# Semiempirical breakdown curves of C\_2N(+\+) and C\_3N(+\+)molecules; application to products branching ratios predictions of physical and chemical processes involving these adducts

Tijani Idbarkach, Thejus Mahajan, Marin Chabot, Karine Béroff, Néstor Aguirre, Sergio Díaz-Tendero, Thibaut Launoy, Arnaud Le Padellec, Luc Perrot, Maëlle Bonnin, et al.

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Tijani Idbarkach, Thejus Mahajan, Marin Chabot, Karine Béroff, Néstor Aguirre, et al.. Semiempirical breakdown curves of C\_2N(+\+) and C\_3N(+\+)molecules; application to products branching ratios predictions of physical and chemical processes involving these adducts. Molecular Astrophysics, 2018, 12, pp.25 - 32. 10.1016/j.molap.2018.06.003. hal-01868314

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<figure><img src="image_1.png" /></figure>

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LA-UR-18-23607 (Accepted Manuscript)

Semiempirical breakdown curves of C2N(+) and C3N(+) molecules; application to products branching ratios predictions of physical and chemical processes involving these adducts

Aguirre Castiblanco, Nestor Fabian

Provided by the author(s) and the Los Alamos National Laboratory (2018-09-26).

**To be published in: Molecular Astrophysics**

**DOI to publisher's version:** 10.1016/j.molap.2018.06.003

**Permalink to record:** http://permalink.lanl.gov/object/view?what=info:lanl-repo/lareport/LA-UR-18-23607

**Disclaimer:**

Approved for public release. Los Alamos National Laboratory, an affirmative action/equal opportunity employer, is operated by the Los Alamos National Security, LLC for the National Nuclear Security Administration of the U.S. Department of Energy under contract DE-AC52-06NA25396. Los Alamos National Laboratory strongly supports academic freedom and a researcher's right to publish; as an institution, however, the Laboratory does not endorse the viewpoint of a publication or guarantee its technical correctness.
Semiempirical breakdown curves of C₂N(+) and C₃N(+), molecules; application to products branching ratios predictions of physical and chemical processes involving these adducts

Tijani IdBarkach, Thejus Mahajan, Marin Chabot, Karine Béroff, Néstor F. Aguirre, Sergio Diaz-Tendero, Thibaut Launoy, Arnaud Le Padellec, Luc Perrot, Maëlle A. Bonnin, Kim Cuong Le, Florian Geslin, Nicolas de Séréville, Fairouz Hammache, Aurélie Jallat, Anne Meyer, Emeline Charon, Thomas Pino, Thibault Hamelin, Valentine Wakelam

PII: S2405-6758(18)30012-5

DOI: 10.1016/j.molap.2018.06.003

Reference: MOLAP 38

To appear in: *Molecular Astrophysics*

Received date: 16 April 2018

Revised date: 11 June 2018

Accepted date: 15 June 2018

Please cite this article as: Tijani IdBarkach, Thejus Mahajan, Marin Chabot, Karine Béroff, Néstor F. Aguirre, Sergio Diaz-Tendero, Thibaut Launoy, Arnaud Le Padellec, Luc Perrot, Maëlle A. Bonnin, Kim Cuong Le, Florian Geslin, Nicolas de Séréville, Fairouz Hammache, Aurélie Jallat, Anne Meyer, Emeline Charon, Thomas Pino, Thibault Hamelin, Valentine Wakelam, Semiempirical breakdown curves of C₂N(+), and C₃N(+), molecules; application to products branching ratios predictions of physical and chemical processes involving these adducts, *Molecular Astrophysics* (2018), doi: 10.1016/j.molap.2018.06.003

<figure><img src="image_2.png" /></figure>
Semiempirical breakdown curves of C₂N⁺ and C₃N⁺ molecules; application to products branching ratios predictions of physical and chemical processes involving these adducts

Tijani IdBarkach¹, Thejus Mahajan², Marin Chabot¹, Karine Béroff²,*, Néstor F.Aguirre³, Sergio Diaz-Tendero⁴, Thibaut Launoy⁵, Arnaud Le Padellec⁶, Luc Perrot¹, Maëlle A.Bonnin², Kim Cuong Le²,ª, Florian Geslin¹, Nicolas de Séréville¹, Fairouz Hammache¹, Aurélie Jallat¹, Anne Meyer¹, Emeline Charon⁷,ᵇ, Thomas Pino², Thibault Hamelin¹, Valentine Wakelam⁸

¹Institut de Physique Nucléaire d'Orsay, IN2P3-CNRS and Université Paris-Sud, F-91406 Orsay Cedex, France

²Institut des Sciences Moléculaires d'Orsay, INP-CNRS and Université Paris-Sud, F-91405 Orsay Cedex, France

³Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States

⁴Departamento de Qimica, Universidad Autonoma de Madrid, 28049 Madrid, Spain

⁵Laboratoire de Chimie Quantique et Photophysique, Université Libre de Bruxelles 1050 Bruxelles, Belgium

⁶Institut de Recherche en Astrophysique et Planétologie CINP-CNRS Univ. Toulouse 3 F-31028 Toulouse, France

⁷Centre de Sciences Nucléaires et de Sciences de la Matière 91400 Orsay Cedex, France

⁸Laboratoire d'Astrophysique de Bordeaux, Université de Bordeaux CNRS, F-33615 Pessac, France

**Abstract :**

We constructed semiempirical breakdown curves (BDC) for C₂N, C₃N, C₂N⁺ and C₃N⁺ molecules. These BDC, which are energy dependent dissociation branching ratios (BR) curves, were used to predict products branching ratios for various processes leading to the formation of C₂N⁺ and C₃N⁺ excited adducts. These processes, of astrochemical interest, are neutral-neutral and ion-molecule reactions, dissociative recombination and charge transfer reactions with He⁺. Model predictions of BR are compared to the literature data and to reported values in the kinetic database for astrochemistry KIDA. With the new BR values, the CₙN abundances in cold cores were simulated.

**Keywords** : Carbon and nitrogen-based molecules ; dissociation branching ratios ; breakdown curves ; astrochemistry ; KIDA database ; cold cores.

<footnote>ªpresent address : Division of Combustion Physics, Department of Physics, Lund University, Sweden</footnote>

<footnote>ᵇpresent address : NIMBE, CEA CNRS, Université Paris Saclay, CEA Saclay 91191 Gif sur Yvette, France</footnote>

<footnote>*Corresponding author</footnote>

<footnote>Email addresses : karine.beroff@u-psud.fr, valentine.wakelam@u-bordeaux.fr</footnote>
1-Introduction

Breakdown curves are energy dependent dissociation branching ratios of an excited
molecule (Vekey 1996). BDCs are specific to the molecule, its size, charge (see below), then
constitute a kind of identity card of the molecule that reflects its intimate electronic
structure. The usefulness of BDC resides in the fact that, based on their knowledge, it is
possible to predict dissociation branching ratios of the molecule following any physical or
chemical process if the associated energy deposit is known. In a recent work (Chabot et al
2013) we showed how it was possible to construct, on both experimental and theoretical
grounds, semiempirical BDC for carbon and hydrocarbon molecules and to use those to
predict product branching ratios for reactions of astrochemical interest. Whereas the
method has its own limitations, it allows to go beyond the usual first order prediction
consisting to affect a BR equal to 1 to the most exothermic reaction. This approximation is
common in astrochemical databases involving thousands of reactions that should somehow
be given a value. With a more realistic estimate, the improvement may be substantial.
Indeed, not only is the number of products much larger than 1 in most cases but the main
channel is not always the most exothermic one as will be seen below.

