The hydrogen-bonded complexes of the nucleobase mimic 2-pyridone (2PY) with seven different fluorinated benzenes (1-, 1,2-, 1,4-, 1,2,3-. 1,3,5-, 1,2,3,4-, and 1,2,4,5-fluorobenzene) are important model systems for investigating the relative importance of hydrogen bonding versus pi-stacking interactions in DNA. We have shown by supersonic-jet spectroscopy that these dimers are hydrogen bonded and not pi-stacked at low temperature (Leist, R.; Frey, J. A.; Leutwyler, S. J. Phys. Chem. A 2006, 110, 4180). Their geometries and binding energies D, were calculated using the resolution of identity (RI) Moller-Plesset second-order perturbation theory method (RIMP2). The most stable dimers are bound by antiparallel N-H... F-C and C-H center dot center dot center dot O=C hydrogen bonds. The binding energies are extrapolated to the complete basis set (CBS) limit, D-e(infinity), using the aug-cc-pVXZ basis set series. The CBS binding energies range from -D-e,(CBS) = 6.4-6.9 kcal/ mol and the respective dissociation energies from -D-0,D-CBS = 5.9-6.3 kcal/mol. In combination with experiment, the latter represent upper limits to the dissociation energies of the pi-stacked isomers (which are not observed experimentally). The individual C-H center dot center dot center dot O=C and N-H center dot center dot center dot F-C contributions to D, can be approximately separated. They are nearly equal for 2PY center dot fluorobenzene; each additional F atom strengthens the C-H center dot center dot center dot O=C hydrogen bond by similar to 0.5 kcal/mol and weakens the C-F center dot center dot center dot H-N hydrogen bond by similar to 0.3 kcal/mol. The single H-bond strengths and lengths correlate with the gas-phase acid-base properties of the C-H and C-F groups of the fluorobenzenes.