We present free energy calculations on the encapsulation of CH4, CHCl3, and CF4 in a dimeric organic host in CHCl3 as solvent. While we can qualitatively reproduce the fact that CHCl3 is observed to be bound only weakly by the host, our calculations predict that the binding of CF4 is only slightly disfavored over the binding of CH4. This is in contrast to experimental results, where no indication of CF4 encapsulation could be found (see note added in proof).