2D structures were selected from the large collection of 2D materials in the "2D atlas". We used VASP to calculate atomic and electronic structures using the generalized gradient approximation based on the PBE parameterization. We accounted for the vdW interaction by adding the Tkatchenko-Scheffler vdW correlation potential. We applied a k-point space of 8 × 8 × 1 for unit cells, and 3 × 3 × 1 for supercells, and an energy cutoff of 400 eV. The energy minimization tolerance is 10 -6 eV, and the force tolerance is 10 -2 eV/Å. For the 267 bilayers in the data set, we calculate the interlayer distance d as the equilibrium distance separating the two layers (that is, the minimum distance between the two layers), and the band gap. Note that the application of VASP for the geometries provided in the "2D atlas" by Miro et al. induces a small strain on the individual layers. However, the presence of small planar strain has a small effect on d and the band gap. For our training set, we perform DFT calculations for the bilayers assembled from 53 monolayer structures, as shown in Table . In selecting these monolayers, we focused on structures that satisfy two criteria: (1) possess trigonal symmetry, and (2) do not suffer from lattice distortions arising from covalent interaction with the adjacent layers. For example, we remove the CdX and ZnX monolayers (X= S, Se, Te) because of the significant layer distortions they exhibit when stacked with other layered materials.