Isomerization between the thermally accessible isomers within the ensemble ensures that LM' is re-populated each TPD cycle, thus LM' acts as a "gateway" isomer that keeps dehydrogenating ethylene on a fraction of the cluster population during repeated TPD cycling. We expect that all of the clusters eventually pass through this gateway during repeated TPD cycling, and become coked. The calculated population of the C2D4-LM' isomer (~3%) is smaller than the population (~25%) suggested by D2 TPD signal, however, we note that isomer populations depend exponentially on their energies, thus amplifying the effects of small DFT errors.