Application of van der Waals density functionals to two dimensional systems based on a mixed basis approach

Abstract A van der Waals (vdW) density functional was implemented with the charge density obtained by the mixed basis approach previously developed for studying two dimensional systems, in which the vdW interaction plays an important role. The basis functions here are taken to be the localized B-splines for the finite non-periodic dimension and plane waves for the two periodic directions. This approach will reduce the size of the basis set, especially for large systems, and therefore is computationally efficient for the diagonalization of the Kohn–Sham Hamiltonian. The nonlocal vdW correlation was treated appropriately according to the layered geometry structure. We applied the present algorithm to calculate the binding energy for graphene and hexagonal boron nitride and the results are consistent with data reported earlier. We also found that, due to the relatively weak vdW interaction, the charge density obtained self-consistently for the whole bilayer system is not significantly different from the simple addition of those for the two individual monolayer systems, except when the interlayer separation is close enough that the strong electron-repulsion dominates. This finding suggests an efficient way to calculate the vdW interaction for large complex systems involving Moire pattern configurations.