In this paper we present the results of our theoretical investigations on the Watson-Crick base pairs of 9-methylguanine - 1-methylcytosine (GC) and 9-methyladenine-1-methylthymine (AT) and the Hoogsteen base pair of 9-methyladenine-1-methylthymine(AT). We have performed full geometry optimization of the bases and the base pairs within the ab initio molecular orbtial (MO) framework at the Hartree-Fock (HF) self-consistent field (SCF) level with the 6-31G* basis set. We have extended these calculations by performing SCF and MP2 calculations, utilizing the Dunning double-zeta plus polarization basis set (DZP), upon the 6-31G* SCF optimized bases and base pairs. Vibrational analyses were performed at the 6-31G* level to enable the calculated interaction energies to be corrected to "predict" a DELAH298 for the base pairs. We have further validated this theoretical model by showing that it reproduces the DELTAH298 for (H2O)2, HCN...HF, and CH3CN...HF. We find that for the AT base pairs, the Hoogsteen orientation is approximately 1 kcal/mol more stable than the Watson-Crick orientation, with a DELTAH298 of -12.8 kcal/mol in excellent agreement with the experimental value of -13.0 kcal/mol. We do not, however, reproduce the experimental value of deltaH298 for Watson-Crick GC of -21.0 kcal/mol; we calculate a DELTAH298 of -25.3 kcal/mol. These ab initio energies are also compared with those found with a recently derived molecular mechanics model. The molecular mechanics calculations do a good job of reproducing the GC base pair energies found quantum mechanically and also lead to AT base pair energies in quite close agreement with experiment.