To uncover the fundamental chemistry of branched alkyl radical reaction with O-2, especially the second oxidation process (O-2 + QOOH), iso-butyl is chosen as a combustion archetype and reactions on the potential energy surfaces of C4H9O2 and C4H9O4 are investigated by using quantum chemical calculations coupled with RRKM/master-equation method. In the present study we calculate the thermodynamics properties, the rate constants and branching ratios for major reaction pathways in a wide temperature range of 298-2400 K and pressure range of 0.01-10 atm. Our study indicates that the treatment of estimating the fate of OOQOOH in the second oxidation process by analogy with similar reaction type and molecular size for the fate of RO2 in the first oxidation process could cause significant deviations. The accurate calculations conform that the rate constants for the second O-2 barrierless addition (QOOH + O-2) is half of the first O-2 barrierless addition (R + O-2). Morever, the accurate thermodynamics and kinetics data determined in the present work are indispensable for the detailed understanding and prediction of ignition properties of larger hydrocarbons. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.