# Revised gas-phase formation network of methyl cyanide: the origin of methyl cyanide and methanol abundance correlation in hot corinos

Lisa Giani, Cecilia Ceccarelli, Luca Mancini, Eleonora Bianchi, Fernando

Pirani, Marzio Rosi, Nadia Balucani

► To cite this version:

Lisa Giani, Cecilia Ceccarelli, Luca Mancini, Eleonora Bianchi, Fernando Pirani, et al.. Revised gas-phase formation network of methyl cyanide: the origin of methyl cyanide and methanol abundance correlation in hot corinos. Monthly Notices of the Royal Astronomical Society, 2025, 526 (3), pp.4535-4556. 10.1093/mnras/stad2892. hal-04960554

HAL Id: hal-04960554

https://hal.science/hal-04960554v1

Submitted on 13 Aug 2025

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# Revised gas-phase formation network of methyl cyanide: the origin of methyl cyanide and methanol abundance correlation in hot corinos

Lisa Giani<sup>1,2*</sup> Cecilia Ceccarelli<sup>1,★</sup> Luca Mancini,<sup>2</sup> Eleonora Bianchi,<sup>3</sup> Fernando Pirani,<sup>2,4</sup> Marzio Rosi<sup>4</sup> and Nadia Balucani<sup>1,2,★</sup>

Accepted 2023 September 20. Received 2023 September 12; in original form 2023 July 3

## ABSTRACT

Methyl cyanide (CH3CN) is one of the most abundant and widely spread interstellar complex organic molecules (iCOMs). Several studies found that, in hot corinos, methyl cyanide and methanol abundances are correlated suggesting a chemical link, often interpreted as a synthesis of them on the interstellar grain surfaces. In this article, we present a revised network of the reactions forming methyl cyanide in the gas phase. We carried out an exhaustive review of the gas-phase CH3CN formation routes, propose two new reactions, and performed new quantum mechanics calculations of several reactions. We found that 13 of the 15 reactions reported in the databases KIDA and UDfA have incorrect products and/or rate constants. The new corrected reaction network contains 10 reactions leading to methyl cyanide. We tested the relative importance of those reactions in forming CH3CN using our astrochemical model. We confirm that the radiative association of CH3⁺ and HCN, forming CH3CNH⁺, followed by the electron recombination of CH3CNH⁺, is the most important CH3CN formation route in both cold and warm environments, notwithstanding that we significantly corrected the rate constants and products of both reactions. The two newly proposed reactions play an important role in warm environments. Finally, we found a very good agreement between the CH3CN predicted abundances with those measured in cold (~10 K) and warm (~90 K) objects. Unexpectedly, we also found a chemical link between methanol and methyl cyanide via the CH3⁺ ion, which can explain the observed correlation between the CH3OH and CH3CN abundances measured in hot corinos.

**Key words:** astrochemistry – ISM: abundances – ISM: molecules.

## 1 INTRODUCTION

Nitriles, that is, organic molecules with a -C≡N (cyano) functional group, comprise a considerable percentage (~15%) of the almost 300 species detected in the interstellar medium (ISM) (https://cdms.astro.uni-koeln.de/classic/molecules and McGuire 2022). They are key intermediates for the formation of biologically relevant molecules and, therefore, are believed to play a central role in pre-biotic chemistry and the origin of life (e.g. Sanchez, Ferris & Orgel 1966; Das, Ghule & Vanka 2019; Meisner, Zhu & Martínez 2019). For instance, nitriles can hydrolyse and participate in multistep synthesis of amino acids (Brack 1998) or RNA precursors (Powner, Gerland & Sutherland 2009; Sutherland 2017).

Nitriles larger than HCN belong to the class of the so-called interstellar complex organic molecules (iCOMs), that is organic molecules containing at least six atoms (Herbst & Van Dishoeck 2009; Ceccarelli et al. 2017). Methyl cyanide (CH3CN, also known as acetonitrile) is the simplest organic nitrile and is one of the first detected (Solomon et al. 1971) and most spread iCOMs. It has been detected in many objects of our Galaxy, remarkably in cold

starless and pre-stellar cores (e.g. Minh et al. 1993; Vastel et al. 2019; Megías et al. 2023), low-mass protostars and hot corinos (e.g. Bottinelli et al. 2004a, b; Taquet et al. 2015; Calcutt et al. 2018; Agúndez et al. 2019; Belloche et al. 2020; Nazari et al. 2021; Bianchi et al. 2022; Mercimek et al. 2022; Nazari et al. 2022; Hsieh et al. 2023) and protoplanetary discs (Öberg et al. 2015; Ilee et al. 2021). Methyl cyanide has also been observed in comets (Ulich & Conklin 1974; Rodgers & Charnley 2001a; Le Roy et al. 2015; Altwegg, Balsiger & Fuselier 2019; Biver et al. 2022), and is one of the nitriles detected in Titan's atmosphere (e.g. Bézard, Marten & Paubert 1993; Marten et al. 2002). Therefore, CH3CN is one of the few pre-biotic species traced through all the formation phases of stars and planetary systems.

As for other iCOMs, the formation route of methyl cyanide is debated (e.g. Ceccarelli et al. 2022; Garrod et al. 2022; Megías et al. 2023) and two major pathways have been invoked in the literature: either gas-phase or grain-surface reactions. In the gas-phase, the sequence of the radiative association of CH3⁺ and HCN leading to CH3CNH⁺ followed by the electron recombination of the protonated methyl cyanide would be the major pathway according to several astrochemical models (Agúndez & Wakelam 2013; Garrod et al. 2022). However, there different suggestions on their rate constants and product yields from the literature (McEwan et al. 1980; Bates 1983; DeFrees, McLean & Herbst 1985; Herbst 1985; Anicich 1993;

<footnote n="1"><sup>1</sup>Univ. Grenoble Alpes, CNRS, IPAG, F-38000 Grenoble, France</footnote>

<footnote n="2"><sup>2</sup>Dipartimento di Chimica, Biologia e Biotecnologie, Universita degli Studi di Perugia, I-06123 Perugia, Italy</footnote>

<footnote n="3"><sup>3</sup>Excellence Cluster ORIGINS, Boltzmannstraße 2, D-85748 Garching bei München, Germany</footnote>

<footnote n="4"><sup>4</sup>Dipartimento di Ingegneria Civile e Ambientale, Universita degli Studi di Perugia, I-06125 Perugia, Italy</footnote>

<footnote>* E-mail: lisa.giani@univ-grenoble-alpes.fr (LG); cecilia.ceccarelli@univ-grenoble-alpes.fr (CC); nadia.balucani@unipg.it (NB)</footnote>
Anicich et al. 1995; Klippenstein et al. 1996) (see the detailed discussion in Section 2).

On the grain-surface, methyl cyanide would be formed either by the ice-assisted association of the CH₃ and CN radicals or by the hydrogenation of C₂N (Garrod, Weaver & Herbst 2008; Garrod et al. 2022). Unfortunately, no experimental or computational data are available for these two processes. In the case of the CH₃ + CN recombination reaction, however, there might be energy barriers because of the interaction of the radicals with water-ice molecules, as observed in similar cases (Enrique-Romero et al. 2019, 2021, 2022). More important than that, it has been demonstrated that the CN radical readily reacts with the water molecules of the ice (Rimola et al. 2018), which makes recombination reactions involving CN radicals on ice highly unlikely.

Astronomical observations can be extremely useful to distinguish which of the two mechanisms prevails and in which environment. For example, the observed correlation between the methyl formate and dimethyl ether abundances has inspired the work by Balucani, Ceccarelli & Taquet (2015), who proposed a chain of gas-phase reactions linking the two species. Likewise, the observed correlation between ethanol, glycolaldehyde, and acetaldehyde abundances has inspired the idea of a chain of gas-phase reactions starting from ethanol, formed on the grain surfaces (e.g. Perrero et al. 2022), and producing other iCOMs (Skouteris et al. 2018). Although an observed correlation does not necessarily imply a direct chemical link (e.g. Belloche et al. 2020), it is worth to consider it.

In this context, a tight correlation between the CH₃OH and CH₃CN column density has recently been observed in a study of several low-mass protostars, the PEACHES survey (Yang et al. 2021). The authors of this study privileged the interpretation that both CH₃OH and CH₃CN are formed on the grain surfaces, since this is the only known route of methanol formation. However, no study has been explicitly carried out to verify whether gas-phase reactions may lead to the observed correlation. Finally, the methyl cyanide deuteration ratio, [CH₂DCN]/[CH₃CN], measured towards the low-mass SVS13-A suggests that, in this source, methyl cyanide was synthesized in the gas-phase during the cold pre-stellar phase, condensed on the grain mantles and, eventually, injected into the gas-phase when the dust temperature reaches the mantles sublimation conditions, upon the heating from the central forming star (Bianchi et al. 2022).

In this work, we focus on the gas-phase reactions leading to the formation of methyl cyanide. To this end, we first carried out a critical search of the literature, starting from the list of reactions reported in the two astrochemical databases KIDA (Kinetic Database for Astrochemistry: Wakelam et al. 2012) and UDfA (UMIST Database for Astrochemistry: McElroy et al. 2013). Only a few of them have been investigated via laboratory experiments under the appropriate experimental conditions. In the cases in which the information was not complete, we performed dedicated quantum mechanics (QM) calculations and estimated the relevant products and rate constants as a function of the temperature. In addition, we propose two new reactions which may contribute to the CH₃CN formation. Also for these reactions, we carried out dedicated QM calculations of the energetics and kinetics. Finally, we obtained astrochemical model predictions using the new chemical network and compared them with the observations of methyl cyanide in cold and warm sources.

The article is organized as follows. Section 2, we present the critical review of the CH₃CN gas-phase formation reactions. The theoretical method for the QM calculations is described in Section 3, while the results of the studied reactions, namely the potential energy surface (PES) and rate constants, are reported in Section 4. The revised network is summarized in Section 5 and the results

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Scheme of the gas-phase reactions involved in the formation of methyl cyanide and listed in Table 1. The numbers on top of each box are those in Table 1 and used in the subsections of Section 2. The colour code of the boxes and arrows is the following: *Green*, reactions correctly reported in the literature/databases; *Blue*, reactions for which we have carried out new QM calculations; *Red*, reactions which we suggest removing from the network; *Orange*, reactions which are updated with a different rate constant derived from the literature; *Black*, reactions not revised in this work; *Magenta*, newly proposed reactions.</figcaption></figure>

obtained using the new network in the astrochemical model are shown in Section 6. We discuss all the results in Section 7. Finally, the conclusions are given in Section 8.

## 2 CRITICAL REVIEW OF THE GAS-PHASE REACTIONS FORMING METHYL CYANIDE

Several gas-phase reactions have been proposed in the literature for the formation of methyl cyanide, most of which are included in the two commonly used astrochemical databases, KIDA and UDfA. However, often rate constants and product branching fractions (BF) have only been guessed on the basis of similar reactions rather than determined in experimental or theoretical studies. Here, we provide a critical review of the reactions contributing to the formation of methyl cyanide which have been considered so far.

Fig. 1 shows the scheme of all reactions invoked in the literature and/or included in the KIDA and UDfA databases, plus two additional reactions that we propose in this work. The reactions are identified by numbers to facilitate the following reading. In Table 1, we list the reactions and separate them in three groups, according to which precursor they form, that is either CH₃CN⁺ or CH₃CNH⁺, or directly CH₃CN. We notice that, the reactions leading to CH₃CN⁺ are rarely taken into account in astrochemical models.

The following subsections report a critical discussion of what is known about each reaction. In some cases, we concluded that products and rate constants used in common databases are not reliable and either we suggested revised values or carried out new theoretical calculations, described in Sections 3 and 4. Table 1 also reports the result of our critical review, namely whether the proposed/literature reactions have reliable rate constants and products, need further investigations, have to be removed or, finally, were unreliable and we carried out new ad hoc QM calculations.
<table><caption>**Table 1.** List of the gas-phase reactions possibly involved in the formation of methyl cyanide that are either considered in the literature, present in the KIDA or UDFA databases, or proposed in this work. The Table is divided in three parts, according to which precursor is formed, that is CH<sub>3</sub>CN<sup>+</sup> or CH<sub>3</sub>CNH<sup>+</sup>, or if CH<sub>3</sub>CN is directly formed, following the scheme of Fig. 1. The numbers in the first column correspond to those in Fig. 1 and used in the subsections of Section 2. Second and third columns indicate reactants and products of each reaction, respectively. The fourth column reports the conclusions of our critical review of the literature for each reaction: 'New QM calculations' means that we carried out new calculations; 'Further investigation needed' means that the characteristics of the reaction (nature of the products and/or its rate constants) indicated in the databases are not reliable but the reaction does not seem to be important for the CH<sub>3</sub>CN formation (based on the astrochemical modelling of Section 6), so we did not carry out new computations; 'Reliable' means that the values in the databases are correct; 'Modified' means that the values have been updated based on the literature search; 'Removed' means that the reaction has been removed because the CH<sub>3</sub>CN is not a product of the reaction. The fifth column indicates our choices after the results of the new QM calculations: 'Removed' if we verified that the reaction does nor produce CH<sub>3</sub>CN; 'Modified' if the calculated parameters are different with respect to those previously used; 'Added' if the reaction has been added to the network.</caption><thead><tr><th>No.</th><th>Reactants</th><th>Products</th><th>Review conclusions</th><th>QM calculation results</th></tr></thead><tbody><tr><td colspan="5" style="text-align:center; font-weight:bold;">Routes to CH<sub>3</sub>CN<sup>+</sup></td></tr><tr><td>1</td><td>C<sub>2</sub>H<sub>2</sub><sup>+</sup> + NH<sub>2</sub></td><td>CH<sub>3</sub>CN<sup>+</sup> + H</td><td>New QM calculations</td><td>Removed</td></tr><tr><td>2</td><td>C<sub>2</sub>H<sub>4</sub><sup>+</sup> + N</td><td>CH<sub>3</sub>CN<sup>+</sup> + H</td><td>New QM calculations</td><td>Removed</td></tr><tr><td>3</td><td>NH<sub>2</sub>CHO + C<sup>+</sup></td><td>CH<sub>3</sub>CN<sup>+</sup> + O</td><td>Further investigation needed</td><td></td></tr><tr><td>4</td><td>H<sub>2</sub>CCN + H<sub>3</sub><sup>+</sup></td><td>CH<sub>3</sub>CN<sup>+</sup> + H<sub>2</sub></td><td>New QM calculations</td><td>Removed</td></tr><tr><td colspan="5" style="text-align:center; font-weight:bold;">Routes to CH<sub>3</sub>CN<sup>+</sup></td></tr><tr><td>5a</td><td>CH<sub>3</sub>CN<sup>+</sup> + H<sub>2</sub></td><td>CH<sub>3</sub>CNH<sup>+</sup> + H</td><td>Reliable</td><td>–</td></tr><tr><td>5b</td><td>CH<sub>3</sub>CN<sup>+</sup> + CH<sub>4</sub></td><td>CH<sub>3</sub>CNH<sup>+</sup> + CH<sub>3</sub></td><td>Reliable</td><td>–</td></tr><tr><td>6</td><td>C<sub>2</sub>H<sub>7</sub><sup>+</sup> + HCN</td><td>CH<sub>3</sub>CNH<sup>+</sup> + CH<sub>4</sub></td><td>Reliable</td><td>–</td></tr><tr><td>7a</td><td>CH<sub>3</sub><sup>+</sup> + HCN</td><td>CH<sub>3</sub>CNH<sup>+</sup> + photon</td><td>Modified</td><td>–</td></tr><tr><td>7b</td><td>CH<sub>3</sub><sup>+</sup> + HNC</td><td>CH<sub>3</sub>CNH<sup>+</sup> + photon</td><td>Removed</td><td>–</td></tr><tr><td>8</td><td>CH<sub>4</sub><sup>+</sup> + HCN</td><td>CH<sub>3</sub>CNH<sup>+</sup> + H</td><td>New QM calculations</td><td>Modified</td></tr><tr><td>9a</td><td>CH<sub>3</sub>OH<sub>2</sub><sup>+</sup> + HCN</td><td>CH<sub>3</sub>CNH<sup>+</sup> + H<sub>2</sub>O</td><td>New QM calculations</td><td>Removed</td></tr><tr><td>9b</td><td>CH<sub>3</sub>OH<sub>2</sub><sup>+</sup> + HNC</td><td>CH<sub>3</sub>CNH<sup>+</sup> + H<sub>2</sub>O</td><td>New QM calculations*</td><td>Added</td></tr><tr><td colspan="5" style="text-align:center; font-weight:bold;">Routes to CH<sub>3</sub>CN</td></tr><tr><td>10a</td><td>CH<sub>3</sub>CNH<sup>+</sup> + NH<sub>3</sub></td><td>CH<sub>3</sub>CN + NH<sub>4</sub><sup>+</sup></td><td>New QM calculations*</td><td>Added</td></tr><tr><td>10b</td><td>CH<sub>3</sub>CNH<sup>+</sup> + e<sup>−</sup></td><td>CH<sub>3</sub>CN + H</td><td>New QM calculations</td><td>Modified</td></tr><tr><td>11a</td><td>CH<sub>3</sub> + CN</td><td>CH<sub>3</sub>CN + photon</td><td>Removed</td><td>–</td></tr><tr><td>11b</td><td>CH<sub>3</sub> + CN<sup>−</sup></td><td>CH<sub>3</sub>CN + e<sup>−</sup></td><td>Further investigation needed</td><td>–</td></tr><tr><td>12</td><td>CH<sub>3</sub>CHCH<sub>2</sub> + CN</td><td>CH<sub>3</sub>CN + C<sub>2</sub>H<sub>3</sub></td><td>Removed</td><td>–</td></tr></tbody></table>

Note. *Reaction proposed in this work.

