According to the Born-Oppenheimer approximation, the excited (2P1/2) spin-orbit state of the fluorine atom will not react with H2 to produce a ground electronic state HF molecule, because this process requires an non-adiabatic transition between the two lowest doublet A' electronic states of the F + H2 system:
However, since the spacing between these electronic states is rather small in the F + H2 reactant valley (the spin-orbit splitting of the fluorine atom is a mere 1.15 kcal/mol - comparable to the j=0 to j=2 rotational spacing of the H2 molecule), there is some reason to be circumspect about the accuracy of the Born-Oppenheimer approximation for this reaction.
In fact, there are three distinct types of coupling that can lead to a non-adiabatic electronic transition, and hence to the reactivity of F*(2P1/2): electronic, spin-orbit, and Coriolis (vibration-rotation) coupling. All three of these effects were included in a quantum reactive scattering calculation on the F + H2 reaction by Millard Alexander, during his sabbatical visit to our group in Oxford in 1998. This calculation involved combining quantum reactive scattering theory with electronic and spin-orbit coupling matrix elements from the group of Hans-Joachim Werner in Stuttgart, and it was fully ab initio from beginning to end.
The above figure shows the resulting cross sections for the reactions of F(2P3/2) and F*(2P1/2) with H2(j=1). The cross section for F* is significantly smaller than that for F at most collision energies, as one would expect from the Born-Oppenheimer approximation. Since the thermal population of the excited F*(2P1/2) spin-orbit state is at most half that of the F(2P3/2) state, one would not therefore expect to see much evidence for the reactivity of F*, and this is borne out by experimental results. Nevertheless, the predicted non-adiabatic reactivity of F* is not completely negligible, and in fact it is larger than the adiabatic reactivity of F at very low collision energies where the spin-orbit energy helps to overcome the reaction barrier.
For more details on electronically non-adiabatic effects in F + H2, see J. Chem. Phys. 109, 5710 (1998) and J. Chem. Phys. 113, 11084 (2000). [Since this work was published attention has turned to the Cl + H2 reaction, in which the spin-orbit splitting and spin-orbit coupling matrix elements are significantly larger. There appears at the moment to be a striking disagreement between theory and experiment for this reaction, as discussed in Science 296, 664 (2002).]