Relevance of the Nuclear Quantum Effects on the Proton/Deuteron Transmission through Hexagonal Boron Nitride and Graphene Monolayers

Abstract

According to recent experiments, atomically thin hexagonal boron nitride and graphene are permeable to protons and deuterons (and not to other atomic species), and the experimental estimates of the activation energy are lower than the theoretical values by about 0.5 eV for the isolated proton–membrane transfer model. Our analysis of the electronic potential energy surfaces along the normal to the transmission direction, obtained using correlated electronic structure methods, suggests that the aqueous environment is essential to stabilize the proton transmission, as opposed to the hydrogen atom. Therefore, the process is examined within a molecular model of H2O–H(D)+–material–H2O. Exact quantum-mechanical scattering calculations are performed to assess the relevance of the nuclear quantum effects, such as tunneling factors and the kinetic isotope effect (KIE). Deuteration is found to affect the thermal reaction rate constants (KIE of 3–4 for hexagonal boron nitride and 20–30 for the graphene) and to effect...