Density functional theory with the M05-2X exchange/correlation functional is used to study the barriers for expulsion of atoms and small molecules (N-2, CO, H-2, Ar, Kr, Xe, H2O) out of open fullerenes (I20) and related molecular containers (C40H20, [5]beltene, cucurbit[5]uril). The reactions are examples where dispersion plays a critical role in determining the barrier heights. Calculations are compared with experimental kinetic data for N-2@I20, CO@I20, and Xe@cucurbit[5]uril (Xe@CB[5]). Comparing the four molecular containers, the activation barriers for escape of an atom or small molecule correlate with the binding energies. A new open-fullerene model container C40H20 (C40) was constructed from C-60 with a constriction at both ends formed by five methylene groups around the rim. The activation barriers for escape of N-2 and CO from the model container are similar to those from the I20 open-cage fullerene. In the case of H2O@C40, charge analysis reveals an interesting charge transfer at the transition state as the escaping guest is "squeezed" out of the host container.