Hybrid density functional theory using the B3LYP functional has been applied to study the energetics of proton translocation in cytochrome oxidase. Redox potentials of the metal centers and the tyrosyl radical have been computed, as well as pK(a) values of important groups along the translocation path. Models with more than 100 atoms have been used with geometries fully optimized in the presence of a dielectric continuum to represent the surrounding enzyme. The models are built from the bovine X-ray structure (20CC), which does not contain water molecules. The main result obtained is that for these models the pK(a) values of propionate A of heme a(3) are actually larger than those of the oxo and hydroxyl groups of the binuclear center, even after an electron has been transferred to heme a(3) from heme a. The consequence of this rather surprising finding is that a proton coming from the inside of the membrane will actually thermodynamically prefer to go to the propionate for further pumping rather than go to the binuclear center for consumption in the oxygen chemistry. Full energetic cycles are constructed for both the case without and the case with a proton gradient across the membrane.