The ab initio determination of the leading long-range term of pairwise additive dispersive interactions, based on the independent analysis of the response properties of the interacting objects, is here considered in the case where these are part of a periodic system. The interaction of a nitrogen molecule with a thin film of hexagonal BN has been chosen as a case study for identifying some of the problems involved, and for proposing techniques for their solution. In order to validate the results so obtained, the interaction energy between N2 and a BN monolayer at different distances has been estimated following a totally different approach, namely by performing post-Hartree–Fock (MP2) supercell calculations using the CRYSTAL+CRYSCOR suite of programs. The results obtained with the two approaches closely agree over a long range, while the limit of validity of the purely dispersive regime can be clearly assessed.