The ortho-to-para ratio of H$_2$Cl$^+$: Quasi-classical trajectory
  calculations and new simulations in light of new observations
  Multi-hydrogenated species with proper symmetry properties can present
different spin configurations, and thus exist under different spin symmetry
forms, labeled as para and ortho for two-hydrogen molecules. We investigated
here the ortho-to-para ratio (OPR) of H$_2$Cl$^+$ in the light of new
observations performed in the z=0.89 absorber toward the lensed quasar PKS
1830-211 with the Atacama Large Millimeter/submillimeter Array (ALMA). Two
independent lines of sight were observed, to the southwest (SW) and northeast
(NE) images of the quasar, with OPR values found to be $3.15 \pm 0.13$ and $3.1
\pm 0.5$ in each region, respectively, in agreement with a spin statistical
weight of 3:1. An OPR of 3:1 for a molecule containing two identical hydrogen
nuclei can refer to either a statistical result or a high-temperature limit
depending on the reaction mechanism leading to its formation. It is thus
crucial to identify rigorously how OPRs are produced in order to constrain the
information that these probes can provide. To understand the production of the
H$_2$Cl$^+$ OPR, we undertook a careful theoretical study of the reaction
mechanisms involved with the aid of quasi-classical trajectory calculations on
a new global potential energy surface fit to a large number of high-level ab
initio data. Our study shows that the major formation reaction for H$_2$Cl$^+$
produces this ion via a hydrogen abstraction rather than a scrambling
mechanism. Such a mechanism leads to a 3:1 OPR, which is not changed by
destruction and possible thermalization reactions for H$_2$Cl$^+$ and is thus
likely to be the cause of observed 3:1 OPR ratios, contrary to the normal
assumption of scrambling.