## 2.1 Reaction [1]: $C_2H_2^+ + NH_2 \rightarrow CH_3CN^+ + H$

The KIDA and UDFA databases report four reactions forming CH<sub>3</sub>CN<sup>+</sup>, namely reactions [1] to [4] of Table 1. Reaction [1] was proposed by Woon & Herbst (2009), who calculated the values of polarizability and dipole moment of several species in order to derive the Langevin rate constant for many ion-neutral reactions. They report a BF of 50% for the proton transfer channel that forms NH<sub>3</sub><sup>+</sup> + CCH, and 50% for the channel that forms CH<sub>3</sub>CN<sup>+</sup> + H. However, reaction [1] can in principle form other products in addition to the products guessed by Woon & Herbst (2009). Therefore, we carried out new QM calculations of the potential energy surface to check whether CH<sub>3</sub>CN<sup>+</sup> is a major reaction product. The results are reported in Section 4.1.

## 2.2 Reaction [2]: $C_2H_4^+ + N \rightarrow CH_3CN^+ + H$

Reaction 2 is cited by Loison, Wakelam & Hickson (2014) with the rate constants measured experimentally by Scott et al. (1999). However, Scott et al. suggested that CH<sub>3</sub>CN<sup>+</sup> is the molecular ion than is formed by the reaction rather than CH<sub>3</sub>CN<sup>+</sup>, as incorrectly written in Loison et al. without an explicit motivation for their assumption.

To clarify the situation, we carried out a theoretical characterization of the PES to determine the main reaction products. The results are reported in Section 4.2.

## 2.3 Reaction [3]: $NH_2CHO + C^+ \rightarrow CH_3CN^+ + O$

As for reaction [1], Woon & Herbst (2009) estimated the products and the Langevin rate constants after calculating the polarizability and dipole moment of the reactants. While it would be useful to revise the products and rate constants of this reaction, this would be time-consuming, so we decided to first assess how important this reaction is in the formation of CH<sub>3</sub>CN<sup>+</sup> using astrochemical modelling (see Section 6). Our conclusions after the modelling is that this route is negligible. Thus, we decided not to investigate this reaction further and the rate constant reported in the KIDA database has been used for the subsequent analysis.

Note that, although the contribution of this reaction is negligible for the formation of methyl cyanide, it may be important in the destruction of NH<sub>2</sub>CHO in environments where carbon is ionized.

## 2.4 Reaction [4]: $H_2CCN + H_3^+ \rightarrow CH_3CN^+ + H_2$

Reaction [4] is part of the same group of the reactions [1] and [3], namely it is based on the theoretical work by Woon & Herbst (2009). H<sub>2</sub>CCN exhibits two resonance structures, consequently it can be protonated both on the carbon atom, forming CH<sub>3</sub>CN<sup>+</sup>, or on the nitrogen atom, forming CH<sub>3</sub>CN<sup>+</sup>. Therefore, as for reactions [1] and [2], we carried out new QM calculations in order to determine which of the two products is formed. The results are reported in Section 4.3.
## 2.5 Reactions [5]: CH₃CN⁺ + H₂/CH₄ → CH₃CNH⁺ + H/CH₃

The two reactions [5a] and [5b], that form CH₃CNH⁺ and subsequently methyl cyanide via reactions [10], have been experimentally studied by Martin & Melton (1960). The authors observed an H-abstraction mechanism for both reactions with large rate constants (k₅ₐ = 5.7 × 10⁻¹⁰ cm³ s⁻¹ and k₅b = 1.7 × 10⁻⁹ cm³ s⁻¹, respectively) and no appreciable temperature dependence (in the range of 100–215 °C).

We note that reaction [5a] is present in the UDfA database but not in that of KIDA, while reaction [5b] is absent from both databases. However, in KIDA, the subsequent reactions involving CH₃CN⁺ do not form CH₃CN (Woon & Herbst 2009; Loison et al. 2014).

In summary, we included these two reactions in the network using the parameters derived in those experimental studies.

## 2.6 Reaction [6]: C₂H₇⁺ + HCN → CH₃CNH⁺ + CH₄

Reaction [6] is reported in the UDfA database with a formation rate constant of CH₃CNH⁺ of 10⁻¹⁰ cm³ mol⁻¹ s⁻¹, based on Mackay et al. (1980). However, only 10% of the reactive flux actually leads to CH₃CNH⁺. The channel that contributes most is instead the one leading to the formation of HCNH⁺ + C₂H₆, via a proton transfer process. Considering the negligible abundance of C₂H₇⁺ in the ISM, it seems unlikely that this reaction is crucial in the formation of methyl cyanide. For this reason, we did not perform new QM calculations and adopted the rate constants reported in the work by Mackay et al. (1980).

## 2.7 Reactions [7]: CH₃⁺ + HCN/HNC → CH₃CNH⁺ + photon

Reactions (7a): CH₃⁺ + HCN → CH₃CNH⁺ + photon

Radiative association between CH₃⁺ and HCN is believed to be the most important route to methyl cyanide formation, followed by the dissociative recombination of CH₃CNH⁺ with an electron (see also Section 6). The first experimental identification of CH₃CNH⁺ as the product of reaction (7a) dates back to 1980 (McEwan et al. 1980). Later, several experiments have been performed in order to understand the reaction mechanism and provide a better estimate of the rate constant (Bass et al. 1981; Illies, Liu & Bowers 1981; Kemper, Bass & Bowers 1985; Anicich, Huntress & McEwan 1986; Knight, Freeman & McEwan 1986; Anicich 1993; Anicich et al. 1995). In the most recent one, Anicich et al. (1995) concluded that CH₃⁺ does react with HCN via a radiative association reaction with a rate constant of 2 × 10⁻¹⁰ cm³ s⁻¹ at room temperature. According to their experiments, the initial stabilized structure is the CH₃NCH⁺ ion but, at pressures > 8 × 10⁻⁵ torr, the association complex can be efficiently stabilized through collisions, resulting in the formation of CH₃CNH⁺. A similar experimental technique has been employed by Luca, Voulot & Gerlich (2002) to study the radiative association of CH₃⁺ + H₂O, with promising results.

Reaction (7a) has also been the subject of some theoretical studies. The rate constant at 10 K has been estimated by Bates (1983) and Herbst (1985) who derived rate constant parameters α = 9 × 10⁻⁹ cm³ s⁻¹ and β = -0.5. The same theoretical approach has been recently used by Tennis, Loison & Herbst (2021) to derive the rate constant for the radiative association of CH₃ and CH₃O. However, given the large uncertainties of the method, which makes use of several approximations, both Bates and Herbst suggested that their rate constant is probably overestimated. In a more recent work by Klippenstein et al. (1996), the rate constant has been derived using a model based on a combination of ab initio QM calculations of

structures, frequencies, and intensities, with the variational transition state theory. The authors derived a rate constant value of 5.76 × 10⁻⁹ cm³ s⁻¹ in the high efficiency limit and for a temperature of 300 K. The comparison with the trajectory calculations by Su & Chesnavich (1982) supports the accuracy of that method, which only slightly overestimates the rate constant value. Unfortunately, the value in the low efficiency limit is not reported by the authors and the high efficiency one should be taken as an upper bound to the rate constant.

An important point to elucidate is the branching fraction for the formation of CH₃CNH⁺ and CH₃NCH⁺, as a function of the temperature. DeFrees et al. (1985) calculated the energies of the two structures CH₃CNH⁺ and CH₃NCH⁺ and their isomerization barrier. The authors propose that while energy is getting lost through relaxation, whether radiatively (as it would likely occur in the ISM) or collisionally (as it occurs in experiments), the complex formed in reaction (7a) can switch between the two isomeric forms. This process can continue until the ion no longer has enough energy to isomerize. DeFrees et al. (1985) concluded that the ratio of formation of protonated methyl isocyanide and protonated methyl cyanide lies in the range 0.1–0.4, when considering the uncertainty in the energy difference between the two protonated isomers.

Later, Le Gal et al. (2019) investigated the impact of the assumed CH₃CNH⁺/CH₃NCH⁺ ratio in reaction (7a) on the modelling of the CH₃NC/CH₃CN abundance ratio in photodissociation regions. Comparing the astrochemical model predictions with the observed ratio, these authors concluded that the best fit is obtained if reaction (7a) has a CH₃CNH⁺/CH₃NCH⁺ ratio of ~ 0.2 (in line with the theoretical calculations of DeFrees et al. 1985). It has to be noted, though, that the modelling itself relied on the best fit of several other poorly known parameters, such as the elemental gaseous O/C ratio and the cosmic-ray ionization rate, so that these conclusions have to be taken with a grain of salt.

In summary, for the analysis presented in Section 6, we decided to use the rate constant value reported by Klippenstein et al. (1996) and to consider that the molecule formed by the radiative association of CH₃⁺ and HCN is CH₃CNH⁺, which corresponds to 80% of the products according to DeFrees et al. (1985). Consequently, the formation of the isomer CH₃NCH⁺, which accounts for the remaining 20%, is not considered in this work since it would require the inclusion of methyl isocyanide and all its formation and destruction pathways in the model, which is beyond the scope of this work.

Reactions (7b): CH₃⁺ + HNC → CH₃CNH⁺ + photon

The reaction of CH₃⁺ with HNC has never been investigated, either experimentally or theoretically. Loison et al. (2014) assumed for this reaction the same rate constant of reaction [7a] in modelling the gas-phase reactions controlling the HCN/HNC abundance ratio. However, this is probably a rough approximation, considering the large uncertainties on the CH₃⁺ + HCN reaction rate constant and branching fractions. Moreover, while in the case of reaction [7a] there are no exothermic channels that compete with the radiative stabilization of the complex, in the case of reaction [7b] the channel of formation of CH₃⁺ + HCN is exothermic by 14 kcal mol⁻¹ (58.6 kJ mol⁻¹). The presence of this exothermic channel identified by DeFrees et al. (1985) makes the radiative association process less likely to be important. Therefore, we decided to remove this reaction from our network.

## 2.8 Reaction [8]: CH₄⁺ + HCN → CH₃CNH⁺ + H

Reaction [8] has been experimentally studied by McEwan, Anicich & Huntress (1981) and Anicich et al. (1986). They measured a global rate constant of 3.3 × 10⁻⁹ cm³ s⁻¹ at room temperature with a
dominant proton transfer mechanism leading to HCNH⁺ + CH₃. A competitive channel forming C₂H₄N⁺ + H has also been identified and reported with a BF of 0.02.

We noticed that KIDA incorrectly uses the global value of the rate constant associated with the formation of CH₃CNH⁺ without taking into account the actual BF of only 2%. Moreover, although McEwan et al. (1981) and Anicich et al. (1986) do not explicitly quote it, the reaction probably forms CH₃NCH⁺ rather than CH₃CNH⁺, considering that it is the nitrogen atom of HCN to interact with the CH₄⁺ ion.

A theoretical study of reaction [8] (which is also of relevance to Titan's ion chemistry) has been performed by Li et al. (2008). They reported the PES with the geometries calculated at B3LYP/6-311G(d,p) level and then the single point energies of the optimized geometries calculated at the CCSD(T)/6-311G++ (3df,2pd) level. Nevertheless, we decided to re-investigate the reaction between HCN and CH₄⁺ at a higher level of theory, focusing only on the exothermic channels of astrochemical interest. We also performed kinetic calculations to compute the rate constant of formation of each product. The results are reported in Section 4.4

## 2.9 Reaction [9]: CH₃OHH₂⁺ + HCN/HNC → CH₃CNH⁺ + H₂O

Reactions [9a]: CH₃OHH₂⁺ + HCN → CH₃CNH⁺ + H₂O

Reaction [9a] is reported in UDfA as a possible source of CH₃CNH⁺. The reaction has been investigated experimentally by Meot-Ner, Karpas & Deakyne (1986), who measured a rate constant of 2.3 × 10⁻¹¹ cm³ s⁻¹ at 340 K. However, this reaction should rather form CH₃NCH⁺ as suggested by the same authors of the experimental study, based on proton affinity considerations (Meot-Ner et al. 1986). As in other cases, no theoretical study is available in the literature for this reaction.

The role of protonated methanol in the synthesis of iCOMs has been recently reconsidered by Taquet, Wirst्रöm & Charnley (2016) and also theoretically analyzed by Skouteris et al. (2019) in the framework of the formation of dimethyl ether. In regions where methanol is very abundant, such as hot cores, hot corinos and molecular shocks, this route of formation of methyl cyanide could be important. For this reason, in this work, we carried out new QM calculations to address which isomeric product among CH₃NCH⁺ or CH₃CNH⁺ is actually formed. The results are reported in Section 4.5.

Reactions [9b]: CH₃OHH₂⁺ + HNC → CH₃CNH⁺ + H₂O

Since the reaction of protonated methanol with HCN likely produces CH₃NCH⁺ rather than CH₃CNH⁺, we also performed new QM calculations for the PES of reaction [9b]. The results are reported in Section 4.5.

## 2.10 Reactions [10]: CH₃CNH⁺ + NH₃/e⁻ → CH₃CN + NH₄⁺/H

Reaction [10a]: CH₃CNH⁺ + NH₃ → CH₃CN + NH₄⁺ The proton transfer to ammonia, first included in astrochemical models by Rodgers & Charnley (2001b), is a process that converts ions into neutral species, alternative to electron-ion recombination. The rates of several proton transfer processes are included in (some) astrochemical models but the parameters are often guessed considering similar reactions. For instance, Taquet et al. (2016) assumed that all the proton transfer reactions are non-dissociative and occur with a rate constant of 4 × 10⁻⁹ cm³ s⁻¹ at 100 K. This assumption is based on the work of Hemsworth et al. (1974), in which the rate constants for a small set of proton transfer reactions involving ammonia are

all reported as having the same order of magnitude, 2 × 10⁻⁹ cm³ s⁻¹ at room temperature. However, relatively small differences (up to a factor of 10) in these rate constants could change the results of the astrochemical models, given their highly non-linear behaviour. For example, QM calculations of the PES and kinetic estimates by Skouteris et al. (2019) for the (CH₃)₂OH⁺ + NH₃ derived a value of 1 × 10⁻⁹ cm³ s⁻¹ in the 10–300 K range.

For this reason, we carried out new QM calculations of this reaction. The results are reported in Section 4.6.

Reactions [10b]: CH₃CNH⁺ + e⁻ → CH₃CN + H Reaction [10b] is an electron-ion recombination reaction. These processes are normally accompanied by the dissociation of the neutralized species since the large amount of energy released is enough to break one or more bonds (Geppert et al. 2006). While in many cases there are multiple bond fissions and the fission of C-C bonds is favored, in the case of the CH₃CNH⁺ + e⁻ reaction a large fraction of the products preserve the C-C-N skeleton, and one or more H atoms are instead lost (Geppert et al. 2007). Indeed, this reaction has been the subject of several experimental studies. In the work by Vigren et al. (2008) and Geppert et al. (2007), the authors derived a thermal rate constant for the electron recombination of CD₃CND⁺ of 8.1 × 10⁻⁷ (T/300)⁻⁰.⁶⁹ cm³ s⁻¹ using the CRYRING ion storage ring (SR). They also reported the presence of two main groups of dissociative recombination channels: those preserving the carbon-chain (65%) and those formed by the breaking of one bond between heavy atoms and leading to small moieties (such as HCN, HNC, and CH₃) (35%). Unfortunately, the authors could not identify the specific products of the CH₃CNH⁺ + e⁻ reaction. In the work by McLain & Adams (2009) instead, flowing afterglow experiments have been used to measure the rate constant for the processes involving the monomer CH₃CNH⁺ and the dimer (CH₃CN)₂H⁺. In the first case they found a power-law dependence of T⁻¹.⁰³ while in the second case of T⁻⁰.⁵.

Since the SR measurement was made with fully deuterated ions and there is some evidence that the rate constants can differ significantly when different isotopes are used (Guberman 2003), we decided to use the value reported by McLain & Adams (2009) for the monomer (e.g. 3.4 × 10⁻⁷ (T/300)⁻¹.⁰³ cm³ s⁻¹) for the global reaction.

Regarding the specific channel leading to the formation of methyl cyanide, Loison et al. (2014) used BFs for four different channels as suggested in the work of Plessis et al. (2012). However, there are several fragmentation pathways which can occur and the description of this system may be more complicated than the one adopted by Loison et al. (2014). In this paper, starting from the experimental works of Geppert et al. (2007) and McLain & Adams (2009), we improved the work by Loison et al. (2014) focusing on the BFs of the products in which the carbon chain is maintained, with the goal of determining the BF of the CH₃CN formation channel. Our results are reported in Section 4.6.

## 2.11 Reactions [11]: CH₃ + CN/CN⁻ → CH₃CN + photon/e⁻

Reactions [11a] and [11b] can directly form CH₃CN. The first one is a radiative association process while the second one is an associative detachment involving a negative ion. These two processes have been proposed by Prasad & Huntress (1980), but the rate constants of both reactions were only guessed and have never been characterized from theoretical or experimental points of view.

