© ESO, 2013

1. Introduction

The latest results obtained by the Cassini-Huygens mission confirmed that the dissociation and ionization of methane of CH₄ and nitrogen N₂ in the high stratosphere of Titan initiates a complex photochemistry of hydrocarbons and nitrogen compounds through molecule-molecule and ion-molecule reactions, which leads to the production of C_nH_p hydrocarbons (up to n = 6 at least; the heaviest hydrocarbon clearly detected is benzene, see for instance Brown et al. 2009, for a comprehensive review of our current knowledge about Titan). The modeling of such an atmospheric system is limited by the lack of kinetic and photolytic data at low temperature (T ∈ [100,150] K) especially for heavy hydrocarbons. Hébrard et al. (2007) pointed out that a great deal of information regarding the larger species (n > 3) is missing from current photochemical models. In particular, only a small fraction of all possible reactions producing or involving C₃-compounds is included in current photochemical models, from which we conclude that several important processes could be missing. To correctly understand how the C₃-, C₄- and C₆-hydrocarbons previously detected in the atmosphere of Titan (CH₃C₂H, C₃H₆, C₃H₈, C₄H₂ and C₆H₆) are produced, it is necessary to complete the chemical scheme for lighter species (i.e., C₂- and C₃-compounds). In a recent study, Hébrard et al. (2012) updated the chemical scheme of C₂-hydrocarbons to provide a solid basis for the study of HCN and HNC neutral productions. In this previous model, we modified various rate constants and branching ratios for reactions involving C and CH. These changes did not play a major role in the chemistry of HCN/HNC but strongly affected C and C₃H_p concentrations. One of the main changes concerned the C + C₂H₂ reaction, which was predicted to lead to the formation of the C₃H₂ adduct (as in all photochemical models of giant planets’ and Titan’s atmospheres where this reaction is present, Lebonnois et al. 2001; Wilson & Atreya 2004; Moses et al. 2005; Lavvas et al. 2008) but in fact leads to the formation of C₃ + H₂ and C₃H + H (see Appendix C). Moreover, Zhang et al. (2010) highlighted the fact that atomic carbon C is likely to be more abundant in Titan’s upper atmosphere than previously predicted. Carbon atoms are indeed efficiently produced by both the H + CH (van Harrevelt et al. 2002) and the N + CN (Daranlot et al. 2012) reactions, whereas they are only very slowly consumed by their reaction with N₂ (Husain & Kirsch 1971) and do not react at all with CH₄ (Husain & Kirsch 1971; Kim et al. 2003). As a result, the C + C₂H₂ (along with C + C₂H₄) reaction is an efficient source of C₃H_p species, such as C₃, a very stable bi-carbene molecule found to be abundant in various interstellar media (Oka et al. 2003; Mookerjea et al. 2010) and in comets (Huggins 1881; Rousselot et al. 2001), but absent from any current models of Titan’s atmosphere. In the present study, we continue our systematic approach to improve the neutral chemical scheme of Titan’s atmosphere, focusing specifically on C₃-hydrocarbons. This work is also important for the modeling of ion-molecule reactions involving C₃H_p species in the ionosphere of Titan, and vice versa. Abundances of neutral species (and their uncertainties) and ion species are indeed strongly coupled (Carrasco et al. 2007). The Ion and Neutral Mass Spectrometer (INMS) instrument onboard Cassini moreover revealed a few neutrals with densities that pure neutral photochemical chemistry could not easily reproduce. This is for example the case for benzene C₆H₆, which has been detected in abundance with the INMS instrument, the production of which is now assumed to involve ion chemistry, and notably dissociative recombinations (Westlake et al. 2012; Plessis et al. 2012).

Another important question clearly points out the need for a careful study of C₃-hydrocarbons chemistry. From an uncertainty propagation study and a global sensitivity analysis point of view, Hébrard et al. (2009) found that C₃H₂ is a key compound in the photochemistry of Titan (i.e., several reactions involving C₃H₂ are responsible for large uncertainties in the abundances of major compounds). It is therefore crucially important to update and complete the chemical scheme related to this compound. Peng et al. (2010) showed a linear increase of the uncertainty factor of species abundance with increasing molecular mass for the three major hydrocarbon families (alkanes, alkenes and alkynes) and a nonlinear uncertainty growth pattern with increasing mass for C_n and C_nH₂ species. Consequently, it is necessary to lower the uncertainties on the current chemical scheme of C₂- and C₃-hydrocarbons to improve the precision of model results for heavy hydrocarbons. This requires us to first evaluate the uncertainties on the computed abundances of C₃-compounds and then to identify the key reactions responsible for the largest of them (following the methodology of Hébrard et al. 2009).

