The objective of this series of investigations is to develop procedures for predicting thermodynamically consistent generic rate rules for abstraction, addition, and isomerization reactions based on state-of-the-art quantum chemical calculations. This paper presents generic rate rules for H-abstraction from alkenes, alkynes, alcohols, aldehydes, and acids by hydrogen atoms. As described in detail in the first paper of this series {Sumathi, R.; Carstensen, H.-H.; Green, W. H., Jr. J. Phys. Chem., in press}, we attempt to describe reaction rates in terms of group additivity. Analysis of ab initio computed transition structures of a series of molecules of a given reaction class reveals the existence of a nearly constant "reactive moiety". We express thermodynamic contributions of these reactive moieties, which we refer to as "supergroups" since they contain several polyvalent atoms, to the entire transition state species in terms of group additivity values. The group additivity value of each "supergroup" is found to be transferable from one molecule to another within a given reaction family and is therefore identified as the characteristic of a given reaction class. The present study in combination with Benson's group additivity tables allows prediction of reaction rates for 15 sets of reactions, which can be used as reasonable estimates in constructing large kinetic models. When available, we compare our estimates with literature data and find good or reasonable agreement. We also analyze the predicted thermodynamic properties for reactants and radicals to provide additional evidence for the reliability of the calculations. Some very small non-nearest-neighbor substituent effects are seen in the calculations, but these are generally too small to be easily discernible from experimental data.