In this paper we intend to pursue the work presented in (Chabot et al 2013) whose
aim is to furnish product branching ratios to the astrochemical databases, in particular the
recent KIDA database dedicated to the interstellar chemistry (Wakelam et al 2012, Wakelam
et al 2015). In place of carbon and hydrocarbon molecules we focused on this paper on C_nN
radicals and their cations C_nN⁺ (n=2-3). Some of them have been detected in the interstellar
medium (ISM) : CCN in IRC+10216 Nebula (Anderson and Ziurys 2014), CCCN in the Taurus
dark cloud (Friberg et al 1980). Despite the large number of molecules containing both
carbon and nitrogen in the ISM, the chemistry of nitrogen containing molecules is not well
documented, exception made of the chemistry relevant to Titan's atmosphere (Dutuit et al
2013). In Loison et al 2014-a the chemistry in dark cloud chemical models of carbon chains
containing H, O, N atoms was reviewed, amongst them the C_nN⁺ families. For the latter
ones, reported values of products BR are based on calculations or estimates but not on
experiments. Generally speaking the numerous works on C_nN⁺, mostly theoretical, refer to
structure calculations in the ground (Ding et al 1998, Maclean et al 2007) or excited (Sadlej
and Roos 1991, Zhang et al 2014) electronic states but very few on the stability and
dissociation BR of these species. This is why the experimental dissociation branching ratios
we present in section 2.2 for excited C₂N⁺ and C₃N⁺ may be of fundamental interest as
well.

The plan of the paper is as follows :

In section 2 the method of construction of semiempirical BDC is presented. It covers
the general principle of the method which is summarised from (Chabot et al 2013), the
description of the experiments with the associated results and the presentation of
semiempirical BDC. In section 3 we use the obtained BDC to predict product BR for various
processes leading to the formation of C₂N(+) or C₃N(+) adducts. It includes some neutral-neutral, ion-molecule reactions, dissociative recombination (DR) process and charge exchange with He⁺ process. In each case we will compare the model predictions with the literature and what is presently reported in KIDA. In section 4 we comment the effect these new BR could have in cold cores environments and conclude.

## 2-Semiempirical method

### 2.1 Principle and validity

The principle of the method has been detailed previously (Chabot et al 2013) and only a brief summary will be given here. The semiempirical method is based on both experimental and theoretical ingredients. From the experimental point of view, we measured all fragmentation branching ratios of C₂N(+) and C₃N(+) molecules excited in high velocity collisions with Helium atoms (see § 2.2). From the theoretical side, we assumed that this fragmentation was of statistical nature, i.e only depending on the molecule internal energy. This assumption was found valid for carbon Cₙ (Martinet et al 2004) and hydrocarbon CₙH (Aguirre et al 2018) molecules. This allowed to express the fragmentation branching ratio along channel j, BRⱼ as :

$$BR_j = \int_0^\infty BDC_j(E) f(E) dE \quad (1)$$

Where f(E) is the normalised internal energy distribution of the excited molecule and BDCⱼ(E) the energy dependent dissociation branching ratio along channel j, also referred as to breakdown curve for channel j (Vekey 1996). As branching ratios, BDCⱼ verify, at each energy :

$$\sum_j BDC_j(E) = 1 \quad (2)$$

Since we measured in the experiments BRⱼ for all channels j and since f(E) was also determined following the procedure recalled in §2.2, we could extract BDCⱼ(E) for all channels j by inversion of equation (1). As explained in (Chabot et al 2013), the BDCⱼ curve was taken the following form :

$$BDC_j(E) = \frac{a_j G_j(E)}{\sum_j a_j G_j(E)} \quad (3)$$

Where Gⱼ has the generic form depicted in Figure 1.
<figure><img src="image_3.png" /><figcaption>Figure 1: Generic form of the G<sub>j</sub> function</figcaption></figure>

The significance of the G<sub>j</sub> form is the following: the probability of decaying along channel j opens at E<sub>diss</sub> (which is the minimum required energy), reaches its maximum at E<sub>sat</sub> and then start to disappear at E<sub>disap</sub> when further dissociation of one of the fragments opens. E<sub>diss</sub> and E<sub>disap</sub> quantities have been calculated using the Coupled cluster CCSD(T)/6-311++G(3df,2d) method for the molecule whose geometry was optimized at the DFT B3LYP/6-311++G(3df, 2d) level. Vibrational energies, entering in the zero-point energy correction, were performed at the same DFT level. A large number of isomers and spin states was investigated. Electronic ground states of the atoms and molecules together with symmetry of the lowest energy isomers of molecules of interest here are presented in Table 1. Similar calculations have been recently reported for hydrocarbon molecules (Sanchez et al 2016).

<table><caption>Table 1: Electronic ground States (GS) and Symmetry Point Groups (Sym.) of atoms and molecules studied in this work. Reported results are for the lowest energy isomers except CCN which is 0.08 eV above CNC and CCN<sup>+</sup> which is 1.09 eV above CNC<sup>+</sup>.</caption><thead><tr><th>species</th><th>C</th><th>N</th><th>C<sub>2</sub></th><th>CN</th><th>CNC</th><th>CCN</th><th>C<sub>3</sub></th><th>C<sub>3</sub>N</th></tr></thead><tbody><tr><td>GS</td><td><sup>3</sup>P<sub>g</sub></td><td><sup>4</sup>S<sub>u</sub></td><td><sup>1</sup>Σ<sup>+</sup><sub>g</sub></td><td><sup>2</sup>Σ<sup>+</sup></td><td><sup>2</sup>Π<sub>g</sub></td><td><sup>2</sup>Π</td><td><sup>1</sup>Σ<sup>+</sup><sub>g</sub></td><td><sup>2</sup>A'</td></tr><tr><td>Sym.</td><td>atom</td><td>atom</td><td>D<sup>∞</sup>h</td><td>C<sup>∞</sup>v</td><td>D<sup>∞</sup>h</td><td>C<sup>∞</sup>v</td><td>D<sup>∞</sup>h</td><td>Cs</td></tr><tr><td>species</td><td>C<sup>+</sup></td><td>N<sup>+</sup></td><td>C<sub>2</sub><sup>+</sup></td><td>CN<sup>+</sup></td><td>CNC<sup>+</sup></td><td>CCN<sup>+</sup></td><td>C<sub>3</sub><sup>+</sup></td><td>C<sub>3</sub>N<sup>+</sup></td></tr><tr><td>GS</td><td><sup>2</sup>P<sub>u</sub></td><td><sup>3</sup>P<sub>g</sub></td><td><sup>4</sup>Σ<sup>-</sup><sub>g</sub></td><td><sup>1</sup>Σ<sup>+</sup></td><td><sup>1</sup>Σ<sup>+</sup><sub>g</sub></td><td><sup>1</sup>Σ</td><td><sup>2</sup>B<sub>2</sub></td><td><sup>3</sup>A'</td></tr><tr><td>Sym.</td><td>atom</td><td>atom</td><td>D<sup>∞</sup>h</td><td>C<sup>∞</sup>v</td><td>D<sup>∞</sup>h</td><td>C<sup>∞</sup>v</td><td>C<sub>2</sub>v</td><td>Cs</td></tr></tbody></table>

The (E<sub>sat</sub>-E<sub>diss</sub>) and (E<sub>disap</sub>-E<sub>end</sub>) differences, which provide the steepness of the ascent and descent of the G<sub>j</sub> curve, were estimated also on theoretical grounds. We used BDC calculations performed by some of the authors using the Microcanonical Metropolis Monte Carlo (MMMC) (Diaz-Tendero et al 2006) and M<sub>3</sub>C (Aguirre et al 2017) statistical fragmentation theories as a guide to estimate these differences. Typical values are 1 to a few eV depending on the number of emitted fragments of the considered channel (Chabot et al 2013). Values of E<sub>diss</sub>, E<sub>sat</sub>, E<sub>disap</sub> and E<sub>end</sub> that enter in the construction of the G<sub>j</sub> functions are given in the appendix (Table A-1) for all channels j of each molecule.
Having constructed the G<sub>j</sub>(E) functions, the a<sub>j</sub> scaling factors were extracted by minimization between measured and predicted BR<sub>j</sub> using the j coupled equations (1)-(3). By this manner semiempirical BDCs were obtained. The errors come from experimental error bars on BR measurements, f(E) distributions and error bars on the (E<sub>sat</sub>-E<sub>diss</sub>) and (E<sub>disap</sub>-E<sub>end</sub>) values. In the Tables of section 3, we give the error bars for all channels calculated by running the minimization code with slightly different inputs : within experimental error bars for measured BRs, with different f(E) distributions compatible with the measurements and with 25% uncertainties for (E<sub>sat</sub>-E<sub>diss</sub>) and (E<sub>disap</sub>-E<sub>end</sub>) quantities.

