# Chemistry of TMC-1 with multiply deuterated species and spin chemistry of H2, H2+, H3+ and their isotopologues

Liton Majumdar, P. Gratier, M. Ruaud, Valentine Wakelam, C. Vastel, O.

Sipilä, F. Hersant, Anne Dutrey, S. Guilloteau

► To cite this version:

Liton Majumdar, P. Gratier, M. Ruaud, Valentine Wakelam, C. Vastel, et al.. Chemistry of TMC-1 with multiply deuterated species and spin chemistry of H2, H2+, H3+ and their isotopologues. Monthly Notices of the Royal Astronomical Society, 2017, 466, pp.4470-4479. 10.1093/mnras/stw3360. hal-01434936

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# Chemistry of TMC-1 with multiply deuterated species and spin chemistry of H₂, H₂⁺, H₃⁺ and their isotopologues

L. Majumdar,<fnref n="1" />,<fnref n="2" />* P. Gratier,<fnref n="1" /> M. Ruaud,<fnref n="1" /> V. Wakelam,<fnref n="1" /> C. Vastel,<fnref n="3" />,<fnref n="4" /> O. Sipilä,<fnref n="5" /> F. Hersant,<fnref n="1" /> A. Dutrey<fnref n="1" /> and S. Guilloteau<fnref n="1" />

Accepted 2016 December 22. Received 2016 December 16; in original form 2016 June 14

## ABSTRACT

Deuterated species are unique and powerful tools in astronomy since they can probe the physical conditions, chemistry and ionization level of various astrophysical media. Recent observations of several deuterated species along with some of their spin isomeric forms have rekindled the interest for more accurate studies on deuterium fractionation. This paper presents the first publicly available chemical network of multiply deuterated species along with spin chemistry implemented on the latest state-of-the-art gas-grain chemical code 'NAUTILUS'. D/H ratios for all deuterated species observed at different positions of TMC-1 are compared with the results of our model, which considers multiply deuterated species along with the spin chemistry of light hydrogen bearing species H₂, H₂⁺, H₃⁺ and their isotopologues. We also show the differences in the modelled abundances of non-deuterated species after the inclusion of deuteration and spin chemistry in the model. Finally, we present a list of potentially observable deuterated species in TMC-1 awaiting detection.

**Key words:** astrochemistry – methods: statistical – ISM: abundances – ISM: evolution – ISM: molecules.

## 1 INTRODUCTION

Until now (as of 2016 February), almost 200 molecules have been detected in the interstellar medium (ISM) or circumstellar shells (as listed by CDMS).<fnref n="1" /> In addition, several deuterated species have been detected in various astrophysical media. Among them there were several detections:

(i) in dark clouds – DCO⁺ (Guelin et al. 1977; van der Tak et al. 2009), DNC (Turner & Zuckerman 1978; van der Tak et al. 2009), HDCO (Loren & Wootten 1985) and D₂CO (Turner 1990);

(ii) in pre-stellar cores – D₂CO (Bacmann 2004), H₂D⁺ (Stark, van der Tak & van Dishoeck 1999; Caselli et al. 2003, 2008; Vastel et al. 2006; Parise et al. 2011), D₂H⁺ (Vastel, Phillips & Yoshida 2004; Parise et al. 2011), N₂D⁺ (Miettinen et al. 2012) and NHD₂ (Roueff et al. 2000);

(iii) towards low-mass and high-mass protostars – D₂CO, HDCO (Bergman et al. 2011), DCOOCH₃ (Demyk et al. 2010;

Margulès et al. 2010), HDO (Coutens et al. 2012, 2014), D₂O (Vastel et al. 2010) and OD (Parise et al. 2012);

(iv) in protoplanetary discs – DCN, DCO⁺ (van Dishoeck, Thi & van Zadelhoff 2003; Guilloteau et al. 2006; Qi et al. 2008; Öberg et al. 2015), N₂D⁺ (Huang & Öberg 2015) and HD (Bergin et al. 2013), the main deuterium reservoir.

The detection of ND₃ in the Barnard 1 cloud (Lis et al. 2002) and CD₃OH in IRAS 16293–2422 (Parise et al. 2004) has shown the possibility of detecting multiply deuterated species in cold and high-density regions. These observations opened new questions regarding the highest deuterium fractionation level that can occur in cold and high-density regions. We have already entered into a new era of astrochemistry where powerful, high-sensitive and high-resolution observational facilities like Atacama Large Millimetre Array are in operation. Thus, there is no doubt that many more singly and multiply deuterated species are going to be observed. By studying the chemistry of these deuterated species, we will be able to diagnose various cold and dense environments where stars are born (see for instance Albertsson et al. 2013 and references therein).

Deuterium chemistry in the gas phase is believed to be controlled by the isotopic exchange reactions between HD and H₃⁺, as the

<footnote n="1">¹Laboratoire d'astrophysique de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France</footnote>

<footnote n="2">²Indian Centre For Space Physics, 43 Chalantika, Garia Station Road, Kolkata 700084, India</footnote>

<footnote n="3">³Université de Toulouse, UPS-OMP, IRAP, F-31028 Toulouse, France</footnote>

<footnote n="4">⁴CNRS, IRAP, 9 Av. Colonel Roche, BP 44346, F-31028 Toulouse Cedex 4, France</footnote>

<footnote n="5">⁵Max-Planck-Institute for Extraterrestrial Physics (MPE), Giessenbachstr. 1, D-85748 Garching, Germany</footnote>

<footnote>* E-mail: liton.icsp@gmail.com</footnote>

<footnote n="1">¹https://www.astro.uni-koeln.de/cdms/molecules</footnote>
reservoir of deuterium is initially locked in the form of HD, via the reaction

$$H_3^+ + HD \rightarrow H_2D^+ + H_2 + 232K. \quad (1)$$

The above backward reaction is endothermic by 232 K and is thus negligible at low temperatures (less than 20 K). H₂D⁺ can react with other abundant molecules (such as CO, N₂) to transfer D-atoms to other species (Ceccarelli et al. 2014). However, this reaction scheme becomes complicated if we consider nuclear spin states for the protonated species. Molecular hydrogen (H₂) has two distinct spin states under the permutation of identical protons. An ortho state (ortho-H₂) when the nuclear spin wavefunction is symmetric and a para state (para-H₂) when the nuclear spin wavefunction is antisymmetric. The energy difference between the rotational ground states of ortho-H₂ and para-H₂ is 170.5 K (Hugo, Asvany & Schlemmer 2009). Consequently if we consider the reaction (1) in backward direction with ortho-H₂ and ortho-H₂D⁺, the reaction becomes exothermic by about 24 K with para-H₃⁺ as one of the products. As a result, the ortho-to-para ratio of H₂ [opr(H₂) from now on in the text] becomes an important parameter in controlling the deuterium fractionation even at low temperature (Flower, Pineau Des Forêts & Walmsley 2006).

The study of deuterium chemistry is a challenging task. The reason is the unavailability of any public data base that provides a network with detailed deuterium chemistry along with spin chemistry of important protonated species. In the past, many authors have studied deuterium fractionation by cloning reactions involving hydrogen-bearing species (Roberts & Millar 2000a,b; Aikawa et al. 2012; Albertsson et al. 2013; Sipilä, Caselli & Harju 2013; Albertsson, Semenov & Henning 2014a; Majumdar, Das & Chakrabarti 2014a,b; Taquet, Charnley & Sipilä 2014; Das et al. 2015). Among these studies, Roberts & Millar (2000a,b) reported one of the first gas-grain chemical models for deuteration, where the chemistry was limited to singly and a few doubly deuterated species along with surface chemistry only for H₂ and HD molecules. Aikawa et al. (2012) considered the chemistry of multiply deuterated species both in the gas phase and on the grain surface but without considering spin-state chemistry. Similar models were also published in Albertsson et al. (2013), Das et al. (2015) and Majumdar et al. (2014a,b) where multiple deuteration was taken into account without considering spin-state chemistry. Sipilä et al. (2013) and Taquet et al. (2014) reported deuterium fractionation models with gas-grain chemistry of deuterated species up to four atoms and the spin chemistry of H₂, H₂⁺, H₃⁺ and their deuterated isotopologues. More recently, Albertsson et al. (2014a) have considered deuterated species with seven atoms whereas Sipilä, Caselli & Harju (2015) have considered six atoms. Both works include spin chemistry. In many cases, deuteration was studied by restricting the number of atoms in the deuterated species, without studying spin chemistry or grain chemistry in detail. The main goal of this paper is to present a more comprehensive deuterium fractionation model, which includes spin chemistry of H₂, H₂⁺, H₃⁺ and their deuterated isotopologues, the chemistry of multiply deuterated species and surface chemistry described in detail in Section 2. This network is the first of its kind to be made public (http://kidaobs.u-bordeaux1.fr/). This paper is structured as follows. In Section 2, we present our new deuterium fractionation model. We give a detailed description of our deuterated network (deuspin.kida.uva.2016 from now in the rest of the text) along with its implementation in the gas-grain code NAUTILUS. We benchmark our model with the other published works. In Section 3, we discuss the general trends of deuterium chemistry. We compare our results with observations and discuss the effect

of inclusion of deuspin.kida.uva.2016 on the predicted modelled abundances for several well-observed non-deuterated species, and discuss some new observable deuterated species in dark clouds. Finally, in Section 4 we draw our conclusions.

# 2 CHEMICAL MODEL AND NETWORK

## 2.1 The nautilus chemical model

To study deuteration together with spin chemistry, we use the NAUTILUS gas-grain chemical model (Reboussin et al. 2014; Ruaud et al. 2015; Wakelam et al. 2015b) under typical cold dense cloud conditions. NAUTILUS is a state-of-the-art chemical code, which can be applied to simulate various types of astronomical environments. Applications of this gas-grain chemical code have already been reported for dense clouds (Wakelam et al. 2015b), low-mass protostellar envelopes (Bottinelli et al. 2014; Majumdar et al. 2016) and the outer regions of protoplanetary discs (Dutrey et al. 2011). NAUTILUS computes the abundances of species (e.g. atoms, ions, radicals and molecules) as a function of time in the gas phase and on the surfaces of interstellar grains. All the equations and the chemical processes included in the model are described in detail in Ruaud et al. (2015). To include the effect of spin chemistry, we then modified all the variables in NAUTILUS relative to H₂ in terms of ortho-H₂ and para-H₂ (from now we will use o, p and m to represent ortho, para and meta states<fnref n="2" /> in the rest of the text).

