A theoretical study of Ne3 using hyperspherical coordinates and a slow variable discretization approach

Abstract

We study theoretically the ground and excited bound states of the bosonic rare gas van der Waals trimer Ne(3). A slow variable discretization approach is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved using basis splines at a series of fixed finite-element methods discrete variable representation hyper-radii. We consider not only zero total nuclear orbital angular momentum, J = 0, states but also J > 0 states. By using the best empirical neon dimer interaction potentials, all the bound state energy levels of Ne(3) will be calculated for total angular momenta up to J = 6, as well as their average root-mean-square radii. We also analyze the wave functions in hyperspherical coordinates for several selected bound states.

Theoretical methods for the rotation–vibration spectra of triatomic molecules: distributed Gaussian functions compared with hyperspherical coordinates

“…Among other things, the authors found: (i) differences with respect to analytical expressions for the energies of a symmetric planar trimer when the vibrational excitation was increased and (ii) a significant contribution from the Coriolis coupling terms. Using the same 2B pairwise potential, Suno [140] performed a HC calculation to obtain the rotational energies up to J = 6. A more extended investigation covering the rotational spectrum between J = 0 and 18 was reported by Yang et al [141] who analyzed energy levels and wave functions of the corresponding Ne 3 bound states in a quantum dynamical calculation.…”

Adiabatic hyperspherical approach to large-scale nuclear dynamics

“…In that case, a diabatic procedure is proposed for accurately solving Eq. (18) [6,27,28]. The slow variable discretization method combined with a complex absorbing potential makes it possible to solve Eq.…”

An improved Lobatto discrete variable representation by a phase optimisation and variable mapping method

“…However, the grid distribution of LDVR is unequal and densely clustering around the two edges of the integration interval, which is not an efficient representation for most of molecular dynamics problem, thus the LDVR method has not been paid much attention in the field of molecular dynamics in the past years. We note that recently Suno has applied the FE-DVR method in hyperspherical coordinates for solving triatomic ro-vibrational eigenstates [61,51].…”