Reaction [11a] is adopted by Loison et al. (2014) with an alternative bimolecular channel leading to H₂CCN + H. This suggestion was based on the work by Yang, Maeda & Ohno (2005) where the PES of the CH₃CN dissociation is considered. However, after the
addition between CH₃ and CN to CH₃CN, an easy dissociation route actually produces CH₂ + HCN through an energy barrier that is below the reactants' energy. The H₂CCN + H channel was not considered in that study. In all cases, since the presence of a competitive exothermic channel makes the probability of the occurrence of radiative association very small, we decided to remove reaction [11a] from our network.

We also decided not to revise reaction [11b] since, based on the astrochemical modelling of Section 6, its role in the formation of CH₃CN is not relevant.

## 2.12 Reaction [12]: CH₃CHCH₂ + CN → CH₃CN + C₂H₃

Another reaction reported in the KIDA and UDfA databases for the direct formation of methyl cyanide is that between propylene (CH₃CHCH₂) and the CN radical. Sims et al. (1993) measured the total rate constant as a function of temperature, using the CRESU technique, and it was found to be very fast. However, it was later demonstrated by Gannon et al. (2007) that CH₃CN is not formed by this reaction. We, therefore, removed reaction [12] from our CH₃CN network.

## 2.13 Summary

We have reviewed a total of seventeen reactions possibly contributing to the formation of methyl cyanide and that are present in the literature and/or in the astrochemical databases of KIDA and UDfA. They can be separated into three groups forming CH₃CN⁺, CH₃CNH⁺, and directly CH₃CN, as detailed in the following.

**CH₃CN⁺ formation:** A first group of four reactions form first CH₃CN⁺ which then forms CH₃CNH⁺ and, finally, CH₃CN. We decided to carry out new QM calculations for the three most important routes of CH₃CN⁺ formation, namely, reactions [1], [2], and [4] of Table 1. Based on the astrochemical modelling of Section 6, instead, reaction [3] has only a negligible role in the methyl cyanide formation, so we leave it to further investigations.

**CH₃CNH⁺ formation:** Eight reactions lead to CH₃CNH⁺ formation. Three of them (reactions [5a], [5b], and [6]) have been already characterized and are correctly included in the astrochemical KIDA and UDfA databases. We carried out new QM calculations for the newly proposed reaction [9b] and for reactions [8] and [9a], which were in need of revision. Reaction [7a] is used with an updated rate constant value derived from the literature, while reaction [7b] is removed from the CH₃CN network because of the occurrence of a competitive bimolecular product channel.

**CH₃CN formation:** Five reactions lead to the CH₃CN formation. We carried out new QM calculations for the newly proposed reaction [10a] and for reaction [10b], which needed revision. Reaction [11a] is removed from the CH₃CN network since it has a competing bimolecular channel (as in the case of the reaction [7b]), while reaction [11b] would need further investigation, not done in this work because it is likely unimportant for CH₃CN formation. Finally, we removed reaction [12] since it has already been studied and found not to form CH₃CN.

Table 1 summarizes the results of the critical review.

# 3 COMPUTATIONAL METHODS

Based on the review of the published articles and our astrochemical simulations, discussed in the previous section (Section 2), we decided to carry out new QM calculations of the PES for eight selected reactions to identify the possible reaction mechanisms and their

products, as described in Section 3.1. We then calculated the rate constants for each channel. Considering that these are barrierless reactions in the entrance channel, we calculated the capture rate constant of each reaction and their branching fractions using the Rice-Ramsperger-Kassel-Markus (RRKM) theory, as described in Section 3.2. The theory makes use of the standard functional V(r) for the potential energy of the two approaching species. In one case, we found that the determination of the so-called C₄ coefficient needed a more detailed characterization, and we used a semi-empirical model described in Section 3.3.

## 3.1 Electronic structure calculations

The PES of the studied systems has been characterized by optimizing the relative stationary points. We used the same computational procedure described in previous works of our group (Rosi et al. 2013; Skouteris et al. 2019), in which the geometries of minima and saddle points have been first optimized with a cost-effective method. Subsequently, single-point calculations were performed employing an expensive method to obtain accurate energy values.

For the first step, all the calculations were performed according to the density functional theory (DFT) with the hybrid B3LYP (Becke 1993; Stephens et al. 1994) functional in conjunction with the correlation consistent valence polarized basis set aug-cc-pVTZ (Dunning 1989). The nature of each stationary point, identified by geometry optimization, has been determined by performing harmonic vibrational frequencies calculations. Moreover, the nature of the saddle points has been assigned through intrinsic reaction coordinate calculations (Gonzalez & Schlegel 1989, 1990). In order to obtain more accurate values of the energy of each stationary point, coupled-cluster single and double excitations augmented by a perturbative treatment of the triple excitations (CCSD(T)) (Bartlett 1981; Raghavachari et al. 1989; Olsen et al. 1996) calculations have been performed with the same basis set. The zero-point-energy (ZPE) correction, calculated using the harmonic vibrational frequencies obtained at the B3LYP/aug-cc-pVTZ level of theory, has been added to the calculated CCSD(T) energies in order to correct them at 0 K.

All calculations have been performed with the GAUSSIAN 09 (Frisch et al. 2009) and GAUSSIAN 16 (Frisch et al. 2016) packages, while the analysis of the vibrational frequencies was performed using the Avogadro package (Hanwell et al. 2012).

## 3.2 Kinetic calculations

Kinetic calculations were performed using a combination of capture and RRKM theories, as described in previous works of our group (Skouteris et al. 2015; Skouteris et al. 2019). The initial bimolecular rate constant leading from the reactants to the first intermediate has been evaluated using capture theory calculations. Capture theory accounts for the long-range attractive forces and assumes that the rate-determining step of a reaction is the formation of an intermediate reaction complex. The energy values for the approaching reactants are fitted to the function:

$$V(r) = -\frac{C_n}{r^n} + b, \quad (1)$$

where r is the distance between the two species, Cₙ is usually determined by fitting the long-range ab initio data, and n is a parameter that depends on the type of system (six for neutral-neutral and four for ion-neutral pairs). Moreover, b is an empirical factor that, for each selected configuration of the reagents, corrects the radial dependence of the interaction for contributions that at long
range add to dispersion and induction attraction components. The capture coefficient is used to evaluate the capture cross-section with the formula:

$$ \sigma(E) = \pi \times 2 \times \left(\frac{C_4}{E}\right)^{1/2}, \qquad (2) $$

where E is the translational energy. The cross-section is then multiplied by the collision velocity ($2E/\mu)^{1/2}$, where $\mu$ is the reduced mass of the system, to obtain the capture rate constant.

Once the intermediate is formed, it can dissociate back to reactants, and the unimolecular rate constant for this back-dissociation is given by the equation:

$$ k_{\text{back}} = k_{\text{capt}} \times \frac{\rho(R)}{\rho(I)}, \qquad (3) $$

where $k_{\text{capt}}$ is the capture rate constant, $\rho(R)$ is the density of states per unit volume for the reactants, and $\rho(I)$ is the density of states for the intermediate.

Finally, we have performed RRKM calculations as follows. The microcanonical rate constant is calculated using the formula:

$$ k_E = \frac{N(E)}{h\rho(E)}, \qquad (4) $$

where $N(E)$ denotes the sum of states in the transition state at energy E, $\rho(E)$ is the reactant density of states at energy E, and h is Planck's constant.

Knowing the capture rate constant and the unimolecular rate constants, it is possible to solve the master equation for the system and consequently derive the branching fractions for the overall reaction as a function of the energy. After that, the rate constants for the formation of each product are determined multiplying the branching fraction for the capture rate constant. Finally, Boltzmann averaging was carried out to obtain temperature-dependent rate constants. The new rate constants were then fitted with the form used in the astrochemical databases and models:

$$ k(T) = \alpha \left( \frac{T}{300K} \right)^{\beta} \exp \left( -\frac{\gamma}{T} \right). \qquad (5) $$

### 3.3 Semi-empirical model

In some cases, specifically for the reactions [9a] and [9b], we used a different method to derive the $C_4$ coefficient, introduced in the previous section, for the reasons that will be explained in Section 4.5. This was obtained by using a semi-empirical potential function described in the following and already used by our group (Marchione et al. 2022).

At large and intermediate separation distances, the total interaction potential $V_{\text{total}}$ is assumed to be:

$$ V_{\text{total}} = V_{\text{ILJ}} + V_{\text{electr}}, \qquad (6) $$

where $V_{\text{electr}}$ is the electrostatic interaction contribution and $V_{\text{ILJ}}$ is the contribution due to non-electrostatic interaction, namely size repulsion plus induction and dispersion attraction. The electrostatic contribution has been evaluated considering the Coulombic interactions between pairs of ESP charges obtained from the CCSD(T)/aug-cc-pVTZ calculations for each atom of the two interacting fragments:

$$ V_{\text{electr}} = \frac{1}{4\pi\epsilon_0} \sum_i \sum_j \frac{q_i q_j}{r_{ij}}. \qquad (7) $$

The non-electrostatic term $V_{\text{ILJ}}$ has been evaluated using the so-called improved Lennard-Jones (ILJ) potential function, which provides

a better reproduction with respect to the classical Lennard-Jones model over both short- and long-range distances (Cappelletti et al. 2008; Pirani et al. 2008). The ILJ potential can be expressed as:

$$ V_{\text{ILJ}} = \epsilon \left[ \frac{m}{n(r) - m} \left( \frac{r_m}{r} \right)^{n(r)} - \frac{n(r)}{n(r) - m} \left( \frac{r_m}{r} \right)^m \right], \qquad (8) $$

where r is the distance between the centre of mass of the reactants, $\epsilon$ and $r_m$ are the well depth and position parameter of the potential, respectively, $m = 4$ for ion-neutral systems and $n(r)$ can be expressed as follows:

$$ n(r) = \beta + 4 \left( \frac{r}{r_m} \right)^2. \qquad (9) $$

$\beta$ is a constant parameter within wide classes of systems, and depends on the nature and hardness of the interacting particles. In our case it is set to 8 since this value is suggested for those cases where the long-range attraction is dominated by electrostatic forces like the ion-permanent dipole and ion-ion components. The $r_m$ and $\epsilon$ parameters, of relevance for this study, have been evaluated from polarizability of the two interacting partners obtained from ab initio calculations.

## 4 RESULTS OF QM CALCULATIONS

In this section we describe the main features of the PES and kinetics calculations for the four studied reactions ([9a], [9b], [10a], and [10b]). Three of them ([9b], [10a], and [10b]) are particularly important for the formation of CH$_3$CN according to the modelling described in Section 6, while reaction [9a] is a case study for which the semi-empirical model described in Section 3.3 has been used. The results for the other four studied reactions ([1], [2], [4], and [8]) are only briefly summarized here, while a more detailed description is provided in Section A, because they are less relevant for the formation of CH$_3$CN.

### 4.1 Reaction [1]: $C_2H_2^+ + NH_2 \rightarrow CH_3CN^+ + H$

We carried out new QM calculations of the PES (see A1) and verified that $CH_3CN^+$ is a very minor product, since it is formed in a non-competitive channel with high energy barriers along the reaction pathway. We, therefore, decided to remove this reaction from the CH$_3$CN network.

### 4.2 Reaction [2]: $C_2H_2^+ + N \rightarrow CH_3CN^+ + H$

Our QM calculations (for the details see A2) show that $CH_2NCH^+$, and not $CH_3CN^+$, is the major product of the reaction. We, therefore, removed this reaction from the CH$_3$CN network.

### 4.3 Reaction [4]: $H_2CCN + H_3^+ \rightarrow CH_3CN^+ + H_2$

Our QM calculations (for the details see A3), show that $CH_2NCH^+$, and not $CH_3CN^+$, is the major product of the reaction. We, therefore, removed this reaction from the network as it does not contribute to the CH$_3$CN formation.

### 4.4 Reaction [8]: $CH_4^+ + HCN \rightarrow CH_3CNH^+ + H$

Our QM calculations (for the details see A4), show that $CH_3 + HCNH^+$ are the major products of the reaction while formation of $CH_3CNH^+$ accounts for only 1%.
<figure><img src="image_3.png" /><figcaption>**Figure 2.** PES of the reactions [9a] (left panel) and [9b] (right panel) of Table 1. The QM calculations are obtained at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level of theory.</figcaption></figure>

## 4.5 Reactions [9]: CH₃OH₂⁺ + HCN/HNC → CH₃CNH⁺ + H₂O

Since calculations on reactions [9a] and [9b] have never been published before and these two reactions are potentially important in the formation of methyl cyanide, we discuss here their cases in detail. Briefly, we can say that reaction [9a] does not form methyl cyanide but rather its isomer, methyl isocyanide. Therefore, we removed this reaction. On the contrary, reaction [9b], never considered before in the literature, forms methyl cyanide and hence, was added to the final network.

### 4.5.1 PES of reactions [9]

$$ \text{Reaction [9a]: } \mathrm{CH_3OH_2^+} + \mathrm{HCN} \rightarrow \mathrm{CH_3NCH^+} + \mathrm{H_2O} $$

Fig. 2 (left panel) reports the PES of reaction [9a]. Three intermediates can be formed directly from the reactants: INT1 and INT2, in which the nitrogen atom points towards one of the two hydrogen atoms of the OH₂ group, or INT3, in which the nitrogen atom of HCN points to the carbon atom of the CH₃ group of protonated methanol.

INT1 and INT2 are characterized by the same energy content and can easily isomerize through a barrier of 33.8 kJ mol⁻¹ (associated with the transition state TS1). Alternatively, the HCN group can move towards the CH₃ group and form INT3, by overcoming a barrier of 71.7 and 71.5 kJ mol⁻¹ (TS2 from INT2 and TS3 from INT2, respectively). INT1 and INT2 could also evolve toward CH₃OH and HCNH⁺ in a proton transfer process. Even if no barrier is involved in the process, this channel is endothermic by 43.7 kJ mol⁻¹ and, therefore, cannot occur under the conditions of interstellar objects.

When INT3 is formed, it can isomerize to INT4 by overcoming a barrier of 34.3 kJ mol⁻¹ (TS4), in which a new C–N bond is formed while the C–O bond is ready to be broken. This allows the water molecule to separate from the intermediate and form the CH₃NCH⁺ + H₂O products (for this channel the enthalpy change is –74.3 kJ mol⁻¹). Therefore, the only exothermic channel of the reaction is the one that forms methyl isocyanide, in agreement with what was suggested by Meot-Ner et al. (1986).

$$ \text{Reaction [9b]: } \mathrm{CH_3OH_2^+} + \mathrm{HNC} \rightarrow \mathrm{CH_3CNH^+} + \mathrm{H_2O} $$

Fig. 2 (right panel) reports the PES of reaction [9b]. There are many similarities with the previous reaction, with two major differences. First, in this case the proton transfer channel is exothermic by 15.5 kJ mol⁻¹, making the formation of CH₃OH + HCNH⁺ a reaction channel competing with the formation of the products of interest. Secondly, TS4 does not form the linear intermediate directly but

it forms first a T-shaped intermediate INT4 and only afterwards is INT5 formed (through TS5 which has been identified as a submerged transition state).

The interesting aspect of these two systems is that there is an "inverse" correlation between the reactants and the products: if the reactant is HCN only the isocyanato isomeric product can be formed (CH₃NCH⁺), while if the reactant is HNC only the cyano isomeric product is formed (CH₃CNH⁺).

### 4.5.2 Kinetics of reactions [9]

$$ \text{Reaction [9a]: } \mathrm{CH_3OH_2^+} + \mathrm{HCN} \rightarrow \mathrm{CH_3CNH^+} + \mathrm{H_2O} $$

Even though the CH₃OH₂⁺ + HCN reaction does not form protonated methyl cyanide, we carried out kinetic calculations because it has been experimentally studied by Meot-Ner et al. (1986) and the measured value (2.3 × 10⁻¹¹ cm³ s⁻¹ at 340 K) provides us with a very important constraint to test our theoretical methods. In this way, we can derive with more confidence the rate coefficient for reaction [9b] which does form protonated methyl cyanide.

As a first attempt, we derived the capture coefficient from the fit of the ab initio data and we obtained a C₄ coefficient equal to 12.7 h Å⁴ and a capture rate constant of 4.2 × 10⁻⁹ cm³ s⁻¹. We then performed the full kinetic calculations and we obtained a rate constant for the formation of CH₃CNH⁺ + H₂O at 340 K of 7.2 × 10⁻¹⁰ cm³ s⁻¹, which is more than one order of magnitude higher than the experimental value found by Meot-Ner et al. (1986).

In order to obtain a value in better agreement with the experimental one, we modelled the entrance potential with a more accurate method using the semi-empirical potential described in Section 3.3. Specifically, the C₄ coefficient was obtained as follows. We first calculated it by averaging over all possible configurations of the reactants and assuming that all the orientations are reactive. Therefore, by definition, the electrostatic contribution is zero because of the compensation between attractive and repulsive effects. With this method we obtained an average C₄ coefficient of 0.78 h Å⁴ and a rate constant for the CH₃CNH⁺ + H₂O channel that is still one order of magnitude too high (1.8 × 10⁻¹⁰ cm³ s⁻¹ at 340 K).

