_{\mathrm{H}}$. Using machine-learning method, we quantized the STM regulation mechanism using five key structural and electronic descriptors, and predicted the $\mathrm{\Delta }{G}_{\mathrm{H}}$ of ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$-STM, which were also extended to ${\mathrm{W}}_2\mathrm{C}{\mathrm{O}}_2$-STM successfully. Our findings highlight the importance of considering second-nearest-neighbor bonding effects in similar delocalized materials systems research.

Figure 1

Overall flow of MXene descriptors discovery.

Figure 2

Top and side views of $3\times 3\times 1$ supercell of Mo-based MXene structures. (a) ${\mathrm{M}}_2\mathrm{C}$ structure: top, fcc and hcp represent the sites where O may be adsorbed; (b) ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$ with functional group O; (c) Single atom-doped model of ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$-STM, STM $=3d, 4d$, and $5d$ metals. $S_0, S_1$, and $S_2$ represent three types of O equivalent positions for H adsorption. $\mathit{Tc}$ atom is excluded due to its radioactivity.

Figure 3

$\mathrm{\Delta }{G}_{\mathrm{H}}$ of ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$-STM. (a)–(c) $\mathrm{\Delta }{G}_{\mathrm{H}}$ of $S_0, S_1$, and $S_2$ sites. Dashed line near 0.094 eV is referencing $\mathrm{\Delta }{G}_{\mathrm{H}}$ of Pt(111) [38].

Figure 4

Structure changes after STM doping. (a) $\mathrm{\Delta }h$: z-axis distance difference between STM and replaced Mo; (b) $\mathrm{\Delta }r$: distance difference after and before STM doped between $S_0$ site and STM in (0,0,1) face; (c) $\mathrm{\Delta }h$ vs atomic number of STM atom; (d) $\mathrm{\Delta }r$ vs atomic number of STM atom. (e) $\mathrm{\Delta }{G}_{\mathrm{H}}$ of $S_0$ sites vs $\mathrm{\Delta }h$; (f) $\mathrm{\Delta }{G}_{\mathrm{H}}$ of $S_0$ sites vs $\mathrm{\Delta }r$.

Figure 5

PDOS of atoms in ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$-STM. (a) STM-$d$-PDOS; (b) C-$p$-PDOS; (c) Mo-$d$-PDOS; and (d) O-$p$-PDOS.

Figure 6

−ICOHP values: (a) $-\mathrm{ICOH}{\mathrm{P}}_{(\mathrm{STM}-\mathrm{O})}$; (b) $-\mathrm{ICOH}{\mathrm{P}}_{(\mathrm{Mo}-\mathrm{O})}$; and (c) $-\mathrm{ICOH}{\mathrm{P}}_{(\mathrm{STM}-\mathrm{Mo})}$.

Figure 7

${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$-STM bonds. Types of $M_0–\mathrm{O}$ bonds (black) at $S_0, S_1$, and $S_2$ sites are STM-O, BTM-O, and BTM-O, respectively, and the bonds of $M_1–\mathrm{O}$ (brown) at $S_0, S_1$, and $S_2$ sites are all BTM-O. BTM is defined as base transition metal, and as stated, STM is defined as single transition metal.

Figure 8

Machine-learning results. (a) Feature selection for ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$-STM; (b) Feature selection for ${\mathrm{W}}_2\mathrm{C}{\mathrm{O}}_2$-STM; (c) SHAP values for five key descriptors of ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$-STM; (d) $\mathrm{\Delta }{G}_{\mathrm{H}}$ predicted by KRR model for ${\mathrm{Mo}}_2\mathrm{C}{\mathrm{O}}_2$-STM with five key descriptors; and (e) $\mathrm{\Delta }{G}_{\mathrm{H}}$ predicted by KRR model for ${\mathrm{W}}_2\mathrm{C}{\mathrm{O}}_2$-STM with five key descriptors.