The doubly excited states of the H2 molecule

We report extensive calculations of energy positions and autoionization widths for the doubly excited states of H${}_2$ between the first and the second ionization thresholds. We present results for 60 doubly excited states of the ${}^{\text{1,3}}{\Sigma }_{\mathrm{g,u}}^{+}$ , ${}^{\text{1,3}}{\Pi }_{\mathrm{g,u}},$ and ${}^{\text{1,3}}{\Delta }_{\mathrm{g,u}}$ symmetries in the range of internuclear distances $\text{0⩽R⩽5}$ a.u. The resonance parameters have been obtained using the Feshbach theory and an $L^2$ representation of the non resonant continuum with B-spline functions. We discuss the main features of the energy correlation diagrams and the corresponding widths. We point out the existence of avoided crossings in the Franck–Condon region that significantly affect the autoionization properties of the doubly excited states. Our data are compared with previous results reported in the literature.