We, therefore, decided to evaluate the electrostatic contribution to the total entrance potential for each specific configuration of the reactants. We found that all orientations with the nitrogen atom of HCN pointing towards CH₃OH₂⁺ are attractive, while all the orientations with the hydrogen atom of HCN pointing towards CH₃OH₂⁺ are repulsive (see Fig. 3). We then concluded that this reaction shows an important steric effect which leads to a lower rate constant. In order to evaluate the steric effect, we developed
<figure><img src="image_4.png" /><figcaption>**Figure 3.** Left panel: Calculated entrance potential energy for reaction [9a], CH₃OH₂⁺ + HCN, as a function of the rotation angle of HCN around its centre of mass, using the semi-empirical model described in Section 3.3. Right panel: The plot shows the adopted reference frame and coordinates used for the representation of the interaction potential between HCN and CH₃OH₂⁺. The rotation of HCN is obtained by keeping the φ angle fixed (90°) while the θ angle is free to vary. For each combination of φ and θ the HCN molecule is translated varying the distance between the centre of mass of the two molecules and the potential is evaluated at each step.</figcaption></figure>

a code which rotates the HCN molecule around its centre of mass and calculates the potential energy curve for each configuration of the reactants. An example of the obtained potentials is shown in Fig. 3.

The derived steric factor, which is given by the ratio between the number of attractive configurations and the total number of configurations, is equal to 0.58 for the formation of INT1, INT2, and INT3. By multiplying the previous rate constant by this factor we obtained a rate of $k = 6.5 \times 10^{-11}$ cm³ s⁻¹ at 340 K, which is only a factor of 2 larger than the experimental value. Therefore, we are confident that our method provides reasonably good estimates of the reaction rate constants for systems of this kind.

The final rate constant as a function of the temperature is shown in Fig. 4. We note that back dissociation plays an important role in determining the trend of the rate constant: the larger the temperature, the lower the rate constant due to the increasing role of back dissociation.

$$ \textit{Reaction [9b]:} \quad \mathrm{CH_3OH_2^+} + \mathrm{HNC} \rightarrow \mathrm{CH_3CNH^+} + \mathrm{H_2O} $$

As discussed before, the reaction between protonated methanol and HNC leads to the formation of protonated methyl cyanide. Using the same methodology described for the reaction [9a], we calculated the C₄ coefficient and the steric factor which is found to be equal to 0.69. However, in this case the main reaction channel is the one leading to CH₃OH + HCNH⁺ with a rate constant of 1.04 × 10⁻⁹ cm³ s⁻¹. The channel leading to CH₃CNH⁺ + H₂O gives only a minor contribution with a BF of only 0.01.

Fig. 4 shows the rate constant as a function of the temperature of the two reactive channels. The contribution of the back dissociation is negligible in this case.

## 4.6 Reactions [10]: CH₃CNH⁺ + NH₃ → CH₃CN + NH₄⁺ or CH₃CNH⁺ + e⁻ → CH₃CN + H

As for the reactions [9a] and [9b], QM calculations of the PES were not previously available in the literature. Since both reactions are important in the formation of methyl cyanide, we discuss their case

in detail below. Here, we summarize the main results for the readers who are not interested in the details: protonated methyl cyanide easily undergoes a proton exchange reaction with ammonia forming methyl cyanide with a rate constants equal to 8.7 × 10⁻¹⁰ cm³ s⁻¹, a value that remains constant in the 10–300 K interval. On the other hand, only about 7% of the protonated methyl cyanide electron recombination produces neutral methyl cyanide. The rate constant scales with $T^{-1.03}$.

### 4.6.1 PES of reactions [10]

**Reactions [10a]:** CH₃CNH⁺ + NH₃ → CH₃CN + NH₄⁺ The schematic PES of reaction [10a] is reported in Fig. 5, left panel. The interaction between protonated methyl cyanide and ammonia gives rise, in a barrier-less process, to an adduct (ADD1) more stable than the reactants by 181.8 kJ mol⁻¹. After that, the dissociation of the adduct into methyl cyanide and ammonium ion occurs (the global enthalpy change is - 70.1 kJ mol⁻¹, in perfect agreement with the differences of proton affinities of ammonia and CH₃CN retrieved from the NIST database (Kramida et al. 2022)).

**Reaction [10b]:** CH₃CNH⁺ + e⁻ → CH₃CN + H Fig. 5, right panel, shows the PES of reaction [10b]. To be noted that only the most relevant channels are reported in the figure. Following the recombination of CH₃CNH⁺ with an electron two intermediates can be formed, trans-CH₃CNH or cis-CH₃CNH, that are stabilized by -593.6 and -574.3 kJ mol⁻¹, respectively, with respect to the reactants. These two intermediates can isomerize through TS1, overcoming barriers of 66.8 and 47.5 kJ mol⁻¹, respectively. The trans-CH₃CNH isomer can dissociate into the CH₂CNH + H products (the enthalpy change for this channel is -418.2 kJ mol⁻¹) by overcoming a barrier of 174.4 kJ mol⁻¹ (TS3). Alternatively, it can isomerize to INT1 (-619.2 kJ mol⁻¹) by transferring a hydrogen atom from the N atom to the C atom via TS2 (barrier of 148.1 kJ mol⁻¹). The fission of a C–H bond in INT1 leads to the formation of CH₃CN + H (the enthalpy change for this channel is -531.7 kJ mol⁻¹) through TS5 (barrier of 116.4 kJ mol⁻¹) while the fission of the C–C bond leads to the formation of CH₃ + HCN (the
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Left panel: Rate constants of reaction [9a], CH₃OH⁺₂ + HCN, as a function of the temperature, for the formation of the CH₃NCH⁺ + H₂O products. The green curve shows the rate constant first obtained from the conventional calculations of the interaction in the entrance channel. The blue curve shows the values when the semi-empirical method, described in Section 3.3, is used to compute the C₄ coefficient of equation (1). Finally, the red curve shows the final values obtained by applying the steric factor, described in the text. The magenta triangle shows the measurements of the rate constant obtained at 340 K by Meot-Ner et al. (1986). Right panel: Rate constants of reaction [9b], CH₃OH⁺₂ + HCN, as a function of the temperature for the products CH₃CNH⁺ + H₂O (green) and CH₃OH + HCNH⁺ (blue), respectively, plus the back dissociation rate (red).</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 5.** PES of the reaction [10a] (left panel) and [10b] (right panel) of Table 1, CH₃CNH⁺ + NH₃ or e⁻. The plots show the results obtained at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level of theory.</figcaption></figure>

enthalpy change for this channel is −550.4 kJ mol⁻¹) through TS4 (barrier of 107.9 kJ mol⁻¹). Also the cis-CH₃CNH intermediate can dissociate into CH₃CN + H by overcoming a barrier of 78.8 kJ mol⁻¹ (TS6) or into CH₃ + HNC (the enthalpy change for this channel is −491.3 kJ mol⁻¹) through TS7 (barrier of 113.0 kJ mol⁻¹). Further fragmentation of CH₃CN or CH₂CNH are possible considering the large amount of available energy and CH₂CN + H + H (a process which is still exothermic by 139.9 kJ mol⁻¹) is a possible reaction outcome. This possibility has been taken into account in the kinetics estimates.

### 4.6.2 Kinetics of reaction [10]

$$ \text{Reactions [10a]: } \mathrm{CH_3CNH^+} + \mathrm{NH_3} \rightarrow \mathrm{CH_3CN} + \mathrm{NH_4^+} $$

Since the back-dissociation of reaction [10a] is negligible, the rate constant is essentially independent of temperature and equal to the capture rate constant 8.7 × 10⁻¹⁰ cm³ s⁻¹ in the investigated

temperature range. This value is in line with the lower limit of values provided by Hemsworth et al. (1974) after the investigation of a limited sample of reactions (~1 × 10⁻⁹ cm³ s⁻¹).

$$ \text{Reaction [10b]: } \mathrm{CH_3CNH^+} + \mathrm{e^-} \rightarrow \mathrm{CH_3CN} + \mathrm{H} $$

In this reaction, cis-CH₃CNH and trans-CH₃CNH intermediates can be initially formed. We solved the master equation starting from the two intermediates separately and derive the product BFs in each case. Then, we take the weighted average of the two BFs by considering the ratio of the density of states of the first two intermediates as an estimate of their relative rate of formation. Even though we could not estimate the rate constant, from our calculations we derived that 60% of the products preserve the carbon chain while 40% of the products are associated with the C–C or C–N bond fission, forming CH₃ + HNC (39%) or CH₃ + HCN (1%). Among the formed species when the C-C-N skeleton is preserved, CH₂CNH has a BF of 53% while CH₃CN has a BF of only 7%. These results are in good agreement with the experimental study of Geppert et al. (2007),
which found that 65% of the products preserve the C-C-N skeleton while 35% are smaller moieties. Finally, we have coupled our BFs with the rate constant measured by McLain & Adams (2009) to derive the rate constant of formation for each set of products. We kept the temperature dependence of $T^{-1.03}$ measured by McLain & Adams (2009) for non-deuterated $CH_3CNH^+$. The final values are reported in Table 2 for the different major products. Note that, since $CH_2CNH$ likely fragments further (as suggested by Loison et al. 2014), we have considered only the global process $CH_2CN + H + H$.

## 5 THE REVISED GAS-PHASE REACTION NETWORK FOR THE METHYL CYANIDE FORMATION

Fig. 2 shows the new scheme of the gas-phase reaction network leading to the formation of methyl cyanide. Table 2 summarizes the reactions, products, and rate constants of the new revised network for the formation of methyl cyanide. The rate constants are given in terms of the parameters $α, β$, and $γ$, following the equation (5), which is commonly used in the astrochemical databases and models. Please note that $α, β$, and $γ$ are the results of the fits of the rate constants as a function of the temperature, in the temperature range marked in the table. Therefore, the $γ$ parameter is sometimes different from zero even in absence of an activation barrier, because it improves analytical fit, as it has been often done in other cases. It is important to emphasize that, in these cases, $γ$ must not be considered as an activation barrier.

The new network consists of ten reactions, forming methyl cyanide or competitive products. The changes with respect to the original ones, summarized in Table 1, are:

(i) Reactions [1], [2], and [4] have been removed because they do not form $CH_3CN^+$, as incorrectly reported in KIDA and UDfA, but its isomer, $CH_2CNH^+$.

(ii) Reaction [3] has not been revised, since its role in the formation of $CH_3CN$ is likely negligible.

(iii) Reactions [5a] and [5b] have been validated based on the literature review. Therefore, they have been included in our network. Note that reaction [5a] is considered in UDfA but not in KIDA, while reaction [5b] is not considered in any of the two databases.

(iv) Reactions [6] is also validated based on the literature review. It has been included in the our network. This process was correctly included in the UDfA but not in KIDA.

(v) Reaction [7a] has been revised and a rate constant smaller by a factor 2 with respect to the one reported in KIDA and UDfA has been adopted in our network.

(vi) Reaction [7b] has been removed because it forms $CH_3^+ + HCN$ and not $CH_3CNH^+$ as incorrectly reported in KIDA and UDfA.

(vii) Reaction [8] mainly forms $CH_3^+ + HCNH^+$ rather than $CH_3CNH^+$ and the rate constant for the formation of $CH_3CNH^+$ is 100 times lower than that reported in KIDA.

(viii) Reaction [9a] has been removed because it does not form $CH_3CNH^+$, as incorrectly reported in UDfA, but its isomer, $CH_3NCH^+$.

(ix) Reaction [9b] has been added (it is not present in KIDA or UDfA) as it forms $CH_3CNH^+$, according to our new QM calculations.

(x) Reaction [10a] has been added (it is not present in KIDA or UDfA) as it forms $CH_3CN$, according to our new QM calculations.

(xi) Reaction [10b] has been modified following our new QM calculations of the BFs. Specifically, the BF for the $CH_3CN$ formation channel has been reduced from 39% to 6.5%.

(xii) Reaction [11a] has been removed since it forms $CH_2 + HCN$ and not $CH_3CN$ as incorrectly reported in KIDA and UDfA.

(xiii) Reaction [11b] has not been revised, since its role in the formation of methyl cyanide is likely negligible.

(xiv) Reaction [12] has been removed since it does not form $CH_3CN$, contrary to what reported in KIDA and UDfA.

To summarize, the remaining formation routes of methyl cyanide are (see also Table 2):

(1) via the formation of $CH_3CN^+$ in the $C^+ + NH_2CHO$ reaction. However, this step was found to be negligible for the formation of $CH_3CN$ following the model described in Section 6.

(2) via $CH_3CNH^+$ which is in turn formed by the reactions of the $CH_3^+, CH_4^+, CH_3OH_2^+$, and $C_2H_4^+$ ions with HCN (or HNC), and from the reactions of $CH_3CN^+$ with $H_2$ or $CH_4$;

(3) the final conversion of the protonated methyl cyanide into $CH_3CN$, via the recombination with $e^-$ of $CH_3CNH^+$ or the proton transfer with $NH_3$. Another possible process is the associative detachment reaction of $CH_3$ with $CN^-$.

## 6 ASTROCHEMICAL MODELLING

In order to understand which gas-phase reactions of the network described in Section 2 (see also Table 1 and Fig. 1) have the largest impact in the formation of $CH_3CN$, we ran simulation with the astrochemical model described in Section 6.1. We considered two general cases with different conditions and where methyl cyanide has been observed, as discussed in Section 7. Specifically, we simulated the chemical evolution of a cold molecular cloud, described in Section 6.2, and a warm protostellar molecular shock, described in Section 6.3, respectively. We emphasize that the goal of the modelling and the focus of the results discussion are to understand the importance of the various reactions in forming methyl cyanide in different conditions and whether the new reaction network is capable to approximately reproduce the observed abundance of methyl cyanide.

### 6.1 Description of the astrochemical model

We used the code MyNahoon, which is a time-dependent gas-phase chemical model based on the Nahoon code originally developed by Wakelam et al. (2005, 2010). Briefly, the code computes the abundances of gaseous species as a function of time for a given temperature $T$ and density $n_H$, and other standard parameters detailed below. The code does not consider reactions occurring on the grain surfaces, except for the formation of $H_2$ molecules. The simulation starts from an initial composition that depends on the object to simulate and that also defines the overall gaseous elemental abundances. It then follows the chemical evolution with time until the age, which also depends on the simulated object, is reached.