The photochemical model used in the present study is derived from the model of Hébrard et al. (2012): details about the model are given in that paper. Our methodology to improve the chemical scheme for C₃-compounds is presented in Sect. 2. The abundances of C₃-hydrocarbons are presented in Sect. 3. In particular, we show the main differences between the present and our previous model (Hébrard et al. 2012) and we present the main reactions that are responsible for the production and loss of the major C₃-hydrocarbons (for the nominal model only). In Sects. 4 and 5 we perform an uncertainty propagation study and a global sensitivity analysis to determine the key reactions responsible for the model result uncertainties for C₃-compounds. This new list of key reactions is discussed in detail in Appendix C.

2. Chemical scheme

2.1. Chemical reactions

Many important photochemical processes involving C₃H_p species in Titan’s atmosphere are found to retain the C₃ carbon backbone whilst changing the corresponding number of H atoms. For example, photodissociations such as the C₃H₆ + hν → C₃H₅ + H reaction lead to lower saturation levels, while the opposite is true for termolecular reactions such as the C₃H₅ + H + M → C₃H₆ + M reaction. There are only a few reactions producing C₃H_p molecules from smaller carbon containing species. These include bimolecular reactions: C + C₂H₂, C + C₂H₄, CH + C₂H₂, CH + C₂H₄, CH + C₂H₆, ¹CH₂ + C₂H₂, ¹CH₂ + C₂H₄, CH₃ + C₂H and termolecular reactions CH₃ + C₂H₃ + M and CH₃ + C₂H₅ + M. The bimolecular reactions dominate at high altitude (above 800 km) and the termolecular reactions dominate at low altitude and higher pressures. In terms of total production flux, the CH₃ + C₂H₃ + M and CH₃ + C₂H₅ + M termolecular reactions are the most efficient.

In the present work, several rate constants have been updated and some reactions have been added. Our new chemical scheme, derived from the chemical scheme presented in Hébrard et al. (2006, 2009, 2012), includes 143 compounds and 944 reactions (102 photodissociation processes, 2 dissociation processes of N₂ by cosmic rays, 737 bimolecular reactions and 103 termolecular reactions). A major change in this update is the introduction of radiative association reactions, following the work of Vuitton et al. (2012). The complete list of reactions is available upon request and can be downloaded from the KIDA database (Wakelam et al. 2012). In the following sections, we explain how we evaluated some unknown rate constants and how we assigned their uncertainty factors in the chemical scheme we propose.

2.2. Photolysis processes

To better describe the photochemistry of the C₃H_p species, we reviewed the parameters important for their photolysis (cross sections, quantum yields and dissociation limits). The photoabsorption cross sections were calculated from formula (3) of van Hemert & van Dishoeck (2008). We also updated the photolysis parameters for C₂H₂ and HC₃N. Table 1 presents the photodissociation limits corresponding to the exit channel exothermicities for barrierless dissociations or to the exit Transition State (TS) energies when the values are known. These values correspond to the product appearance only if photodissociation arises from the unimolecular decay of a molecule in an excited vibrational level of the electronic ground state formed by a non-radiative transition from the electronically excited state. Experimental branching ratio determinations are very scarce. Uncertainties on these branching ratios are therefore very large, particularly below 200 nm where many exit channels are possible. We discuss of the quantum yields and dissociation limits in Appendix A for all species presented in Table 1 along with the absorption cross sections for selected important species.

