Role of quantum-size effects in the dehydrogenation of CH4on 3d TMnclusters: DFT calculations combined with data miningElectronic supplementary information (ESI) available: The data employed for the figures, as well as complementary analyses and additional technical details, are reported within the ESI. See DOI: 10.1039/d1cy01785c

In this work, we report a theoretical investigation of the role of quantum-size effects (QSEs) in the dehydrogenation of methane (CH4) on 3d transition-metal clusters, TMn, where TM = Fe, Co, Ni, and Cu, and n= 4–15. Our calculations were based on density functional theory combined with the unity bond index-quadratic exponential potential (UBI-QEP) approach and data mining (Spearman rank correlation, clustering). We found viaclustering techniques that QSEs or the chemical species, TMs, do not affect the adsorption modes (geometric orientation of the molecules) of CH4, CH3, CH3+ H, and H on the TMnclusters. However, QSEs play a crucial role in modulating the magnitude of the adsorption energy, reaction energy, dissociation energy, and activation energy, in particular, for Cunclusters due to the unpaired electron for clusters with an odd number of electrons. Through the UBI-QEP approach, we found small activation energy barriers for small Fenclusters and larger ones for Ninclusters, i.e., QSEs can be explored to tune energy barriers. These findings are supported by Spearman analysis; however, we could not identify a general trend due to the quantum-size effects that correlate activation energy with the adsorption and dissociation energies for the studied systems.