For the gas-phase reaction network, we used the GRETOBAPE network, described in Tinacci et al. (2023), and the new network of Table 2 for the methyl cyanide formation (see also Fig. 6). Briefly, the GRETOBAPE network is based on the KIDA2014 network Wakelam et al. (2015), upgraded following studies from our and other groups (e.g. Loison et al. 2014; Balucani et al. 2015; Neufeld et al. 2015; Vazart et al. 2016; Skouteris et al. 2018; Blázquez et al. 2020; Codella et al. 2020; Vazart et al. 2020). We want to point out
<table><caption>**Table 2.** Revised network for the formation of methyl cyanide in the gas-phase. For each reaction (column 1), the rate constants are given in terms of α (in cm³ s⁻¹) (column 2), β (column 3), and γ (in K, column 4). They follow the formalism of equation (5), except for reaction [3] where the Ion-pol formalism is employed instead (Wakelam et al. 2012). The rate constants are valid for the range of temperatures indicated in column 5. Note that the number of each reaction refers to those in Table 1. The reactions preceded by a star are those revised based on either a careful literature search or our dedicated QM calculations presented in Section 4; those preceded by a plus are taken from the databases, but they need to be verified; the remaining reactions are confirmed after our critical review of Section 2. For comparison, columns 6 to 11 report the values listed in the KIDA (Wakelam et al. 2012) and UDfA (McElroy et al. 2013) databases, respectively.</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Reaction</th><th colspan="6">Revised network</th><th colspan="3">KIDA</th><th colspan="3">UDfA</th></tr><tr><th>α</th><th>β</th><th>γ</th><th>T(K)</th><th>α</th><th>β</th><th>γ</th><th>α</th><th>β</th><th>γ</th></tr></thead><tbody><tr><td colspan="12">(i) Routes to CH<sub>3</sub>CN<sup>+</sup></td></tr><tr><td>3</td><td>+ NH<sub>2</sub>CHO + C<sup>+</sup></td><td>→</td><td>CH<sub>3</sub>CN<sup>+</sup> + O</td><td>1.67 × 10<sup>-1</sup></td><td>1.55 × 10<sup>-9</sup></td><td>6.62</td><td>10–300</td><td>1.67 × 10<sup>-1</sup></td><td>1.55 × 10<sup>-9</sup></td><td>6.62</td><td>—</td><td>—</td><td>—</td></tr><tr><td colspan="12">(ii) Routes to CH<sub>3</sub>CNH<sup>+</sup></td></tr><tr><td>5a</td><td>CH<sub>3</sub>CN<sup>+</sup> + H<sub>2</sub></td><td>→</td><td>CH<sub>3</sub>CNH<sup>+</sup> + H</td><td>5.7 × 10<sup>-10</sup></td><td>0.0</td><td>0.0</td><td>10–300</td><td>—</td><td>—</td><td>—</td><td>5.7 × 10<sup>-10</sup></td><td>0.0</td><td>0.0</td></tr><tr><td>5b</td><td>CH<sub>3</sub>CN<sup>+</sup> + CH<sub>4</sub></td><td>→</td><td>CH<sub>3</sub>CNH<sup>+</sup> + CH<sub>3</sub></td><td>1.7 × 10<sup>-9</sup></td><td>0.0</td><td>0.0</td><td>10–300</td><td>—</td><td>—</td><td>—</td><td>1.7 × 10<sup>-9</sup></td><td>0.0</td><td>0.0</td></tr><tr><td>6</td><td>C<sub>2</sub>H<sub>7</sub><sup>+</sup> + HCN</td><td>→</td><td>CH<sub>3</sub>CNH<sup>+</sup> + CH<sub>4</sub></td><td>2.2 × 10<sup>-10</sup></td><td>-0.5</td><td>0.0</td><td>10–300</td><td>—</td><td>—</td><td>—</td><td>2.2 × 10<sup>-10</sup></td><td>-0.5</td><td>0.0</td></tr><tr><td>7a</td><td>*</td><td>CH<sub>3</sub><sup>+</sup> + HCN</td><td>→</td><td>CH<sub>3</sub>CNH<sup>+</sup> + hν</td><td>5.7 × 10<sup>-9</sup></td><td>-0.5</td><td>0.0</td><td>10–300</td><td>9.0 × 10<sup>-9</sup></td><td>-0.5</td><td>0.0</td><td>9.0 × 10<sup>-9</sup></td><td>-0.5</td><td>0.0</td></tr><tr><td>8</td><td>*</td><td>CH<sub>4</sub><sup>+</sup> + HCN</td><td>→</td><td>CH<sub>3</sub> + HCNH<sup>+</sup></td><td>3.9 × 10<sup>-9</sup></td><td>0.0</td><td>0.0</td><td>10–300</td><td>3.3 × 10<sup>-9</sup></td><td>0.0</td><td>0.0</td><td>—</td><td>—</td><td>—</td></tr><tr><td>9b</td><td>*</td><td>CH<sub>3</sub>OH<sub>2</sub><sup>+</sup> + HNC</td><td>→</td><td>CH<sub>3</sub>CNH<sup>+</sup> + H</td><td>3.2 × 10<sup>-11</sup></td><td>0.0</td><td>0.0</td><td>10–300</td><td>3.3 × 10<sup>-9</sup></td><td>0.0</td><td>0.0</td><td>—</td><td>—</td><td>—</td></tr><tr><td>*</td><td>*</td><td>CH<sub>3</sub>OH<sub>2</sub><sup>+</sup> + HNC</td><td>→</td><td>CH<sub>3</sub>CNH<sup>+</sup> + H<sub>2</sub>O</td><td>3.0 × 10<sup>-11</sup></td><td>0.0</td><td>0.0</td><td>10–300</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>*</td><td>*</td><td>CH<sub>3</sub>OH<sub>2</sub><sup>+</sup> + HNC</td><td>→</td><td>CH<sub>3</sub>OH<sup>+</sup> + HCNH<sup>+</sup></td><td>1.0 × 10<sup>-9</sup></td><td>0.0</td><td>0.0</td><td>10–300</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td colspan="12">(iii) Routes to CH<sub>3</sub>CN</td></tr><tr><td>10a</td><td>*</td><td>CH<sub>3</sub>CNH<sup>+</sup> + NH<sub>3</sub></td><td>→</td><td>CH<sub>3</sub>CN + NH<sub>4</sub><sup>+</sup></td><td>8.7 × 10<sup>-10</sup></td><td>0.0</td><td>0.0</td><td>10–300</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>10b</td><td>*</td><td>CH<sub>3</sub>CNH<sup>+</sup> + e<sup>-</sup></td><td>→</td><td>CH<sub>3</sub>CN + H</td><td>2.2 × 10<sup>-8</sup></td><td>-1.03</td><td>0.0</td><td>10–300</td><td>1.3 × 10<sup>-7</sup></td><td>-0.5</td><td>0.0</td><td>5.3 × 10<sup>-7</sup></td><td>-0.7</td><td>0.0</td></tr><tr><td>*</td><td>*</td><td>CH<sub>3</sub>CNH<sup>+</sup> + e<sup>-</sup></td><td>→</td><td>CH<sub>2</sub>CN + H + H</td><td>1.8 × 10<sup>-7</sup></td><td>-1.03</td><td>0.0</td><td>10–300</td><td>8.8 × 10<sup>-8</sup></td><td>-0.5</td><td>0.0</td><td>—</td><td>—</td><td>—</td></tr><tr><td>*</td><td>*</td><td>CH<sub>3</sub> + HCN</td><td>→</td><td>CH<sub>3</sub> + HCN</td><td>3.4 × 10<sup>-10</sup></td><td>-1.03</td><td>0.0</td><td>10–300</td><td>6.0 × 10<sup>-8</sup></td><td>-0.5</td><td>0.0</td><td>—</td><td>—</td><td>—</td></tr><tr><td>*</td><td>*</td><td>CH<sub>3</sub> + HNC</td><td>→</td><td>CH<sub>3</sub> + HNC</td><td>1.4 × 10<sup>-7</sup></td><td>-1.03</td><td>0.0</td><td>10–300</td><td>6.0 × 10<sup>-8</sup></td><td>-0.5</td><td>0.0</td><td>2.8 × 10<sup>-7</sup></td><td>-0.7</td><td>0.0</td></tr><tr><td>11b</td><td>+</td><td>CH<sub>3</sub> + CN<sup>-</sup></td><td>→</td><td>CH<sub>3</sub>CN + e<sup>-</sup></td><td>1.0 × 10<sup>-9</sup></td><td>0.0</td><td>0.0</td><td>10–300</td><td>1.0 × 10<sup>-9</sup></td><td>0.0</td><td>0.0</td><td>1 × 10<sup>-9</sup></td><td>0.0</td><td>0.0</td></tr></tbody></table>
<figure><img src="image_7.png" /><figcaption>**Figure 6.** Scheme of the new gas-phase reaction network leading to the formation of methyl cyanide, following the revision summarized in Section 5. The numbers on top of each box are those in Table 2. The green boxes mark the reactions which have been verified to be correct while the black boxes mark reactions that would need further investigations (but are unlikely important in the formation of methyl cyanide).</figcaption></figure>

<table><caption>**Table 3.** Initial elemental abundances relative to H nuclei adopted for the cold molecular cloud modelling. The abundances are adapted from Jenkins (2009).</caption><thead><tr><th>Element</th><th>Abundance</th><th>Element</th><th>Abundance</th></tr></thead><tbody><tr><td>He</td><td>9.0 × 10<sup>-2</sup></td><td>P<sup>+</sup></td><td>2.0 × 10<sup>-10</sup></td></tr><tr><td>C<sup>+</sup></td><td>1.7 × 10<sup>-5</sup></td><td>Na<sup>+</sup></td><td>2.0 × 10<sup>-9</sup></td></tr><tr><td>O</td><td>2.6 × 10<sup>-5</sup></td><td>Mg<sup>+</sup></td><td>7.0 × 10<sup>-9</sup></td></tr><tr><td>N</td><td>6.2 × 10<sup>-6</sup></td><td>Fe<sup>+</sup></td><td>3.0 × 10<sup>-9</sup></td></tr><tr><td>S<sup>+</sup></td><td>8.0 × 10<sup>-8</sup></td><td>Cl<sup>+</sup></td><td>1.0 × 10<sup>-9</sup></td></tr><tr><td>Si<sup>+</sup></td><td>8.0 × 10<sup>-9</sup></td><td>F<sup>+</sup></td><td>1.0 × 10<sup>-9</sup></td></tr></tbody></table>

here that the GRETOBAPE network is cleaned up version where endothermic reactions present in the original KIDA2014 network have been removed.

## 6.2 Cold molecular cloud

### 6.2.1 Modelling and adopted parameters

To simulate a generic molecular cloud, where methyl cyanide has been detected, we assumed the following parameters: gas temperature $T = 10$ K, H-nuclei density $N_H = 2 \times 10^4$ cm$^{-3}$, cosmic-ray (CR) ionization rate $\zeta_{CR} = 3 \times 10^{-17}$ s$^{-1}$, visual extinction $A_\nu = 20$ mag, gas-to-dust ratio in mass equal to 0.01, dust grain radius $a_d = 0.1$ µm, and grain density 3 g cm$^{-3}$.

We aimed at simulating the evolution of a typical translucent cloud into a molecular cloud. For this reason, as initial conditions, all elements with an ionization potential below 13.6 eV are ionized (C, S, Si, P...) while the elements with larger ionization potential are neutral (N and O). Hydrogen is assumed to be fully molecular. The adopted elemental abundances are summarized in Table 3.

<figure><img src="image_8.png" /><figcaption>**Figure 7.** Abundance (with respect to H$_2$) of methyl cyanide as a function of time, using the original network (purple) and the revised network (green). The yellow band shows the measured abundance of methyl cyanide in the TMC-1 cold cloud (see Table 5).</figcaption></figure>

### 6.2.2 Results of the modelling

In order to see the effect of the new reaction network, we ran the cold cloud model using both the old and the new networks. Fig. 7 shows the methyl cyanide abundance as a function of time, using the revised and the original reaction networks, respectively. As predicted by other astrochemical models for several C-bearing species, the CH$_3$CN abundance has a peak at ~$10^5$ yr, when ionized carbon becomes neutral but is not yet mostly locked into CO.

With both the networks, the methyl cyanide formation follows the two steps summarized in Section 5: (1) the CH$_3$CNH$^+$ formation, dominated by the radiative association of CH$_3^+$ with HCN, followed by (2) the formation of CH$_3$CN, dominated by the electron recombination of CH$_3$CNH$^+$. In other words, the major reactions involved in the methyl cyanide formation in cold molecular clouds are [7a] and [10b].

That said, it is important to emphasize that, in the revised network, the rate constants of these two reactions have been modified. The rate constant of reaction [7a] has been decreased from $9.0 \times 10^{-9}$ to $5.7 \times 10^{-9}$ cm$^3$ s$^{-1}$ (see Section 2.6), and the BF of formation of CH$_3$CN in reaction [10b] has been lowered from 39% to 7% (see Section 4.6). The new values adopted for reactions [7a] and [10b] affect the CH$_3$CN abundance, which decreases by one order of magnitude with respect to the one obtained using the original network.

Finally, we searched for the impact of the new reaction network on species other than CH$_3$CN. The most affected ones are CH$_3^+$, CH$_3$, HCN, and HNC, which in turn are involved in the formation of C$_2$H$_2^+$, C$_2$H$^+$, C$_3$N, and CH$_4^+$. However, the abundances predicted using the new network differ by less than one order of magnitude with respect to those predicted by the original network.

## 6.3 Warm molecular protostellar shock

### 6.3.1 Modelling and adopted parameters

Young protostars are known to have spectacular ejections of matter which cause shocks when they hit the surrounding quiet environment. From the chemical point of view, the passage of the shock has two major effects: (i) it heats and compresses the gas and (ii) species frozen on the icy grain mantles are sputtered and injected into the
<table><caption>**Table 4.** Parameters used to model the passage of the shock (Section 6.3). The upper half table lists the adopted H₂ density, n<sub>H₂</sub>, temperature, T, age, t<sub>shock</sub> and cosmic-ray ionization rate, ζ<sub>CR</sub>, of the gas after the passage of the shock. The lower half table lists the adopted abundance of the species injected into the gas-phase from the grain mantle after the passage of the shock.</caption><thead><tr><th colspan="2">Physical parameters of the shocked gas</th></tr><tr><th>Parameter</th><th>L1157-B1 value</th></tr></thead><tbody><tr><td>n<sub>H2</sub> (cm<sup>-3</sup>)</td><td>4 &times; 10<sup>5</sup></td></tr><tr><td>T (K)</td><td>90</td></tr><tr><td>t<sub>shock</sub> (yr)</td><td>200–3000</td></tr><tr><td>&zeta;<sub>CR</sub> (s<sup>-1</sup>)</td><td>6 &times; 10<sup>-16</sup></td></tr><tr><td colspan="2">Abundances (wrt H) of the injected species</td></tr><tr><th>Species</th><th>L1157-B1 value</th></tr><tr><td>H<sub>2</sub>O</td><td>1 &times; 10<sup>-4</sup></td></tr><tr><td>CO<sub>2</sub></td><td>3 &times; 10<sup>-5</sup></td></tr><tr><td>CO</td><td>1 &times; 10<sup>-4</sup></td></tr><tr><td>CH<sub>3</sub>OH</td><td>8 &times; 10<sup>-6</sup></td></tr><tr><td>NH<sub>3</sub></td><td>5.6 &times; 10<sup>-5</sup></td></tr><tr><td>H<sub>2</sub>CO</td><td>1 &times; 10<sup>-6</sup></td></tr><tr><td>OCS</td><td>2 &times; 10<sup>-6</sup></td></tr><tr><td>SiO</td><td>1 &times; 10<sup>-6</sup></td></tr><tr><td>Si</td><td>1 &times; 10<sup>-6</sup></td></tr><tr><td>CH<sub>3</sub>CH<sub>2</sub></td><td>4 &times; 10<sup>-8</sup></td></tr><tr><td>CH<sub>3</sub>CH<sub>2</sub>OH</td><td>6 &times; 10<sup>-8</sup></td></tr><tr><td>SiH<sub>4</sub></td><td>1 &times; 10<sup>-7</sup></td></tr></tbody></table>

gas phase. As a result, molecular shocks are warm (~80–100 K) and dense (≥10⁵ cm⁻³) regions with much larger abundances of some species with respect to cold molecular clouds.

In order to simulate the chemical composition of the gas after the passage of a shock, we adopt a two-step procedure where we first compute the chemical abundances of the cold molecular cloud (previous subsection) and then we suddenly (i) increase the gas temperature (but not the dust one, which remains roughly the same before the shock event) and the H nuclei number density and (ii) (artificially) inject into the gas large abundances of species that are known to be present on the grain icy mantles, because of the sputtering and shattering of the grains. Although the physics is slightly different, a similar modelling can be also considered a fair enough simulation of what happens in hot cores and hot corinos, which are regions heated by the central forming star and where the grain icy mantles sublimate (e.g. see the recent review by Ceccarelli et al. 2022).

In practice, our model has two steps, as follows.

Step 1: We first compute the steady-state chemical composition of a cold molecular cloud at 10 K with a H nuclei number density of 2 × 10⁴ cm⁻³ and with the parameters described in Section 6.2.

Step 2: We increase the gas temperature to 90 K, H nuclei number density to 8 × 10⁵ cm⁻³, and we inject into the gas the grain-mantle species reported in Table 4 with the abundances listed in the table. We then leave the chemical composition evolve for 10⁴ yr.

The values adopted for the physical parameters and abundances of the injected species are based on the astronomical observations of the prototypical molecular outflow shock L1155-B1, for which our group carried the same model described here in previous works (e.g. Codella et al. 2017; Podio et al. 2017; Codella et al. 2020). Please note, though, that the modelling also approximately describes the chemical evolution of hot corinos, where similarly to the molecular shock, the components of the grain mantles are injected into the gas-phase (because of their thermal sublimation).

<figure><img src="image_9.png" /><figcaption>**Figure 8.** Abundances (with respect to H₂) of methyl cyanide and other species involved in its formation as a function of time from the passage of the shock: CH₃CN (red), HCN (blue), CH₃⁺ (orange), and CH₃CNH⁺ (green). The yellow band shows the CH₃CN abundance observed towards the L1157-B1 shocked region (see Table 5).</figcaption></figure>

### 6.3.2 Results of the modelling

Fig. 8 shows the post-shock evolution of the gas-phase abundance of methyl cyanide and other species involved in its formation as a function of time. As in the case of the molecular cloud, the production of methyl cyanide requires first the formation of CH₃CNH⁺, which can then be converted into CH₃CN. However, some reactions that were not important in the cold cloud, become relevant in the shock case thanks to the injection in the gas-phase of species such as methanol and ammonia, which are abundant grain mantle components (Table 4). In particular, CH₃CN is mainly formed by the reaction of CH₃CNH⁺ with ammonia (90 per cent) while the electron recombination of CH₃CNH⁺ accounts for the ~10 per cent of the formation of CH₃CN. In turn, 90% of the CH₃CNH⁺ is produced by the radiative association of CH₃⁺ with HCN and the remaining 10% by the reaction of CH₃OH⁺ with HNC. In summary, the major reactions entering in the methyl cyanide formation in the shock are [7a], [9b], [10a], and [10b].

Finally, as for the cold molecular cloud (Section 6.2) we searched for the impact of the new network on the other species of the model: they are minor and the difference in the predicted abundances before and after the network modification are less than a factor ten.

## 7 DISCUSSION

Methyl cyanide is commonly observed almost ubiquitously in the ISM. Here, we focus in particular on the solar-type star forming regions. Table 5 summarizes the CH₃CN observations towards cold cores, low-mass protostars and hot corinos, protoplanetary discs, and the only protostellar shock where it was detected, L1157-B1. More specifically, Table 5 lists the derived CH₃CN column densities and abundances (with respect to H₂, when it is available). It also reports the measured abundance ratio between methanol and methyl cyanide, as methanol is the most abundant iCOM. Assuming that both species are present in the same region, their abundance ratio is a more reliable value with respect to the absolute abundance of methyl cyanide.