2.3. Methodology for the chemical review

The reactions and rate constants were updated following the same procedure used to complete the photochemistry of HCN and HNC (Hébrard et al. 2012). First, a systematic literature search was performed (particularly for the reactions of C, CH and ¹CH₂ reactions with C₂H₂ and C₂H₄). When no information was found, we performed density functional theory (DFT) calculations at the M06-2X/cc-pVTZ level using the Gaussian09 software package (Frisch et al. 2009) to evaluate the presence and the values of any energetic barriers to the entrance valley for the important reactions (in terms of production and/or loss rate). For some critical reactions or when DFT results were ambiguous, we also performed MRCI+Q/cc-pVTZ calculations using the Molpro software package (Werner et al. 2010). When no energetic barrier was found present, the value of the considered rate constant was estimated using long-range forces, mainly through dispersion interactions (Stoecklin & Clary 1992; Georgievskii & Klippenstein 2005) and by taking into account the electronic degeneracy, γ_el. We investigated certain association reactions that play a major role in Titan’s atmosphere but are not well characterized, particularly in the low-pressure region. We present in Appendix B a semi-empirical model (called “k_association − ρ”), based on the calculations of Vuitton et al. (2012) and also on various experimental rate constants, which has allowed us to estimate values of the low-pressure limiting rate constant for associations reactions, k₀, as a function of the vibrational density of states of the adduct, ρ(E₀). We also applied this model to some radiative association processes addressed by Vuitton et al. (2012) as well as in earlier calculations.

Many of the reactions involved in the atmosphere of Titan are of the type atom/radical + radical or atom/radical + unsaturated compound. For these processes, there is often competition between the formation of bimolecular products and adduct stabilization. Adduct stabilization A + B → C designates the conjugation of the termolecular reaction A + B + M → C + M and the radiative association A + B → C + hν. When bimolecular product formation occurs through a distinct mechanism, we can easily separate the bimolecular channel from the adduct formation channel. For example, for H atom abstraction in the reactions of H and CH₃ with some hydrocarbon radicals, there is either a direct pathway or an adduct formation pathway followed by an elimination. However, the TSs for this latter type of system leading from the adduct to H₂ or CH₄ products are generally located above the energy of the separated reagents, as is the case for the H + C₂H₅ → C₂H₄ + H₂ (Irle & Morokuma 2000) and the CH₃ + C₂H₅→ CH₄ + C₂H₄ reactions (Zhu et al. 2004). For the H + C₂H₃ reaction, the TSs leading to H₂ and C₂H₂ are below the entrance level (Chang et al. 1998) but an experimental study by Monks et al. (1995) strongly indicated that H₂ + C₂H₂ formation occurs mainly through a direct mechanism. Therefore we considered here that H-atom abstraction is always a direct channel, clearly separated from the other bimolecular product channels that arise from adduct formation. When bimolecular product formation occurs through the same first step as adduct formation, i.e., through addition, we cannot separate bimolecular product formation from adduct stabilization. A good example is the H + C₂H₅ → C₂H₆/CH₃ + CH₃ reaction. Here, bimolecular product formation competes with adduct stabilization and with redissociation to the reagents. The main effect of the existence of an exit bimolecular channel from the adduct is to reduce the fraction of adduct stabilization at low pressure, which leads to a lower value for the low-pressure limiting rate constant k₀. For small systems (CH_p, C₂H_p) with an open bimolecular exit channel from the adduct, adduct stabilization is negligible when compared with bimolecular reaction for pressures below 0.1−1 Torr (corresponding to altitudes greater than ~200 km in Titan’s atmosphere). In most cases we can therefore neglect adduct stabilization. For large systems or when the bimolecular exit TSs are located close to the entrance level, adduct stabilization cannot be ignored. To deal with such systems we must consider a multiple-well treatment using the master equation for each system, which is beyond the scope of this study. Instead, we used experimental values for the termolecular reaction rate constant (when these were available in the literature) or we estimated them using our semi-empirical “k_association − ρ” model, dividing k₀ (and k_r) values by factors between 10 and 1000, depending on the size of the system and the position of the exit TS to take into account the effect of the open bimolecular exit channel. When the radiative association was estimated to be very weak (<10^-16 cm³ molecule^-1 s^-1), it was neglected. When there is a competition between adduct stabilization and bimolecular product formation, we considered that the total rate constant was a constant leading to k_bimolecular = k_∞ − k_adduct (see Appendix B). This competitive behaviour is always considered at the outset, but can be neglected for most reactions. Exceptions include the H + C₂H₅, H + C₃H, H + l,t-C₃H₂ and H + C₃H₇ reactions (for which the k₀ values are low) and the H + C₃H₆, H + C₄H₃, CH₃ + C₂H₃ and CH₃ + C₃H₃ reactions (for which the k₀ values are high). This competitive behavior is neglected for all other investigated reactions as our results are relevant only for altitudes above 200 km. However, many association reactions may play a more important role at altitudes lower than 200 km, for example the C₂H + alkenes reactions (Woon & Park 2009). Details on how rate constants and uncertainty factors were calculated are given in Appendix B.

