Nuclear quantum effects in two-hydrogen intermediates on graphene-embedded transition metal atoms

The formation of hydrogen molecules (H₂) on surfaces is a fundamental process with profound environmental and industrial implications. While classical models have generally explained H₂ formation, recent studies highlight substantial nuclear quantum effects (NQEs) on surfaces like transition metals and graphene. Here, we explore NQEs on a series of graphene-embedded single transition metal atoms, where the presence of novel two-hydrogen intermediates in H₂ formation introduces new complexities. Using density functional theory calculations, ab initio path-integral molecular dynamics simulations, and ring-polymer instanton rate theory, we investigate the structure, interactions, and kinetics of these intermediates. Notably, nuclear quantum fluctuations have been found to enhance the structural flexibility of binding dihydrogen. Moreover, quantum tunneling increases the formation rate constants of two-hydrogen intermediates over a broad temperature range. These findings deepen our understanding of H₂ adsorption and formation on graphene-embedded transition metals, emphasizing the role of NQEs in theoretical models.