In the following, we first compare our results with the observations towards two sources representative of cold and warm environments
<table><caption>**Table 5.** CH₃CN abundances measured towards cold clouds, hot corinos, protoplanetary discs, and protostellar shocks.</caption><thead><tr><th>Source</th><th>N<sub>CH3CN</sub> (cm<sup>-2</sup>)</th><th>Abundance/H<sub>2</sub></th><th>N<sub>H2</sub> (cm<sup>-2</sup>)</th><th>CH<sub>3</sub>OH/CH<sub>3</sub>CN</th><th>N<sub>CH3OH</sub> (cm<sup>-2</sup>)</th><th>Reference</th></tr></thead><tbody><tr><td colspan="7"><strong>Prestellar cores</strong></td></tr><tr><td>TMC-1 (cyanopolyynes peak)</td><td>(4–5) × 10<sup>12</sup></td><td>(0.8–8.0) × 10<sup>-10</sup></td><td>(0.6–5) × 10<sup>22</sup></td><td>7–10</td><td>(3–5) × 10<sup>13</sup></td><td>[1,2]</td></tr><tr><td>L1544 (dust peak)</td><td>(5–9) × 10<sup>11</sup></td><td>(5–9) × 10<sup>-11</sup></td><td>1.0 × 10<sup>22</sup></td><td>30–80</td><td>(2–4) × 10<sup>13</sup></td><td>[3,4]</td></tr><tr><td>L1517B (dust peak)</td><td>(1.5–2.7) × 10<sup>11</sup></td><td>(2–10) × 10<sup>-12</sup></td><td>(3–4) × 10<sup>22</sup></td><td>30–80</td><td>(8–12) × 10<sup>12</sup></td><td>[5]</td></tr><tr><td>L1498 (methanol peak)</td><td>(0.9–1.1) × 10<sup>11</sup></td><td>(1.3–1.5) × 10<sup>-11</sup></td><td>7 × 10<sup>21</sup></td><td>80–100</td><td>8.7 × 10<sup>12</sup></td><td>[6]</td></tr><tr><td>L1521E</td><td>(3–6) × 10<sup>11</sup></td><td>(2–4) × 10<sup>-11</sup></td><td>1.6 × 10<sup>22</sup></td><td>30–100</td><td>(1.7–3.2) × 10<sup>13</sup></td><td>[7,8]</td></tr><tr><td colspan="7"><strong>Hot corinos</strong></td></tr><tr><td>IRAS 16293–2422 A</td><td>(7–9) × 10<sup>16</sup></td><td>(2–3) × 10<sup>-8</sup></td><td>4 × 10<sup>24</sup></td><td>100–250</td><td>(0.9–1.7) × 10<sup>19</sup></td><td>[9,10,11]</td></tr><tr><td>IRAS 16293–2422 B</td><td>(3–5) × 10<sup>16</sup></td><td>(2–4) × 10<sup>-9</sup></td><td>> 1.2 × 10<sup>25</sup></td><td>160–400</td><td>(0.8–1.2) × 10<sup>19</sup></td><td>[9,10,12]</td></tr><tr><td>SVS13-A</td><td>(5–50) × 10<sup>15</sup></td><td>< 5 × 10<sup>-7</sup></td><td>> 1 × 10<sup>22</sup></td><td>100–1400</td><td>(5–7) × 10<sup>18</sup></td><td>[13,14]</td></tr><tr><td>NGC 1333 IRAS 2A</td><td>(1.6–3.2) × 10<sup>16</sup></td><td>(3–6) × 10<sup>-9</sup></td><td>5 × 10<sup>24</sup></td><td>100–500</td><td>(3–8) × 10<sup>18</sup></td><td>[15]</td></tr><tr><td>NGC 1333 IRAS 4A</td><td>(5–10) × 10<sup>16</sup></td><td>(1.3–2.7) × 10<sup>-9</sup></td><td>4 × 10<sup>25</sup></td><td>80–440</td><td>(0.8–2.2) × 10<sup>19</sup></td><td>[15]</td></tr><tr><td>B1-c</td><td>(5–10) × 10<sup>15</sup></td><td>—</td><td>—</td><td>130–480</td><td>(1.3–2.5) × 10<sup>18</sup></td><td>[16]</td></tr><tr><td>L1551-IRS5</td><td>> 1 × 10<sup>17</sup></td><td>—</td><td>> 5 × 10<sup>22</sup></td><td>—</td><td>> 1 × 10<sup>19</sup></td><td>[17,18]</td></tr><tr><td>HOPS-108</td><td>(1.8–2.2) × 10<sup>16</sup></td><td>< 7 × 10<sup>-7</sup></td><td>> 3 × 10<sup>22</sup></td><td>230–780</td><td>(5–14) × 10<sup>18</sup></td><td>[19]</td></tr><tr><td>Cep E-A</td><td>(0.9–1.9) × 10<sup>15</sup></td><td>(2–5) × 10<sup>-9</sup></td><td>4 × 10<sup>23</sup></td><td>180–710</td><td>(3–7) × 10<sup>17</sup></td><td>[20]</td></tr><tr><td colspan="7"><strong>Protoplanetary discs</strong></td></tr><tr><td>TW Hydrae</td><td>(1.3–1.6) × 10<sup>12</sup></td><td>—</td><td>—</td><td>1.8–5.0</td><td>(3–6) × 10<sup>12</sup></td><td>[21,22]</td></tr><tr><td>MWC 480</td><td>(1.4–2.2) × 10<sup>12</sup></td><td>—</td><td>—</td><td>—</td><td>—</td><td>[23]</td></tr><tr><td>V4046 Sgr</td><td>(4–8) × 10<sup>12</sup></td><td>—</td><td>—</td><td>—</td><td>—</td><td>[23]</td></tr><tr><td>GM Aur</td><td>(1.9–2.3) × 10<sup>12</sup></td><td>—</td><td>—</td><td>—</td><td>—</td><td>[24]</td></tr><tr><td>AS 209</td><td>(1.5–1.9) × 10<sup>12</sup></td><td>—</td><td>—</td><td>—</td><td>—</td><td>[24]</td></tr><tr><td>HD 163 296</td><td>(2–3) × 10<sup>12</sup></td><td>—</td><td>—</td><td>—</td><td>—</td><td>[24]</td></tr><tr><td>MWC 480</td><td>(3–4) × 10<sup>12</sup></td><td>—</td><td>—</td><td>—</td><td>—</td><td>[24]</td></tr><tr><td colspan="7"><strong>Protostellar shocks</strong></td></tr><tr><td>L1157-B1</td><td>(0.6–10) × 10<sup>12</sup></td><td>(0.3–5) × 10<sup>-9</sup></td><td>2 × 10<sup>21</sup></td><td>770–5000</td><td>(3–8) × 10<sup>15</sup></td><td>(see text)</td></tr></tbody></table>

Notes. [1] Cabezas et al. (2021);[2] Soma et al. (2015);[3] Vastel et al. (2014);[4] Vastel et al. (2019);[5] Megías et al. (2023);[6] Jiménez-Serra et al. (2021);[7] Nagy et al. (2019);[8] Scibelli et al. (2021);[9] Bottinelli et al. (2004b);[10] Calcutt et al. (2018);[11] Manigand et al. (2020);[12] Jørgensen et al. (2016);[13] Bianchi et al. (2022);[14] Hsieh et al. (2023);[15] Taquet et al. (2015);[16] Nazari et al. (2021);[17] Mercimek et al. (2022);[18] Bianchi et al. (2020);[19] Chahine et al. (2022);[20] Ospina-Zamudio et al. (2018);[21] Loomis et al. (2018);[22] Walsh et al. (2016);[23] Bergner et al. (2018);[24] Ilee et al. (2021).

(Section 7.1): TMC-1 and L1517-B1, respectively. We then discuss the possible origin of the observed correlation between the methyl cyanide and methanol abundances, due to the chemical gas-phase link of these two species (Section 7.2).

## 7.1 Model predictions versus observations

### 7.1.1 Cold environment representative: TMC-1

TMC-1 (cyanopolyyne peak) is a cold starless core in the Taurus molecular cloud (distance of 141 ± 9 pc; Zucker et al. 2019), which shows an exceptional richness in C-bearing species. Given its peculiarity, it has been extensively studied in several spectral surveys where carbon chains and rings were detected (Fuente et al. 2019; McGuire et al. 2020; Cernicharo et al. 2022, and references therein). The kinetic temperature of the gas has been estimated to be 11 ± 1 K (Fehér et al. 2016). CH₃CN has been observed with an abundance of (with respect to H₂) ~(0.8–8) × 10⁻¹⁰ (see Table 5).

Fig. 7 shows the predicted CH₃CN abundance as a function of time (see Section 6.2) compared to that observed towards TMC-1. The predictions obtained with the old network slightly overproduce methyl cyanide with respect to the measured value. On the contrary, the predictions obtained using the new network (Section 5 and Table 2) agree with the lowest estimate of the measured CH₃CN.

Methyl cyanide is detected also towards other four cold cores: L1544 (e.g. Jiménez-Serra et al. 2016; Vastel et al. 2019), L1498 (Jiménez-Serra et al. 2021), L1521E (Nagy et al. 2019) an L1517B

(Megías et al. 2023). Their abundance, which is computed assuming that the species is present throughout the entire core, has been estimated to be between 2 × 10⁻¹² and 9 × 10⁻¹¹ (see Table 5). However, these abundances have to be taken as lower limits of the real ones, because, as discussed in several previous works (e.g. Vastel et al. 2014; Ceccarelli et al. 2022), very likely iCOMs lines in cold objects are emitted in the skins of the cores and not throughout the entire core. Therefore, the H₂ column density where the iCOMs are present is smaller than that assumed, leading to a lower limit of the estimated abundance. Considering this large uncertainty, we cannot assess if our model estimation is in agreement with the observations, nevertheless it is not in contradiction.

### 7.1.2 Warm environment representative: L1157-B1

L1157-B1 is a well studied region of shocked gas, produced by the impact of a protostellar jet, driven by the Class 0 protostar L1157-mm, with the surrounding medium. Thanks to its rich chemistry, L1157-B1 is considered one of the best example to study the chemistry triggered by the passage of a protostellar shock, whose result is the injection of (some of) the dust grain mantles components into the gas-phase. Several molecules have been imaged towards L1157-B1, and, in particular, iCOMs such as CH₃OH, CH₃CHO, and NH₂CHO (Codella et al. 2017, 2020).

To our best knowledge, L1157-B1 is the only shocked regions where methyl cyanide has been detected so far. The images obtained
with the Plateau de Bure interferometer (now called NOEMA: https://iram-institute.org/observatories/noema/) show that CH3CN maps the B1 bow-shock/cavity structure, which extends over a region of about 20 arcsec (Codella et al. 2009). The temperature and density in this region has been the subject of several studies (e.g. Lefloch et al. 2012; Codella et al. 2020; Feng et al. 2022). Specifically, the non-LTE analysis of the methanol lines indicate a gas temperature equal to ~90 K and a gas density equal to ~5 × 10⁵ cm⁻³ (Codella et al. 2020). In addition, the observed [CH₃OH]/[CH₃CN] abundance ratio across the region is equal to 770–5000 (Codella et al. 2009). Using this ratio and the methanol abundance derived by Codella et al. (2020), the derived CH₃CN abundance (with respect to H₂) is equal to 1.5–4 × 10⁻⁶.<fnref n="1" />

Fig. 8 shows the CH3CN abundance predicted by the model, described in Section 6.3, against the observations towards L1557-B1. The agreement between the predictions and the observations are extremely good for shock ages larger than about 1000 yr, in line with the age of the L1157-B1 shock passage estimated by Podio et al. (2017).

## 7.2 The correlation between methyl cyanide and methanol

As mentioned in Section 1, a correlation between the measured abundances of CH3CN and CH3OH has been observed in a large sample of hot corinos (Belloche et al. 2020; Yang et al. 2021). Note that, in the case of Yang et al. (2021), the correlation is observed between the CH3OH and CH3CN column densities normalized with respect to the intensity of the continuum, as a proxy of the H2 column density. However, these authors do not explicitly derive the H2 column density and, consequently, the CH3OH and CH3CN abundances.

The [CH3OH]/[CH3CN] abundance ratio is rather constant and about 380 (see Table 5), over a relatively large range of methyl cyanide and methanol abundances, about two orders of magnitude. The constant ratio led Yang et al. (2021) to suggest the possibility that both species are formed on the grain surfaces. On the other hand, Belloche et al. (2020) ruled out that the observed methyl cyanide–methanol correlation implies a chemical link between the two species, based on the argument that CH3CN is mostly formed in the gas-phase and CH3OH on the grain surfaces. In order to understand whether the CH3CN gas-phase and CH3OH grain-surface formation really cannot reproduce the observed correlation, we ran the model used to reproduce the observations of L1157-B1 (Section 6.3) and approximately applicable also to the case of hot corinos. Specifically, we obtained the time-dependent CH3CN and CH3OH predicted abundances as a function of the CH3OH abundance.

Fig. 9 shows the results of the simulations along with the observations. Please note that, in the model the methanol abundance is the one injected, which differs from that observed because methanol is consumed forming other iCOMs. Therefore, in the plot, we consider the measured CH3OH abundance as a lower limit to the injected one. The figure shows the predicted [CH3OH]/[CH3CN] abundance ratio as a function of the methanol abundance, for different evolutionary times. For times larger than about 4 × 10⁴ yr,

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Comparison of observed and predicted [CH3OH]/[CH3CN] abundance ratio as a function of the methanol abundance (with respect to H2). The yellow box shows the range of the observed [CH3OH]/[CH3CN] ratio, derived using the values reported in Table 5. The red solid line represents the average value of the observed ratios. The model predicted [CH3OH]/[CH3CN] ratio (blue curves) is shown for three different times: 10 800 (dotted line), 40 000 (dashed line), and 75 000 (solid line) yr, respectively.</figcaption></figure>

the predicted [CH3OH]/[CH3CN] abundance ratio does not depend on the injected CH3OH abundance, in the range of the estimated methanol abundance of the hot corinos, and it is very similar to the observed value (300–340 versus 380). At ~10⁴ yr, the ratio varies within a factor 3.

The (unexpected) chemical link between methyl cyanide and methanol is the cation CH₃⁺, which is, on the one hand, the bottleneck precursor of methyl cyanide and, on the other hand, the product of the methanol reaction with H₃⁺. Specifically, methyl cyanide is mainly formed by the reaction CH₃⁺ + HCN → CH₃CNH⁺ followed by the electron recombination or proton transfer to ammonia (our reactions [7a] and [10a] of Table 2), as also discussed for the case of L1157-B1 (Section 6.3). On the other hand, once methanol is injected into the gas-phase by the grain mantle sublimation, the reaction CH₃OH + H₃⁺ → CH₃⁺ + H₂ + H₂O is the dominant production route of CH₃⁺. This reaction was studied experimentally by Lee, Drucker & Adams (1992), who measured that 53% of the reaction goes into the channel CH₃⁺ + H₂ + H₂O, while the protonation, that leads to the formation of CH₃OH₂⁺ + H₂, represents only the 12% of the products.

In summary, our simulations, obtained with the cleaned and most up-to-date gas-phase reaction network GRETOBAPE (Tinacci et al. 2023), demonstrate that the observed methyl cyanide–methanol correlation is due to the gas-phase formation of methyl cyanide that involves the cation CH₃⁺, which, in turn, is formed by the methanol once it is in the gas-phase. Thus, methanol is the grandmother of methyl cyanide.

As a final and general comment, the methyl cyanide–methanol correlation is an illustrative example of the danger to interpret the observed correlation of two species, both to assign a presumed chemical link or to exclude it. Only a careful and dedicated modelling using our best knowledge of the chemical networks can help us to assess or rule out a possible real chemical link. We remind here the cases of methyl formate and dimethyl ether (Balucani et al. 2015), glycolaldehyde and ethanol (Skouteris et al. 2018) and glycolaldehyde and acetaldehyde (Vazart et al. 2020), all cases where

<footnote n="1">¹First, we obtained the methanol abundance from the methanol column density (3–8 × 10⁻¹⁵ cm⁻²) derived by the non-LTE analysis of several CH₃OH lines towards L1157-B1 observed by Codella et al. (2020). We then divided it by the H₂ column density (2 × 10²¹ cm⁻²) derived by Lefloch et al. (2012) from the non-LTE analysis of several CO lines ($N_{CO} = 2 × 10^{17}$ cm⁻²) and assuming the standard [CO]/[H₂] = 1 × 10⁻⁴ value. Finally, we obtained a methanol abundance (with respect to H₂) equal to (1.5–4) × 10⁻⁶ and a methyl cyanide abundance of 0.3–5 × 10⁻⁹.</footnote>
the observed correlations can have a chemical-link explanation when the correct gas-phase reactions are considered.

## 8 CONCLUSIONS

In this work, we present a critical review of the 15 gas-phase reactions leading to the formation of methyl cyanide invoked in the literature and reported in the two major astrochemical databases, KIDA and UDfA. We also propose two new reactions involving protonated methanol and ammonia. We carried out new quantum mechanics calculations for eight of the 17 reactions, using a combination of DFT and CCSD(T) methods for the electronic structure calculations of the relevant potential energy surfaces and RRKM theory for the kinetic.

As a result of this study, we found that 13 of the 15 reactions reported in the KIDA and UDfA databases have incorrect products and/or rate constants. Specifically: (i) we removed three reactions based on the literature review; (ii) we removed four reactions based on our new QM calculations; (iii) we modified the rate constants of one (important) reaction based on the literature search; (iv) we modified the rate constants and products of two reactions following our results; (v) we added two new reactions, whose products and rate constants were calculated and compared with existing experiments; (vi) two reactions require further investigation but, since they are not important for the methyl cyanide formation, they were not studied here. We provide a new cleaned reaction network for the formation of methyl cyanide which consists of ten reactions, reported in Table 2.

