A theoretical study of the mechanism of oxygen atom transfer from hydrogen peroxide and an alkyl hydrogen peroxide is described. Ab initio molecular orbital calculations were carried out with the 6-31G* basis set (and larger basis sets for selected reactions). All key equilibrium geometries and transition states were optimized at the MP2 level; barriers were calculated at the MP4SDTQ level with use of the MP2 optimized geometry. The barrier for HOOH --> H2OO is ca. 54 kcal/mol. The reverse reaction, H2OO --> HOOH, shows no barrier at the MP4 level when the HF optimized geometries are used, but it does have a barrier of 3.9 or 3.7 kcal/mol when the geometry is optimized at the MP2 or MP4 level, respectively. By contrast, a comparatively high barrier (27 kcal/mol) is found for H3NO --> H2NOH, which is relatively insensitive to correlation effects on the geometry. The oxidation of ammonia by hydrogen peroxide is shown to be a 2-step process dominated by a 1,2-hydrogen shift (54-kcal/mol barrier) followed by a facile S(N)2-like displacement (2-kcal/mol barrier) to afford H3NO + H2O. The active bonds in the transition state are generally shorter when optimized at the MP2, CASSCF, CISD, and QCISD levels than at the HF level. All four levels agree that the barrier for oxygen transfer from water oxide is very low. The NH3 + H2O2 reaction has been compared to the two identity reactions, H2O + H2O2 and NH3 + H3NO, and an orbital interaction picture has been developed to explain the differences. The high barrier for the 1,2-hydrogen shift (e.g. HOOH --> H2OO) that must precede all of the oxygen transfers can be dramatically lowered by adding one or two molecules of solvent water. The solvent water forms a cyclic transition state and allows the hydrogen shift to occur by a 1,4 mechanism involving a proton relay. Likewise, one and two molecules of water are shown to decrease the barrier for NH3 + H2O2 by ca. 20 kcal/mol per solvent water relative to isolated reactants or ca. 10 kcal/mol per water relative to solvated reactants. The same behavior is found for CH3OOH. These data suggest that the accepted mechanism for oxygen atom transfer from the hydroperoxide functional group involving a direct displacement in concert with a 1,2-hydrogen shift must be modified to include the energetics of the 1,2-hydrogen shift. An ionic pathway for oxidation of NH3 with H2O2 catalyzed by one water where the hydrogen is transferred after the rate-limiting oxygen transfer has a barrier 4.3 kcal/mol higher than the above concerted process.