  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.
