The process of insertion of molecular oxygen and nitrogen into polyhedral oligomeric silsesquioxanes (POSS) has been investigated theoretically. Using ab initio methods, the N-2 interaction with the POSS has been described with restricted Hartree-Fock (RHF) with a triple-zeta basis set, while systems involving O-2 require restricted open shell (ROHF) wave functions, to account for their open-shell ground states. This insertion process is described in terms of the energetic change that the system X-2::POSS undergoes when the gas molecule passes from the exterior to the interior of the cage through the largest of its faces. The formation of the cluster occurs through a transition structure that has been characterized for each system. The barrier is a function of the dimension of the face of the POSS and, hence, of the cage dimensions. The results of the calculation are consistent with experimental observations that the O-2 molecules pass through a given membrane more easily than N-2.