4 8 16 32 hyper-radius  (a.u.) 0 1000 2000 3000 4000 5000 6000 adiabatic potentials (cm -1 ) (0,0) (0,1) (0,2) (0,3) (0,4) (0,5) (0,6) (0,7) (0,8) (1,0) (1,1) (1,2) H$_{2}$(v$_{d}$,j) FIG. 6: (Color online) The lowest H − 3 hyperspherical adiabatic curves ( U$_{a}$ ( ρ ) in Eq. (13)) for J = 0 of A ′ 1 irrep (solid black lines) and of A ′ 2 irrep (dashed red lines). The curves of the E ′ irrep are not displayed, as they are very similar to the A ′ 1 and A ′ 2 curves for energies smaller than 4000 cm − 1 above the lowest dissociation limit H$_{2}$(0 , 0) + H $^{−}$, and would be indistinguishable on this scale. A couple of avoided crossings located around 4000 cm − 1 are marked. Each curve is labelled at large R with the pair of indexes ( v$_{d}$,j ) corresponding to the rovibrational state of the H$_{2}$ molecule. The energy origin is set to the lowest dissociation limit H$_{2}$(0 , 0) + H $^{−}$. The closed circles on the (0,6) curve exemplifies the density of grid points in R used in the calculations. labelled with the set of quantum numbers J , j ,Ω, v$_{t}$ , v$_{d}$ ,Γ. In agreement with Ref. [10], we found four vibrational energies levels of the A ′ 1 irrep and one other level of the A ′ 2 irrep . We also found four more vibrational levels of the A ′ 2 irrep . Although their energies are located above the v$_{d}$ = 0 , j = 0 dissociation threshold, they are stable because they cannot dissociate due to the symmetry restriction. Their binding energies are given in the table 16