A new method based on free energy calculations is proposed for discriminating between promoters that can form sI, sII, and sH hydrogen clathrates. The method is validated by comparing results of this computational approach to known experimental data reporting which type of clathrate structure is formed with the help of a particular promoter molecule. Good agreement is found. The free energy results confirm a well-known simple rule of thumb based on the van der Waals volume of the promoter molecules to distinguish between potential sH or sII hydrate formers. The method predicts an unusually strong temperature dependence of the stability of hydrogen clathrate hydrates for some hitherto untested promoter molecules, which can be exploited if easy release of hydrogen is required.