so only the even parity is allowed. The hyperradius ρ can vary in the interval [0, ∞ ). In this study, it varies from 1 a.u. to 120 a.u. for H − 3 a.u. and from 1 a.u. to 80 a.u. for D − 3 . In the numerical calculation, we have used equal masses m = 1837 . 3621 a.u. for all three atoms in the H − 3 molecule. This value is the sum of the hydrogen mass and one third of electron mass. Similarly, we took m = 3670 . 8162 a.u. (which is the sum of the deuterium mass and one third of electron mass) for D − 3 . The resulting adiabatic potentials of A ′ 1 and A ′ 2 irreps are shown in Fig. 6 for H − 3 and in Fig. 7 for D − 3 . The curves of E ′ irrep are not shown in Figs. 6 and 7: The lowest E ′ curves are almost identical to the A ′ 1 and A ′ 2 curves and would be indistinguishable from them in the figures because for low vibrational levels, the energies of levels are independent on the symmetry ( A ′ $_{1}$, A ′ $_{2}$, or E ′ ) of wave functions with respect to the proton exchange between the dimer and the H − ion. (We assume here that the dimer is in a particular rovibrational state such that the proton exchange is made without changing the dimer state. The energy does depend on the H$_{2}$ rovibrational state). At large ρ , all adiabatic curves dissociate into an atom+dimer system characterized by the rovibrational state ( v$_{d}$, j ) of the dimer. Some of the adiabatic curves in Figs. 6 and 7 exhibit avoided crossings at energies above ∼ 4000 cm − $^{1}$: Dynamic coupling between hyperspherical adiabatic states is mostly determined by the avoided crossings and responsible for nuclei exchange above the potential barrier identified in Fig. 2. Such transitions are much less probable at smaller energies as each adiabatic state is only weakly coupled to other adiabatic states of the same irrep . As a consequence, only one component ϕ$_{a}$ in the expansion of Eq. (11) is dominant. Each adiabatic state for a given irrep Γ is correlated with a definite pair of quantum numbers ( v$_{d}$, j ), and can be approximately characterized by these two quantum numbers. The value Ω of the projection of the H$_{2}$ angular momentum j on the axis connecting the dimer with the atom is also a relevant quantum number. For J = 0, Ω is always zero and, therefore is not specified in Figs. 6 and 7. To characterize completely a bound state of the trimer, an additional quantum number v$_{t}$ is needed for the excitation within each adiabatic state (along the hyperradius). Therefore, the bound states are characterized by four approximate quantum numbers Ω , j, v$_{t}$, v$_{d}$ and two exact quantum numbers J and Γ. At high energies, the mixing between different Ω , j, v$_{t}$, v$_{d}$ for given J and Γ becomes important. We summarized in Table II the present H − 3 bound state energies and those of Ref. [10] 15