In the model, several types of chemical reactions are considered in the gas phase by following the kida.uva.2014 chemical network of Wakelam et al. (2015a). These reactions can be classified in four categories: bimolecular reactions between neutral species, between charged species and between neutral and charged species, unimolecular reactions (i.e. photoreactions with direct UV photons and UV photons produced by the de-excitation of H₂ excited by the cosmic ray particles), and direct ionization and dissociation by cosmic ray particles. Here, the interstellar ice is modelled by a one phase rate equation approach (Hasegawa, Herbst & Leung 1992), i.e. there is no differentiation between the species in the mantle and on the surface. In our model, the gas and the grains are coupled to each other via four interaction processes: physisorption of gas-phase species on to grain surfaces, diffusion of the accreted species, reaction at the grain surface and evaporation to the gas phase. These evaporation processes can also be of various types. The evaporation mechanisms considered here are as follows: thermal (which are inefficient at dense cloud conditions), induced by cosmic-rays (Hasegawa & Herbst 1993) and chemical as defined by Garrod, Wakelam & Herbst (2007). According to Wakelam et al. (2014), photodesorption induced by cosmic ray secondary photons is less efficient than chemical desorption. This is why we did not consider it in our model. Any species can diffuse by thermal hopping only with a barrier of 0.5 × E_D where E_D is the species binding energy. By following Garrod et al. (2007), we consider that approximately 1 per cent of the products are allowed to desorb due to chemical desorption. We do not take into account the cosmic ray-induced

<footnote n="2">² Here ortho, para and meta stand for different nuclear spin symmetries for a species. For example, H₂ has two spin states i.e. ortho (I=1 and gI=3), para (I=0 and gI=1), whereas D₃⁺ has three spin states i.e. ortho (I=1,2 and gI=16), para (I=0, gI=1) and meta (I=1,3 and gI=10). Among others, H₂⁺, H₃⁺, D₂⁺, H₂D⁺ and D₂H⁺ have only ortho and para spin states. Here, I and gI stand for nuclear spin angular momenta and nuclear spin statistical weights, respectively. See Hugo et al. (2009) for more details.</footnote>
<table><caption>**Table 1.** Initial abundances used in our model.</caption><thead><tr><th>Element</th><th>Abundance relative to H</th></tr></thead><tbody><tr><td>o-H<sub>2</sub></td><td>3.75 × 10<sup>-1</sup></td></tr><tr><td>p-H<sub>2</sub></td><td>1.25 × 10<sup>-1</sup></td></tr><tr><td>He</td><td>9 × 10<sup>-2</sup></td></tr><tr><td>N</td><td>6.2 × 10<sup>-5</sup></td></tr><tr><td>O</td><td>2.4 × 10<sup>-4</sup></td></tr><tr><td>C<sup>+</sup></td><td>1.7 × 10<sup>-4</sup></td></tr><tr><td>S<sup>+</sup></td><td>8 × 10<sup>-8</sup></td></tr><tr><td>Si<sup>+</sup></td><td>8 × 10<sup>-9</sup></td></tr><tr><td>Fe<sup>+</sup></td><td>3 × 10<sup>-9</sup></td></tr><tr><td>Na<sup>+</sup></td><td>2 × 10<sup>-9</sup></td></tr><tr><td>Mg<sup>+</sup></td><td>7 × 10<sup>-9</sup></td></tr><tr><td>P<sup>+</sup></td><td>2 × 10<sup>-10</sup></td></tr><tr><td>Cl<sup>+</sup></td><td>1 × 10<sup>-9</sup></td></tr><tr><td>F</td><td>6.68 × 10<sup>-9</sup></td></tr><tr><td>HD</td><td>1.60 × 10<sup>-5</sup></td></tr></tbody></table>

diffusion mechanism (CRD) since for high visual extinction, effect of CRD is negligible (see Reboussin et al. 2014).

To simulate deuterium chemistry together with spin chemistry in dark clouds, the model is used with homogeneous physical conditions and integrated over $10^7$ yr. The initial elemental abundances reported in Table 1 are the same as in Hincelin et al. (2011) with deuterium and fluorine elemental abundances relative to hydrogen of $1.6 \times 10^{-5}$ (Linsky et al. 2006) and $6.68 \times 10^{-9}$ (Neufeld, Wolfire & Schilke 2005), respectively. The species are assumed to be initially in an atomic form as in diffuse clouds except for hydrogen and deuterium, which are initially in $H_2$ and HD forms, respectively. All elements (e.g. C, S, Si, Fe, Na, Mg, Cl and P) with an ionization potential lower than 13.6 eV are initially singly ionized. For our standard model, we have used a C/O ratio of 0.7 (i.e. the oxygen elemental abundance is $2.4 \times 10^{-4}$). The opr($H_2$) is initially set to its statistical value of 3. The model was run with a dust and gas temperature of 10 K, a total proton density of $2 \times 10^4$ cm$^{-3}$, a cosmic ray ionization rate of $1.3 \times 10^{-17}$ s$^{-1}$ and a visual extinction of 30 mag.

## 2.2 Developed chemical network from kida 2014

The initial gas-phase chemical network was adapted from the kida.uva.2014 network<fnref n="3" /> (Wakelam et al. 2015a, which includes 489 species composed of 13 elements: H, He, C, N, O, Si, S, Fe, Na, Mg, Cl, P, F) linked with 7509 reactions. Our starting network includes various updates of the HCN/HNC chemistry by Loison, Wakelam & Hickson (2014b), carbon chemistry by Loison et al. (2014a), branching ratios for reactions forming $C_{n=2-10}^{(0,+)}$, $C_{n=2-4}H^{(0,+)}$ and $C_3H_2^{(0,+)}$ from Chabot et al. (2013), and also various new data sheets from KIDA data base. This network has been extended to include the spin states of $H_2$, $H_2^+$ and $H_3^+$ and their deuterated isotopologues.

To add the spin states of $H_2$, $H_2^+$ and $H_3^+$ into kida.uva.2014, we applied the method described by Sipilä et al. (2015) in which the branching ratios are calculated using Oka's method (Oka 2004). In this method, selection rules for reactive collisions involving different spin species are derived using angular momentum algebra. Branching ratios resulting from this method correspond to pure nuclear spin statistical weights under the assumption that

the nuclei are completely mixed in the reaction. Following Sipilä et al. (2015), we applied the same method to all reactions except charge-transfer reactions, where we assume that spin states are conserved. We have added an activation energy of 170 K to the $\gamma$ coefficient [of the temperature-dependent rate coefficients $k(T) = \alpha(T/300)^\beta e^{-\gamma/T}$] for the reactions where $o-H_2$ is formed (see Albertsson et al. 2014a for similar methods). The formation of $o-H_2$ and $p-H_2$ in reactions that involve species, whose spin states are not tracked (i.e. other than $H_2$, $H_2^+$ and $H_3^+$), is handled with the 'recombination' approach described in detail in section 2.3.1 of Sipilä et al. (2015). Our deuteration routine is similar to the one described in Albertsson et al. (2013), where deuterons are substituted for protons in the reactions, and branching ratios are calculated assuming complete scrambling. Here, we do not consider the spin chemistry of multiply deuterated species. For multiply deuterated species, the calculation of nuclear spin-state branching ratios is more complicated than for hydrogenated species since there is no one-to-one correspondence between angular momentum and symmetry representations. In this work, we include the spin-state chemistry of the deuterated isotopologues involved in the $H_3^+$ + $H_2$ reaction system (which is essential in the present context) from tables III and IV of Hugo et al. (2009) complemented by important reactions involving light hydrogen and deuterium-bearing species ($H_3^+$, $H_2D^+$, HD etc.) from Flower, Pineau des Forêts & Walmsley (2004) and Walmsley, Flower & Pineau des Forêts (2004). We also included dissociative recombination reactions for $H_3^+$ and its deuterated forms from Pagani et al. (2009). We have added all these important reactions as Supporting Information online, in the format of kida.uva.2014 network. In addition, we have added several important reactions from the literature: important reactions for deuterations from Albertsson et al. (2013) and water deuteration chemistry from Talukdar & Ravishankara (1996) and Bergin, Neufeld & Melnick (1999). The entire network considered here is available on the KIDA<fnref n="4" /> web site.

Our network for surface reactions and gas-grain interactions is based on the one from Garrod et al. (2007) with several additional processes from Ruaud et al. (2015). We extended our network to include deuteration by assuming statistical branching ratios (see for instance Taquet et al. 2014 for the same method). According to Taquet et al. (2013), although deuterated isotopologues have the higher mass, they seem to show similar binding energies to their hydrogenated counterpart. Therefore, by following these studies and also due to the unavailability of binding energies for deuterated species, we assume the same binding energies for all deuterated and non-deuterated species. Finally, we have nearly 7700 reactions on grain surface linked with the 111 000 reactions in gas phase. If we sum up all these modifications, the deuspin.kida.uva.2016 network has the following characteristics:

(i) spin chemistry of light hydrogen bearing species ($H_2$, $H_2^+$, $H_3^+$) essential to take into account the deuterium fractionation properly;

(ii) spin chemistry of $H_3^+$ + $H_2$ reacting system and their isotopologues from Hugo et al. (2009);

(iii) chemistry of multiply deuterated species;

(iv) extension of the kida.uva.2014 network to include full deuterium fractionation for species containing any of the 13 elements (H, He, C, N, O, Si, S, Fe, Na, Mg, Cl, P, F);

<footnote n="3">³ http://kida obs.u-bordeaux1.fr/</footnote>

<footnote n="4">⁴ http://kida obs.u-bordeaux1.fr/</footnote>
<figure><img src="image_2.png" /><figcaption>**Figure 1.** Gas-phase abundance of ortho- and para-H₂ with respect to *n*<sub>H</sub> as a function of time.</figcaption></figure>

(v) all reactions are written in the same format as in the KIDA data base for the different types so that in future, users can export this network easily without any confusion.

