Three-Dimensional Wave Packet Approach for the Quantum Transport of Atoms through Nanoporous Membranes

Quantum phenomena are relevant to the transport of light atoms and molecules through nanoporous two-dimensional (2D) membranes. Indeed, confinement provided by (sub-)nanometer pores enhances quantum effects such as tunneling and zero point energy (ZPE), even leading to quantum sieving of different isotopes of a given element. However, these features are not always taken into account in approaches where classical theories or approximate quantum models are preferred. In this work we present an exact three-dimensional wave packet propagation treatment for simulating the passage of atoms through periodic 2D membranes. Calculations are reported for the transmission of $^3$He and $^4$He through graphdiyne as well as through a holey graphene model. For He-graphdiyne, estimations based on tunneling-corrected transition state theory are correct: both tunneling and ZPE effects are very important but competition between each other leads to a moderately small $^4$He/$^3$He selectivity. Thus, formulations that neglect one or another quantum effect are inappropriate. For the transport of He isotopes through leaky graphene, the computed transmission probabilities are highly structured suggesting widespread selective adsorption resonances and the resulting rate coefficients and selectivity ratios are not in agreement with predictions from transition state theory. Present approach serves as a benchmark for studies of the range of validity of more approximate methods.