In all cases where a comparison between experiment and model predictions was possible, a good agreement was found for products branching ratios (Chabot et al 2013). This was the case for dissociative recombination (DR) of C<sub>4</sub><sup>+</sup>, C<sub>2</sub>H<sup>+</sup> and C<sub>3</sub>H<sub>2</sub><sup>+</sup> measured nearby storage rings. Also the semiempirical BDC were found in very good agreement with BDC calculations performed within the more sophisticated Microcanonical Metropolis Monte Carlo (MMMC) method for the C<sub>n</sub> carbon clusters (see the case of C<sub>7</sub> in Chabot et al 2013).

The statistical approach is expected to work when many states contribute to the studied
process. According to Herbst (1978) this is the case in Dissociative Recombination and in
chemical reactions already in very small systems (triatomics) when concerned with
integrated properties such as products branching ratios irrespectively of their internal state.
A statistical approach appears meaningful also in the case of photodissociation by a broad
photon energy range. By contrast, photodissociation at specific energy may exhibit some
strong dynamical response (see for instance the phototodissociation of CH<sub>4</sub> near the Lyman-
α in Gans et al 2011) that the model, as all other dynamical processes, is unable to treat.

## 2.2 Experiments : dissociation BR, internal energy distribution of C<sub>2</sub>N<sup>(+)</sup> and C<sub>3</sub>N<sup>(+)</sup>

Experiments have been performed at the Tandem accelerator in Orsay with beams of C_nN^+ molecules of, respectively, 4.6 MeV (n=2) and 6.0 MeV (n=3) kinetic energy colliding with helium atoms. Both projectiles have the same impact velocity v=2.2 a.u (120 keV/amu). The exact value of v does not matter much, the main goal being to produce in the collision excited molecular species of known internal energy and to measure the associated dissociation branching ratios. It was found that dissociation branching ratios of C_n (n≤5) were not dependent on v, within experimental error bars, over the [2-4] a.u velocity range (Wohrer et al 2000). It reflects the fact that their is little change of internal energy with v in this velocity domain. In the collision, excited C_nN^+ and C_nN species were produced by electronic excitation and charge transfer processes respectively. The associated fragmentation was recorded using the dedicated AGAT spectrometer (Launoy et al 2017). Briefly, AGAT consists of a collision chamber hosting the helium jet, an electrostatic analyser for deflecting fragments according to their charge over mass ratio and a detection chamber where 10 solid-state silicon detectors, suitably positioned, intercepted the fragments. The time window for detection of fragments was [0-150ns], long enough so as to record the total fragmentation. It was theoretically checked (Diaz-Tendero 2005) for the dissociation of a C_5
cluster excited in similar conditions and analysed with the same setup. On the other hand, the evolution with n of Cn dissociative branching ratios let us deduce that it is the case at least up to sizes n=10 (Mezdari 2005). The current signals issued from the detectors were used to extract the masses of the fragments. Because the current signal shapes for N and C were very close, some of the channels could not be resolved by the shape analysis method (Chabot et al 2002). In order to get all channels resolved, we used for detection of neutrals an original CCD position sensitive detector associating the position and mass information (Chabot et al 2011).

In Tables 2-5 are presented measured dissociation branching ratios for C₂N, C₃N, C₂N⁺ and C₃N⁺ excited in HVC. Dissociation branching ratios for all channels j have been measured and reported. Their number is increasing with the size and the charge of the molecule. The rate of intact cations is not measured in the experiment. Being reported in the third columns of Tables 2-5 are the dissociation energies calculated as explained in § 2.1. These dissociation energies are computed for the lowest energy isomers of both the parent and the fragments. This is a kind of approximation since the isomer state of the fragment is not known in these experiments. Accordingly the channel notations of Tables 2-5 should be understood as isomer unresolved notations.

An instructive information comes from the number of fragments N<sub>f</sub> of the dissociation channel, reported in columns 4 of Tables 2-5. Indeed this number strongly correlates with the internal energy of the species since channels with two fragments (N<sub>f</sub>=2) typically require 6 eV whereas channels with N<sub>f</sub>=3 and N<sub>f</sub>=4 require around 12 eV and 18 eV respectively (with the exception of C₂N⁺ for which all energies are shifted by 3 eV towards higher values). Experimental BR(N<sub>f</sub>), obtained by summing experimental BR<sub>j</sub> associated to the same value of N<sub>f</sub> (see columns 5 in Tables 2-5), were used to extract the internal energy distribution of the species f(E). This was done by using equation (1) in which BR<sub>j</sub> is replaced by BR(N<sub>f</sub>) and BDC<sub>j</sub> (E) replaced by BDC<sub>N<sub>f</sub></sub>(E) (BDC<sub>N<sub>f</sub></sub>(E) is the sum of BDC<sub>j</sub> (E) for channels j having the same N<sub>f</sub> value).

An analytical form for f(E) was assumed, made of two half Gaussian distributions centered and joining at E0 and having standard deviation σL (low energy side) and σH (high energy side). This form is flexible enough to reproduce all possible shapes and physically meaningful distributions (in particular the decrease of the distribution at high energy). The values we found for E0, σL and σH in the case of the four studied molecules are reported in Table 6. They show quite broad energy distributions peaking around 5/8 eV for neutral molecules, 13/14 eV for cationic molecules and extending up to 25 eV (neutrals) and 40 eV (cations). Note that the distributions obtained with cations are perfectly explained by the excitation process of atoms composing the molecule (Mahajan et al 2018). This distribution is not expected to change more with the collision velocity, especially in the high velocity range (v≥2-3 a.u). Indeed, in ion-atom collisions, probabilities of excitation processes decrease with
but the relative populations of {n,l} final states (n, l principal and orbital angular momentum quantum numbers respectively) are basically unchanged (Kirchner et al 2000).

As a general remark on these results of Tables 2-5 we note that, within a given number of emitted fragments, channels requiring the lowest energy are having the larger BR. Exception arises for the C₃ +N channel which is having a very small BR although the dissociation energy is close to the lowest energy one (see Table 3). In fact the existence of a barrier along the C₃ + N reaction coordinate has already been invoked in the literature (Loison et al 2014-a) and estimated to be about 1 eV in KIDA (Smith and Loison 2011). We checked the height of this barrier by calculating the energy profile of the C₃N(^4A") → C₃(^1Σ⁺g) + N(^4S_u) reaction. Results are shown in Figure 2. Relative energy as a function of the reaction coordinate (a.u) computed at the B3LYP/6-311++G(3df,2p) level of theory is shown in black. The blue points in Figure 2 correspond to relative energies at the critical points in the reaction (reactant, transition state and products) computed at the CCSD(T)/6-311++G(3df,2p) level over the B3LYP geometry. The CCSD(T) calculations provide a barrier height of 0.4 eV for the reverse reaction, smaller than previously estimated. In any case this barrier is likely to reduce the C₃ + N outgoing channel reported in Table 3 since the required energy is not 5.57eV but 5.97eV.

