The primary purpose of the present study is to resolve the discrepancy that exists between the two most recently published dissociation energies for the fluorine molecule [D-0(F-2)] and, consequently, for the associated heats of formation of the fluorine atom [Delta H-f(0)degrees(F)]. We hope to provide a reliable, well-established theoretical estimate for these thermochemical quantities. To this end, a high-accuracy coupled-cluster-based composite ab initio model chemistry has been utilized. The protocol involves contributions of up to pentuple excitations in coupled-cluster theory augmented with basis set extrapolation techniques and additional corrections beyond the nonrelativistic and Born-Oppenheimer approximations. The augmented core-valence correlation consistent basis set families, aug-cc-pCVXZ, have been successively used, in some cases, up to octuple-zeta quality. Our best theoretical results for D-0(F-2) and Delta H-f(0)degrees(F) obtained in this study are 154.95 +/- 0.48 and 77.48 +/- 0.24 kJ/mol, respectively. Because conflicting theoretical results are also reported about the existence of a barrier along the dissociation curve of F-2, extensive multireference configuration interaction and coupled-cluster calculations have been performed using reference orbitals taken from all-electron complete active space self-consistent field computations. Extrapolations from the results obtained with the aug-cc-pCVXZ (X = T, Q, 5) basis sets clearly indicate that the barrier indeed exists. It is located at 3.80 +/- 0.20 angstrom along the dissociation curve with a height of 42 +/- 10 mu E-h (similar to 0.11 +/- 0.03 kJ/mol). Because of the neglect of this effect during the evaluation of the raw experimental data used to obtain D-0(F-2) = 154.52 +/- 0.12 kJ/mol and Delta H-f(0)degrees(F) = 77.26 +/- 0.06 kJ/mol [Stevens; et al. J. Phys. Chem. A 2010, 114, 13134], an additional error should be attached to these latter values. Obviously, the barrier does not affect either the experimental results, D-0(F-2) = 154.92 +/- 0.10 kJ/mol and Delta H-f(0)degrees(F) = 77.46 +/- 0.05 kJ/mol [Yang; et al. J. Chem. Phys. 2005, 122, 134308; 2007, 127, 209901], which are based on the ion-pair dissociation of the molecule, or the data calculated theoretically. It is also noteworthy that our best estimates are in excellent agreement with those obtained from the ion-pair dissociation experiment.