The structure-reactivity relationship for the catalytic performance of cationic oxygen- and sulfur-containing Ga clusters in high-silica zeolite in ethane dehydrogenation is derived from the results of DFT calculations. Computed Gibbs free energy changes for the active site regeneration step via H2 desorption are used as a reactivity descriptor that reflects strength of the active Lewis acid-base pairs. It is shown that the activation free energies as well as the free energy changes of the initial C-H bond activation and final H2 recombination elementary steps of the catalytic cycle scale linearly with the values of free energy change of the active site regeneration. The energetics of the intermediate step involving alkene desorption via ß-C-H cleavage does not apparently depend on the properties of the active site. The relationship obtained points to the optimum composition and structure of the intrazeolite Ga cluster for the catalytic dehydrogenation of light alkanes.