Forbidden "ortho"--"para" electric dipole transitions in H${}_2^{+}$ ion

We present the first systematic calculation of the electric dipole forbidden transitions in the homonuclear molecular ion H${}_2^{+}$. We get that the transition rate from the ground “ortho” $(v\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}0,N\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}1,J\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}1\mathrm{/}2)$ state to the ground “para” $(v\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}0,N\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}0,J\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}1\mathrm{/}2)$ state is $4.9\text{\hspace{0.17em}⁣}\times \text{\hspace{0.17em}⁣}{10}^{-14}$ s${}^{-1}$ that corresponds to the lifetime of $6.4\text{\hspace{0.17em}⁣}\times \text{\hspace{0.17em}⁣}{10}^5$ yr. The Einstein coefficient $A_{n{n}^{\mathrm{\prime }}}$ for the $(v\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}1,N\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}1,J\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}1\mathrm{/}2)\text{\hspace{0.17em}⁣}\to \text{\hspace{0.17em}⁣}(v\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}0,N\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}0,J\text{\hspace{0.17em}⁣}=\text{\hspace{0.17em}⁣}1\mathrm{/}2)$ transition is equal to $0.12\text{\hspace{0.17em}⁣}\times \text{\hspace{0.17em}⁣}{10}^{-9}$ s${}^{-1}$, which is of “comparable” order with the values for quadrupole transitions in H${}_2^{+}$. It gives hope that the “ortho”–“para” transitions in H${}_2^{+}$ can be induced by the laser spectroscopy.