The IMOMO (integrated molecular orbital+molecular orbital) method was used to accurately calculate and compare with the experiment for the single-bond C-H and C-C bond dissociation energies of a series of hydrocarbons, R-1-R-2--> R-1+R-2, where R-1 is H or CH3, while the largest R-2 considered is 1,1-diphenylethyl, C(C6H5)(2)(CH3). While the geometries and zero point vibrational energies were obtained at the hybrid density function (B3LYP/6-31G) level for the real system, a small system, H-CH3 or CH3-CH3, was used as the "model" in the IMOMO energy calculation, for which a high level method is used. Of a large number of IMOMO combinations tested, the combination of the modified Gaussian-2 method (G2MSr) with the restricted open-shell second-order Moller-Plesset perturbation method (ROMP2), the IMOMO(G2MSr:ROMP2/6-31G(d)) method, yields the best results, and can be used for bond dissociation energy predictions of very large molecules. Finally, the IMOMO(G2MSr:ROMP2/6-31G(d)) method was used to predict the C-H bond dissociation energy in H-C(C6H5)(3) and the C-C bond dissociation energy in CH3-C(C6H5)(3), neither of which is available experimentally. These predicted values are 75.9 and 64.1 kcal/mol, respectively, which are smaller than any other C-H and C-CH3 BDE studied in this paper.