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 { as opposed to the hydrogenatom { transmission. 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 e ects, such as tunneling factors and the kinetic isotope e ect (KIE). Deuteration is found to a ect the thermal reaction rate constants (KIE of 3-4 for hexagonal boron nitride and 20-30 for the graphene) and to e ectively lower the barriers to the proton transfer by 0.2 and 0.4 eV for the two membranes, respectively. This lowering e ect is reduced for the deuteron by approximately a factor of three. A more comprehensive description of the proton transmission is likely to require an extended explicit aqueous environment.
