Regulation of two-layer hydrogen adsorption in Metal-doped MXenes: few-shot learning, mechanisms, and transferability

MXenes are promising hydrogen-storage materials with high surface areas and tunable electronic structures, but whether single-atom doping can balance first-layer chemisorption and second-layer physisorption remains unclear. In this work, a combined density functional theory and few-shot machine learning framework was constructed to investigate the thermodynamic stability and two-layer hydrogen adsorption behavior of M 1.89 M′ 0.11 X systems. Prediction reliability under limited data was improved by 1000 repeated training runs and an average overfitting-rate evaluation. TabPFN gave the most robust formation-energy prediction, with the lowest overfitting rate of 47.2% and only a 0.042 eV validation–test root mean square error (RMSE) difference; the Voting Regressor predicted first-layer adsorption energy with an RMSE of 0.087 eV, and the XGB classifier identified second-layer Kubas-type adsorption with a test-set area under the receiver operating characteristic curve of 0.952. Formation-energy analysis shows that 5 d dopants stabilize MXenes by enhancing metal–nonmetal orbital hybridization. First-layer adsorption is more tunable in carbides and governed by electron number and electronegativity, whereas nitrides more readily form moderate second-layer Kubas interactions. Screening by formation energy, first-layer weakening, and second-layer enhancement identifies Ti 1.89 Zr 0.11 N as the optimal candidate, with a 16.90% increase in gravimetric hydrogen storage capacity, 8.61% first-layer weakening, and E ad2 = −0.234 eV. The regulation patterns were further extended to MBenes.