2.4. Importance of isomers

In reconsidering the chemical network for C₃ hydrocarbon species, we have found it necessary to introduce several isomers of species already present in the chemical scheme for two main reasons. Firstly, if the various isomers are present at sufficiently high densities, they might be distinguished by observations. Secondly, the different isomers may also have different chemical reactivity than the other species present in the model and introducing them might open some new chemical pathways that were absent from the previous model. As a result, some reactions with new isomers could also be key reactions because they could prove to be a significant source of uncertainties in the current photochemical model. In the present study, we have introduced the isomers of two compounds: C₃H and C₃H₂. We did not consider the isomers of the other C₃-compounds for several reasons. One isomer of C₃H₃ is considerably more stable than the others. For C₃H₇, we considered only one isomer because n-C₃H₇ and i-C₃H₇ have been shown to have similar reactivities (Tsang 1988). Nevertheless, reactions involving these isomers as reactants are likely to have different products, so it will be necessary to differentiate between these isomers when studying heavier hydrocarbons (C_n-compounds, n > 3). It is also important to note that the reactivity of N(⁴S) with the various isomers introduced can give different products. Future studies of the inclusion of nitrogen in complex organic compounds for Titan’s atmosphere should therefore pay particular attention to these reactions.

3. Photochemical model results

First, we stress the limitations of our model. Microphysics of particles in Titan’s lower stratosphere and troposphere as well as the attenuation of solar photons by aerosols and the impact of cosmic rays in the lower atmosphere are not taken in account in our model (except for the dissociation of N₂). As a consequence, the results presented here for altitudes below approximately 200 km are not fully relevant. It is also important to note that including aerosols in the model would introduce additional uncertainties in the calculations of the actinic flux and of condensation processes. The propagation of these uncertainties is not treated in the present model. Due to the absence of coupling with ions in the upper atmosphere, the total production and loss of some neutral compounds is only poorly constrained above 800 km (Plessis et al. 2012). The aim of the present work is to improve the neutral photochemistry of Titan’s atmosphere (which will serve as a basis for future modeling studies including ion-molecule reactions), not to constrain some physical parameters (like the eddy diffusion coefficient). The incident solar flux at every level in the atmosphere was calculated as a function of the diurnally averaged unattenuated solar flux at the top of the atmosphere for a medium solar activity (normalized from Thuillier et al. 2004).

3.1. Comparison with the previous model of Hébrard et al. (2012)

To illustrate how the model results have been affected by the improvement of the chemical scheme for C₃-compounds, we compare our results with the recent model of Hébrard et al. (2012) (quoted as “previous model” in the following). We first checked to what extent the update of the chemical scheme for C₃H_p compounds affected the abundances of nitrogen compounds, C₂-hydrocarbons and C_n-hydrocarbons (n > 3). For nitrogen compounds, the difference between the previous and the present model results are small and always within the error bars of the model, whatever the altitude. For hydrocarbons, the situation depends on the compounds (see Fig. 1). For some compounds, the difference is noticeable but still lies within the error bars of the model (like C₂H₆ and C₄H₁₀). For other compounds the difference is outside the error bars of the model (like C₂H₂ and C₆H₆) and can reach several orders of magnitude (like C₄H₂ and C₄H₆).

More evidently, the present update has a noticeable effect on the abundances of many C₃-compounds, mainly C₃, C₃H, C₃H₂, C₃H₃, C₃H₄ and C₃H₆. Comparisons between the previous and the present models are presented in Figs. 2 and 3. For the other C₃-compounds the differences are less pronounced between the two models and are within the error bars of the model (see also Figs. 4−7).

3.2. Main production and loss processes

In the following, the main processes that contribute to the production or the loss of a given compound are given at the steady state for the nominal set of rate constants (unperturbed by the Monte-Carlo procedure explained in Sect. 4). Values in parentheses give the relative importance in percentage terms of the total production or loss rates. The emphasis is placed on compounds that show pronounced differences between the previous and the present model. Owing to the uncertainty factors attached to all reactions and all abundances, the relative importance of each reaction to the total production and loss rates might be very different in the Monte-Carlo runs than in the nominal one.

