Effects of basis set superposition error on DFT model of C$_2$N/graphene bilayer

We investigated the structural and energetic properties of the C$_2$N/graphene bilayer using the electron density functional theory. We compared two approaches for wave function decomposition: plane waves (PW) and localized pseudoatomic orbitals (PAOs). We showed that for the weakly bonded bilayer, it is essential to consider correction to the basis set superposition error in binding energy calculations and geometry optimization. Otherwise, the interlayer binding energy and layer separation could be overestimated by 45–90 % and underestimated by 4–12 %, respectively. Also, to have the quantitative agreement between PAOs and PW results, the atomic-like basis set should be optimized. Overall, calculated with dispersion corrections, the interlayer binding energy (0,17–0,22 J/m$^2$) is of the van der Waals nature.