We report a high-precision calculation of the photodetachment energy of the hydrogen anion ${\mathrm{H}}^{-}$, also known as the electron affinity of the hydrogen atom. The nonrelativistic bound-state energy is obtained using an exact three-body approach, and supplemented by leading relativistic, quantum-electrodynamic, finite-nuclear-size, and hyperfine corrections. Our result is $6083.06447\left(68\right){\mathrm{cm}}^{-1}$ for the detachment to the hydrogen ground-state hyperfine level $(F=0)$, which is 220 times more precise than the best experimental determination to date, $6082.99\left(15\right){\mathrm{cm}}^{-1}$, as reported by Lykke et al. [Phys. Rev. A 43, 6104 (1991)]. Beyond their intrinsic interest, these results provide critical input for antihydrogen physics, where controlled photodetachment of ${\overline{\mathrm{H}}}^{+}$ offers a path to producing ultracold antihydrogen (and its isotopes) for precision experiments. We further determine the photodetachment thresholds for ${}^2\mathrm{H}^{-}$ and ${}^3\mathrm{H}^{-}$ into the ground hyperfine states of the corresponding hydrogenic atoms, yielding $6086.70679\left(68\right){\mathrm{cm}}^{-1}$ for ${}^2\mathrm{H}(F=1/2)$ and $6087.87924\left(68\right){\mathrm{cm}}^{-1}$ for ${}^3\mathrm{H}(F=0)$.

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• Atomic & molecular structure
• Relativistic & quantum electrodynamic effects in atoms, molecules,& ions
• Atoms