3.2.1. Carbon trimer C₃

C₃ was introduced in the previous model, but was described by only a limited network of reactions. As shown in Fig. 2, the present update of the earlier reaction scheme has a dramatic effect on the abundance of C₃ in the lower atmosphere and C₃ is now the most abundant C₃H_p species above 700 km. The main source for C₃ at high altitudes is the C + C₂H₂ reaction, whereas at lower altitudes, the H + l-C₃H and, especially, the H + c-C₃H processes take over gradually. The main processes responsible for the loss of C₃ in the lower atmosphere are the termolecular reactions, $\begin{array}{ccc}\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}& \mathrm{\to }& \mathrm{c}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}\mathrm{H}\mathrm{(}\mathrm{39}\mathrm{\%}\mathrm{at}\mathrm{600}\mathrm{km}\mathrm{)}\\ \mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}& \mathrm{\to }& \mathrm{l}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}\mathrm{H}\mathrm{(}\mathrm{39}\mathrm{\%}\mathrm{at}\mathrm{600}\mathrm{km}\mathrm{)}\mathit{.}\end{array}$These associations were not present in the previous model. The photolysis of C₃ leading to the formation of C₂ and C represents 18% of the total loss at 600 km.

3.2.2. 2-cyclopropyn-1-yl c-C₃H and 2-propynylidyne l-C₃H

Cyclic C₃H (c-C₃H) and linear C₃H (l-C₃H) are predicted to have similar abundances (within a factor 2) but their relatively low densities throughout the atmosphere, as a result of their high reactivity with atomic hydrogen H, probably prevent a differentiation in their putative detection. Their profiles differ noticeably from C₃H profile (which was considered as a single species in the previous model) below 700 km, where several important reactions for C₃H were missing. For instance, at 600 km, the main processes responsible for their production are $\begin{array}{ccc}\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}& \mathrm{\to }& \mathrm{l}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}\mathrm{H}\mathrm{\left(}\mathrm{99.4}\mathrm{\%}\mathrm{\right)}\\ \mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}& \mathrm{\to }& \mathrm{c}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}\mathrm{H}\mathrm{\left(}\mathrm{80.8}\mathrm{\%}\mathrm{\right)}\\ \mathrm{H}\mathrm{+}\mathrm{l}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}\mathrm{H}& \mathrm{\to }& \mathrm{c}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}\mathrm{H}\mathrm{+}\mathrm{H}\mathrm{\left(}\mathrm{13.4}\mathrm{\%}\mathrm{\right)}\mathit{.}\end{array}$None of these reactions were present in our previous model. We found that both C₃H isomers have a similar reactivity with the other species present in the model. We also note (see Sect. 5) that two reactions involving l-C₃H are key reactions for the production of the carbon trimer C₃.

3.2.3. Cyclopropenylidene c-C₃H₂

Cyclic C₃H₂ (c-C₃H₂) is by far the most abundant C₃H₂ isomer. Nevertheless, the importance of the propadienylidene l-C₃H₂ and propynylidene t-C₃H₂ isomers lies in their different reactivity with many compounds. As an example, N(⁴S) is supposed to react only with t-C₃H₂ to produce HC₃N. Also, the three isomers react differently with CH₃ to produce C₂H₃, which is involved in many subsequent reactions. Figure 2 clearly shows that c-C₃H₂ is even more abundant in the present work than total C₃H₂ in the previous model (which was considered as a single species previously). Many reactions participate in the production of c-C₃H₂ in the upper atmosphere of Titan (above 800 km, which corresponds to the altitude where the total production rate of c-C₃H₂ is at its maximum), including $\begin{array}{ccc}\mathrm{H}\mathrm{+}\mathrm{t}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{2}}& \mathrm{\to }& \mathrm{c}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{2}}\mathrm{+}\mathrm{H}\mathrm{\left(}\mathrm{46}\mathrm{\%}\mathrm{\right)}\\ {\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}\mathrm{h}\mathit{\nu }& \mathrm{\to }& \mathrm{c}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{2}}\mathrm{+}\mathrm{H}\mathrm{\left(}\mathrm{27}\mathrm{\%}\mathrm{\right)}\\ \mathrm{CH}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{2}}& \mathrm{\to }& \mathrm{c}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{2}}\mathrm{+}\mathrm{H}\mathrm{\left(}\mathrm{22}\mathrm{\%}\mathrm{\right)}\mathit{.}\end{array}$This production is counterbalanced by the photolysis of c-C₃H₂, which represents 93% of its total loss around 1000 km. None of these reactions were present in our previous model.

