Gerade-ungerade mixing in the hydrogen molecule

In homonuclear molecules, such as ${\mathrm{H}}_2$, the rovibrational levels close to the dissociation threshold do not have definite symmetry with respect to the inversion of electronic variables. This effect—the gerade-ungerade mixing—results from interactions between magnetic moments of electrons and protons. We calculate this mixing on the level of adiabatic approximation and numerically solve the system of nuclear differential equations. It turns out that the corrections to the dissociation energy of rovibrational levels resulting from the mixing are negligible in comparison with the present accuracy of experiments. As a coproduct, an accurate clamped nuclei potential for the $b$ ${}^3{\Sigma }_u^{+}$ state has been obtained.