The Connectivity-Based Hierarchy (CBH) is a generalized method we have developed recently to accurately predict the thermochemical properties of large closed-shell organic molecules hydrocarbons as well as nonhydrocarbons. The performance of the different rungs of the hierarchy was initially evaluated using density functional theory. In this study, we have carried out a wave function-based analysis of the CBH method to analyze the influence of electron correlation effects on the reaction energies and enthalpies of formation. For a test set containing unstrained molecules, all levels of theory (HF, MP2, and CCSD(T)) yield small reaction energies and accurate enthalpies of formation even with modest-sized polarized double-zeta or triple-zeta basis sets. For an initial test set of five strained molecules, however, the computed reaction energies are not small, though correlated schemes still yield accurate enthalpies of formation. Thus, small reaction energies cannot be used as the principal criterion to calibrate the success of thermochemical reaction schemes for molecules possessing special features (such as ring strain or aromaticity). Overall, for the relatively large nonaromatic molecules considered in this study, the mean absolute deviation with the MP2 method at the isoatomic CBH-2 rung is comparable to that with the more expensive CCSD(T) method at the higher CBH-3 rung.