3.2.4. Propargyl radical C₃H₃

C₃H₃ is much more abundant in the upper atmosphere in the present model than in the previous one. However, the main reactions that contribute to the total production rate are similar in the two models. For instance, at 1000 km, these are: $\begin{array}{ccc}\mathrm{C}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{4}}& \mathrm{\to }& {\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}\mathrm{H}\mathrm{\left(}\mathrm{45.2}\mathrm{\%}\mathrm{\right)}\\ \mathrm{C}{\mathrm{H}}_{\mathrm{2}}\mathrm{CC}{\mathrm{H}}_{\mathrm{2}}\mathrm{+}\mathrm{h}\mathit{\nu }& \mathrm{\to }& {\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}\mathrm{H}\mathrm{\left(}\mathrm{38.9}\mathrm{\%}\mathrm{\right)}\\ \mathrm{C}{\mathrm{H}}_{\mathrm{3}}{\mathrm{C}}_{\mathrm{2}}\mathrm{H}\mathrm{+}\mathrm{h}\mathit{\nu }& \mathrm{\to }& {\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}\mathrm{H}\mathrm{\left(}\mathrm{7.1}\mathrm{\%}\mathrm{\right)}\\ 1\mathrm{C}{\mathrm{H}}_{\mathrm{2}}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}\mathrm{H}2& \mathrm{\to }& {\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}\mathrm{H}\mathrm{\left(}\mathrm{4.8}\mathrm{\%}\mathrm{\right)}\mathit{.}\end{array}$The increase in the abundance of C₃H₃ comes from a nonlinear competition between reactions involving atomic hydrogen H (H + c-C₃H₂, H + C₃H₃) and C₃H₄ isomers photodissociation.

3.2.5. Propene C₃H₆

C₃H₆ is found to be much more abundant in the present model compared to the previous one. At 1000 km, the main reactions that contribute to the production of this molecure are $\begin{array}{ccc}\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{5}}& \mathrm{\to }& {\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{6}}\mathrm{\left(}\mathrm{61.8}\mathrm{\%}\mathrm{\right)}\\ \mathrm{CH}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{6}}& \mathrm{\to }& {\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{6}}\mathrm{+}\mathrm{H}\mathrm{\left(}\mathrm{36.7}\mathrm{\%}\mathrm{\right)}\mathit{.}\end{array}$The rate constant of the first addition reaction has been updated since the previous model to include radiative association. Whilst termolecular reaction is negligible at this altitude, radiative association is seen to be important even if the rate is predicted to be relatively slow.

4. Uncertainty propagation study

4.1. Method

The methodology used to study the propagation of uncertainties in the model is described in Hébrard et al. (2007, 2009). In this study, we performed 900 Monte-Carlo runs to obtain statistically significant results. The integration time for each run was set to 10¹² s for simplicity and to limit the computation time. This time is sufficient to reach a steady state for each run. The uncertainty factor was set to 1.2 for all photodissociation rates for simplicity (see Peng et al. (2012) for a valuable discussion about uncertainties on photodissociation rates). A detailed investigation of all sources of uncertainties in these photodissociations rates (arising mainly from uncertainties in absorption cross sections and quantum yields) is beyond the scope of the present paper but should be performed in the future to improve the present model.

4.2. Results

Abundance distribution types depend on the compound and can vary with altitudes: distributions are not always normal or log-normal for a given altitude. In this case, quantiles are useful measures to represent the distributions. Consequently, Figs. 4−6 display both the 5th and 15th 20-quantiles and the 1st and 19th 20-quantiles, which represent the intervals containing respectively 50% and 90% of the abundance profiles for several important species in Titan’s atmosphere.

The main conclusion of these results is that although the agreement in terms of abundance is good, the current accuracy of photochemical models is quite poor for C₃H_p compounds (compared to uncertainties on observations when available), especially below 800 km. Theoretical and experimental studies are clearly required to improve the situation. We see in the next section that global sensitivity analysis can pinpoint the key reactions that are responsible for these large uncertainties.

Observational data are presented to give an idea of the agreement between our photochemical model (using a mean eddy diffusion coefficient K(z), Hörst et al. 2008) and available observations for C₃-compounds. We did not try to better constrain K(z) because of the current limitations of our model and uncertainties on the model results.

