Dispersion interactions are commonly included in density functional theory (DFT) calculations through the addition of an empirical correction. In this study, a modification is made to the damping function in DFT-D2 calculations to describe repulsion at small internuclear distances. The resulting Atomic Interactions Represented By Empirical Dispersion (AIRBED) approach is used to model the physisorption of molecules on surfaces such as graphene and hexagonal boron nitride, where the constituent atoms of the surface are no longer required to be included explicitly in the density functional theory calculation but are represented by a point charge to capture electrostatic effects. It is shown that this model can reproduce the structures predicted by full DFT-D2 calculations to a high degree of accuracy. The significant reduction in computational cost allows much larger systems to be studied, including molecular arrays on surfaces and sandwich complexes involving organic molecules between two surface layers.