The CH4 + HO2 center dot reaction is studied by using explicitly correlated coupled-cluster theory with singles and doubles (CCSD-R12) in a large 19s14p8d6f4g3h basis (9s6p4d3f for H) to approach the basis-set limit at the coupled-cluster singles-doubles level. A correction for connected triple excitations is obtained from the conventional CCSD(T) coupled-cluster approach in the correlation-consistent quintuple-zeta basis (cc-pV5Z). The highly accurate results for the methane reaction are used to calibrate the calculations of the hydroperoxylradical hydrogen abstraction from other alkanes. For the alkanes CnH2n+2 with n = 2 -> 4, the reactions are investigated at the CCSD(T) level in the correlation-consistent triple-zeta (cc-pVTZ) basis. The results are adjusted to the benchmark methane reaction and compared with those from other approaches that are commonly used in the field such as CBS-QB3, CBS-APNO, and density functional theory. Rate constants are computed in the framework of transition state theory, and the results are compared with previous values available.