Role of quantum-size effects in the dehydrogenation of CH4 on 3d TMn clusters: DFT calculations combined with data mining

Abstract

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, TM_n, 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 via clustering 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 TM_n clusters. However, QSEs play a crucial role in modulating the magnitude of the adsorption energy, reaction energy, dissociation energy, and activation energy, in particular, for Cu_n clusters 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 Fe_n clusters and larger ones for Ni_n clusters, 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.