A new intermolecular interaction potential for the adenine dimer has been developed with the help of a combination of symmetry-adapted perturbation theory and density functional theory (DFT-SAPT). Supermolecular intermolecular interaction energy computations on hydrogen-bonded and stacked adenine dimers at B3LYP-D, MP2, SCS-MP2, SCS-MI-MP2 and CCSD(T) levels showed that DFT-SAPT is in a very good agreement with CCSD(T). The developed ab initio intermolecular potential has been used to predict the cluster structure of adenine dimers, trimers and tetramers. These global cluster optimizations reproduced adenine dimers reported in the literature and moreover new low-energy structures were also located. For trimers and tetramers, new hydrogen-bonded and stacked low-energy structures have also been found. The current findings suggest that the new ab initio potential can further be exploited to reveal the structure and energy of much larger supramolecular adenine clusters.