The　1-methylallyl　(C(4)H(7)1-3)　allylic　radical　is　an　important　intermediate　species　in　oxidation　of　linear　C4　unsaturated　hydrocarbons　(1-butene,　2-butene,　and　1,3-butadiene).　This　study　reports　the　first　high-level　quantum　chemical　calculations　for　an　undisclosed　reaction　class　of　this　radical　at　intermediate　to　high　temperatures:　direct　H-atom　abstraction　from　terminal　methyl　group　by　molecular　oxygen.　Moreover,　we　systematically　calculated　rate　constants　for　primary,　secondary,　and　tertiary　H-atom　abstraction　from　the　C-4,　C-5,　and　C-6　allylic　radicals,　respectively.　Our　results　can　be　further　used　as　rate　rules　for　kinetic　model　development　of　unsaturated　hydrocarbon　oxidation.　All　calculations　were　implemented　using　two　different　ab　initio　solvers:　Gaussian　and　ORCA,　three　sets　of　ab　initio　methods,　and　two　different　kinetic　solvers:　MultiWell　and　PAPR.　Temperature　dependent　rate　constants　and　thermochemistry　were　carried　out　based　on　transition　state　theory　and　statistical　thermodynamics,　respectively.　H-atom　abstraction　from　the　primary　site　of　C4　allylic　radical　is　found　to　be　faster　than　that　from　secondary　and　tertiary　sites　of　C5　and　C6　allylic　radicals,　contrary　to　common　understanding.　Barrier　heights　predicted　by　different　ab　initio　solvers　and　methods　are　about　4-5　kcal/mol　different,　which　results　in　a　factor　of　4-86　difference　in　rate　constant　predictions　depending　on　the　temperature.　Using　the　Gaussian　solver　with　Method　2　is　found　to　be　the　most　effective　combination　of　predicting　accurate　rate　constants　when　compared　against　experimental　data.　When　comparing　two　kinetic　solvers,　both　reaction　rate　coefficients　and　species　thermochemistry　show　good　agreement　at　a　wide　range　of　temperatures,　except　for　the　rate　coefficients　calculated　for　C5　and　C6　reactions　(about　a　factor　of　5-17　and　3-4　differences　were　obtained,　respectively).　From　an　application　point　of　view,　we　incorporated　the　calculation　results　into　the　AramcoMech2.0　model,　and　found　systematic　improvements　for　predicting　ignition　delay　time,　laminar　flame　speed　and　speciation　targets　of　2-butene　oxidation.