Kinetics for the reactions of allylic isobutenyl radical (C-C(C)-C) with molecular oxygen are analyzed by using quantum Rice-Ramsperger-Kassel (QRRK) theory for k(E) and master equation analysis for falloff. Thermochemical properties and reaction path parameters are determined by ab initio-Merller-Plesset (MP2-(full)/6-31g(d) and MP4(full)/6-31g(d,p)//MP2(full)/6-31g(d)), complete basis set model chemistry (CBS-4 and CBS-q with MP2(full)/6-31g(d) and B3LYP/6-31g(d) optimized geometries), and density functional (B3LYP/6-31g(d) and B3LYP/6-311+g(3df,2p)//B3LYP/6-31g(d)) calculations. An elementary reaction mechanism is constructed to model the experimental system, isobutene oxidation. The forward and reverse rate constants for initiation reaction C2C=C + O-2 C <-> C-C(C)-C + HO2 are determined to be 1.86 x 10(9) T-1.301 exp(-40939 cal/RT) (cm(3) mol(-1) s(-1)) and 6.39 x 10(8) x T-0.944 exp(-123.14 cal/RT) (cm(3) mol(-1) s(-1)), respectively. Calculations on 2,5-dimethylhexa-1,5-diene, methacrolein, isobutene oxides, and acetone product formation from reaction of isobutene oxidation mechanism are compared with experimental data. Reaction of allylic isobutenyl radical + O-2 forms an energized peroxy adduct [C=C(C)COO .]* with a shallow well (ca. 21 kcal/mol), which predominantly dissociates back to reactants. The reaction channels of the C=C(C)COO .* adduct include reverse reaction to reactants, stabilization to C=C(C)COO. radical, O-O bond fission to C=C(C)CO . + O, isomerization via hydrogen shift with subsequent beta -scission or R .O-OH bond cleavage. The C-C(C)COO.* adduct can also cyclize to four- or five-member cyclic peroxide-alkyl radicals. All the product formation pathways of allylic isobutenyl radical with O-2 involve barriers that are above the energy of the initial reactants. This results in formation of isomers that exist in steady state concentration at early time in oxidation, at low to moderate temperatures. The primary reaction is reverse dissociation back to reactants, with slower reactions from the distributed isomers to new products. The concentration of allylic isobutenyl radical accumulates to relatively high levels and the radical is consumed mainly through radical-radical processes in moderate temperature isobutene oxidation. Reactions of C=C(C)COO . cyclization to four or five-member cyclic peroxides require relative high barriers due to the near complete loss of pi bond energy for the terminal double bond's twist needed in the transition states. These barriers are calculated as 28.02 (24.95) and 29.72 (27.98) kcal/mol at CBS-q//MP2(full)/6-31g(d) level with A factors of 2.42 x 10(10) (3.28 x 10(10)) and 3.88 x 10(10) (6.09 x 10(10)) s(-1) at 743 K, respectively, for four- and five-member ring cyclization. Data in parentheses are calculation at B3LYP/6-311+g(3df,2p)//B3LYP/6-31g(d). A new reaction path is proposed: C=C(C . )COOH <-> C=C(C . )CO . + OH <-> C=Y(CCOC) + OH, which is responsible for methylene oxirane formation (Y = cyclic). The reaction barrier for the C=C(C)COOH reaction to C=C(C)CO + OH is evaluated as 42.45 (41.90) kcal/mol with an A factor of 4 x 10(15) s(-1). The reaction barrier of C=C(C . )COOH --> TS5 --> C=Y(CCOC) + OH is calculated as 42.14 kcal/mol with an A factor of 6.95 x 10(11) s(-1) at 743 K.