The reaction pathways for the gallium nitride GaN growth by gas phase reaction of trimethylgallium (TMG) with ammonia is studied theoretically. Water is the most important impurity in ammonia, therefore its reaction with TMG is investigated as a possible source of oxygen impurity in GaN. Gallium oxide (GaO) formed by the reaction between TMG and H2O is predicted to be one of the possible source of oxygen impurity in GaN. The mechanisms and energetics of these reactions in the gas phase have been investigated by density functional B3LYP/[LANL2DZ-ECP + 6-31G(d,p)] method and ab initio MP2/[LANL2DZ-ECP + 6-31G(d,p)], CCSD(T)/[LANL2DZ-ECP + 6-31G(d,p)]//B3LYP/[LANL2DZ-ECP + 6-31G(d,p)] CCSD(T)/[LANL2DZ-ECP + 6-31G(d,p)]//MP2/[LANL2DZ-ECP + 6-31G(d, p)], and CCSD(T)/[LANL2DZ-ECP + Ahlrichs-VTZP]//MP2/ [LANL2DZ-ECP + Ahlrichs-VTZP] methods. Both the reactions of TMG with NH3 and H2O are modeled using pre-equilibrium charge-transfer complexes (CH3)(3)Ga:NH3 (C1) and (CH3)(3)Ga:OH2 (C2) having binding energies of 18.8 and 12.4 kcal/mol, respectively. The first step of the methane elimination reaction from the complexes proceeds through the saddle points TS1 and TS1a having activation barriers 37.0 and 22.6 kcal/mol for Cl and C2, respectively. The first CH4 elimination step is exothermic for both the cases, but the exothermicity is 15.0 kcal/mol greater for CH4 elimination from C2. The next step of methane elimination from the stable reaction intermediates (CH3)(2)GaNH2 and (CH3)(3)GaOH has a very high activation barrier of 76.0 and 67.8 kcal/mol via saddle points TS2 and TS2a, respectively. The calculated reaction rates at 298.15 K for both the reactions are low but are comparable to each other. The total rate constant k(tot) for GaN formation is 2.07 x 10(-60) cm(3) molecule(-1) s(-1), and that for GaO formation is 6.85 x 10(-62) cm(3) molecule(-1) s(-1).