A sub-monolayer of atomic sodium was deposited on LiF(001) at 40-90 K. The adsorbed sodium atoms and clusters were dosed with HBr, to form HBr···Na_n /LiF(001) (n = 1,2,...) complexes which were then irradiated by 610 nm laser-light to induce charge-transfer reactions. The reaction-product atomic H(g) was observed leaving the surface, by two-color Rydberg-atom TOF spectroscopy. The H-atom translational energy in its "fast" (0.9 eV) component exhibited structure (40±10 meV spacing) attributed to vibration of the NaBr residue at the surface following photoinduced reaction in Na···HBr. The cross-section of the harpooning event was obtained as 7.5 ·10^-19 cm² for the "fast" H-atom reaction-product, and 2.4 ·10^-19 cm² for the "slow" component (0.1 eV). Investigation of the coverage and temperature dependences of the H-atom signal and of Temperature Programmed Desorption (TPD) and X-ray photoelectron spectra gave an activation barrier for surface diffusion of Na-atoms E_diff <170 meV. High-level ab initio calculations were employed to interpret the TOF and TPD spectra. The reaction precursors and products, Na-HBr, Na⁺-HBr, Na₂-HBr, Na₂Br, NaBr, and NaBr-HBr, were investigated in terms of potential energy surfaces, equilibrium structures, binding energies and vibrational frequencies.