## 2.3 Benchmarking spin and deuterium chemistry

H₂, D₂, H₃⁺, H₂D⁺, D₂H⁺ and D₃⁺ along with their spin isomers are the main species that dictate deuterium fractionation at low temperature (see for instance Ceccarelli et al. 2014 and references therein). In addition, deuterium fractionation strongly depends on the initial opr(H₂) considered. Ortho- and para-H₂ are formed on the surfaces of interstellar grains with a statistical ratio of 3:1 (Watanabe et al. 2010) and proton-exchange reactions in the gas phase then convert ortho-H₂ into para-H₂ (see Ceccarelli et al. 2014 and references therein for more discussions). In our model, we set an initial ratio of 3:1, in agreement with the experimental findings of Watanabe et al. (2010).

Before applying our model to a dense core (e.g. a TMC-1 like environment), we have benchmarked our model with other published works. The importance of spin-state chemistry is now widely accepted and has been tested in different stages of star formation process: diffuse clouds (Albertsson et al. 2014b), starless/pre-stellar cores (Pagani et al. 2009; Sipilä et al. 2013) and protostellar systems (Taquet et al. 2013). But in all cases, spin-state chemistry was discussed to address particular issues by adopting various types of physical and chemical model making a direct comparison with our model very difficult. Two things can be compared though: the time-scale for gas-phase ortho-H₂ to para-H₂ conversion and abundance profiles for the two spin isomers of H₃⁺. Fig. 1 shows the evolution of the ortho and para forms of H₂ in the gas phase under dense core conditions. In our model, opr(H₂) becomes unity at around few times 10⁵ yr and drops down to 10⁻³ or below after this. This is consistent with the result of Sipilä et al. (2013). Fig. 2 shows the evolution of the ortho and para forms of H₃⁺. At 10⁷ yr, the abundances of o-H₃⁺ and p-H₃⁺ are, respectively, 1.45 × 10⁻⁹⁰ and 1.73 × 10⁻⁹⁰. Sipilä et al. (2015) reported 2.00 × 10⁻⁹⁰ for o-H₃⁺ under the same conditions.

To validate deuterium chemistry with associated spin chemistry, one basic test would be to compare the abundance profile of H₂D⁺, D₂H⁺ and D₃⁺ with other models, since they are the major species controlling the deuterium fractionation. In order to perform a more realistic comparison, we ran our model with a similar initial opr(H₂)=10⁻³ (i.e. kinetically equilibrated H₂ at low temperature, see Faure et al. 2013) mentioned in Sipilä et al. (2015). Fig. 3 shows

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Gas-phase abundance of ortho and para forms of H₃⁺ with respect to *n*<sub>H</sub> as a function of time.</figcaption></figure>

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Gas-phase abundance of various isotopologues of H₃⁺ with respect to *n*<sub>H</sub> as a function of time.</figcaption></figure>

the abundances of all the isotopologues of H₃⁺. At 10⁷ yr, the abundances of o-H₂D⁺, p-H₂D⁺, o-D₂H⁺, p-D₂H⁺, o-D₃⁺, p-D₃⁺ and m-D₃⁺ are, respectively, 7.0 × 10⁻¹⁰, 4.7 × 10⁻¹⁰, 1.4 × 10⁻¹⁰, 2.2 × 10⁻¹¹, 8.5 × 10⁻¹², 2.1 × 10⁻¹³ and 1.1 × 10⁻¹¹. In fig. 3 of Sipilä et al. (2015), at 10⁷ yr the reported abundances of o-H₂D⁺ and p-D₂H⁺ are, respectively, 4.0 × 10⁻¹⁰ and 1.0 × 10⁻¹¹ under the same conditions, within a factor of 2 in agreement with our model. These differences are quite minor considering the differences in the starting networks (our work is based on kida.uva.2014 network whereas Sipilä et al. 2015 used osu_03_2008 network). But we have found the similar trend for all the isotopologues of H₃⁺ as described in Sipilä et al. (2015), i.e. abundances are much higher at late times and this is attributed due to the depletion of their main reaction partners (e.g. CO) on to grain surfaces.

# 3 RESULTS AND DISCUSSION

## 3.1 General trends of deuterium chemistry

Using the model described above, we have investigated general trends of deuterium chemistry in the ISM. For this purpose, we selected two deuterated ions (DCO⁺, N₂D⁺) and several deuterated neutrals (NH₂D, DCN, DNC, HDCO, C₂D, C₃H₃D, C₄D, DC₃N, DC₅N, HDCS) as they have been observed in TMC-1 (see for instance Albertsson et al. 2013, and references therein). The abundances predicted by our model are shown in Fig. 4 as a function
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Abundance with respect to $n_H$ as a function of time of a selection of deuterated species observed in dense cores. Dotted lines correspond to non-deuterated species and solid lines correspond to deuterated species.</figcaption></figure>

of time. Our model shows that the abundance of HCO⁺ increases with time and its formation is very efficient after $10^2$ yr due to the reaction between HOC⁺ and o-H₂. Around this time, most of the gas-phase H₂ is in the form of o-H₂. For DCO⁺, we observe a very rapid fall in abundance between $10^5$ and $10^6$ yr. Around this time, H₂O becomes an efficient destruction partner of DCO⁺ since the formation of H₂O is very efficient (due to its highly abundant precursors H₃O⁺ and o-H₂). After $10^6$ yr, we observe an increase in abundance for DCO⁺ due its efficient formation via the reaction o-H₂D⁺ + CO. Around this time o-H₂D⁺ becomes highly abundant due to low opr(H₂). For the other deuterated ion N₂D⁺, we observe a similar trend as with DCO⁺. Between $10^5$ and $10^6$ yr, N₂D⁺ is destroyed efficiently by H₂O to form H₂DO⁺. Similarly, after $10^6$ yr, rapid formation of N₂D⁺ is due to the efficient formation via the reaction of o-H₂D⁺ + N₂.

Among the deuterated neutrals, we observe a slightly different behaviour for NH₂D and C₃H₃D as compared to deuterated ions. For NH₃ and NH₂D, we find an increase in the abundances after $10^5$ yr. Around this time both NH₃ and NH₂D are formed via the dissociative recombination reactions of NH₄⁺ and NH₃D⁺. Both these ions are formed back again from various ion-molecular destruction reactions of NH₃ and NH₂D by the ions HCO⁺, H₃O⁺. After $10^6$ yr, the abundance of NH₃ drops quickly due its efficient depletion on to grain surface. But C₃H₄ and C₃H₃D show an increase in abundance in between $10^5$ and $10^6$ yr due to their efficient formation via the barrierless surface reactions s-H + s-C₃H₃ and s-H + s-C₃H₂D (here, 's' represents species on the surface of grains). For the rest of the deuterated neutrals, we observe a general trend between $10^5$ and $10^6$ yr i.e. abundances decrease. DNC, which is an isomer of DCN, shows a decrease in abundance around this time by several orders of

magnitude. This is due to the efficient destruction of DNC by highly abundant p-H₃⁺. HCN shows a peak in the abundance at $10^6$ yr due to its high abundant precursors H₂CN⁺ and p-H₂. HDCO is less destroyed than the other species at later times because its main destruction path is O + HDCO. DC₃N, DC₅N and HDCS, on the contrary, show a rapid fall in the abundance in between $10^5$ and $10^6$ yr due to their efficient destruction by highly abundant p-H₃⁺ and HCO⁺. In Table 2, we have listed major reactions of production and destruction for these species at high- and low-opr(H₂) regimes.

