Explicitly correlated averaged coupled-pair functional methods have been used to compute the ground-state Born-Oppenheimer potential energy surface for the F + HH' -> FH + H' reaction at the F + HH' and FH + H' asymptotes, the (FHH)-H-...', and (FHH)-H-... van der Waals wells, the reaction transition state, and at points along the intrinsic reaction coordinate connecting all of these stationary points. To these energies, corrections for spin-orbit coupling and scalar relativistic effects were added to produce total electronic energies whose accuracy is demonstrated to be very high (e.g., 0.1 kcal mol(-1)). The final data are used to refine the two-body parts of the currently best three-dimensional potential energy surface for this reaction, to predict several spectroscopic parameters of the species involved, and to offer accurate estimates of the title reaction's exothermicity (32.0 kcal mol(-1)) and activation barrier (1.8 kcal mol(-1)) as well as the geometry of the transition state.