The eigenstates Ψ of three particles interacting through a potential V depending only on the three internuclear distances are obtained by solving the Schr¨ odinger equation with the following Hamiltonian expressed in hyperspherical coordinates ρ, ω in the center-of-mass frame [54]: − 1 2 µ ρ − 5 ∂ ∂ρ ρ 5 ∂ ∂ρ + Λ 2 2 µρ 2 + V , (6) where µ = $_{m/}$√$_{3 is the three-body reduced mass and}$ m is the mass of each of the three identical particles. The operator Λ above is the grand angular momentum [58, 59]. It depends only on the set ω of five angles, which include the three Euler angles (for the orientation of the molecular frame in the lab frame) and the hyperangles θ and φ . If the total angular momentum J = 0, Λ depends only on the two hyperangles. The explicit form of Λ 2 is given, for example, by Eq. (27) of Ref. [59]: Λ 2 = − 4 sin(2 θ ) ∂ ∂θ sin(2 θ ) ∂ ∂θ − 4 sin $^{2}$( θ ) ∂ 2 ∂φ 2 (7) + 2 J 2 X 1 − sin θ + 2 J 2 Z 1 + sin θ + J 2 Y sin 2 θ + 4 i cos θJ$_{Y}$ sin 2 θ ∂ ∂φ , where J$_{X}$ , J$_{Y}$ , and J$_{Z}$ are the components of the angular momentum along the principal axes of inertia. The orientation of the axes is approximately indicated in Fig. 1. After rescaling the wave function Ψ as Ψ = ρ − 5 / $^{2}$ψ , the Hamiltonian for the new function ψ is written as The eigenfunctions ψ ( ρ, ω ) of the above Hamiltonian are sought as an expansion over the basis functions y$_{a,j}$ ( ρ, ω ) with unknown coefficients c$_{a,j}$ : H = T$_{ρ}$ + H$_{ad}$ , where (8) T$_{ρ}$ = − 1 2 µ ∂ 2 ∂ρ 2 and (9) H$_{ad}$ = Λ 2 + 15 / 4 2 µρ 2 + V . (10) ψ ( ρ, ω ) = ∑ a,j y$_{a,j}$ ( ρ, ω ) c$_{a,j}$ (11) y$_{a,j}$ ( ρ, ω ) = π$_{j}$ ( ρ ) ϕ$_{a,j}$ ( ω ) (12) The basis functions y$_{a,j}$ ( ρ, ω ) are constructed as products where the functions π$_{j}$ ( ρ ) are DVR-like functions localized at DVR grid points ρ$_{j}$ along the hyper-radius. As in our earlier study [60, 61], here we used the plane wave DVR functions. 13