<table><caption>Table 2: Measured dissociation branching ratios BR<sub>j</sub> of the excited C<sub>2</sub>N molecule along channel j (second column) and as a function of the number of fragments N<sub>f</sub> (last column). The BR<sub>j</sub> for intact (non fragmented) molecule is given in the first line. In the third column is reported the calculated dissociation energy of channel j i.e the minimum energetical cost for dissociation along this channel.</caption><thead><tr><th>Channel j</th><th>BR<sub>j</sub> (abs.err)</th><th>Dissociation Energy (eV)</th><th>N<sub>f</sub></th><th>BR(N<sub>f</sub>) (abs.err)</th></tr></thead><tbody><tr><td>C<sub>2</sub>N</td><td>0.36(0.02)</td><td></td><td>1</td><td>0.36(0.02)</td></tr><tr><td>CN +C</td><td>0.45(0.02)</td><td>4.89</td><td>2</td><td>0.55(0.03)</td></tr><tr><td>C<sub>2</sub> +N</td><td>0.10(0.01)</td><td>6.23</td><td></td><td></td></tr><tr><td>C +C +N</td><td>0.09(0.02)</td><td>12.21</td><td>3</td><td>0.09(0.02)</td></tr></tbody></table>

<table><caption>Table 3: same legend as Table 2 for the excited C<sub>3</sub>N molecule.</caption><thead><tr><th>Channel j</th><th>BR<sub>j</sub> (abs.err)</th><th>Dissociation Energy (eV)</th><th>N<sub>f</sub></th><th>BR(N<sub>f</sub>)(abs.err)</th></tr></thead><tbody><tr><td>C<sub>3</sub>N</td><td>0.22(0.02)</td><td></td><td>1</td><td>0.22(0.02)</td></tr><tr><td>C<sub>3</sub> +N</td><td>0.04(0.01)</td><td>5.57</td><td>2</td><td>0.46(0.05)</td></tr><tr><td>C<sub>2</sub>N +C</td><td>0.12(0.02)</td><td>6.60</td><td></td><td></td></tr><tr><td>C<sub>2</sub> +CN</td><td>0.30(0.02)</td><td>5.51</td><td></td><td></td></tr><tr><td>CN +C +C</td><td>0.17(0.03)</td><td>11.49</td><td>3</td><td>0.29(0.05)</td></tr><tr><td>C<sub>2</sub> +N +C</td><td>0.12(0.02)</td><td>12.82</td><td></td><td></td></tr><tr><td>N +C +C +C</td><td>0.03(0.01)</td><td>18.82</td><td>4</td><td>0.03(0.01)</td></tr></tbody></table>
<table><caption>Table 4: Measured dissociation branching ratios BR<sub>j</sub> of the excited C<sub>2</sub>N<sup>+</sup> molecule along channel j (second column) and as a function of the number of fragments N<sub>f</sub> (last column). In the third column is reported the calculated dissociation energy of channel j i.e the minimum energetical cost for dissociation along this channel.</caption><thead><tr><th>Channel j</th><th>BR<sub>j</sub> (abs.err)</th><th>Dissociation Energy (eV)</th><th>N<sub>f</sub></th><th>BR(N<sub>f</sub>)(abs.err)</th></tr></thead><tbody><tr><td>CN +C<sup>+</sup></td><td>0.218(0.015)</td><td>6.39</td><td rowspan="4">2</td><td rowspan="4">0.47(0.03)</td></tr><tr><td>C +CN<sup>+</sup></td><td>0.145(0.007)</td><td>8.86</td></tr><tr><td>C<sub>2</sub> +N<sup>+</sup></td><td>0.025(0.002)</td><td>11.02</td></tr><tr><td>N +C<sub>2</sub><sup>+</sup></td><td>0.086(0.004)</td><td>8.24</td></tr><tr><td>C +C +N<sup>+</sup></td><td>0.112(0.005)</td><td>17.01</td><td rowspan="2">3</td><td rowspan="2">0.53(0.03)</td></tr><tr><td>C +N +C<sup>+</sup></td><td>0.414(0.03)</td><td>13.71</td></tr></tbody></table>

<table><caption>Table 5: same legend as Table 4 for the excited C<sub>3</sub>N<sup>+</sup> molecule</caption><thead><tr><th>Channel j</th><th>BR<sub>j</sub> (abs.err)</th><th>Dissociation Energy (eV)</th><th>N<sub>f</sub></th><th>BR(N<sub>f</sub>)(abs.err)</th></tr></thead><tbody><tr><td>C<sub>2</sub>N<sup>+</sup> +C</td><td>0.148(0.003)</td><td>4.52</td><td rowspan="6">2</td><td rowspan="6">0.40(0.03)</td></tr><tr><td>C<sub>2</sub><sup>+</sup> +CN</td><td>0.086(0.007)</td><td>5.43</td></tr><tr><td>C<sup>+</sup> +C<sub>2</sub>N</td><td>0.064(0.005)</td><td>6.02</td></tr><tr><td>C<sub>3</sub><sup>+</sup> +N</td><td>0.052(0.002)</td><td>5.45</td></tr><tr><td>CN<sup>+</sup> +C<sub>2</sub></td><td>0.033(0.003)</td><td>7.40</td></tr><tr><td>N<sup>+</sup> +C<sub>3</sub></td><td>0.012(0.0015)</td><td>8.28</td></tr><tr><td>C<sup>+</sup> +CN +C</td><td>0.14(0.01)</td><td>10.91</td><td rowspan="5">3</td><td rowspan="5">0.41(0.03)</td></tr><tr><td>C<sup>+</sup> +C<sub>2</sub> +N</td><td>0.076(0.006)</td><td>12.25</td></tr><tr><td>C<sub>2</sub><sup>+</sup> +N +C</td><td>0.108(0.008)</td><td>12.76</td></tr><tr><td>CN<sup>+</sup> +C+C</td><td>0.053(0.005)</td><td>13.38</td></tr><tr><td>N<sup>+</sup> +C<sub>2</sub> +C</td><td>0.038(0.003)</td><td>15.54</td></tr><tr><td>C<sup>+</sup> +N+C+C</td><td>0.155(0.011)</td><td>18.23</td><td rowspan="2">4</td><td rowspan="2">0.19(0.02)</td></tr><tr><td>N<sup>+</sup> +C+C+C</td><td>0.035(0.003)</td><td>21.53</td></tr></tbody></table>

<table><caption>Table 6: Parameters of the internal energy distributions (see text) of C<sub>2</sub>N, C<sub>3</sub>N, C<sub>2</sub>N<sup>+</sup> and C<sub>3</sub>N<sup>+</sup> molecules fragmenting along Tables 2-5.</caption><thead><tr><th></th><th>E<sub>0</sub> (abs.err)</th><th>σ<sub>L</sub>(abs.err)</th><th>σ<sub>R</sub>(abs.err)</th></tr><tr><th></th><th>eV</th><th>eV</th><th>eV</th></tr></thead><tbody><tr><td>C<sub>2</sub>N</td><td>5(0.5)</td><td>3(1)</td><td>6(0.5)</td></tr><tr><td>C<sub>3</sub>N</td><td>8.5(0.5)</td><td>6.5(1)</td><td>7(1)</td></tr><tr><td>C<sub>2</sub>N<sup>+</sup></td><td>13.5(1)</td><td>4(1)</td><td>7(1)</td></tr><tr><td>C<sub>3</sub>N<sup>+</sup></td><td>13(1)</td><td>8(1)</td><td>9(1)</td></tr></tbody></table>
domain » and far from curve crossings. In case there is an internal energy distribution f(E_a) associated to the studied process, BR are obtained using equation (1).