## 3.2 Gas-phase D/H ratios in TMC-1: comparison with observations and previous models

In the past, molecular D/H ratios observed towards TMC-1 were compared by various gas-grain chemical models (see for instance Roberts & Millar 2000b; Albertsson et al. 2013). Roberts & Millar (2000b) have studied the chemical evolution with deuterium fractionation for temperatures 10–100 K and densities $3 \times 10^3–3 \times 10^8$ cm⁻³. They used a time-dependent gas-phase model based on the UMIST’95 data base. Their chemical network consists of ~300 species linked by >5000 reactions, and only includes singly deuterated species and limited surface chemistry for H₂ and HD. Recently, Albertsson et al. (2013) have also studied deuterium fractionation with their newly constructed chemical network, which contains 55 000 reactions in gas phase. But they restricted their study to avoid reactions with –OH end groups and also they did not consider spin chemistry of H₂, H₂⁺ and H₃⁺ and their isotopologues. We did the same type of comparison but using our more complete model. In Table 3, we report molecular D/H ratios for several deuterated species observed in different positions of
<table><caption>**Table 2.** Main reactions of production and destruction for observed deuterated species in TMC-1 cloud in the high- and low-opr(H₂) regimes. Here 10⁵ and 10⁶ yr correspond to high- and low-opr(H₂) regimes, respectively.</caption><thead><tr><th>Species</th><th>Formation<br>(10<sup>5</sup> yr)</th><th>Destruction<br>(10<sup>5</sup> yr)</th><th>Formation<br>(10<sup>6</sup> yr)</th><th>Destruction<br>(10<sup>6</sup> yr)</th></tr></thead><tbody><tr><td>NH<sub>2</sub>D</td><td>NH<sub>3</sub>D<sup>+</sup> + e<sup>-</sup> → H+NH<sub>2</sub>D</td><td>H<sub>3</sub>O<sup>+</sup> + NH<sub>2</sub>D → NH<sub>3</sub>D<sup>+</sup> + H<sub>2</sub>O<br>HCO<sup>+</sup> + NH<sub>2</sub>D → NH<sub>3</sub>D<sup>+</sup> + CO</td><td>NH<sub>3</sub>D<sup>+</sup> + e<sup>-</sup> → H+NH<sub>2</sub>D</td><td>H<sup>+</sup> + NH<sub>2</sub>D → NH<sub>2</sub>D<sup>+</sup> + H<br>HCO<sup>+</sup> + NH<sub>2</sub>D → NH<sub>3</sub>D<sup>+</sup> + CO</td></tr><tr><td>HDCO</td><td>O + CH<sub>2</sub>D → HDCO + H</td><td>O + HDCO → H + CO + OD<br>O + HDCO → D + CO + OH</td><td>s-H + s-DCO → HDCO</td><td>HCO<sup>+</sup> + HDCO → H<sub>2</sub>DCO<sup>+</sup> + CO<br>p-H<sub>3</sub><sup>+</sup> + HDCO → H<sub>3</sub>CO<sup>+</sup> + HD</td></tr><tr><td>DCN</td><td>CH<sub>2</sub>D<sup>+</sup> + HC<sub>3</sub>N → DCN +<br>c-C<sub>3</sub>H<sub>3</sub><sup>+</sup><br>N + DCO → DCN + O<br>N + CHD → DCN + H</td><td>CH<sub>3</sub><sup>+</sup> + DCN → C<sub>2</sub>H<sub>3</sub>DN<sup>+</sup><br>p-H<sub>3</sub><sup>+</sup> + DNC → H<sub>2</sub>CN<sup>+</sup> + HD<br>HCO<sup>+</sup> + DNC → HDCN<sup>+</sup> + CO<br>o-H<sub>3</sub><sup>+</sup> + DNC → HDCN<sup>+</sup> + o-H<sub>2</sub></td><td>HDCN<sup>+</sup> + p-H<sub>2</sub> → p-H<sub>3</sub><sup>+</sup> +<br>DCN</td><td>HCO<sup>+</sup> + DCN → HDCN<sup>+</sup> + CO<br>p-H<sub>3</sub><sup>+</sup> + DCN → H<sub>2</sub>CN<sup>+</sup> + HD<br>o-H<sub>3</sub><sup>+</sup> + DCN → HDCN<sup>+</sup> + o-H<sub>2</sub></td></tr><tr><td>DNC</td><td>N + CHD → DNC + H</td><td>O + C<sub>2</sub>D → CD + CO<br>C<sub>2</sub>D + C<sub>3</sub> → C<sub>5</sub> + D<br>C + C<sub>4</sub>D → C<sub>5</sub> + D<br>O + C<sub>4</sub>D → C-C<sub>3</sub>D + CO</td><td>C + NHD → DNC + H<br>C<sub>2</sub>H<sub>2</sub>D<sup>+</sup> + e<sup>-</sup> → C<sub>2</sub>D + H + H</td><td>o-H<sub>3</sub><sup>+</sup> + DCN → HDCN<sup>+</sup> + o-H<sub>2</sub><br>HCO<sup>+</sup> + DNC → HDCN<sup>+</sup> + CO<br>p-H<sub>3</sub><sup>+</sup> + DNC → H<sub>2</sub>CN<sup>+</sup> + HD<br>o-H<sub>3</sub><sup>+</sup> + DNC → HDCN<sup>+</sup> + o-H<sub>2</sub><br>C<sub>2</sub>D + C<sub>3</sub> → C<sub>5</sub> + D</td></tr><tr><td>C<sub>2</sub>D</td><td>C + CHD → C<sub>2</sub>D + H<br>O + C-C<sub>3</sub>D → C<sub>2</sub>D + CO</td><td>C<sub>2</sub>D + C<sub>3</sub> → C<sub>5</sub> + D<br>C + C<sub>4</sub>D → C<sub>5</sub> + D<br>O + C<sub>4</sub>D → C-C<sub>3</sub>D + CO</td><td>C + C-C<sub>3</sub>HD → C<sub>4</sub>D + H</td><td>HCO<sup>+</sup> + C<sub>4</sub>D → C<sub>4</sub>HD<sup>+</sup> + CO<br>p-H<sub>3</sub><sup>+</sup> + C<sub>4</sub>D → C<sub>4</sub>H<sub>2</sub><sup>+</sup> + HD<br>o-H<sub>3</sub><sup>+</sup> + C<sub>4</sub>D → C<sub>4</sub>H<sub>2</sub><sup>+</sup> + HD<br>DCO<sup>+</sup> + e<sup>-</sup> → CO + D<br>DCO<sup>+</sup> + H<sub>2</sub>O → H<sub>2</sub>DO<sup>+</sup> + CO</td></tr><tr><td>C<sub>4</sub>D</td><td>C + C-C<sub>3</sub>HD → C<sub>4</sub>D + H</td><td>DCO<sup>+</sup> + H<sub>2</sub>O → H<sub>2</sub>DO<sup>+</sup> + CO<br>DCO<sup>+</sup> + C → CD<sup>+</sup> + CO<br>DCO<sup>+</sup> + HCN → HDCN<sup>+</sup> + CO</td><td>o-H<sub>2</sub>D<sup>+</sup> + CO → DCO<sup>+</sup> + o-H<sub>2</sub><br>HCO<sup>+</sup> + D → DCO<sup>+</sup> + H</td><td>N<sub>2</sub>D<sup>+</sup> + CO → DCO<sup>+</sup> + N<sub>2</sub></td></tr><tr><td>DCO<sup>+</sup></td><td>HCO<sup>+</sup> + D → DCO<sup>+</sup> + H<br>CH<sub>2</sub>D<sup>+</sup> + O → DCO<sup>+</sup> + o-H<sub>2</sub></td><td>N<sub>2</sub>D<sup>+</sup> + H<sub>2</sub>O → H<sub>2</sub>DO<sup>+</sup> + N<sub>2</sub><br>N<sub>2</sub>D<sup>+</sup> + CO → DCO<sup>+</sup> + N<sub>2</sub></td><td>o-H<sub>2</sub>D<sup>+</sup> + N<sub>2</sub> → N<sub>2</sub>D<sup>+</sup> + o-H<sub>2</sub><br>p-H<sub>2</sub>D<sup>+</sup> + N<sub>2</sub> → N<sub>2</sub>D<sup>+</sup> + p-H<sub>2</sub><br>N<sub>2</sub>H<sup>+</sup> + D → N<sub>2</sub>D<sup>+</sup> + H</td><td>HCO<sup>+</sup> + C-C<sub>3</sub>HD → C<sub>3</sub>H<sub>2</sub>D<sup>+</sup> + CO<br>p-H<sub>3</sub><sup>+</sup> → C<sub>3</sub>H<sub>3</sub><sup>+</sup> + HD<br>C + C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub>D + H<br>C + C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub> + HD</td></tr><tr><td>N<sub>2</sub>D<sup>+</sup></td><td>N<sub>2</sub>H<sup>+</sup> + D → N<sub>2</sub>D<sup>+</sup> + H</td><td>C + C-C<sub>3</sub>HD → C<sub>4</sub>D + H<br>C + C-C<sub>3</sub>HD → C<sub>4</sub>H + D<br>C + C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub>D + H<br>C + C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub> + HD</td><td>H + C<sub>3</sub>H<sub>3</sub>D → C-C<sub>3</sub>HD + o-H<sub>2</sub><br>H + C<sub>3</sub>H<sub>3</sub>D → C-C<sub>3</sub>HD + p-H<sub>2</sub><br>s-H + s-C<sub>3</sub>H<sub>2</sub>D → C<sub>3</sub>H<sub>3</sub>D</td><td>HCO<sup>+</sup> + C-C<sub>3</sub>HD → C<sub>3</sub>H<sub>2</sub>D<sup>+</sup> + CO<br>p-H<sub>3</sub><sup>+</sup> → C<sub>3</sub>H<sub>3</sub><sup>+</sup> + HD<br>C + C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub>D + H<br>C + C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub> + HD</td></tr><tr><td>c-C<sub>3</sub>HD</td><td>c-C<sub>3</sub>H<sub>2</sub>D<sup>+</sup> + e<sup>-</sup> → c-C<sub>3</sub>HD + H</td><td>C + C-C<sub>3</sub>HD → C<sub>4</sub>D + H<br>C + C-C<sub>3</sub>HD → C<sub>4</sub>H + D<br>C + C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub>D + H<br>C + C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub> + HD</td><td>C + CHDCN → DC<sub>3</sub>N + H<br>C<sub>3</sub>HDN<sup>+</sup> + e<sup>-</sup> → DC<sub>3</sub>N + H<br>CN + C<sub>4</sub>HD → DC<sub>5</sub>N + H</td><td>HCO<sup>+</sup> + DC<sub>3</sub>N → C<sub>3</sub>HDN<sup>+</sup> + CO<br>p-H<sub>3</sub><sup>+</sup> + DC<sub>3</sub>N → HC<sub>3</sub>NH<sup>+</sup> + HD<br>HCO<sup>+</sup> + DC<sub>5</sub>N → C<sub>5</sub>HDN<sup>+</sup> + CO</td></tr><tr><td>C<sub>3</sub>H<sub>3</sub>D</td><td>s-H + s-C<sub>3</sub>H<sub>2</sub>D → C<sub>3</sub>H<sub>3</sub>D</td><td>C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub>D + H<br>C + C<sub>3</sub>H<sub>3</sub>D → C<sub>4</sub>H<sub>2</sub> + HD</td><td>C + s-C<sub>3</sub>H<sub>2</sub>D → C<sub>3</sub>H<sub>3</sub>D</td><td>p-H<sub>3</sub><sup>+</sup> + DC<sub>5</sub>N → H<sub>2</sub>CS<sup>+</sup> + HD<br>p-H<sub>3</sub><sup>+</sup> + DC<sub>5</sub>N → H<sub>2</sub>CS<sup>+</sup> + HD</td></tr><tr><td>DC<sub>3</sub>N</td><td>C + CHDCN → DC<sub>3</sub>N + H</td><td>p-H<sub>3</sub><sup>+</sup> + DC<sub>3</sub>N → HC<sub>3</sub>NH<sup>+</sup> + HD<br>o-H<sub>3</sub><sup>+</sup> + DC<sub>3</sub>N → HC<sub>3</sub>NH<sup>+</sup> + HD</td><td>C + CHDCN → DC<sub>3</sub>N + H<br>C<sub>3</sub>HDN<sup>+</sup> + e<sup>-</sup> → DC<sub>3</sub>N + H<br>CN + C<sub>4</sub>HD → DC<sub>5</sub>N + H</td><td>HCO<sup>+</sup> + DC<sub>3</sub>N → H<sub>2</sub>CS<sup>+</sup> + HD<br>HCO<sup>+</sup> + DC<sub>5</sub>N → C<sub>5</sub>HDN<sup>+</sup> + CO</td></tr><tr><td>DC<sub>5</sub>N</td><td>C<sub>5</sub>H<sub>2</sub>DN<sup>+</sup> + e<sup>-</sup> → DC<sub>5</sub>N +<br>o-H<sub>2</sub></td><td>o-H<sub>3</sub><sup>+</sup> + DC<sub>5</sub>N → H<sub>2</sub>C<sub>5</sub>N<sup>+</sup> + HD<br>p-H<sub>3</sub><sup>+</sup> + HDCS → H<sub>3</sub>CS<sup>+</sup> + HD</td><td>S + CH<sub>2</sub>D → H + HDCS</td><td>p-H<sub>3</sub><sup>+</sup> + DC<sub>5</sub>N → H<sub>2</sub>C<sub>5</sub>N<sup>+</sup> + HD<br>p-H<sub>3</sub><sup>+</sup> + HDCS → H<sub>2</sub>CS<sup>+</sup> + HD</td></tr><tr><td>HDCS</td><td>S + CH<sub>2</sub>D → H + HDCS</td><td>HCO<sup>+</sup> + HDCS → H<sub>2</sub>DCS<sup>+</sup> + CO</td><td>S + CH<sub>2</sub>D → H + HDCS</td><td>p-H<sub>3</sub><sup>+</sup> + HDCS → H<sub>2</sub>CS<sup>+</sup> + HD<br>p-H<sub>3</sub><sup>+</sup> + HDCS → H<sub>3</sub>CS<sup>+</sup> + HD</td></tr></tbody></table>