We tested the impact of the revised network on the predicted abundance of methyl cyanide via modelling two cases, representatives of cold and warm environments: TMC-1 and L1157-B1, respectively. First, the abundance of methyl cyanide predicted using the revised reaction network compares very well with that observed in TMC-1 and L1157-B1, respectively. Secondly, we found that four reactions dominate the formation of CH₃CN (the numbers refer to those in Table 2):

<table><tr><td>(7a)</td><td>CH<sub>3</sub><sup>+</sup> + HCN → CH<sub>3</sub>CNH<sup>+</sup> + hν</td></tr><tr><td>(9b)</td><td>CH<sub>3</sub>OH<sub>2</sub><sup>+</sup> + HNC → CH<sub>3</sub>CNH<sup>+</sup> + H<sub>2</sub>O</td></tr><tr><td>(10b)</td><td>CH<sub>3</sub>CNH<sup>+</sup> + e<sup>-</sup> → CH<sub>3</sub>CN + H</td></tr><tr><td>(10a)</td><td>CH<sub>3</sub>CNH<sup>+</sup> + NH<sub>3</sub> → CH<sub>3</sub>CN + NH<sub>4</sub><sup>+</sup></td></tr></table>

Reactions [7a] and [10b] were already present in the KIDA or UDfA databases but with incorrect rate constants, that we modified. Specifically, for reaction [7a] we adopted a lower rate constant following the values derived in previous work, while for reaction [10b] we adopted new calculated BFs and corrected the temperature dependence of the rate constant. These two reactions are confirmed to be the dominant ones in the formation of methyl cyanide in cold environments. Reactions [9b] and [10a] instead have been newly added to the network following the theoretical calculations presented in this work, and they are found to be particularly important in warm environments.

Finally, we demonstrate that the correlation between the methyl cyanide and methanol, observed in the hot corinos where the two species are detected, can be explained by the fact that methanol is the grandmother of methyl cyanide. The link between the two species is the cation CH₃⁺, which is, on the one hand, the bottleneck of the reaction that dominates the CH₃CN gas-phase formation and, on the other hand, the product of the gas-phase reaction of H₃⁺ with CH₃OH, which is a grain-surface product.

To summarize, this work major conclusions are: (1) methyl cyanide can efficiently form in the gas-phase in both cold and warm regions

of the ISM, and (2) the correlation between methyl cyanide and methanol observed in hot corinos by other authors is likely the result of the gas-phase reaction of methanol, a grain-surface product, with H₃⁺, which produces CH₃⁺ which is the bottleneck for the gas-phase formation of methyl cyanide.

As final comment, we notice that, so far, gas-phase reactions can explain the observed correlations of four couples of iCOMs: methyl formate and dimethyl ether (Balucani et al. 2015), glycolaldehyde and ethanol (Skouteris et al. 2018), glycolaldehyde and acetaldehyde (Vazart et al. 2020) and methyl cyanide and methanol (this work). Therefore, astronomical observations are a powerful tool to understand the chemistry of iCOMs and their correlations probably tell us of real chemical links, which is up to us to discover and which are not necessarily that the couple is formed on the grain-surfaces, as often assumed.

## ACKNOWLEDGEMENTS

This project has received funding within the European Union's Horizon 2020 research and innovation programme from the European Research Council (ERC) for the project 'The Dawn of Organic Chemistry' (DOC), grant agreement No 741002, and from the Marie Skłodowska-Curie for the project-Astro-Chemical Origins' (ACO), grant agreement No 811312. The authors thank the Herla Project (http://hscw.herla.unipg.it) - 'Università degli Studi di Perugia' and the 'Dipartimento di Ingegneria Civile e Ambientale' of the University of Perugia within the project 'Dipartimenti di Eccellenza 2018-2022' for allocated computing time. Some computations presented in this paper were performed using the GRICAD infrastructure (https://gricad.univ-grenoble-alpes.fr), which is partly supported by the Equip@Meso project (reference ANR-10-EQPX-29-01) of the programme Investissements d'Avenir supervised by the Agence Nationale pour la Recherche. EB acknowledges the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC 2094-390783311.

## DATA AVAILABILITY

The data underlying this article are available in the article and in its online supplementary material.

## REFERENCES

Agúndez M., Marcelino N., Cernicharo J., Roueff E., Tafalla M., 2019, A&A, 625, A147

Agúndez M., Wakelam V., 2013, Chem. Rev., 113, 8710

Altwegg K., Balsiger H., Fuselier S. A., 2019, ARA&A, 57, 113

Anicich V. G., 1993, J. Phys. Chem. Ref. Data, 22, 1469

Anicich V. G., Huntress W. T., Jr, McEwan M. J., 1986, J. Phys. Chem., 90, 2446

Anicich V. G., Sen A. D., Huntress W. T., Jr, McEwan M. J., 1995, J. Chem. Phys., 102, 3256

Balucani N., Ceccarelli C., Taquet V., 2015, MNRAS, 449, L16

Bartlett R. J., 1981, Annu. Rev. Phys. Chem., 32, 359

Bass L. M., Kemper P. R., Anicich V. G., Bowers M. T., 1981, J. Am. Chem. Soc., 103, 5283

Bates D., 1983, ApJ, 270, 564

Becke A., 1993, J. Chem. Phys., 98, 5648

Belloche A. et al., 2020, A&A, 635, A198

Bergner J. B., Guzmán V. G., Öberg K. I., Loomis R. A., Pegues J., 2018, ApJ, 857, 69

Bézard B., Marten A., Paubert G., 1993, AAS/Division for Planetary Sciences Meeting Abstracts #2525.09,
Bianchi E. et al., 2020, MNRAS, 498, L87

Bianchi E. et al., 2022, A&A, 662, A103

Biver N., Boissier J., Bockelée-Morvan D., Crovisier J., Cottin H., Cordiner M., Roth N., Moreno R., 2022, A&A, 668, A171

Blázquez S. et al., 2020, Phys. Chem. Chem. Phys., 22, 20562

Bottinelli S. et al., 2004a, ApJ, 615, 354

Bottinelli S. et al., 2004b, ApJ, 617, L69

Brack A., 1998, The Molecular Origins of Life: Assembling Pieces of the Puzzle. Cambridge Univ. Press, Cambridge

Cabezas C., Endo Y., Roueff E., Marcelino N., Agúndez M., Tercero B., Cernicharo J., 2021, A&A, 646, L1

Calcutt H. et al., 2018, A&A, 616, A90

Cappelletti D., Pirani F., Bussery-Honvault B., Gomez L., Bartolomei M., 2008, Phys. Chem. Chem. Phys., 10, 4281

Ceccarelli C. et al., 2017, ApJ, 850, 176

Ceccarelli C. et al., 2023, ASP Conf. Ser., 534, 379

Cernicharo J., Agúndez M., Cabezas C., Marcelino N., Tercero B., Pardo J. R., Fuentetaja R., de Vicente P., 2022, Eur. Phys. J. Web Conf., 265, 00041

Chahine L. et al., 2022, A&A, 657, A78

Codella C. et al., 2009, A&A, 507, L25

Codella C. et al., 2017, A&A, 605, L3

Codella C. et al., 2020, A&A, 635, A17

Das T., Ghule S., Vanka K., 2019, ACS Cent. Sci., 5, 1532

DeFrees D., McLean A., Herbst E., 1985, ApJ, 293, 236

Dunning T. H., Jr, 1989, J. Chem. Phys., 90, 1007

Enrique-Romero J., Rimola A., Ceccarelli C., Ugliengo P., Balucani N., Skouteris D., 2019, ACS Earth Space Chem., 3, 2158

Enrique-Romero J., Ceccarelli C., Rimola A., Skouteris D., Balucani N., Ugliengo P., 2021, A&A, 655, A9

Enrique-Romero J., Rimola A., Ceccarelli C., Ugliengo P., Balucani N., Skouteris D., 2022, ApJS, 259, 39

Fehér O., Tóth L. V., Ward-Thompson D., Kirk J., Kraus A., Pelkonen V. M., Pintér S., Zahorecz S., 2016, A&A, 590, A75

Feng S., Liu H. B., Caselli P., Burkhardt A., Du F., Bachiller R., Codella C., Ceccarelli C., 2022, ApJ, 933, L35

Frisch M. J. et al., 2009, Gaussian09 Revision E.01

Frisch M. J. et al., 2016, Gaussian~16 Revision C.01

Fuente A. et al., 2019, A&A, 624, A105

Gannon K. L., Glowacki D. R., Blitz M. A., Hughes K. J., Pilling M. J., Seakins P. W., 2007, J. Phys. Chem. A, 111, 6679

Garrod R. T., Jin M., Matis K. A., Jones D., Willis E. R., Herbst E., 2022, ApJS, 259, 1

Garrod R. T., Weaver S. L. W., Herbst E., 2008, ApJ, 682, 283

Geppert W. D. et al., 2006, Faraday Discuss., 133, 177

Geppert W. D. et al., 2007, J. Phys.: Conf. Ser., 88, 012068

Gonzalez C., Schlegel H. B., 1989, J. Chem. Phys., 90, 2154

Gonzalez C., Schlegel H. B., 1990, J. Phys. Chem., 94, 5523

Guberman S. L., 2003, in Guberman S. L., ed., Dissociative Recombination of Molecular Ions with Electrons. Springer, New York, p. 187

Hanwell M. D., Curtis D. E., Lonie D. C., Vandermeersch T., Zurek E., Hutchison G. R., 2012, J. Cheminform., 4, 1

Hemsworth R., Payzant J., Schiff H., Bohme D., 1974, Chem. Phys. Lett., 26, 417

Herbst E., 1985, ApJ, 291, 226

Herbst E., Van Dishoeck E. F., 2009, ARA&A, 47, 427

Hsieh T.-H. et al., 2023, A&A, 669, A137

Ilee J. D. et al., 2021, ApJS, 257, 9

Illies A., Liu S., Bowers M., 1981, J. Am. Chem. Soc., 103, 5674

Irvine W. M. et al., 1988, ApJ, 334, L107

Jenkins E. B., 2009, ApJ, 700, 1299

Jiménez-Serra I. et al., 2016, ApJ, 830, L6

Jiménez-Serra I., Vasyunin A. I., Spezzano S., Caselli P., Cosentino G., Viti S., 2021, ApJ, 917, 44

Jørgensen J. K., et al., 2016, A&A, 595, A117

Kemper P. R., Bass L. M., Bowers M. T., 1985, J. Phys. Chem., 89, 1105

Klippenstein S. J., Yang Y.-C., Ryzhov V., Dunbar R. C., 1996, J. Chem. Phys., 104, 4502

Knight J., Freeman C., McEwan M., 1986, J. Am. Chem. Soc., 108, 1404

Kramida A., Ralchenko Y. U., Reader J., and NIST ASD Team, 2022, NIST Atomic Spectra Database (ver. 5.10), [Online]. Available at: https://ph ysics.nist.gov/asd [2017, April 9], National Institute of Standards and Technology, Gaithersburg, MD.

Le Gal R., Brady M. T., Öberg K. I., Roueff E., Le Petit F., 2019, ApJ, 886, 86

Le Roy L. et al., 2015, A&A, 583, A1

Lee H. S., Drucker M., Adams N. G., 1992, Int. J. Mass Spectrom. Ion Process., 117, 101

Lefloch B. et al., 2012, ApJ, 757, L25

Li Y., Liu H.-l., Huang X.-r., Geng C.-y., Sun C.-c., Tang A.-c., 2008, J. Phys. Chem. A, 112, 2693

Loison J.-C., Wakelam V., Hickson K. M., 2014, MNRAS, 443, 398

Loomis R. A., Cleeves L. I., Öberg K. I., Aikawa Y., Bergner J., Furuya K., Guzman V. V., Walsh C., 2018, ApJ, 859, 131

Luca A., Voulot D., Gerlich D., 2002, in 11th Annual Conference of Doctoral Students WDS'02: Ion-Trapping Apparatus for Studies on Reactions between Ions and Neutral Carbon Species. WDS, Chemnitz, p. 294

Mackay G., Vlachos G., Bohme D.-K., Schiff H., 1980, Int. J. Mass Spectrom. Ion Phys., 36, 259

Manigand S. et al., 2020, A&A, 635, A48

Marchione D., 2022, J. Phys. Chem. A, 126, 3569–3582

Marten A., Hidayat T., Biraud Y., Moreno R., 2002, Icarus, 158, 532

Martin T., Melton C., 1960, J. Chem. Phys., 32, 700

McElroy D., Walsh C., Markwick A., Cordiner M., Smith K., Millar T., 2013, A&A, 550, A36

McEwan M., Anicich V., Huntress W., Jr, 1981, Int. J. Mass Spectrom. Ion Phys., 37, 273

McEwan M., Anicich V., Huntress W., Kemper P., Bowers M., 1980, Chem. Phys. Lett., 75, 278

McGuire B. A. et al., 2020, ApJ, 900, L10

McGuire B. A., 2022, ApJS, 259, 30

McLain J., Adams N., 2009, Planet. Space Sci., 57, 1642

Megías A., Jiménez-Serra I., Martín-Pintado J., Vasyunin A. I., Spezzano S., Caselli P., Cosentino G., Viti S., 2023, MNRAS, 519, 1601

Meisner J., Zhu X., Martínez T. J., 2019, ACS Cent. Sci., 5, 1493

Meot-Ner M., Karpas Z., Deakyne C. A., 1986, J. Am. Chem. Soc., 108, 3913

Mercimek S. et al., 2022, A&A, 659, A67

Minh Y. C., Irvine W. M., Ohishi M., Ishikawa S., Saito S., Kaifu N., 1993, A&A, 267, 229

Nagy Z., Spezzano S., Caselli P., Vasyunin A., Tafalla M., Bizzocchi L., Prudenzano D., Redaelli E., 2019, A&A, 630, A136

Nazari P. et al., 2021, A&A, 650, A150

Nazari P. et al., 2022, A&A, 668, A109

Neufeld D. et al., 2015, A&A, 577, A49

Öberg K. I., Guzmán V. V., Furuya K., Qi C., Aikawa Y., Andrews S. M., Loomis R., Wilner D. J., 2015, Nature, 520, 198

Olsen J., Jo/rgensen P., Koch H., Balkova A., Bartlett R. J., 1996, J. Chem. Phys., 104, 8007

Ospina-Zamudio J., Lefloch B., Ceccarelli C., Kahane C., Favre C., López-Sepulcre A., Montarges M., 2018, A&A, 618, A145

Perrero J., Enrique-Romero J., Martínez-Bachs B., Ceccarelli C., Balucani N., Ugliengo P., Rimola A., 2022, ACS Earth Space Chem., 6, 496

Pirani F., Brizi S., Roncaratti L. F., Casavecchia P., Cappelletti D., Vecchio-cattivi F., 2008, Phys. Chem. Chem. Phys., 10, 5489

Plessis S., Carrasco N., Dobrijevic M., Pernot P., 2012, Icarus, 219, 254

Podio L. et al., 2017, MNRAS, 470, L16

Powner M. W., Gerland B., Sutherland J. D., 2009, Nature, 459, 239

Prasad S. S., Huntress W. T. J., 1980, ApJS, 43, 1

Raghavachari K., Trucks G. W., Pople J. A., Head-Gordon M., 1989, Chem. Phys. Lett., 157, 479

Rimola A., Skouteris D., Balucani N., Ceccarelli C., Enrique-Romero J., Taquet V., Ugliengo P., 2018, ACS Earth Space Chem., 2, 720

Rodgers S., Charnley S., 2001a, MNRAS, 320, L61

Rodgers S., Charnley S., 2001b, ApJ, 546, 324

Sanchez R. A., Ferris J. P., Orgel L. E., 1966, Science, 154, 784

Scibelli S., Shirley Y., Vasyunin A., Launhardt R., 2021, MNRAS, 504, 5754
Scott G. B., Fairley D. A., Freeman C. G., McEwan M. J., Anicich V. G., 1999, *J. Phys. Chem. A*, 103, 1073

Sims I. R., Queffelec J.-L., Travers D., Rowe B. R., Herbert L. B., Karthäuser J., Smith I. W., 1993, *Chem. Phys. Lett.*, 211, 461

Skouteris D., Balucani N., Faginas-Lago N., Falcinelli S., Rosi M. 2015, *A&A*, 584, 8

Skouteris D., Balucani N., Ceccarelli C., Vazart F., Puzzarini C., Barone V., Codella C., Lefloch B., 2018, *ApJ*, 854, 135

Skouteris D., Balucani N., Ceccarelli C., Faginas Lago N., Codella C., Falcinelli S., Rosi M., 2019, *MNRAS*, 482, 3567

Solomon P. M., Jefferts K. B., Penzias A. A., Wilson R. W., 1971, *ApJ*, 168, L107

Soma T., Sakai N., Watanabe Y., Yamamoto S., 2015, *ApJ*, 802, 74

Stephens P. J., Devlin F. J., Chabalowski C. F., Frisch M. J., 1994, *J. Phys. Chem.*, 98, 11623

Su T., Chesnavich W. J., 1982, *J. Chem. Phys.*, 76, 5183

Sutherland J. D., 2017, *Nat. Rev. Chem.*, 1, 0012

Taquet V., López-Sepulcre A., Ceccarelli C., Neri R., Kahane C., Charnley S. B., 2015, *ApJ*, 804, 81