<figure><img src="image_4.png" /><figcaption>Figure 3 : Semiempirical BDC for C₂N, C₃N, C₂N⁺ and C₃N⁺ molecules</figcaption></figure>

## 3- Semiempirical products branching ratios

Using BDCs of Figure 3, products branching ratios for physical and chemical processes leading to excited adducts C₂N⁺ and C₃N⁺ of known internal energy E_a were predicted. The processes we considered below are neutral-neutral reactions, ion-molecule reactions, dissociative recombination (DR) and charge exchange reaction with He⁺.

In the calculation of the internal energy of the adduct E_a, we supposed that the reaction occurred between reactants in their electronic ground states towards the adduct in its electronic ground state. This energy is equal to the dissociation energy of the adduct in its electronic ground state towards reactants in their electronic ground states (reverse pathway, see equation (4)). The E_a energies are reported in bold in Tables 7-10. Similarly, the exothermicity ΔE of the reaction (reactants to products) was calculated by supposing that the products were in their electronic ground states. ΔE has been calculated by difference
between the adduct internal energy and the dissociation energy of the adduct towards the considered outgoing channel (or the dissociation energy increased by a barrier height when pertinent), see equation (5). Exothermicities are reported in the last column of Tables 7-10; positive values correspond to exothermic reactions.

$$E_a = E_{diss}(\text{adduct} \rightarrow \text{reactants}) \qquad (4)$$

$$\Delta E = E_a - E_{diss} (\text{adduct} \rightarrow \text{products}) \qquad (5)$$

These assumptions are not always valid. Ground state to ground state reaction is sometimes forbidden, for spin conservation violation or symmetry breaking reasons. We checked, for all reactions, whether the reaction between reactants and products was spin allowed and whether the adduct was possibly the lowest energy isomer of the molecule in its electronic ground state. For that, we used the electronic ground states characteristics of atoms and molecules involved in the processes (presented in Table 1) and the known selection rules (see appendix B of Chabot et al 2013). We indicate in the legend of Tables 7-10 when the reaction is spin forbidden (¶) and also when spin and/or symmetry considerations preclude the formation as an adduct of the lowest energy isomer of the molecule in its electronic ground state (*). In the first case (¶), since the model is not able to predict whether a spin forbidden reaction will be closed, slowed down or will occur with a normal rate (Schwarz 2004) we introduced this uncertainty in the error bars of the predicted values. We recommend to use in chemical models the predicted values with the associated large unsymmetrical error bars given in Tables 7-10. When the adduct cannot be the lowest energy isomer in its electronic ground state, we checked whether the adduct could possibly be a close-in-energy isomer of the molecule in its electronic ground state (calculations of many isomers were performed as indicated before). In all cases an excited isomer of the adduct was found to be compatible with spin and symmetry considerations. Then, symmetry considerations never precluded strictly the reaction to occur. We recommend to use the predicted branching ratios for these reactions identified with the * sign.

### 3.1 Neutral-Neutral reactions

Reactions between neutral reactants leading to intermediate C₂N and C₃N adducts are reported in Table 7. In addition to the adduct internal energy Eₐ and reaction exothermicities ΔE, given in column 5 and 6 respectively, we present in column 3 semiempirical product branching ratios predicted by the model and in column 4 values found in the KIDA database.

Considering reaction with C₂ + N reactants we note that a single outgoing channel different from the entrance one, C + CN, is open so that the BR of this one has to be 1. For this reaction the adduct cannot be C₂N in the lowest energy isomer and in its electronic ground state for spin and symmetry reasons. According to our calculations of isomers, there exists an isomer having a ⁴A" (Cs) ground electronic state, situated 1.107eV above the lowest
energy one (CNC in the $^2\Pi_g$ state), through which the reaction could occur. The complete pathway of this reaction has been recently elucidated (Loison et al 2014-b).

<table><caption>Table 7: Branching ratios (BR) for Neutral-Neutral reactions. $E_a$ represents the internal energy of the neutral adduct and $ΔE$ the exothermicity of the reaction. *: the reaction cannot proceed through the electronic ground state of the adduct lowest energy isomer.</caption><thead><tr><th>Reactants</th><th>Products</th><th>Model BR (abs.err)</th><th>KIDA BR</th><th>E<sub>a</sub> (eV)</th><th>ΔE (eV)</th></tr></thead><tbody><tr><td>C<sub>2</sub> + N</td><td>C+CN*</td><td>1</td><td>1</td><td>6.23</td><td>1.34</td></tr><tr><td rowspan="2">CNC+C</td><td>C<sub>2</sub>+CN</td><td>0.90(0.05)</td><td></td><td rowspan="2">6.60</td><td>1.09</td></tr><tr><td>C<sub>3</sub>+N*</td><td>0.10(0.05)</td><td></td><td>0.63</td></tr><tr><td rowspan="2">CCN+C</td><td>C<sub>2</sub>+CN</td><td>0.90(0.05)</td><td>1</td><td rowspan="2">6.68</td><td>1.17</td></tr><tr><td>C<sub>3</sub>+N*</td><td>0.10(0.05)</td><td></td><td>0.71</td></tr></tbody></table>

We consider next the CNC + C and CCN + C reactions because CCN + C is the reaction treated in KIDA. It is possible to treat different reactants isomers within the model since, depending on the isomer, we may get different $E_a$ values and then different model predictions. By contrast, because the experimental results of §2.2 are isomer unresolved, we have generally no access to the products isomers. Model predictions are identical between the two reactions and give $C_2 + CN$ as very dominant, in accordance with KIDA. Prediction for $C_3 + N$ is associated with a large error bar so that it is difficult to estimate the role of the barrier height of 0.4 eV in this reaction. Note that without barrier the model prediction for $C_3 + N$ is 0.11 (0.03). Although a minor channel we may mention that the reaction leading to $C_3 + N$ products cannot occur through the electronic ground state of the $C_3N$ lowest energy isomer for spin and symmetry considerations. But the reaction can proceed through the $^4A''$ (Cs) state of an excited $C_3N$ isomer situated, according to our calculations, 3.90 eV above the lowest energy one. The $C_3 + N \rightarrow C_2 + CN$ reaction has not been reported in the Table 7 because this spin forbidden reaction is unlikely to occur due to the barrier of 0.4 eV preventing the addition of N to $C_3$.

## 3.2 Ion-molecule reactions

In Table 8 are reported model predictions for ion molecule reactions leading to intermediate $C_2N^+$ and $C_3N^+$ adducts. As mentioned before the isomer state of the products cannot be derived from the model; unresolved isomer product is indicated in brackets (for instance [$C_2N^+$]). We note that, for a given couple of reactants, many outgoing channels with significant branching ratios are predicted by the model, at variance with KIDA where often one channel only, corresponding to the largest exothermicity, is supposed to be populated. This channel is sometimes corresponding to our main outgoing channel (case of $CN^+ + C$ reactants for instance) but sometimes not (cases of $C_2 + N^+$ and $CN^+ + C_2$ reactants). The $C^+$ +
CCN reaction is of interest because predictions for two products channels are reported in KIDA, based on the work of (Loison et al 2014-a). In this work, DFT calculations showed no barrier for CCCN⁺ and CCNC⁺ formation. Calculated branching ratios are in good agreement with the model predictions for [C₂N⁺]⁺C and C₂⁺ +CN products. The reaction leading to C₃⁺ +N products, of rather small branching ratio (~10% as predicted by the model), is not considered in (Loison et al 2014-a).

