The temperature variation of the CH+ + H reaction rate coefficients: a puzzle finally understood?

CH+ was the first molecular ion identified in the interstellar medium and is found to be ubiquitous in interstellar clouds. However, its formation and destruction paths are not well understood, especially at low temperatures. A new theoretical approach based on the canonical variational transition state theory was used to study the H + CH+ reactive collisions. Rate coefficients for formation of C+ ions are calculated as a function of temperature. We considered the participation of a direct path and an indirect path in which the reactants should overcome an entropic barrier to form a van der Waals complex or pass through a CH2+ intermediate complex, respectively. We show that the contribution of both pathways to the formation of C+ has to be taken into account. The new reactive rate coefficients for the title reaction, complemented by reactive data for CH+/CH2+ in the H/H2/He mixture, have been used to simulate the corresponding kinetics experimentally measured using an Atomic Beam 22 Pole Trap apparatus at low temperature. A good agreement with the experimental findings was found at 50 K. At a lower temperature, the model overestimates the formation of C+. This shows that secondary reactions are not responsible for the weak C+ production in the experiments at such temperature. Then, we discuss the possible impact of non-adiabatic effects in the study of the H + CH+ reactive collisions and we found that such effects can be responsible for the decrease of the H + CH+ rate coefficients at low temperature. This study offers an explanation for the disagreement between H + CH+ theoretical and experimental rate coefficients which has been going on for 20 years and highlights the need for performing non-adiabatic studies for this simple chemical reaction.


S2. Kinetic modelling
The CH + + H reaction was modeled assuming steady-state conditions and solving the kinetic equations as a function of time and using the initial reactant concentrations.

S3. Quasi-classical trajectory (QCT) dynamics
For the QCT calculations, trajectories were made with the classical molecular dynamics with quantum transition (MDwQT) program 2-3 on the potential energy surface of Stoecklin and Halvick 4 .First, 10000 trajectories were running with the maximum impact parameter settled at 10 bohrs and dynamics were stopped when the distance between the atoms is larger than 22 bohrs.The results are showed in Figure S1.

Figure S1. Various processes probability for the CH + + H collision as a function of time at different kinetic energies. The numbers inside each plot are the observed fraction of the process.
From these results, it can be seen that the reactive process is dominant at low energies but in competition with the inelastic process (dissociation of the CH2 +* into the product).This is consistent with the microcanonical rate coefficients computed in this work.
By analyzing the reaction probabilities, we can observe distinct patterns.At high energies, the probability for the consumption of the pre-reactive complex (CH2 +* or CH + …H) is a Boltzmann function.Initially, low reaction probabilities are found.Then, it is followed by a gradual increase before a constant decrease.This behavior aligns with the presence of both direct and indirect reaction paths.At low energy, the probabilities are rapidly increasing and then suddenly decreasing.This behavior suggests that the indirect path is strongly dominant under adiabatic conditions.7][8][9][10][11][12] Additionally, 5x10⁵ trajectories were performed for 10 K and 50 K and 1x10 6 trajectories for temperatures above 100 K (Figure S2).The maximum impact parameter used for all the trajectories was 40 bohrs.Figure S2 indicates that when the temperature is decreasing, larger impact parameters play an increasingly important role.Such large impact parameters correspond to very long (in time) trajectories that lead to spiral-shaped orbits before reacting.

Figure S2. Contour plot of the number of trajectories as a function of the impact parameter and total time of the trajectories.
The thermal rate coefficients were calculated using such conditions (see purple values in Figure S3) and are in good agreement with the Langevin limiting value and with the exact quantum results 7 (1.38x10 - cm³ s -1 , 1.26x10 -9 cm³ s -1 and 1.22x10 -9 cm³ s -1 , respectively).However, we observe in Figure S3 that when the maximum time allowed for the reactive process is reduced, the thermal rate coefficients are also reduced, in a nearly quantitative agreement with the results of the present microcanonical model.Thus, longer time trajectories may yield to secondary collisions or to other phenomena, as those labelled as R5-R7 in the main text.This microscopical dynamical picture can be used to justify the direct (fast) and indirect (slow) mechanism allowing to produce only a gradual decay of the reactive rate coefficients when reducing temperature.The wb97xd/aug-cc-pvdz level of theory used for the non-adiabatic molecular dynamics is benchmarked versus experimental and theoretical values of reference.We computed the equilibrium geometry of CH2 + in both its ground and first excited electronic states and compare our results to those obtained by MRCI and CCSD(T) calculations of reference and to experimental measurement.The comparison is shown in Table S3.The similarities between the results obtained with the different level of theory and the experimental data show that wb97xd/aug-cc-pvdz level of theory used in this work can provide a good representation of the geometrical evolution in the regions around the CH2 + and the Renner-Teller crossing using the on-the-fly dynamics.

Figure S3 . 1 s - 1 )
Figure S3.Effect of the maximum time allowed for the reactive process on the thermal rate coefficients

Table S3 .
Comparison of the equilibrium geometry of CH2 + in the ground and first excited electronic states calculated at the wb97xd/aug-cc-pvdz level of theory with data available in the literature.