When a hydrogen in an excited state transits back to the ground state, a photon (or series of photons) is emitted in accordance with the selection rules.

When two free hydrogen atoms in the ground state $1s$ (and with the same wave function parity) approach each other the atomic orbitals interact and a $\sigma(ss)$ molecular orbital is formed and energy is released. The bond Enthalpy for $\mathrm{H\_2}$ is $-436\;\mathrm{kJ/mol}$, which can be converted to about $-4.53\:\mathrm{eV}$ per bond formed and corresponds to the VIS/near UV part of the electromagnetic spectrum.

I've always believed that this energy would be released also as a photon (or a series of photons) but is that really true? Or could it manifest itself as an increase in kinetic energy of the formed $\mathrm{H\_2}$ molecule? Can either be derived from quantum mechanical principles?