<table><caption>**Table 3.** Comparison of observed D/H ratios for different positions of TMC-1 cloud with predictions from our model (T = 10 K, n<sub>H</sub> = 2 × 10⁴ cm⁻³, time = 10⁵ yr), Roberts & Millar (2000a) and Albertsson et al. (2013).</caption><thead><tr><th>Species</th><th>Our model</th><th>Roberts & Millar (2000a)</th><th>Albertsson et al. (2013)</th><th>Observation</th><th>Observed positions and Refs.</th></tr></thead><tbody><tr><td>NH<sub>2</sub>D/NH<sub>3</sub></td><td>4.3 × 10<sup>-2</sup></td><td>8.4 × 10<sup>-2</sup></td><td>5.2 × 10<sup>-2</sup></td><td>9.0 × 10<sup>-3</sup>-1.4 × 10<sup>-2</sup></td><td>TMC1-N (1)</td></tr><tr><td>HDCO/H<sub>2</sub>CO</td><td>2.1 × 10<sup>-2</sup></td><td>4.2 × 10<sup>-2</sup></td><td>2.3 × 10<sup>-2</sup></td><td>5.9 × 10<sup>-3</sup>-1.1 × 10<sup>-2</sup></td><td>TMC1-CP (2)</td></tr><tr><td>DCN/HCN</td><td>0.4 × 10<sup>-2</sup></td><td>0.9 × 10<sup>-2</sup></td><td>2.4 × 10<sup>-2</sup></td><td>2.3 × 10<sup>-2</sup></td><td>TMC1-CP (3)</td></tr><tr><td>DNC/HNC</td><td>0.6 × 10<sup>-2</sup></td><td>1.5 × 10<sup>-2</sup></td><td>1.6 × 10<sup>-2</sup></td><td>1.5 × 10<sup>-2</sup></td><td>TMC1-CP (2)</td></tr><tr><td>C<sub>2</sub>D/C<sub>2</sub>H</td><td>0.4 × 10<sup>-2</sup></td><td>1.1 × 10<sup>-2</sup></td><td>1.5 × 10<sup>-2</sup></td><td>1.0 × 10<sup>-2</sup></td><td>TMC1-CP (4)</td></tr><tr><td>C<sub>4</sub>D/C<sub>4</sub>H</td><td>2.3 × 10<sup>-3</sup></td><td>0.4 × 10<sup>-2</sup></td><td>1.0 × 10<sup>-2</sup></td><td>4.0 × 10<sup>-3</sup></td><td>TMC1-CP (5)</td></tr><tr><td>DCO<sup>+</sup>/HCO<sup>+</sup></td><td>0.3 × 10<sup>-2</sup></td><td>1.9 × 10<sup>-2</sup></td><td>1.8 × 10<sup>-2</sup></td><td>2.0 × 10<sup>-2</sup></td><td>TMC1-N (1)</td></tr><tr><td>N<sub>2</sub>D<sup>+</sup>/N<sub>2</sub>H<sup>+</sup></td><td>0.2 × 10<sup>-2</sup></td><td>2.5 × 10<sup>-2</sup></td><td>0.8 × 10<sup>-2</sup></td><td>8.0 × 10<sup>-2</sup></td><td>TMC1-N (1)</td></tr><tr><td>c-C<sub>3</sub>HD/c-C<sub>3</sub>H<sub>2</sub></td><td>1.6 × 10<sup>-2</sup></td><td>0.6 × 10<sup>-2</sup></td><td>1.3 × 10<sup>-2</sup></td><td>8.0 × 10<sup>-2</sup>-1.6 × 10<sup>-1</sup></td><td>TMC1-CP (6)</td></tr><tr><td>C<sub>3</sub>H<sub>3</sub>D/C<sub>3</sub>H<sub>4</sub></td><td>4.4 × 10<sup>-2</sup></td><td>8.3 × 10<sup>-2</sup></td><td>1.6 × 10<sup>-2</sup></td><td>5.4 × 10<sup>-2</sup>-6.5 × 10<sup>-2</sup></td><td>TMC1-CP (7)</td></tr><tr><td>DC<sub>3</sub>N/HC<sub>3</sub>N</td><td>0.7 × 10<sup>-2</sup></td><td>0.7 × 10<sup>-2</sup></td><td>0.9 × 10<sup>-2</sup></td><td>3.0 × 10<sup>-2</sup>-1.0 × 10<sup>-1</sup></td><td>TMC1-CP (8)</td></tr><tr><td>DC<sub>5</sub>N/HC<sub>5</sub>N</td><td>0.3 × 10<sup>-2</sup></td><td>2.3 × 10<sup>-2</sup></td><td>1.2 × 10<sup>-2</sup></td><td>1.3 × 10<sup>-2</sup></td><td>TMC1-CP (9)</td></tr><tr><td>HDCS/H<sub>2</sub>CS</td><td>1.6 × 10<sup>-2</sup></td><td>4.0 × 10<sup>-2</sup></td><td>1.8 × 10<sup>-2</sup></td><td>2.0 × 10<sup>-2</sup></td><td>TMC1-CP (10)</td></tr><tr><td>c-C<sub>3</sub>D<sub>2</sub>/c-C<sub>3</sub>HD</td><td>0.5 × 10<sup>-2</sup></td><td>-</td><td>-</td><td>4 × 10<sup>-2</sup></td><td>TMC1-C (11)</td></tr></tbody></table>

References: (1) Tiné et al. (2000); (2) Turner (2001); (3) Wootten (1987); (4) Millar, Bennett & Herbst (1989); (5) Turner (1989); (6) Bell et al. (1988); (7) Gerin et al. (1992); (8) Howe et al. (1994); (9) MacLeod, Avery & Broten (1981); (10) Minowa et al. (1997); (11) Spezzano et al. (2013).

