Polyphenylene superhoneycomb network (PSN) and covalent triazine framework (CTF) are experimentally realized periodically porous graphene derivatives. Such ultrathin layers with homogeneously distributed pores of controllable sizes are highly desirable for applications in molecular separations such as water purification. The permeation energy barrier is expected to be a function of not only the pore size, but also the specific permeation trajectory as determined by hydrogen bonding interactions at the water-pore interface. Here, we report a detailed first-principles study of permeation of a single H2O molecule through a mono layer PSN and CTF-0, as well as its diffusion behavior inside a bilayer PSN. The calculated energy barrier of 1.44 eV indicates the infeasibility of using PSN as a water permeation membrane. However, the barrier decreases considerably to 0.94 eV when three C-H pairs at the pore are replaced with N atoms into CTF-0. Inside a bilayer PSN, we find facile interlayer sliding as well as interlayer expansion owing to out-of-plane reorientation of the H2O molecule. In all cases, the functional groups at the pore significantly alter the orientation of the H2O molecule and the corresponding barriers. Such atomistic insights at the porous interface would provide a valuable guidance in advancing rational pore design principles. (C) 2018 Elsevier Inc. All rights reserved.