<table><caption>Table 8: Branching ratios (BR) for Ion-molecule reactions. Eₐ represents the internal energy of the ionic adduct and ΔE the exothermicity of the reaction. ⚫: this value corresponds to the sum of the two isomers CNC⁺ and CCN⁺. *: the reaction cannot proceed through the electronic ground state of the adduct lowest energy isomer; ¶: the reaction is spin forbidden for ground state reactants towards ground state products.</caption><thead><tr><th>Reactants</th><th>Products</th><th>Model BR (abs.err)</th><th>KIDA BR</th><th>E<sub>a</sub> (eV)</th><th>ΔE (eV)</th></tr></thead><tbody><tr><td>C<sub>2</sub><sup>+</sup> + N</td><td>C<sup>+</sup> + CN</td><td>1</td><td>1</td><td>8.24</td><td>1.85</td></tr><tr><td rowspan="2">CN<sup>+</sup> + C</td><td>C<sup>+</sup> + CN*</td><td>0.72(+0.07/-0.05)</td><td rowspan="2">1</td><td rowspan="2">8.86</td><td>2.47</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + N*</td><td>0.28(+0.05/-0.07)</td><td>0.62</td></tr><tr><td rowspan="3">N<sup>+</sup> + C<sub>2</sub></td><td>CN<sup>+</sup> + C*</td><td>0.40(0.05)</td><td rowspan="3">1</td><td rowspan="3">11.02</td><td>2.16</td></tr><tr><td>C<sup>+</sup> + CN*</td><td>0.39(0.05)</td><td>4.63</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + N*</td><td>0.21(0.04)</td><td>2.78</td></tr><tr><td>C<sub>3</sub><sup>+</sup> + N</td><td>[C<sub>2</sub>N<sup>+</sup>] + C</td><td>1</td><td></td><td>5.45</td><td>0.93</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + CN</td><td>[C<sub>2</sub>N<sup>+</sup>] + C</td><td>1</td><td></td><td>5.43</td><td>0.91</td></tr><tr><td rowspan="3">C<sup>+</sup> + CNC</td><td>[C<sub>2</sub>N<sup>+</sup>] + C</td><td>0.58(0.06)</td><td rowspan="3"></td><td rowspan="3">6.02</td><td>1.50</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + CN</td><td>0.30(0.06)</td><td>0.59</td></tr><tr><td>C<sub>3</sub><sup>+</sup> + N</td><td>0.12(0.04)</td><td>0.57</td></tr><tr><td rowspan="3">C<sup>+</sup> + CCN</td><td>[C<sub>2</sub>N<sup>+</sup>] + C</td><td>0.58(0.06)</td><td rowspan="3">0.7<sup>+</sup><br>0.3</td><td rowspan="3">6.10</td><td>1.58</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + CN</td><td>0.30(0.06)</td><td>0.67</td></tr><tr><td>C<sub>3</sub><sup>+</sup> + N</td><td>0.12(0.04)</td><td>0.65</td></tr><tr><td rowspan="3">CN<sup>+</sup> + C<sub>2</sub></td><td>[C<sub>2</sub>N<sup>+</sup>] + C<sup>¶</sup></td><td>0.35(+0.03/-0.35)</td><td rowspan="3">1</td><td rowspan="3">7.40</td><td>2.88</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + CN<sup>¶</sup></td><td>0.28(+0.03/-0.28)</td><td>1.97</td></tr><tr><td>C<sup>+</sup> + [C<sub>2</sub>N]<sup>*</sup></td><td>0.23(+0.77/-0.03)</td><td>1.38</td></tr><tr><td rowspan="3">N<sup>+</sup> + C<sub>3</sub></td><td>C<sub>3</sub><sup>+</sup> + N<sup>¶</sup></td><td>0.12(+0.02/-0.12)</td><td></td><td></td><td>1.95</td></tr><tr><td>[C<sub>2</sub>N<sup>+</sup>] + C</td><td>0.33(+0.15/-0.04)</td><td rowspan="3"></td><td rowspan="3">8.28</td><td>3.76</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + CN</td><td>0.25(+0.15/-0.03)</td><td>2.85</td></tr><tr><td>C<sup>+</sup> + [C<sub>2</sub>N]</td><td>0.22(+0.14/-0.03)</td><td>2.26</td></tr><tr><td rowspan="2"></td><td>C<sub>3</sub><sup>+</sup> + N</td><td>0.11(+0.13/-0.02)</td><td rowspan="2"></td><td rowspan="2"></td><td>2.83</td></tr><tr><td>CN<sup>+</sup> + C<sub>2</sub><sup>¶</sup></td><td>0.09(+0.02/-0.09)</td><td>0.88</td></tr></tbody></table>
For a few cases in Table 8 (identified by the sign ¶), reaction from reactants in their electronic ground states towards products in their electronic ground states is spin forbidden. As explained before uncertainties on these reactions are completely included in the error bars.

As in the case of neutral-neutral reactions, the intermediate complex involved in the reaction could sometimes not be the adduct of Table 1. This concerned six channels, identified by the * sign. In all cases an adduct satisfying spin and symmetry considerations was found. Those adducts were : ³B₂(C2v), situated 2 eV above the adduct of Table 1, for the five first reactions stamped with * leading to a C₂N⁺ adduct ; ¹A'(Cs), situated 0.6 eV above the adduct of Table 1, for the last reaction stamped with * leading to a C₃N⁺ adduct.

### 3.3 Dissociative recombination (DR)

In Table 9 are reported branching ratios predictions following DR in electron- CNC⁺, electron-CCN⁺ and electron-C₃N⁺ collisions. The internal energy of the neutral adduct Eₐ has been taken equal to its ionization potential (IP), assuming that the DR process proceeds mainly with electron kinetic energy small as compared to IP (Mitchell 2015).

Although the internal energy of the neutral adduct differs in CNC⁺ +e⁻ and CCN⁺ +e⁻ reactions, it is seen from Figure 3 that both reactions lead to equal model predictions for BR. This is in agreement with estimations of (Loison et al 2014-a) reported in KIDA. The model predicts a strong dominance of the C+CN products channel, as reported in KIDA.

<table><caption>Table 9: Branching ratios (BR) for Dissociative Recombination. Eₐ represents the internal energy of the neutral adduct and ΔE the exothermicity of the reaction. ¶: the reaction is spin forbidden for ground state reactants towards ground state products.</caption><thead><tr><th>Reactants</th><th>Products</th><th>Model BR (abs.err)</th><th>KIDA BR</th><th>E<sub>a</sub> (eV)</th><th>ΔE (eV)</th></tr></thead><tbody><tr><td rowspan="2">CNC<sup>+</sup> +e<sup>-</sup></td><td>C+CN</td><td>0.77(+0.23/-0.03)</td><td>0.95</td><td rowspan="2">9.66</td><td>4.77</td></tr><tr><td>C<sub>2</sub> +N<sup>¶</sup></td><td>0.23(+0.03/-0.23)</td><td>0.05</td><td>3.43</td></tr><tr><td rowspan="2">CCN<sup>+</sup> +e<sup>-</sup></td><td>C+CN</td><td>0.77(+0.23/-0.03)</td><td>0.95</td><td rowspan="2">10.67</td><td>5.78</td></tr><tr><td>C<sub>2</sub> +N<sup>¶</sup></td><td>0.23(+0.03/-0.23)</td><td>0.05</td><td>4.44</td></tr><tr><td rowspan="4">C<sub>3</sub>N<sup>+</sup> +e<sup>-</sup></td><td>C<sub>2</sub>+CN</td><td>0.56(0.05)</td><td rowspan="4">1</td><td rowspan="4">11.76</td><td>6.25</td></tr><tr><td>C +[C<sub>2</sub>N]</td><td>0.32(0.03)</td><td>5.16</td></tr><tr><td>C<sub>3</sub> +N</td><td>0.09(0.02)</td><td>5.79</td></tr><tr><td>C+C+CN</td><td>0.03(0.02)</td><td>0.27</td></tr></tbody></table>