5. Global sensitivity analysis: determination of key reactions

The technique we used to determine the key reactions is based on the computation of Rank Correlation Coefficients (RCCs) between reaction rate constants and mole fractions at different altitudes. It has been previously used and described in Carrasco et al. (2007), Dobrijevic et al. (2008) and Hébrard et al. (2009). The greater the absolute value of the RCC, the more significant the contribution of a given reaction rate to the uncertainty on the mole fraction of a given species. Consequently, all reactions with a high RCC absolute value should be targeted to improve the accuracy of the model. The power of this technique to improve photochemical models has already been demonstrated for Titan by Hébrard et al. (2009) and for Neptune by Dobrijevic et al. (2010).

Tables 2 and 3 give RCCs for the main C₃-species. The RCC threshold has been arbitrarily set to 0.2. This choice gives for each compound a reasonable set of reactions allowing us to pinpoint only the most significant ones. Thirty key reactions were identified for four representative altitudes. We see that association reactions in general are predicted to be significant in all parts of the atmosphere. The termolecular reaction H + C₂H₂ → C₂H₃ in particular is a key reaction for all but one of the C₃-compounds, listed in Tables 2 and 3. Comments on some of these reactions are given in Appendix C.

The reaction N(²D) + HCN → CH + N₂ is also a main key reaction for HCN (see Hébrard et al. 2012). A discussion about the reaction H + CH → C + H₂ can be found as a datasheet in the KIDA database (Wakelam et al. 2012). Details about these two reactions are therefore not repeated here.

6. Conclusion

We have performed a systematic study of all potentially important processes that produce or consume C₃H_p compounds. This extensive review has led us to make recommendations for a large number of reaction rates and therefore to improve significantly the chemical schemes published so far for Titan’s atmosphere. Several photolysis processes were updated and the rate constants and branching ratios for many bimolecular reactions between neutral species were updated/reinvestigated. A new semi-empirical model based on previous calculations and various experimental data was implemented to allow us to predict the rates of the most important termolecular reactions and radiative associations for Titan’s atmosphere. Our update of the chemical network relating to C₃H_p substantially modified the overall chemical scheme of Titan’s atmosphere. We showed that several important reactions were indeed missing from our previous model (Hébrard et al. 2012) and also from other current photochemical models. This improvement of the C₃H_p chemistry has noticeable effects on the abundances of C₂- and C_n-compounds (n > 3), which are more or less pronounced, depending on the compound. For some species the differences brought about by the update stay within the error bars of the previous model (such as for C₂H₆), whereas for other compounds the differences lead to predicted abundances outside the error bars of the previous model (such as for C₂H₂, C₂H₄, C₆H₆). In some cases, the update has resulted in a change in predicted abundance of several orders of magnitude (for example, C₄H₂ is over two orders of magnitude less abundant at low altitudes in the updated model). We showed in particular that a careful update of the chemical scheme for a given family of compounds can have a drastic effect (or no effect at all) for other seemingly unrelated compounds. It is therefore important to complete the chemical scheme as far as possible before creating a reduced scheme that can be able to correctly predict the abundance of all the atmospheric constituents.

We found that many of the main processes involving the C₃H_p species in Titan’s atmosphere recycle C₃H_p species (which essentially changes the degree of saturation of the C₃ backbone), either through photodissociations or through reactions with H atoms. There are only a few reactions that produce C₃H_p species: bimolecular reactions such as C + C₂H₂, C + C₂H₄, CH + C₂H₂, CH + C₂H₄, CH + C₂H₆, ¹CH₂ + C₂H₂, ¹CH₂ + C₂H₄ and CH₃ + C₂H₃ and association reactions like CH₃ + C₂H₃ and CH₃ + C₂H₅.

We found that some C₃-molecules such as the carbon trimer C₃, the cyclopropenylidene radical c-C₃H₂ and the propargyl radical C₃H₃ present predicted abundances high enough to be potentially present in the Cassini/INMS data and should therefore be considered in models that aim to interpret these spectra.

The present work confirms previous studies Hébrard et al. (2007, 2009, 2012) that demonstrated that the uncertainties in the results of current photochemical models of Titan’s atmosphere could be very important and that the theoretical/experimental determination of rate constants and branching ratios at low temperature is crucial to better constrain in fine some physical parameters.

Among all the new processes introduced in the present chemical scheme, some are important reactions for the production and loss of C₃-compounds and/or are also identified as key reactions (reactions for which the uncertainty factors need to be lowered to improve the predictivity of photochemical models) by uncertainty propagation and global sensitivity analysis. We showed in this study only the most significant key reactions for C₃-compounds. The complete list of all main key reactions for Titan’s atmosphere (concerning all species for which observational data are available) will be available from the KIDA database.

