Atomic-scale species (atoms and clusters) have attracted much attention as potential highly active catalysts. Synthesizing such catalysts that may be stable under synthesis or reaction conditions is a challenge. In this work, we used density functional theory to model the growth of Cu clusters on the TiO2 support, including sintering and oxidation. Oxidation of supported Cu was preferred over sintering due to metal-support interactions. Ab initio thermodynamics calculations showed that O2 readily oxidized most clusters, while H2O was a mild oxidant. CO2 did not oxidize any clusters at relevant temperatures. Thermodynamics would suggest that oxidation of Cu atoms/clusters would readily occur, but kinetic analysis suggested otherwise. O2 adsorption was weak over the TiO2 surface, as well as most oxidized clusters. O2 dissociation barriers were low over nonoxidized Cu clusters, but quite high (1.88 eV) over single Cu atoms. Our results suggest that lone Cu atoms are stabilized on the surface, due to a high diffusion barrier (necessary for sintering) and a high O2 dissociation barrier (necessary for oxidation). We performed experiments that indeed support the premise that lone Cu atoms occur on the surface. Cu species were deposited on TiO2, and any Cu2+ species (indicative of oxidized Cu clusters) were removed after thermal treatment in various environments. Only Cu0 and Cu1+ species existed after thermal treatment. Lone adsorbed Cu atoms had a +1 oxidation state. Combined, our calculations and experiments indicate that Cu1+ species (lone adsorbed Cu atoms) are dominant. The kinetics of oxidation/diffusion rather than thermodynamics limits the growth/oxidation of Cu. In summary, we show that metal-support interactions are key for synthesizing stable atomic-scale catalysts, since they can strongly influence key processes such as diffusion/oxidation.