For C₃N⁺ + e⁻, the main products are found to be C₂ +CN as predicted by the model and reported in KIDA. The role of the barrier along the C₃ + N outgoing channel is found rather small since, without barrier, the predicted BR is 0.07 (0.02). It is in any case a small outgoing channel as compared to the C + [C₂N] of near exothermicity. This last reaction has a BR far from being negligible and should then be considered in databases.
3.4 Charge exchange reactions with He⁺

In Table 10 products of charge exchange between CNC, CCN, C₃N and He⁺ are reported. As well known from ion-atom collisions, charge exchange at low velocity occurs between electronic states of equal energy (energy matching) (Olson 1981). The same is found for ion-molecule collision as shown for instance in a recent investigation of the charge exchange reaction between He⁺ and dimethyl ether (Cernuto et al 2017). Helium, which has a large IP (24.6 eV), captures then an electron from an inner valence shell of the molecule, resulting in a large internal energy of the molecular ion ΔIP= IP (He)-IP (molecule) (Chabot et al 2010). The adducts of interest here are the excited molecular ions CNC⁺, CCN⁺ and C₃N⁺ after charge exchange and not the intermediate complexes [C₂NHe⁺] or [C₃NHe⁺] that are formed during the collision. Accordingly we have for those Eₐ=ΔIP. We used our calculated IP of CNC, CCN and C₃N (equal to 9.66 eV, 10.67 eV and 11.76 eV respectively<sup>footnote 1)</sup>) in order to extract Eₐ values, reported in bold in column 5 of Table 10. Exothermicities of the reactions ΔE were calculated with equation (5) as before.

<table><caption>Table 10: Branching ratios (BR) following charge exchange reactions in collisions of CNC, CCN and C₃N with He⁺. Eₐ values give the internal energies of the adducts CNC⁺, CCN⁺ and C₃N⁺ after charge exchange and ΔE are the exothermicities of the reactions.</caption><thead><tr><th>Reactants</th><th>Products (+ He)</th><th>Model BR (abs.err)</th><th>KIDA BR</th><th>E<sub>a</sub> (eV)</th><th>ΔE (eV)</th></tr></thead><tbody><tr><td rowspan="5">CNC + He<sup>+</sup></td><td>C<sup>+</sup> + C + N</td><td>0.30(0.15)</td><td></td><td rowspan="5">14.93</td><td>1.22</td></tr><tr><td>C<sup>+</sup> + CN</td><td>0.25(0.10)</td><td></td><td>8.54</td></tr><tr><td>CN<sup>+</sup> + C</td><td>0.25(0.07)</td><td></td><td>6.07</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + N</td><td>0.15(0.05)</td><td></td><td>6.69</td></tr><tr><td>N<sup>+</sup> + C<sub>2</sub></td><td>0.05(0.02)</td><td></td><td>3.91</td></tr><tr><td rowspan="5">CCN + He<sup>+</sup></td><td>C<sup>+</sup> + C + N</td><td>0.0</td><td></td><td rowspan="5">13.92</td><td>0.21</td></tr><tr><td>C<sup>+</sup> + CN</td><td>0.38(0.05)</td><td>1</td><td>7.53</td></tr><tr><td>CN<sup>+</sup> + C</td><td>0.38(0.05)</td><td></td><td>5.06</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + N</td><td>0.20(0.03)</td><td></td><td>5.68</td></tr><tr><td>N<sup>+</sup> + C<sub>2</sub></td><td>0.04(0.02)</td><td></td><td>2.90</td></tr><tr><td rowspan="7">C<sub>3</sub>N + He<sup>+</sup></td><td>C<sup>+</sup> + C + CN</td><td>0.25(0.04)</td><td></td><td rowspan="7">12.81</td><td>1.90</td></tr><tr><td>C<sub>3</sub><sup>+</sup> + N</td><td>0.18(0.04)</td><td></td><td>7.36</td></tr><tr><td>[C<sub>2</sub>N<sup>+</sup>] + C</td><td>0.15(0.07)</td><td></td><td>8.29</td></tr><tr><td>CN<sup>+</sup> + C<sub>2</sub></td><td>0.14(0.03)</td><td></td><td>5.41</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + CN</td><td>0.12(0.06)</td><td>1</td><td>7.38</td></tr><tr><td>C<sup>+</sup> + [C<sub>2</sub>N]</td><td>0.09(0.05)</td><td></td><td>6.79</td></tr><tr><td>N<sup>+</sup> + C<sub>3</sub></td><td>0.03(0.01)</td><td></td><td>4.53</td></tr><tr><td></td><td>C<sup>+</sup> + C<sub>2</sub> + N</td><td>0.02(0.01)</td><td></td><td></td><td>0.56</td></tr></tbody></table>

Due to the large internal energies of the molecular ions, fragmentation into three fragments is rather important, exception made of CCN⁺ whose internal energy (13.92 eV) is close from
the opening of the first three-fragment channel ($C^+ + C + N$ that requires 13.71 eV). That was already noted in $C_n$, $C_nH$ and $C_3H_2 + He^+$ reactions (Chabot et al 2013) whereas, from mass spectra and the abundance of $HCO^+$, authors from (Cernuto et al 2017) could estimate a very large contribution of channels with three or four fragments as well. Fragmentation along channels with three fragments has a large energetic cost. Accordingly the corresponding exothermicity of the reaction is rather small. This behaviour is apparently non statistical. In fact within a pure statistical fragmentation process it is found that the system prefers to spend the internal energy for breaking chemical bonds (producing more fragments) rather than by dissipating the energy in fragment's internal energy or fragments kinetic energy (Diaz-Tendero et al 2006). In that respect channels reported in KIDA as main products and corresponding to maximum exothermicities (two-fragments channels) are out of the game. The database should be updated for these charge exchange reactions.

## 4-Discussion about the astrophysical implications and conclusions

Using the Nautilus astrochemical model, we simulated the expected abundances of $C_nN$ molecules in cold cores conditions. Nautilus is a gas-grain astrochemical model. Based on micro-physical parameters (such as rate coefficients for gas-phase reactions), this numerical model computes the species abundances in interstellar conditions as a function of time by solving a set of kinetic differential equations. The model includes a large number of chemical processes in the gas-phase. It also takes into account the interactions with the interstellar grains (adsorption on the surfaces and desorption from the surfaces) and the reactions at the surface of the grains (treated with the Langmuir-Hinselwood approach). The model is described in details in Ruaud et al. (2016) while the chemical parameters are described in Loison et al. (2017). For this work, the gas-phase network has been updated with the new branching ratios presented in this paper. We have run the model for typical cold core conditions, i.e. a gas and dust temperature of 10 K, a proton density of $2 \times 10^5 \text{cm}^{-3}$, and a high visual extinction preventing any direct photochemistry. Figure 4 presents the results of our simulations for CN, CCN, $C_3N$, and $C_5N$. In fact, under cold core conditions, the model results are not affected by the chemical updates. Indeed, species having an abundance of more than $10^{-12}$ (with respect to H) were modified by less than 5% at all times, which is not significant. One interesting point however is that the CCN predicted abundance is the same or higher as the ones of the two other detected species (i.e. $C_3N$ and $C_5N$). This molecule has been detected in the circumstellar envelop of IRC + 10216 (Anderson & Ziurys 2014) where the conditions are different from cold cores but, as far as we know, not in cold cores. We however could not find any published upper limits. In our model, CCN is formed by the dissociative recombination of $CH_2CN^+$ and $CH_3CN^+$, and the neutral-neutral reaction $N + \text{CCH} -> \text{H} + \text{CCN}$. Note that errors on the predicted abundances of Figure 4 may be important due to uncertainties on the rates of contributing processes. Their estimates would require an extensive work, that goes beyond the scope of this paper. On the other hand,
observational constraints on CCN abundance in cold cores would be of great help to constrain the model.