Positions: TMC1-N (α<sub>J2000</sub> = 04h41m21s.01, δ<sub>1950</sub> = +25°48m11s), TMC1-CP (α<sub>J2000</sub> = 04h41m41s.88, δ<sub>2000</sub> = +25°41m27s), TMC1-C (α<sub>J2000</sub> = 04h41m16s.1, δ<sub>2000</sub> = +25°49m43.8s).
<table><caption>**Table 4.** Effect of deuteration and spin chemistry on molecular abundances (relative to H₂) at best chemical age obtained by comparing the models to the observed values in TMC-1.</caption><thead><tr><th>Species</th><th>TMC-1</th><th>NoDS</th><th>DS</th><th>Species</th><th>TMC-1</th><th>NoDS</th><th>DS</th></tr></thead><tbody><tr><td>OH</td><td>3(-7)</td><td>3.2(-8)</td><td>2.6(-9)</td><td>NH<sub>3</sub><sup>a</sup></td><td>2.45(-8)</td><td>6.6(-9)</td><td>3.7(-11)</td></tr><tr><td>H<sub>2</sub>O</td><td>&lt;7(-8)</td><td>3.1(-7)</td><td>1.8(-5)</td><td>N<sub>2</sub>H<sup>+</sup></td><td>2.8(-10)</td><td>7.9(-11)</td><td>7.5(-11)</td></tr><tr><td>O<sub>2</sub><sup>a</sup></td><td>&lt;7.7(-8)</td><td>7.3(-7)</td><td>3.2(-9)</td><td>CN</td><td>7.4(-10)</td><td>2.7(-8)</td><td>9.4(-9)</td></tr><tr><td>CO</td><td>1.7(-4)</td><td>6.0(-5)</td><td>6.7(-5)</td><td>HCN<sup>a</sup></td><td>1.1(-8)</td><td>8.7(-8)</td><td>2.6(-10)</td></tr><tr><td>HCO<sup>+</sup></td><td>9.3(-9)</td><td>4.2(-9)</td><td>1.0(-9)</td><td>HNC</td><td>2.6(-8)</td><td>3.1(-8)</td><td>4.8(-8)</td></tr><tr><td>H<sub>2</sub>CO</td><td>5(-8)</td><td>1.2(-8)</td><td>1.4(-9)</td><td></td><td></td><td></td><td></td></tr><tr><td>CH<sub>3</sub>OH<sup>a</sup></td><td>3.2(-9)</td><td>7.3(-10)</td><td>4.8(-9)</td><td></td><td></td><td></td><td></td></tr><tr><td></td><td></td><td></td><td></td><td>CH<sub>3</sub>CN<sup>a</sup></td><td>6(-10)</td><td>4.2(-10)</td><td>2.2(-7)</td></tr><tr><td>C<sub>2</sub>O<sup>a</sup></td><td>6(-11)</td><td>6.9(-13)</td><td>2.1(-11)</td><td>CH<sub>2</sub>CHCN</td><td>1(-9)</td><td>1.2(-11)</td><td>1.3(-12)</td></tr><tr><td>CH<sub>2</sub>CO</td><td>6(-10)</td><td>9.0(-10)</td><td>2.0(-10)</td><td>C<sub>3</sub>N</td><td>6(-10)</td><td>1.9(-9)</td><td>8.6(-10)</td></tr><tr><td>CH<sub>3</sub>CHO</td><td>6(-10)</td><td>2.3(-12)</td><td>5.3(-12)</td><td>HC<sub>3</sub>N</td><td>1.6(-8)</td><td>1.0(-8)</td><td>1.0(-7)</td></tr><tr><td>C<sub>3</sub>O</td><td>1(-10)</td><td>7.7(-9)</td><td>7.9(-10)</td><td>HNC<sub>3</sub></td><td>3.8(-11)</td><td>4.1(-10)</td><td>3.6(-10)</td></tr><tr><td>CH</td><td>2.0(-8)</td><td>2.0(-9)</td><td>3.5(-9)</td><td></td><td></td><td></td><td></td></tr><tr><td>C<sub>2</sub>H</td><td>7.2(-9)</td><td>3.1(-9)</td><td>1.5(-9)</td><td></td><td></td><td></td><td></td></tr><tr><td>c-C<sub>3</sub>H</td><td>1.03(-9)</td><td>3.2(-9)</td><td>2.8(-9)</td><td></td><td></td><td></td><td></td></tr><tr><td>l-C<sub>3</sub>H</td><td>8.4(-11)</td><td>2.4(-9)</td><td>1.5(-9)</td><td>C<sub>5</sub>N</td><td>3.1(-11)</td><td>2.1(-10)</td><td>5.6(-11)</td></tr><tr><td>c-C<sub>3</sub>H<sub>2</sub></td><td>5.8(-9)</td><td>2.6(-8)</td><td>2.6(-10)</td><td>HC<sub>5</sub>N</td><td>4(-9)</td><td>4.8(-10)</td><td>1.03(-9)</td></tr><tr><td>l-C<sub>3</sub>H<sub>2</sub></td><td>2.1(-10)</td><td>2.1(-8)</td><td>9.2(-9)</td><td>CH<sub>3</sub>C<sub>5</sub>N</td><td>7.4(-11)</td><td>4.8(-13)</td><td>5.1(-12)</td></tr><tr><td>CH<sub>3</sub>C<sub>2</sub>H</td><td>6(-9)</td><td>2.7(-10)</td><td>8.4(-12)</td><td>HC<sub>7</sub>N</td><td>1(-9)</td><td>3.9(-11)</td><td>1.7(-10)</td></tr><tr><td></td><td></td><td></td><td></td><td>HC<sub>9</sub>N</td><td>5(-10)</td><td>1.3(-12)</td><td>5.8(-11)</td></tr><tr><td>C<sub>4</sub>H</td><td>7.1(-8)</td><td>1.0(-9)</td><td>8.0(-10)</td><td></td><td></td><td></td><td></td></tr><tr><td>C<sub>4</sub>H<sup>-</sup></td><td>&lt;3.7(-12)</td><td>1.7(-11)</td><td>1.9(-11)</td><td>NO</td><td>2.7(-8)</td><td>7.0(-8)</td><td>6.8(-10)</td></tr><tr><td>H<sub>2</sub>C<sub>4</sub></td><td>7(-10)</td><td>2.7(-8)</td><td>1.9(-11)</td><td>HNCO</td><td>4(-10)</td><td>3.2(-13)</td><td>4.0(-11)</td></tr><tr><td>C<sub>5</sub>H</td><td>8(-10)</td><td>5.2(-10)</td><td>1.0(-10)</td><td></td><td></td><td></td><td></td></tr><tr><td>CH<sub>3</sub>C<sub>4</sub>H</td><td>1(-9)</td><td>6.1(-11)</td><td>3.8(-11)</td><td></td><td></td><td></td><td></td></tr><tr><td>C<sub>6</sub>H</td><td>4.1(-10)</td><td>3.7(-11)</td><td>3.7(-11)</td><td>H<sub>2</sub>S</td><td>&lt;5(-10)</td><td>4.5(-11)</td><td>2.1(-10)</td></tr><tr><td>C<sub>6</sub>H<sup>-</sup></td><td>1.0(-11)</td><td>4.2(-12)</td><td>1.0(-11)</td><td>CS</td><td>2.9(-9)</td><td>2.6(-9)</td><td>2.2(-9)</td></tr><tr><td>H<sub>2</sub>C<sub>6</sub></td><td>4.7(-11)</td><td>9.7(-11)</td><td>6.8(-12)</td><td>HCS<sup>+</sup></td><td>3(-10)</td><td>2.7(-12)</td><td>2.0(-12)</td></tr><tr><td>C<sub>8</sub>H</td><td>4.6(-11)</td><td>9.3(12)</td><td>1.4(-11)</td><td>H<sub>2</sub>CS</td><td>7(-10)</td><td>1.37(-10)</td><td>2.1(-10)</td></tr><tr><td>C<sub>8</sub>H<sup>-</sup></td><td>2.1(-12)</td><td>8.1(-13)</td><td>2.3(-12)</td><td>C<sub>2</sub>S<sup>a</sup></td><td>7(-9)</td><td>6.8(-11)</td><td>1.5(-9)</td></tr><tr><td></td><td></td><td></td><td></td><td>C<sub>3</sub>S</td><td>1(-9)</td><td>6.2(-10)</td><td>4.7(-10)</td></tr><tr><td>OCS</td><td>2.2(-9)</td><td>2.7(-10)</td><td>6.0(-10)</td><td>SO<sup>a</sup></td><td>1.5(-9)</td><td>3.9(-9)</td><td>9.6(-12)</td></tr><tr><td>NS</td><td>8.0(-10)</td><td>3.6(-11)</td><td>1.6(-13)</td><td>SO<sub>2</sub><sup>a</sup></td><td>3(-10)</td><td>2.4(-10)</td><td>2.4(-13)</td></tr></tbody></table>

Notes. *a(b)* refers to *a* × 10<sup>6</sup>. Abundances correspond to the positions TMC-1 α<sub>J2000</sub> = 04<sup>h</sup>41<sup>m</sup>41<sup>s</sup>88, δ<sub>J2000</sub> = +25°41<sup>m</sup>27<sup>s</sup> (cyanopolyene peak). See Agúndez & Wakelam (2013) for more details. DS refers to modelled abundances with deuteration and spin chemistry taken into account. NoDS refers to modelled abundances without deuteration and spin chemistry.

<sup>a</sup>Fig. 6 shows the shift in the chemical time-scale for the affected species (bold face) to reach the peak abundances.

TMC-1 together with the abundances obtained with our model at 10<sup>5</sup> yr. For comparison, we also list the molecular D/H ratios reported by Roberts & Millar (2000b) and Albertsson et al. (2013) for the same physical conditions and the same age.

Our modelled abundances are in reasonable agreement with the observed ones. The D/H ratios predicted by our model are slightly smaller than the ones reported by Roberts & Millar (2000b) and Albertsson et al. (2013). This can be explained by the fact that our network includes essential spin chemistry to take into account deuterium fractionation properly and the others do not. Considering ortho and para species, reaction (1) becomes efficient in the backward direction. This results in efficient destruction of H<sub>2</sub>D<sup>+</sup>, which in turn globally reduces the abundances of deuterated species. This is the reason why we observe smaller molecular D/H ratios as compared to the other models.

### 3.3 Effect of essential spin chemistry and deuteration on the observed non-deuterated species in TMC-1

One of the goals of this study is to quantify the effect of essential spin chemistry and deuteration on the abundances of non-deuterated species. For that, we have run two models: (1) with deuteration and

spin chemistry (DS) and (2) without deuteration and spin chemistry (NoDS). We then focus on the gas-phase species observed in the cold core TMC-1. In Table 4, we report the observed abundances in TMC-1 collected by Agúndez & Wakelam (2013) together with the abundances predicted by our two models. To define the ‘chemical age’ for TMC-1 for both models, we have calculated the mean confidence level following the prescription of Garrod et al. (2007) to fit with the TMC-1 observations. First, we construct a lognormal distribution about each observational value, and then identify its defining standard deviation, σ, with an appropriate error factor (erf) on the observed value. Finally, the ‘confidence’, κ<sub>i</sub>, that the modelled abundance (X<sub>model, i</sub>, for species i) is associated with the observed value (X<sub>obs, i</sub>) is defined as

$$ \kappa_i = \text{erfc} \left( \frac{|\log(X_{\text{model},i}) - \log(X_{\text{obs},i})|}{\sqrt{2\sigma}} \right), \quad (2) $$

where erfc is the complementary error function (erfc = 1 - erf); κ<sub>i</sub> ranges between zero and unity. In our case, we define σ = 1; hence one standard deviation corresponds to one order of magnitude higher or lower than the observed value. Fig. 5 represents the mean confidence level calculated using the method described above. As it can be seen, the DS model (~37 per cent) has a strong impact
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Comparison between the modelled abundances for non-deuterated species and the abundances observed in TMC-1 (see text). NoDS means the model without spin and deuterium chemistry whereas DS means the model with spin and deuterium chemistry.</figcaption></figure>

on the general confidence level as compared to the NoDS model (~45 per cent) at its maximum. The use of the DS model suggests a best-fitting chemical age for TMC-1 of $10^5$ yr whereas the NoDS model gives $3 \times 10^5$ yr. At the time of best agreement, for both the DS and NoDS models, ~50 per cent and ~60 per cent of the observed species in TMC-1 are reproduced within a factor of 10. But all these estimates are very much dependent on the initial opr(H$_2$) and our estimates are only valid for the initial statistical ratio of 3:1. For example, in order to perform more realistic age estimates

for TMC-1, it needs to be done in the context of parameter-space exploration with assumed opr(H$_2$) and this is out of scope of the current work. In Table 4, we have reported abundances for all the observed non-deuterated species using the above two models at their best chemical age.

