Bimetallic Re-Pt is a widely used catalyst in petroleum reforming to obtain high-octane gasoline, but experimental and theoretical information of such systems at the subnanometer scale-namely, as cluster aggregates-is currently lacking. Thus, in this work, we performed a density functional theory-based global optimization study to determine the physicochemical properties of the most stable Re-Pt gas-phase clusters up to six atoms for all compositions. Our results indicate that in these putative global minima (GM) geometries, Re atoms tend to aggregate, while most Pt atoms remain separated from each other. This is even observed in Pt-rich clusters-an indication of the strength of the Re-Re and Re-Pt bonds over pure Pt-Pt ones-due to a strong, directional hybridization of the Re half-filled 5d and the nearly full Pt 5d states. We observe that doping monometallic Pt clusters even with a single Re atom increases their binding energy values and widens the bimetallic cluster highest occupied molecular orbital-lowest unoccupied molecular orbital gap. As catalysis occurs at elevated temperatures, we explore the concept of cluster fluxionality for Re-Pt minima in terms of the calculated isomer occupation probability, P(T). This allows us to quantify the abundance of GM and low-energy isomer configurations as a function of temperature. This is done at size 5 atoms due to the wide isomer observed variety. Our calculations indicate that for pure Re5, the P(T) of the GM configuration substantially decreases after 750 K. Especially, for Re4Pt1, the GM is the dominant structure up to nearly 700 K when the second-energy isomer becomes the stable one. Although no ordering changes are seen for Re3Pt2, Re2Pt3, and Re1Pt4, we do observe a structural transition-between the GM and the second isomer-for pure Pt5 above 1000 K. We expect this type of combined first-principles analysis to add to the overall, continuous understanding of the stability and energetics of ultrafine and highly-dispersed Re-Pt petroleum-reforming catalysts and the scarce available information on this particular bimetallic system.