Ab initio molecular orbital theory calculations are performed at the complete basis set (CBS-Q) level to determine thermochemical parameters (ΔfH298, S298, CTp) of alcohols, methyl ethers, formates, acetates, hydroperoxides, methyl alkylperoxides and the corresponding methoxy, primary and secondary alkoxy radicals derived from these molecular families. A consistent set of 12 Benson groups transferable among these six molecular families is derived from CBS-Q results via regression together with 20 hydrogen bond increment (HBI) group values for estimating the thermochemistry of oxymethyl (˙CH2OX), oxyethyl (CH3CH˙OX), oxyisopropyl ((CH3)2C˙OX) with varying substituent X (= H, CH3, C(O)H, C(O)CH3, OH, OCH3) and alkoxycarbonyl (ROC(O)˙) radicals. These new groups are useful in estimating the thermochemistry of large oxygenated molecules and radicals involved in complex chemical reaction mechanisms. The kinetics of nearly 50 elementary bimolecular hydrogen abstraction reactions belonging to eight different reaction families viz., (i) CH3OX + H˙ → ˙CH2OX + H2, (ii) CH3OX + ˙CH3 → ˙CH2OX + CH4, (iii) CH3CH2OX + H˙ → CH3C˙HOX + H2, (iv) CH3CH2OX + ˙CH3 → CH3C˙HOX + CH4, (v) (CH3)2CHOX + H˙ → (CH3)2C˙OX + H2, (vi) HC(O)OR + H˙ → ˙C(O)OR + H2, (vii) HC(O)OR + ˙CH3 → ˙C(O)OR + CH4, (viii) ROOH + H˙ → ROO˙ + H2 are studied using transition state theory coupled with CBS-Q energetics. The calculated barrier height within a given reaction family varies with the nature of the β substituents. The reliability of the calculated variations in the barrier height with varying β substituents is determined through comparison of the calculated rate constants with the scarcely available experimental data. Thermodynamically consistent generic rate rules have been derived in terms of group additivity. New transferable supergroup values corresponding to the thermochemistry of the reactive moiety in transition structures are developed. The effect of non-next neighbor substituents on the enthalpy of the supergroup is quantified using Evans–Polanyi relations.