We carried out a theoretical study on geometries, relative energies of stationary points, and reaction rate constants for ethyl + O-2, propyl + O-2, and butyl + O-2 reactions, which are important reactions in the low-temperature oxidation of corresponding alkanes. Geometries with CCSD(T)/aug-cc-pVTZ for the ethyl + O-2 system are adopted as the benchmark to choose a proper exchange-correlation functional for geometry optimization. Our results show that B3LYP with 6311+G(d,p) can provide reliable structures for this system, and structures of the other two systems are determined with this functional. The performances of the explicitly correlated CCSD(T)-F12a and the locally correlated DLPNO-CCSD(T) methods on barrier heights and reaction energies are evaluated by comparing their results with those of CCSD(T)/aug-cc-pVQZ for the ethyl + O-2 system. Our results indicate that reliable energy differences for this system are achieved with CCSD(T)-F12a using the cc-pVDZ-F12 basis set, and this method is employed in calculating single-point energies for the other two systems. The single-reference equation-of motion spin-flip coupled-cluster method is adopted to obtain the potential energy surface of the barrierless reaction C2H5. + O-2 -> CH3CH2OO, and the results are compared with those using broken-symmetry density functional theory and the Morse potential. Differences between energies with these methods are <1.6 kcal/mol, but the difference in the rate constants could be sizable at temperatures <500 K, and rate constants obtained in this work are reliable only for temperatures >500 K. Pressure dependent rate constants for these reactions are determined using the Rice-Ramsperger-Kassel- Marcus/Master equation method. The obtained reaction energies, barrier heights, and rate constants could be valuable for reactions between the large alkane radical and O-2, which are important in the low-temperature combustion of fuels such as kerosene and gasoline.