Hydrogen bonding between base pairs in nucleic acids is a key determinant of their structures. We have examined the distance dependence of the hydrogen bonding of AT-WC (Watson-Crick), GC-WC, and AT-H (Hoogsteen) base pairs using ab initio quantum mechanics, LMP2/cc-pVTZ(-f) energies at HF/cc-pVTZ(-f) optimized geometries. From these curves, we have extracted Morse potentials between the H atoms and the acceptor atoms that accurately reproduce the quantum mechanical energies for a range of geometries. Using these parameters, we have calculated the complexation energies of the remaining 26 possible pairwise combinations, and the agreement with previously reported ab initio calculations is excellent. We have also extracted off-diagonal Lennard-Jones 12-6 parameters to be used with the popular AMBER95 and CHARMM95 force fields that significantly improve their descriptions of the base-pairing energy and optimum geometry.