Symmetry and structure of rotating H3+

Abstract

We present a global study of how the relative equilibria of the H 3 ϩ ion change as the angular momentum J increases. A relative equilibrium is a classical trajectory for which the molecule rotates about a stationary axis without changing its shape. The study confirms previous results which show that the geometry of the minimum energy relative equilibria changes from an equilateral triangle to a symmetric linear configuration at around Jϭ47. The series of bifurcations and stability changes that accompany this transition is presented in detail. New results include the discovery that the rotating equilateral triangle remains linearly stable for a large range of angular momentum values beyond the point where it ceases to be a minimum of the total energy. A third type of relative equilibrium, a rotating isosceles triangle, is also found to be linearly stable in the approximate range Jϭ0-34. Both the equilateral and isosceles triangle configurations lose stability via Hamiltonian-Hopf bifurcations. The frequencies and symmetry species of the normal modes of the stable relative equilibria are computed and harmonic quantization is used to predict how the symmetries of the lowest lying quantum states will change as J increases. Energy level clustering due to tunneling between symmetry-equivalent relative equilibria is described.

Assigning vibrational polyads using relative equilibria: application to ozone

“…It will be equally interesting to study continuation of RE to high energies (cf. [29]) in order to understand the breakdown of the polyad approximation.…”

“…We do it in a somewhat different context [29]. We opted for the very well-developed continuation package CONTENT [30], 3 which can be easily adapted for our purposes by introducing a free dummy parameter λ in the equations of motioṅ…”

Strand spaces and rank functions:more than distant cousins

“…We have shown elsewhere 33,34 that relative equilibria can be used to obtain new approximations for the qualitative analysis of quantum levels. This can be done for any relative equilibrium but the most experimentally relevant for the Stark effect is the P relative equilibrium.…”

“…This is not uncommon: any given rotating molecular system is likely to exhibit several such bifurcations as the angular momentum is increased. 33,34 Of course molecular systems are not integrable. However integrable approximations often provide useful models.…”

“…Relative equilibria have been used as ''organizing centers'' for molecular spectra at high angular momenta in much the same way as equilibria are used for vibrational and low angular momentum spectra. [30][31][32][33][34] They appear in families parametrized by total angular momentum and typically undergo a number of bifurcations as the angular momentum is increased. Hamiltonian Hopf bifurcations occur when two normal mode frequencies become equal and then complex, resulting in loss of stability.…”