By investigating closely, we found three types of differences: (1) DS model results different from NoDS but in better agreement with the TMC-1 observation as compared to NoDS (Case I); (2) DS model results different from NoDS but in less agreement with the TMC-1 observation as compared to NoDS (Case II); (3) differences between the two models and the observations are both within a factor of 10 (Case III). The differences between the agreements are caused by changes in the chemical time-scales. This can be clearly seen from Fig. 6 where we have shown the most affected oxygen-, nitrogen- and sulphur-bearing species for which the chemical time-scales for reaching their peak have changed. Here, we will focus on the detailed chemistry for Case I and Case II, which shows the effect of deuteration and ortho-para chemistry on the observed non-deuterated species. For Case I, we found molecules such as O$_2$, CH$_3$OH, C$_2$O, H$_2$C$_4$, HC$_5$N, C$_2$S, C$_6$H$^-$ and C$_8$H$^-$, and for Case II we found CH$_3$C$_2$H, NH$_3$, HCN, CH$_3$CN, CH$_2$CHCN, SO and SO$_2$. The rest of the species belong to Case III.

Among the Case I species, O$_2$ forms via the gas-phase reaction O + OH in both models. But in model DS, as can be seen from Table 4, the abundance of OH is almost 10 times lower than in the NoDS model, which in turn produces less O$_2$. In the DS model, OH forms via the gas-phase photodissociation of H$_2$O and by the neutral-neutral reaction O + H$_2$CO → H + OH + CO that has an activation barrier, while in the NoDS model, OH forms via the

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Abundance with respect to n$_H$ for a selection of O, N and S bearing species and for two models: left-hand panel – DS Model with spin and deuterium chemistry; right-hand panel – NoDS model without spin and deuterium chemistry.</figcaption></figure>
<table><caption>**Table 5.** New set of observable gas-phase deuterated species in TMC-1 awaiting detection (for example with the IRAM-30 m telescope).</caption><thead><tr><th>Species</th><th>Line</th><th>A<sub>ij</sub> (s<sup>-1</sup>)</th><th>E<sub>up</sub> (K)</th><th>Frequency (GHz)</th><th>n(x)/n(H)</th><th>Line intensity (K)</th></tr></thead><tbody><tr><td>c-C<sub>3</sub>D</td><td>3 1 3 → 2 1 2</td><td>2.2(−7)</td><td>9.41</td><td>116.73 (JPL)<sup>a</sup></td><td>2.0(−10)</td><td>0.18</td></tr><tr><td>CH<sub>2</sub>ND</td><td>2 0 2 → 1 0 1</td><td>5.4(−6)</td><td>8.43</td><td>117.08 (JPL)<sup>a</sup></td><td>3.2(−11)</td><td>0.005</td></tr><tr><td>DNCCC</td><td>9 8 7 → 8 8 8</td><td>1.9(−8)</td><td>19.01</td><td>79.20 (JPL)<sup>a</sup></td><td>5.2(−11)</td><td>0.019</td></tr><tr><td>C<sub>4</sub>HD</td><td>9 0 9 → 8 0 8</td><td>4.11(−5)</td><td>18.30</td><td>76.27 (CDMS)</td><td>2.3(−9)</td><td>0.13</td></tr><tr><td>DNO</td><td>2 0 2 → 1 0 1</td><td>5.0(−6)</td><td>10.52</td><td>146.117 (JPL)<sup>a</sup></td><td>1.7(−11)</td><td>0.003</td></tr></tbody></table>

Notes. The table is limited to species with relative abundances ≥10<sup>-11</sup>.

a(b) refers to a × 10<sup>6</sup>.

<sup>a</sup>http://spec.jpl.nasa.gov/.

fast dissociative recombination of H<sub>3</sub>O<sup>+</sup>. CH<sub>3</sub>OH forms via the dissociative recombination reaction of CH<sub>3</sub>OH<sub>2</sub><sup>+</sup> in the gas phase at 10<sup>5</sup> yr in the DS model, whereas in the NoDS model, it forms via the surface reaction s-H + s-CH<sub>3</sub>O and is destroyed rapidly via the barrierless gas-phase reaction CH<sub>3</sub>OH + C. Reaction s-H + s-CH<sub>3</sub>O becomes the main production reaction from 10<sup>6</sup> yr in model DS i.e. well after the gas-phase spin conversion of ortho-to-para H<sub>2</sub>. C<sub>2</sub>O is produced in model DS as well as in model NoDS via the gas-phase reaction C + HCO. But, we found that, C<sub>2</sub>O is more abundant in the DS model as compared to the NoDS model. This is due to the chemistry of HCO. HCO is produced in the NoDS model via the grain surface reaction s-H + s-CO, which has a high activation barrier of 2500 K, and in the DS model it is produced via the barrierless reaction CH<sub>2</sub> + O. We produce less C<sub>4</sub>H<sub>2</sub> in model DS due to the highly efficient destruction of this species via the barrierless gas-phase reaction C + C<sub>4</sub>H<sub>2</sub>, whereas in the NoDS model, this destruction process is not very efficient. For HC<sub>5</sub>N, we have better agreement with the observation and also it is more abundant in model DS than the NoDS. In both models, HC<sub>5</sub>N forms via the dissociative recombination of H<sub>2</sub>C<sub>5</sub>N<sup>+</sup>. But in model DS, HC<sub>5</sub>N is efficiently destroyed by p-H<sub>3</sub><sup>+</sup> to form H<sub>2</sub>C<sub>5</sub>N<sup>+</sup>, which recombine again to form HC<sub>5</sub>N. For C<sub>2</sub>S, we observe that it is more abundant in DS model than NoDS model. This is due to the effect of the barrierless gas-phase reaction O + C<sub>2</sub>S. This reaction destroys C<sub>2</sub>S more rapidly in NoDS model as compared to the DS model. Among the anions, C<sub>6</sub>H<sup>−</sup> and C<sub>8</sub>H<sup>−</sup> both are efficiently produced in model DS as compared to NoDS, since, in model DS, the rate of production via the dissociative recombination reactions of C<sub>6</sub>H and C<sub>8</sub>H is very high due to high opr(H<sub>2</sub>).

Among the Case II species, CH<sub>3</sub>C<sub>2</sub>H is produced efficiently in model NoDS due to its formation on the surface via the barrierless reaction s-H + s-CH<sub>2</sub>CCH. Among the others, the chemistry of NH<sub>3</sub> and HCN has already been discussed in our earlier section. For CH<sub>3</sub>CN, we observe a very high abundance in model DS as compared to the NoDS model. CH<sub>3</sub>CN is produced by the dissociative recombination reaction of CH<sub>3</sub>CNH<sup>+</sup> in both models but in model NoDS, it is destroyed by several other ion-molecule reactions with HCO<sup>+</sup>, H<sub>3</sub><sup>+</sup>, H<sub>3</sub>O<sup>+</sup> and C<sup>+</sup>, whereas in model DS, it is only destroyed by p-H<sub>3</sub><sup>+</sup>. We observe that CH<sub>2</sub>CHCN is less abundant in model DS, since it is destroyed by several reactions of ortho- and para-H<sub>3</sub><sup>+</sup> to form C<sub>3</sub>H<sub>3</sub>NH<sup>+</sup>, whereas in the NoDS model, it is destroyed mainly by HCO<sup>+</sup>. SO is mainly produced by the neutral-neutral reaction S + OH in model DS and OH is among the highly affected species in model DS. This corresponds to the decrease in abundance of SO in model DS. For SO<sub>2</sub>, it is formed on the surface in DS model via the reaction s-O + s-SO, whereas in model NoDS, it is formed by the neutral-neutral gas-phase reactions OH + SO, O + SO. But its decrease in abundance in DS model is due to the efficient gas-phase destruction reaction C + SO<sub>2</sub>. The decrease in

the abundance of NS in model DS as compared to NoDS is due to the efficient destruction by the various atoms i.e. C, O and N.

### 3.4 Some new observable deuterated species in TMC-1 from our model

In Table 5, we list a set of potentially new observable deuterated species in TMC-1. For predicting the observability (in the frequency range of 73–180 GHz) of all the species (for which frequencies are known) listed in Table 5, we have used the CASSIS<sup>5</sup> interactive spectrum analyser to calculate the line intensities under local thermodynamic equilibrium (LTE) conditions (though LTE might not be reasonable for some of those transitions at 10<sup>4</sup> cm<sup>-3</sup>, see for other alternatives in Liszt & Pety 2016). For our calculations, we assume excitation temperature = 5 K (to take into account the fact that the populations of the molecular levels might not be at LTE), FWHM = 1 km s<sup>-1</sup>, H<sub>2</sub> column density = 10<sup>22</sup> cm<sup>-2</sup> and no beam dilution to simulate typical dark cloud conditions. We list only the brightest transitions along with their Einstein coefficients and upper level energies in Table 5.

