Molecular hydrogen insertion in and release from four molecular containers, spherophanes, have been studied with different computational methods. It has been found that dispersion interactions are very important in these systems; they govern their stability and the potential energy barriers. The calculated energy barriers are very high so that H-2 could not enter to/release from the cavity of the spherophanes through the benzene rings. The hydrogen molecule would rather prefer to follow the 4H-approach. The M05-2X/6-31G(d) results show that the encapsulation of H-2 inside these spherophanes is stabilizing. The energy barriers for H-2 to enter to (to release from) the spherophanes' cages are compared with those of open fullerenes. (C) 2009 Elsevier B.V. All rights reserved.