A detailed computational study of a copper-catalyzed aerobic cross-dehydrogenative coupling reaction has been conducted. To select a reliable method to describe the thermochemistry of a single electron transfer (SET) process, benchmark calculations have been performed. M06/6-311+g(d,p) is appropriate to evaluate the thermochemistry of the SET process for the system involving iminium species. The computational results support an SET mechanism, but also uncover an alternative mechanism in which O2 is directly involved in a hydrogen-abstracting step. A comparative study with tert-butylhydroperoxide (TBHP) as the oxidant has also been performed. The computations reveal several competitive pathways, including a radical pathway, a CuIII pathway, and an SET mechanism for the Cu/TBHP system.