  The formation of hydrides by gas-phase reactions between H2 and a heavy
element atom is a very selective process. Reactions with ground-state neutral
carbon, oxygen, nitrogen, and sulfur atoms are very endoergic and have high
energy barriers because the H2 molecule has to be fragmented before a hydride
bond is formed. In cold interstellar clouds, these barriers exclude the
formation of CH, OH, NH, and SH radicals through hydrogen abstraction
reactions. Here we study a very energetically unfavorable process, the reaction
of N(4S) atoms with H2 molecules. We calculated the reaction rate coefficient
for H2 in different vibrational levels, using quantum methods for v=0-7 and
quasi-classical methods up to v=12. Owing to the high energy barrier, these
rate coefficients increase with v and also with the gas temperature. We
implemented the new rates in the Meudon PDR code and studied their effect on
models with different ultraviolet (UV) illumination conditions. In strongly
UV-irradiated dense gas (Orion Bar conditions), the presence of H2 in highly
vibrationally excited levels (v>7) enhances the NH abundance by two orders of
magnitude (at the PDR surface) compared to models that use the thermal rate
coefficient for reaction N(4S) + H2 -> NH + H. The increase in NH column
density across the PDR is a factor of ~25. We explore existing Herschel/HIFI
observations of the Orion Bar and Horsehead PDRs. We report a 3-sigma emission
feature at the ~974 GHz frequency of the NH N_J=1_2-0_1 line toward the Bar.
The emission level implies N(NH)~10^13 cm^-2, which is consistent with PDR
models using the new rate coefficients for reactions between N and UV-pumped
H2. This formation route dominates over hydrogenation reactions involving the
less abundant N+ ion. JWST observations will soon quantify the amount and
reactivity of UV-pumped H2 in many interstellar and circumstellar environments.
