Regulation mechanisms of electron-delocalized single transition metal-doped Mo2CO2 MXene hydrogen evolution reaction catalysts

Two-dimensional (2D) Mo-based MXenes $({\mathrm{Mo}}_n+1{C}_n{T}_x)$ 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 $(\mathrm{\ensuremath{\Delta}}{G}_{\mathrm{H}})$ 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 $\mathrm{\ensuremath{\Delta}}{G}_{\mathrm{H}}$ 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 $\mathrm{\ensuremath{\Delta}}{G}_{\mathrm{H}}$. Using machine-learning method, we quantized the STM regulation mechanism using five key structural and electronic descriptors, and predicted the $\mathrm{\ensuremath{\Delta}}{G}_{\mathrm{H}}$ 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.