In this paper, we have presented new branching ratios for a number of reactions involved in the chemistry of the interstellar molecules C<sub>n</sub>N. Despite the fact that the new values do not significantly change the model results, they will be included in the KIDA databases and should be included in current astrochemical models. In fact, because of the non-linear behavior of these models, the importance of the reactions depends on the specific network used and the physical conditions (Wakelam et al. 2010).

<figure><img src="image_5.png" /><figcaption>Figure 4: Species abundances computed by our astrochemical model as a function of time for cold core conditions. The horizontal lines are the observed values in the cold core TMC-1 (Cyanopolyyne Peak) (refs: Crutcher et al 1984 for CN, Ohishi & Kaifu 1998 for C<sub>3</sub>N, Guélin et al. 1998 for C<sub>5</sub>N).</figcaption></figure>

**Acknowledgments:**

VW research is funded by an ERC Starting Grant (3DICE, grant agreement 336474). The authors acknowledge the support of the CNRS program Physique et Chimie du Milieu Interstellaire (PCMI) co-funded by the Centre National d'Etudes Spatiales (CNES) and of the P2IO LabEx (ANR-10-LABX-0038) within the framework of the emblematic program « Evolution de la matière du milieu interstellaire aux exoplanètes avec le JWST ». TL is funded by a fellowship of the Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture-FRIA.

**Footnotes :**1: Recent measurements give 9.78 (0.04) eV and 10.82 (0.03) eV for CNC and CCN molecules respectively (Garcia et al 2017).
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Appendix

In this appendix, we give in the Table A-1 the values of E<sub>diss</sub>, E<sub>sat</sub>, E<sub>disap</sub> and E<sub>end</sub> used for the construction of the G<sub>j</sub> functions for all j channels of each molecule. These quantities are calculated or derived from theoretical work (see text).

<table><caption>Table A-1: Values of the E<sub>diss</sub>, E<sub>sat</sub>, E<sub>disap</sub> and E<sub>end</sub> quantities entering in the G<sub>j</sub> functions for all channels j of each molecule.</caption><thead><tr><th>Molecule</th><th>Channel j</th><th>E<sub>diss</sub> (eV)</th><th>E<sub>sat</sub> (eV)</th><th>E<sub>disap</sub>(eV)</th><th>E<sub>end</sub> (eV)</th></tr></thead><tbody><tr><td rowspan="4">C<sub>2</sub>N</td><td>C<sub>2</sub>N</td><td>0</td><td>0.01</td><td>4.89</td><td>5.39</td></tr><tr><td>CN + C</td><td>4.89</td><td>5.39</td><td>12.21</td><td>13.71</td></tr><tr><td>C<sub>2</sub> + N</td><td>6.23</td><td>6.73</td><td>12.21</td><td>13.71</td></tr><tr><td>C + C + N</td><td>12.21</td><td>13.71</td><td>40.00</td><td>42.5</td></tr><tr><td rowspan="6">C<sub>3</sub>N</td><td>C<sub>3</sub>N</td><td>0</td><td>0.005</td><td>5.51</td><td>5.515</td></tr><tr><td>C<sub>3</sub> + N</td><td>5.97</td><td>6.47</td><td>12.82</td><td>14.32</td></tr><tr><td>C<sub>2</sub> + CN</td><td>5.51</td><td>6.01</td><td>11.49</td><td>12.99</td></tr><tr><td>C<sub>2</sub> + N + C</td><td>6.60</td><td>7.1</td><td>11.49</td><td>12.99</td></tr><tr><td>CN + C + C</td><td>11.49</td><td>12.99</td><td>18.82</td><td>21.32</td></tr><tr><td>C<sub>2</sub> + N + C</td><td>12.82</td><td>14.32</td><td>18.82</td><td>21.32</td></tr><tr><td rowspan="5">C<sub>2</sub>N<sup>+</sup></td><td>N + C + C</td><td>18.82</td><td>21.32</td><td>40.00</td><td>42.5</td></tr><tr><td>CN + C<sup>+</sup></td><td>6.39</td><td>6.89</td><td>13.71</td><td>15.21</td></tr><tr><td>N + C<sub>2</sub><sup>+</sup></td><td>8.24</td><td>8.74</td><td>13.71</td><td>15.21</td></tr><tr><td>C + CN<sup>+</sup></td><td>8.86</td><td>9.36</td><td>13.71</td><td>15.21</td></tr><tr><td>C<sub>2</sub> + N<sup>+</sup></td><td>11.02</td><td>11.52</td><td>17.01</td><td>18.51</td></tr><tr><td rowspan="5">C<sub>3</sub>N<sup>+</sup></td><td>C + N + C<sup>+</sup></td><td>13.71</td><td>15.21</td><td>40.00</td><td>42.5</td></tr><tr><td>C + N<sup>+</sup> + C</td><td>17.01</td><td>18.51</td><td>40.00</td><td>42.5</td></tr><tr><td>C<sub>2</sub>N<sup>+</sup> + C</td><td>4.52</td><td>4.57</td><td>10.91</td><td>12.41</td></tr><tr><td>C<sub>3</sub><sup>+</sup> + N</td><td>5.45</td><td>5.95</td><td>12.25</td><td>13.75</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + CN</td><td>5.43</td><td>5.93</td><td>10.91</td><td>12.41</td></tr><tr><td rowspan="10">C<sub>2</sub>N<sup>+</sup></td><td>C<sup>+</sup> + C<sub>2</sub>N</td><td>6.02</td><td>6.52</td><td>10.91</td><td>12.41</td></tr><tr><td>CN<sup>+</sup> + C<sub>2</sub></td><td>7.40</td><td>7.90</td><td>12.25</td><td>13.75</td></tr><tr><td>N<sup>+</sup> + C<sub>3</sub></td><td>8.28</td><td>8.78</td><td>15.54</td><td>17.04</td></tr><tr><td>C<sup>+</sup> + C + CN</td><td>10.91</td><td>12.41</td><td>18.23</td><td>20.73</td></tr><tr><td>C<sup>+</sup> + C<sub>2</sub> + N</td><td>12.25</td><td>13.75</td><td>18.23</td><td>20.73</td></tr><tr><td>C<sub>2</sub><sup>+</sup> + N + C</td><td>12.76</td><td>14.26</td><td>18.23</td><td>20.73</td></tr><tr><td>CN<sup>+</sup> + C + C</td><td>13.38</td><td>14.88</td><td>18.23</td><td>20.73</td></tr><tr><td>N<sup>+</sup> + C<sub>2</sub> + C</td><td>15.54</td><td>17.04</td><td>21.53</td><td>24.03</td></tr><tr><td>C<sup>+</sup> + N + C + C</td><td>18.23</td><td>20.73</td><td>40.00</td><td>43.5</td></tr><tr><td>N<sup>+</sup> + C + C + C</td><td>21.53</td><td>24.03</td><td>40.00</td><td>43.5</td></tr></tbody></table>