The computation of the vibrational levels is relatively standard and it is related on early works on variational methods . For the present study, it has been performed with the help of our home-made pseudo-spectral Fortran code, TI_Schrod . It allows us to solve the time-independent Schrödinger equation with a Hamiltonian expressed in terms of the three internal coordinates, q = [R 1 , R 2 , θ]. The 3D-quantum vibrational bound states are expanded on a direct product of one-dimensional harmonic oscillator basis sets, and thus, ρ(q) associated with the non-Euclidean volume element is equal to one (ρ(q) = 1). Furthermore, the integration procedure is performed using the direct product of Gauss-Hermite quadrature grids.