In , we see that, contrary to expectation, there is no correlation between the static (0 K) binding energies and the cavity size. It is surprising to see that strong binding (E bind latt < -35 kJ/mol) can occur with packing coefficients as small as 25% and as large as 80%. Methane is generally less strongly bound than CO 2 and Xe. Methane is however not as strongly penalized by the loss of entropy as CO 2 , presumably because methane molecules are quite free to rotate in the clathrates, which carbon dioxide, being a linear molecule cannot. The two structures that bind CO 2 the strongest are oF0_R-3_17 and oF0_R-3_20, these both belong to the class of hexagonal R3-symmetric structures that strongly resemble hydroquinone clathrates, see also the very similar ofluorophenol structure in Fig 2 . These two structures bind CO 2 with a heat of desorption of -60 kJ/mol and -52 kJ/mol, respectively, which can be compared to the isosteric enthalpy of adsorption of CO 2 on active charcoal which is typically between 15 and 25 kJ/mol , nanoporous carbon 16 to 33 kJ/mol , and amine-functionalized mesoporous silicas 65-78 kJ/mol . The guest molecules introduce new lattice vibrational modes in the crystals, which give the clathrates a stabilizing contribution to the free energy. In Fig (middle) we show the spread in F bind vib calculated at 300 K. Again, there is a wide range, and no apparent correlation with respect to the packing coefficient of the guest molecules. The heat of desorption q takes the anharmonic thermal motion of the guest into account and should be a good estimate of the experimental isosteric heat of adsorption. It is calculated as an average over all simulations at all temperatures and pressures for each clathrate. The results are shown in the bottom panel of Fig 3 . We can compare the heats of desorption calculated from static (0 K) lattice energies with the more realistic estimate q from the grand canonical ensembles, see There is a correlation, as expected, but it is weak. Hence, using only lattice energies to assess the affinity of gases in clathrates at There is no correlation between the static binding energy E bind latt and the size of the cavity. (middle) The vibrational contribution to the free energy is also independent of the cavity size. (bottom) The ensemble-average heat of desorption q ranges approximately from -15 to -30 kJ/mol for CH4 and -20 to --50 kJ/mol for the other gases. Again, there is no correlation between the adsorption energy q and the size of the cavity.