As we know from the improved methods valence bond theory (VB), as well as molecular orbital theory (MO-LCAO), the wave function of the $\ce{H2}$ molecule consist of two terms, which belong to covalent and ion structure, respectively: $$\psi =\psi_\mathrm{cov} + \lambda\psi_\mathrm{ion}.$$
According to quantum mechanics, there is a nonzero probability $\propto\lambda^2$ for the ionic state wave-function term. Such reaction should lead to the $\ce{H2}$ molecule dissociation products $\ce{H+}$ (proton) and anion $\ce{H-}$: $$\ce{H2 -> H+ + H-}.$$
Have such processes been observed in nature?