Hyperridge of triply excited states

We present a theory for the definition and the reliable calculation of correlated wave functions of a special class of triply excited states and for their rigorous geometrical analysis. This class is named the three-electron ionization ladder (THEIL) and refers to the simultaneous excitation of three electrons in valence states near threshold. Application to the Li THEIL of ${}_{}{}^4{}_{}{}^{}\mathrm{S}$ ° symmetry reveals impressive localization properties. In analogy with a similar analysis of the ‘‘two-electron ionization ladder,’’ which leads smoothly to the so-called ‘‘Wannier ridge’’ at the E=0 threshold, the present results suggest the existence of a ‘‘hyperridge’’ at E=0 with the following properties: (1) The ion core and the three electrons lie in a plane, (2) ‖${\mathrm{r}}_1$‖=‖${\mathrm{r}}_2$‖=‖${\mathrm{r}}_3$‖, and (3) ${\theta }_{12}$=${\theta }_{23}$=${\theta }_{31}$. .AE