### 4 CONCLUSIONS

In this work, we present the first publicly available chemical network of multiply deuterated species along with spin chemistry of H<sub>2</sub>, H<sub>2</sub><sup>+</sup>, H<sub>3</sub><sup>+</sup> and their isotopologues. We also benchmarked our new model by comparing with existing works. Observed molecular D/H ratios at different positions of TMC-1 have been compared with our new comprehensive astrochemical model. By introducing an extensive description of deuteration along with nuclear spin-state processes, we found that the chemical time-scale for reaching the peak abundance of some non-deuterated species has changed by a factor of a few in some cases. Finally, we report a new set of potentially observable deuterated species in TMC-1.

### ACKNOWLEDGEMENTS

LM, PG, MR, VW and FH thank ERC starting grant (3DICE, grant agreement 336474) for funding during this work. VW, PG, AD, SG, FH and CV also acknowledge the French program Physique et Chimie du Milieu Interstellair (PCMI) funded by the Conseil National de la Recherche Scientifique (CNRS) and Centre National d'Etudes Spatiales (CNES). LM would like to thank Holger S. P. Müller for useful comments on the manuscript. We would like to thank the anonymous referee for constructive comments that helped to improve the manuscript.

<footnote n="5"><sup>5</sup>http://cassis.irap.omp.eu</footnote>
REFERENCES

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

Aikawa Y., Wakelam V., Hersant F., Garrod R. T., Herbst E., 2012, ApJ,
760, 40

Albertsson T. Semenov D. A., Vasyunin A. I., Henning T., Herbst E., 2013, ApJS, 207, 27

Albertsson T., Semenov D., Henning T., 2014a, ApJ, 784, 39

Albertsson T., Indriolo N., Kreckel H., Semenov D., Crabtree K. N., Henning T., 2014b, ApJ, 787, 44

Bacmann A., 2004, Balt. Astron., 13, 402

Bell M. B., Avery L. W., Matthews H. E., Feldman P. A., Watson J. K. G., Madden S. C., Irvine W. M., 1988, ApJ, 326, 924

Bergin E. A., Neufeld D. A., Melnick G. J., 1999, ApJ, 510, L145

Bergin E. A. et al., 2013, Nature, 493, 644

Bergman P., Parise B., Liseau R., Larsson B., 2011, A&A, 527, A39

Bottinelli S., Wakelam V., Caux E., Vastel C., Aikawa Y., Ceccarelli C., 2014, MNRAS, 441, 1964

Caselli P., van der Tak F. F. S., Ceccarelli C., Bacmann A., 2003, A&A, 403, L37

Caselli P., Vastel C., Ceccarelli C., van der Tak F. F. S., Crapsi A., Bacmann A., 2008, A&A, 492, 703

Ceccarelli C., Caselli P., Bockelée-Morvan D., Mousis O., Pizzarello S., Robert F., Semenov D., 2014, Protostars and Planets VI. Univ. Arizona Press, Tucson, AZ, p. 859

Chabot M., Béroff K., Gratier P., Jallat A., Wakelam V., 2013, ApJ, 771, 90

Coutens A. et al., 2012, A&A, 539, A132

Coutens A. et al., 2014, MNRAS, 445, 1299

Das A., Majumdar L., Sahu D., Gorai P., Sivaraman B., Chakrabarti S. K., 2015, ApJ, 808, 21

Demyk K., Bottinelli S., Caux E., Vastel C., Ceccarelli C., Kahane C., Castets A., 2010, A&A, 517, A17

Dutrey A. et al., 2011, A&A, 535, A104

Faure A., Hily-Blant P., Le Gal R., Rist C., Pineau des Forêts G., 2013, ApJ,
770, L2

Flower D. R., Pineau des Forêts G., Walmsley C. M., 2004, A&A, 427, 887

Flower D. R., Pineau Des Forêts G., Walmsley C. M., 2006, A&A, 449, 621

Garrod R. T., Wakelam V., Herbst E., 2007, A&A, 467, 1103

Gerin M., Combes F., Wlodarczak G., Encrenaz P., Laurent C., 1992, A&A, 253, L29

Guelin M., Langer W. D., Snell R. L., Wootten H. A., 1977, ApJ, 217, L165

Guilloteau S., Piétu V., Dutrey A., Guélin M., 2006, A&A, 448, L5

Hasegawa T. I., Herbst E., 1993, MNRAS, 261, 83

Hasegawa T. I., Herbst E., Leung C. M., 1992, ApJS, 82, 167

Hincelin U., Wakelam V., Hersant F., Guilloteau S., Loison J. C., Honvault P., Troe J., 2011, A&A, 530, A61

Howe D. A., Millar T. J., Schilke P., Walmsley C. M., 1994, MNRAS, 267, 59

Huang J., Öberg K. I., 2015, ApJ, 809, L26

Hugo E., Asvany O., Schlemmer S., 2009, J. Chem. Phys., 130, 164302

Linsky J. L. et al., 2006, ApJ, 647, 1106

Lis D. C., Roueff E., Gerin M., Phillips T. G., Coudert L. H., van der Tak F. F. S., Schilke P., 2002, ApJ, 571, L55

Liszt H. S., Pety J., 2016, ApJ, 823, 124

Loison J.-C., Wakelam V., Hickson K. M., Bergeat A., Mereau R., 2014a,
MNRAS, 437, 930

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

Loren R. B., Wootten A., 1985, ApJ, 299, 947

MacLeod J. M., Avery L. W., Broten N. W., 1981, ApJ, 251, L33

Majumdar L., Das A., Chakrabarti S. K., 2014a, A&A, 562, A56

Majumdar L., Das A., Chakrabarti S. K., 2014b, ApJ, 782, 73

Majumdar L., Gratier P., Vidal T., Wakelam V., Loison J.-C., Hickson K. M., Caux E., 2016, MNRAS, 458, 1859

Margulès L. et al., 2010, ApJ, 714, 1120

Miettinen O., Harju J., Haikala L. K., Juvela M., 2012, A&A, 538, A137

Millar T. J., Bennett A., Herbst E., 1989, ApJ, 340, 906

Minowa H., Satake M., Hirota T., Yamamoto S., Ohishi M., Kaifu N., 1997, ApJ, 491, L63

Neufeld D. A., Wolfire M. G., Schilke P., 2005, ApJ, 628, 260

Öberg K. I., Furuya K., Loomis R., Aikawa Y., Andrews S. M., Qi C., van Dishoeck E. F., Wilner D. J., 2015, ApJ, 810, 112

Oka T., 2004, J. Mol. Spectrosc., 228, 635

Pagani L. et al., 2009, A&A, 494, 623

Parise B., Castets A., Herbst E., Caux E., Ceccarelli C., Mukhopadhyay I., Tielens A. G. G. M., 2004, A&A, 416, 159

Parise B., Belloche A., Du F., Güsten R., Menten K. M., 2011, A&A, 526, A31

Parise B. et al., 2012, A&A, 542, L5

Qi C., Wilner D. J., Aikawa Y., Blake G. A., Hogerheijde M. R., 2008, ApJ, 681, 1396

Reboussin L., Wakelam V., Guilloteau S., Hersant F., 2014, MNRAS, 440, 3557

Roberts H., Millar T. J., 2000a, A&A, 361, 388

Roberts H., Millar T. J., 2000b, A&A, 364, 780

Roueff E., Tiné S., Coudert L. H., Pineau des Forêts G., Falgarone E., Gerin M., 2000, A&A, 354, L63

Ruaud M., Loison J. C., Hickson K. M., Gratier P., Hersant F., Wakelam V., 2015, MNRAS, 447, 4004

Sipilä O., Caselli P., Harju J., 2013, A&A, 554, A92

Sipilä O., Caselli P., Harju J., 2015, A&A, 578, A55

Spezzano S. et al., 2013, ApJ, 769, L19

Stark R., van der Tak F. F. S., van Dishoeck E. F., 1999, ApJ, 521, L67

Talukdar R. K., Ravishankara A., 1996, Chem. Phys. Lett., 253, 177

Taquet V., Peters P. S., Kahane C., Ceccarelli C., López-Sepulcre A., Toubin C., Duflot D., Wiesenfeld L., 2013, A&A, 550, A127

Taquet V., Charnley S. B., Sipilä O., 2014, ApJ, 791, 1

Tiné S., Roueff E., Falgarone E., Gerin M., Pineau des Forêts G., 2000, A&A, 356, 1039

Turner B. E., 1989, ApJ, 347, L39

Turner B. E., 1990, ApJ, 362, L29

Turner B. E., 2001, ApJS, 136, 579

Turner B. E., Zuckerman B., 1978, ApJ, 225, L75

van der Tak F. F. S., Müller H. S. P., Harding M. E., Gauss J., 2009, A&A, 507, 347

van Dishoeck E. F., Thi W.-F., van Zadelhoff G.-J., 2003, A&A, 400, L1

Vastel C., Phillips T. G., Yoshida H., 2004, ApJ, 606, L127

Vastel C., Caselli P., Ceccarelli C., Phillips T., Wiedner M. C., Peng R., Houde M., Dominik C., 2006, ApJ, 645, 1198

Vastel C. et al., 2010, A&A, 521, L31

Wakelam V., Vastel C., Aikawa Y., Coutens A., Bottinelli S., Caux E., 2014, MNRAS, 445, 2854

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

Wakelam V., Loison J.-C., Hickson K. M., Ruaud M., 2015b, MNRAS, 453, L48

Walmsley C. M., Flower D. R., Pineau des Forêts G., 2004, A&A, 418, 1035

Watanabe N., Kimura Y., Kouchi A., Chigai T., Hama T., Pirronello V., 2010, ApJ, 714, L233

Wootten A., 1987, in Vardya M. S., Tarafdar S. P., eds, Proc. IAU Symp. 120, Astrochemistry. Reidel, Dordrecht, p. 311

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