In oxy-fuel combustion, the pure oxygen (O-2), diluted with CO2 is used as oxidant instead air. Hence, the combustion products (CO2 and H2O) are free from pollution by nitrogen oxides. Moreover, high pressures result in the near liquid density of CO2 at supercritical state (sCO(2)). Unfortunately, the effects of sCO(2) on the combustion kinetics are far from being understood. To assist in this understanding, in this work we are using quantum chemistry methods. Here we investigate potential energy surfaces of important combustion reactions in the presence of the carbon dioxide molecule. All transition states and reactant and product complexes are reported for three reactions: H2CO + HO2 -> HCO + H2O2 (R1), 2HO(2) -> H2O2 + O-2 (R2), and CO + OH -> CO2 + H (R3). In reaction R3, covalent binding of CO2 to the OH radical and then the CO molecule opens a new pathway, including hydrogen transfer from oxygen to carbon atoms followed by CH bond dissociation. Compared to the bimolecular OH + CO mechanism, this pathway reduces the activation barrier by 5 kcal/mol and is expected to accelerate the reaction. In the case of hydroperoxyl self-reaction 2HO(2) -> H2O2 + O-2 the intermediates, containing covalent bonds to CO2 are found not to be competitive. However, the spectator CO2 molecule can stabilize the cyclic transition state and lower the barrier by 3 kcal/mol. Formation of covalent intermediates is also discovered in the H2CO + HO2 -> HCO + H2O2 reaction, but these species lead to substantially higher activation barriers, which makes them unlikely to play a role in hydrogen transfer kinetics. The van der Waals complexation with carbon dioxide also stabilizes the transition state and reduces the reaction barrier. These results indicate that the CO2 environment is likely to have a catalytic effect on combustion reactions, which needs to be included in kinetic combustion mechanisms in supercritical CO2.