Reliable estimates of high-pressure-limit reaction rates as a function of temperature are essential for the development of reaction sets that can be used to model complex chemical processes. As these reaction rates depend primarily on the thermodynamic properties of the reactants and the corresponding transition state, this work attempts to predict these properties within the framework of group additivity. Using ab initio calculations at the CBS-Q level, with additional HF/6-31G(d') potential energy surfaces (PES) to define the hindrance potential for internal rotations, we calculate heats of formation (Delta H-f(298)), entropies (S-298), and heat capacity values (C-p(T)) of species involved in prototypical H abstraction reactions. From these, we derive new group additivity values (GAV) for transition-state-specific moieties. The new GAV allow rapid calculation of reaction rates for entire reaction families with good accuracy. This work presents a detailed description of the methodology and has its focus on H abstraction from alkanes by H and CH3. Subsequent papers will apply this methodology to derive GAV for other reaction families of interest in combustion processes.