Taquet V., Wirstöm E. S., Charnley S. B., 2016, *ApJ*, 821, 46

Tennis J., Loison J.-C., Herbst E., 2021, *ApJ*, 922, 133

Tinacci L., Ferrada-Chamorro S., Ceccarelli C., Pantaleone S., Ascenzi D., Maranzana A., Balucani N., Ugliengo P., 2023, *ApJS*, 266, 38

Ulich B., Conklin E., 1974, *Nature*, 248, 121

Vastel C., Ceccarelli C., Lefloch B., Bachiller R., 2014, *ApJ*, 795, L2

Vastel C., Loison J. C., Wakelam V., Lefloch B., 2019, *A&A*, 625, A91

Vazart F., Calderini D., Puzzarini C., Skouteris D., Barone V., 2016, *J. Chem. Theory Comput.*, 12, 5385

Vazart F., Ceccarelli C., Balucani N., Bianchi E., Skouteris D., 2020, *MNRAS*, 499, 5547

Vigren E. et al., 2008, *Phys. Chem. Chem. Phys.*, 10, 4014

Wakelam V. et al., 2012, *ApJS*, 199, 21

Wakelam V. et al., 2015, *ApJS*, 217, 20

Wakelam V., Herbst E., Le Bourlot J., Hersant F., Selsis F., Guilloteau S., 2010, *A&A*, 517, A21

Wakelam V., Selsis F., Herbst E., Caselli P., 2005, *A&A*, 444, 883

Walsh C. et al., 2016, *ApJ*, 823, L10

Woon D. E., Herbst E., 2009, *ApJS*, 185, 273

Yang X., Maeda S., Ohno K., 2005, *J. Phys. Chem. A*, 109, 7319

Yang Y.-L. et al., 2021, *ApJ*, 910, 20

Zucker C., Speagle J. S., Schlafly E. F., Green G. M., Finkbeiner D. P., Goodman A. A., Alves J., 2019, *ApJ*, 879, 125

## APPENDIX A: EXTRA RESULTS

$$ \text{A1 Reaction [1]: } C_2H_2^+ + NH_2 \rightarrow CH_3CN^+ + H $$

### A1.1 PES of reaction [1]

Fig. A1 shows the PES of the reaction between $C_2H_2^+$ and $NH_2$. The initial intermediate addition intermediate INT1 (localized at -476.8 kJ mol⁻¹ with respect to the reactants energy asymptote) can evolve in three different ways via isomerization to: i) INT2 through TS2 (+234.4 kJ mol⁻¹); ii) INT3 through TS1 (+250.8 kJ mol⁻¹) and iii) INT5 through TS3 (+244.3 kJ mol⁻¹). INT2 can, in turn, isomerize to INT4 by overcoming a barrier of 91.8 kJ mol⁻¹ (TS6), or to INT9 by overcoming a barrier of 197.7 kJ mol⁻¹ (TS5) or to INT5 by overcoming a barrier of 350.8 kJ mol⁻¹ (TS4). INT3, instead, can isomerize to INT6 through TS7 (+98.3 kJ mol⁻¹), while INT5 can isomerize to INT7 through TS9 (+51.6 kJ mol⁻¹). Additionally, INT4 can isomerize to INT8, the most stable intermediate in the PES (located 665.1 kJ mol⁻¹ below the reactants energy asymptote), through TS8 (barrier of 45.4 kJ mol⁻¹). Alternatively, INT4 can eliminate an $H_2$ molecule and form $CH_2CN^+ + H_2$ (with a global enthalpy change of -253.2 kJ mol⁻¹). INT6 can instead isomerize to INT7 through TS11 (barrier of 226.4 kJ mol⁻¹) or it can form $NH_3^+ + CCH$ (globally, this is a proton transfer process) with an enthalpy change of -5.7 kJ mol⁻¹ with respect to the reactants. INT9 can isomerize to INT10 via TS13 (77.8 kJ mol⁻¹) or into INT11 via TS12 (34.2 kJ mol⁻¹). INT11, in turn, can evolve into INT12 through TS14 (barrier of 76.9 kJ mol⁻¹). INT7 can lose an H-atom and form $NH_2CCH^+ + H$ (the enthalpy change for this channel is -176.1 kJ mol⁻¹) or $CH_2CNH^+ + H$ (the enthalpy change for this channel is -253.7 kJ mol⁻¹). The fission of the N-H bond in INT8 leads to the formation of $CH_3CN^+ + H$ through TS15 (+628.0 kJ mol⁻¹), otherwise the fission of the C-C bond leads to the formation of $CH_3^+ + HNC$ in a barrier-less process. Similar processes can be observed starting from the INT10 intermediate, which can form $CH_3NC^+ + H$ through TS16, or $CH_3^+ + HNC$. Finally, the fission of the C-H bond in INT12 (TS17) forms $CH_2NCH^+ + H$ in a channel with an enthalpy change of -208.9 kJ mol⁻¹. We remark that TS15, TS16, and TS17 were identified as submerged transition states and therefore are reported with the same energy of the respective products.

<figure><img src="image_11.png" /><figcaption>**Figure A1.** PES of the reaction [1] in Table 1, $C_2H_2^+ + NH_2$. The plot shows the results obtained at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level of theory.</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>**Figure A2.** PES of the reaction [2] of Table 1, C₂H₄⁺ + N. The plot shows the results obtained at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level of theory.</figcaption></figure>

### A1.2 Kinetics of reaction [1]

For this system we did not run RRKM calculations. However, we can say that the channel leading to the formation of CH₃CN⁺ has probably a negligible BF with respect to the other channels because it is much less exothermic (−41.4 kJ mol⁻¹) than the other channels and its formation pathway is characterized by very high energy barriers. In particular, INT8 can lose an H atom and form CH₃CN⁺ only by overcoming a barrier of 628.0 kJ mol⁻¹, while the competing process from the same intermediate INT8 and leading to CH₃⁺ and HNC is barrier-less and leads to the formation of much more stable products (for this channel ΔH°₀ = −221.9 kJ mol⁻¹). For the proton transfer process we could not find a direct channel connecting the reactants to the products via a single adduct. The NH₃⁺ + CCH products can be formed in a multistep process that requires the formation of INT1, INT3, and then INT6. In conclusion, from the analysis of the PES it is obvious that this reaction cannot be an important source of CH₃CN⁺ as considered in the usual databases and we decided to remove it from our network. RRKM calculation to derive the specific BFs are postponed to a future work.

form INT9 through TS11 (representing a barrier of 228.1 kJ mol⁻¹) or INT8 through TS8 (barrier of 0.7 kJ mol⁻¹). INT6 can isomerize to INT7 through TS10 (barrier of 70.2 kJ mol⁻¹) and both of them can lose an H atom and form CH₃NC⁺ (ΔH°₀ = −35.8 kJ mol⁻¹), or CH₂NCH⁺ (ΔH°₀ = −52.7 kJ mol⁻¹), respectively. INT8 can instead form CH₂CNH⁺ + H in the most exothermic channel (ΔH°₀ = −265.1 kJ mol⁻¹), overcoming a barrier of 131.8 kJ mol⁻¹ (TS16). INT8 can also isomerize to INT10 through TS15 (barrier of 201.1 kJ mol⁻¹), while INT9 can isomerize to INT10 through TS14 (barrier of 31.1 kJ mol⁻¹). INT10 can in turn isomerize to INT11 by overcoming a barrier of 151.8 kJ mol⁻¹ (TS19), otherwise it can lose an H atom and form CH₂CNH⁺ through TS18 (barrier of 72.4 kJ mol⁻¹). INT7 can also lose an H-atom and form CH₃CN⁺ by overcoming a barrier of 190.0 kJ mol⁻¹ (TS20).

The possibility of ISC from the triplet surface to the more stable singlet surface has not been explored at this level of calculations. Moreover, we have only considered the channels leading to products that retain the CCN chain while those involving the breaking of the C–C or the C–N bond have been neglected. A complete investigation of the reaction is postponed to a possible future work.

$$ \textbf{A2 Reaction [2]:} \quad C_2H_4^+ + N \rightarrow CH_3CN^+ + H $$

### A2.1 PES of reaction [2]

Fig. A2 shows the PES for the reaction between N atoms and C₂H₄⁺ ions in their fundamental states (⁴S) and (²A), respectively. The initial intermediate INT1 (in the triplet state) can isomerize to INT2, INT3, or INT6 by overcoming barriers of 194.0 kJ mol⁻¹ (TS1), 48.9 kJ mol⁻¹ (TS2), and 223.7 kJ mol⁻¹ (TS3), respectively. INT2 can, in turn, isomerize to INT5 via TS4 by overcoming a barrier of 71.6 kJ mol⁻¹ or into INT4 by overcoming a barrier which is localized above the energy of the reactants (TS5, +0.72 kJ mol⁻¹). INT3 can instead isomerize to INT6 through a barrier of 243.7 kJ mol⁻¹ (TS6), or it can lose an H atom and form CH₂NCH⁺, the second most exothermic product (ΔH°₀ = −220.3 kJ mol⁻¹), by overcoming a barrier of 154.7 kJ mol⁻¹ (TS7). INT4 can isomerize to INT8 through a barrier of 67.8 kJ mol⁻¹ (TS9), while INT5 can

### A2.2 Kinetics of reaction [2]

In this reaction the most favourable channel is the one leading to CH₂NCH⁺ + H since in can be formed after only one isomerization of the initial intermediate and is highly exothermic (−220.3 kJ mol⁻¹). The formation of all other CH₃NC⁺, CH₂CNH⁺, and CH₃CN⁺ isomers require at least four isomerization before dissociation into the products. Given that the channel leading to CH₃CN⁺ (the product considered in the databases) is much less exothermic than those forming its CH₃NC⁺ and CH₂CNH⁺isomers, and that it requires more isomerization to be formed with respect to CH₃NC⁺, it should not be considered the major product of the reaction. Because we were solely interested in the formation of CH₃CN⁺, we chose to remove this reaction from our CH₃CN network without performing kinetic calculations.

However, since CH₂CNH⁺ and CH₂NCH⁺ are of relevance for the formation of the CH₂CN radical (observed in the ISM (Irvine
<figure><img src="image_13.png" /><figcaption>**Figure A3.** PES of the reaction [4] of Table 1, CH₂CN + H₃⁺. In the plot the B3LYP/aug-cc-pVTZ energies are reported in black, while the CCSD(T)/aug-cc-pVTZ energies are reported in red.</figcaption></figure>

et al. 1988) and possibly linked to CH₃CN) further investigations are needed but postponed to a future work.

$$ \text{A3 Reaction [4]: H}_2\text{CCN} + \text{H}_3^+ \rightarrow \text{CH}_3\text{CN}^+ + \text{H}_2 $$

### A3.1 PES of reaction [4]

The cyanomethyl radical CH₂CN exists in two resonant forms, the first one with a C-N triple bond and the unpaired electron on the terminal carbon atom, and the second one with double C–C and C–N bonds and the unpaired electron on the N atom. Since the form with the radical on the N atom is the favoured one, we expect the

protonation by H₃⁺ to be more favourable on the N atom than that on the C atom. This is confirmed by the PES showed in Fig. A3: the reactants can form two adducts which are almost isoenergetic with their exit channels leading to CH₃CN⁺ + H₂ (ΔH₀ = -121.9 kJ mol⁻¹) and CH₂CNH⁺ + H₂ (ΔH₀ = -334.2 kJ mol⁻¹), respectively. In particular ADD1 is localized at -6.9 kJ mol⁻¹ with respect to the energy of the products at the B3LYP level, a difference that almost disappears at the CCSD(T) level, while ADD2 is localized below the products both at CCSD(T) and B3LYP level (-8.0 and -6.7 kJ mol⁻¹, respectively). Once the adducts are formed, they can eliminate an H₂ molecule without any barrier.

### A3.2 Kinetics of reaction [4]

Considering that the most relevant C₂H₂N form is the one with the unpaired electron on the N atom, and that the channel of formation of CH₂CNH⁺ is 213 kJ mol⁻¹ more exothermic than the channel of formation of CH₃CN⁺, we concluded that the main product of this reaction is CH₂CNH⁺ and not CH₃CN⁺ as instead considered in the databases. We therefore decided to remove the reaction from our CH₃CN network but, as for reaction [2], the formation of CH₂CNH⁺ is still of interest and opens new questions on the connection between CH₃CN and CH₂CN.

$$ \text{A4 Reaction [8]: CH}_4^+ + \text{HCN} \rightarrow \text{CH}_3\text{CNH}^+ + \text{H} $$

### A4.1 PES of reaction [8]

Fig. A4 shows the global PES starting with the barrier-less addition of HCN on CH₄⁺. Two initial adducts can be formed without any entrance barrier, ADD1 and ADD2, localized at -70.3 and -232.3 kJ mol⁻¹ with respect to the reactants, respectively. However, ADD1 easily converts into ADD2 through a saddle point that has been identified at the B3LYP level, but not at the CCSD(T) level. For this

<figure><img src="image_14.png" /><figcaption>**Figure A4.** PES of the reaction [8] of Table 1, CH₄⁺ + HCN. The plot shows the results obtained at the CCSD(T)/aug-cc-pVTZ//B3LYP/aug-cc-pVTZ level of theory.</figcaption></figure>
reason, ADD1 formation is not relevant for the kinetic of the reaction. Once ADD2 is formed, a proton transfer can occur to form the CH 3 + HCNH⁺ products (ΔH°0 = -184.0 kJ mol⁻¹). Alternatively, ADD2 can rearrange into two different intermediates, INT1 or INT2, through a barrier of 36.1 kJ mol⁻¹ (TS1) and 36.5 kJ mol⁻¹ (TS2), respectively. INT1 can isomerize to four different minima: i) INT3, by overcoming a barrier of 1.4 kJ mol⁻¹ (TS3), ii) INT4 through a barrier of 170.3 kJ mol⁻¹ (TS5), iii) INT6 through a barrier of 266.0 kJ mol⁻¹ (TS8), and iv) ADD3 through a barrier of 103.3 kJ mol⁻¹ (TS4). INT1 can also directly dissociate into CH 3 CNH⁺ + H (ΔH°0 = -234.3 kJ mol⁻¹) by overcoming a barrier of 105.9 kJ mol⁻¹ (TS6). INT2 can, instead, isomerize to INT5 via TS9 (barrier of 32.4 kJ mol⁻¹) or INT7 via TS7 (barrier of 186.0 kJ mol⁻¹). INT3 can, in turn, isomerize to INT5, through TS10 (barrier of 229.4 kJ mol⁻¹), to ADD3 through TS11 (barrier of 104.1 kJ mol⁻¹), or it can dissociate into CH 3 CNH⁺ + H by overcoming a barrier of 106.8 kJ mol⁻¹ (TS12). INT4 can also form CH 3 CNH⁺ + H through TS14 (163 kJ mol⁻¹), while INT7 can dissociate into CH 3 NCH⁺ + H (ΔH°0 = -187.8 kJ mol⁻¹) by overcoming a barrier of 138.4 kJ mol⁻¹ (TS15). ADD3 can proceed to a complete proton transfer and form CH 3 + HCNH⁺, as it was the case for ADD2. ADD1 can isomerize, at least in principle, to INT6 through TS16 (-35.1 kJ mol⁻¹ with respect to the reactants), which in turn can fragment into CH 2 CNH⁺ + H 2 , the least exothermic channel of the reaction (ΔH°0 = -40.0 kJ mol⁻¹) by overcoming TS17 localized at -4.4 kJ mol⁻¹. Our work is in agreement with the one by Li et al. (2008), but a new transition state (TS12) and two additional intermediates (INT5 and ADD3) have been found, as well as a connection between the reactants and ADD1.

A4.2 Kinetics of reaction [8]

We characterized the entrance channel using the electronic structure
calculations described in Section 3.2 and we calculated a capture rate
constant of 3.9 × 10⁻⁹ cm³ s⁻¹. This global value has been used to
derive the rate constants for each channel: 3.9 × 10⁻⁹ cm³ s⁻¹ for
the proton transfer channel that forms CH₃ + HCNH⁺; 3.2 × 10⁻¹¹

<figure><img src="image_15.png" /><figcaption>**Figure A5.** Rate constants of reaction [8], CH₄⁺ + HCN, as a function of the temperature for the products CH₃ + HCNH⁺ (blue), CH₃CNH⁺ + H (green) and CH₃NCH⁺ + H (red), respectively. The plot also reports the measurements at room temperature of the rate constant of the CH₃ + HCNH⁺ product (Bass et al. 1981; Anicich et al. 1986).</figcaption></figure>

cm³ s⁻¹ for the channel leading to CH₃CNH⁺ + H; and 3.0 × 10⁻¹⁵
cm³ s⁻¹ for the channel leading to CH₃NCH⁺ + H. The BF of the
channel leading to CH₂CHN⁺ + H₂ is negligible with respect to the
other three.

The obtained rate constants as a function of the temperature are
shown in Fig. A5. There is no dependence on the temperature since
the back-dissociation is negligible being the first intermediate formed
with a large energy gain (−232.3 kJ mol⁻¹).

Finally, our calculated rate constant at 300 K for the proton transfer
channel forming CH₃ + HCNH⁺ agrees very well with the two
experimental measurements by Bass et al. (1981) and Anicich et al.
(1986).

This paper has been typeset from a TeX/LA TeX file prepared by the author.