Our model does not take into account ionic chemistry, which is known to have a noticeable impact on the abundances of neutral species (see Plessis et al. 2012). As a consequence, it is important to keep in mind that the abundances of some compounds presented in our study might be significantly affected by the coupling of our neutral chemical scheme with a ionospheric model. This is the case in particular for C₃. Considering the Proton Affinity of C₃ (767 kJ mol^-1, Hunter & Lias 1998) and because exothermic proton transfer reactions generally do not present a barrier, C₃ will react with the most abundant ions in Titan’s ionosphere (HCNH⁺, CH$\begin{array}{c}\mathrm{+}\\ \mathrm{5}\end{array}$, C₂H$\begin{array}{c}\mathrm{+}\\ \mathrm{3}\end{array}$, C₂H$\begin{array}{c}\mathrm{+}\\ \mathrm{5}\end{array}$), which will lead to C₃H⁺ formation. Ionic chemistry is likely to be a strong sink for C₃ because C₃H⁺ loss will be dominated by its reaction with CH₄ (Raksit & Bohme 1983).

The next step of the present study should be the improvement of C₄H_p chemistry (photolysis and neutral reactions). Considering the results we present here, we may expect that such an update of the chemical scheme could have a significant impact on the abundances of many compounds (even lighter ones).

This study might also help us to better understand the complexification of organic compounds in Titan’s atmosphere.

Acknowledgments

E.H. acknowledges support from the European Research Council (ERC Starting Grant 209622: E3ARTHs).

References

Appendix A: Cross sections and quantum yield of several compounds

Appendix A.1: Photolysis of C₂H₂

C₂H₂ photodissociation was reconsidered using the latest measurements, which lead exclusively to the formation of C₂H + H between 121.6 and 193 nm (Kovàcs et al. 2010; Läuter et al. 2002).

Appendix A.2: Photolysis of C₃

C₃(${}^{\mathrm{1}}\mathrm{\Sigma }_{\mathit{g}}^{\mathrm{+}}$) has two main transitions, the ${}^{\mathrm{1}}\mathrm{\Pi }_{\mathit{u}}{\mathrm{\leftarrow }}^{\mathrm{1}}{\mathrm{\Sigma }}_{\mathit{g}}^{\mathrm{+}}$ transition around 405 nm and the ${}^{\mathrm{1}}\mathrm{\Sigma }_{\mathit{u}}^{\mathrm{+}}{\mathrm{\leftarrow }}^{\mathrm{1}}{\mathrm{\Sigma }}_{\mathit{g}}^{\mathrm{+}}$ transition around 165 nm (Monninger et al. 2002; van Hemert & van Dishoeck 2008; Chang & Graham 1982). Because the dissociation limit is equal to 7.62 eV (162.7 nm) (Baulch et al. 2005; Martin & Taylor 1995; Gingerich et al. 1994), only the ${}^{\mathrm{1}}\mathrm{\Sigma }_{\mathit{u}}^{\mathrm{+}}{\mathrm{\leftarrow }}^{\mathrm{1}}{\mathrm{\Sigma }}_{\mathit{g}}^{\mathrm{+}}$ transition leads to photodissociation. The photodissociation cross section was calculated using the oscillator strengths calculated by van Hemert & van Dishoeck (2008) with a constant width at half maximum Δλ = 20 nm and taking into account the dissociation energy equal to 735.22 kJ mol^-1.

Appendix A.3: Photolysis of C₃H and C₃H₂

c-C₃H, l-C₃H, c-C₃H₂, l-C₃H₂ and t-C₃H₂ photodissociation cross sections were calculated using the oscillator strengths calculated by van Hemert & van Dishoeck (2008) with a constant width at half maximum Δλ = 20 nm. These five radicals absorb in the UV and visible part of the spectrum where the solar flux is highest. Therefore the photodissociation will be dominated by these absorptions, which mainly lead to C-H bond rupture. The photodissociations of c-C₃H and l-C₃H are dominated by the visible and near-UV regions and should yield only C₃ + H. The products of c-C₃H₂ and l-C₃H₂ photodissociation were derived from Mebel et al. (1998), Park et al. (2006) and Großet al. (2008) and were set to l-C₃H + H (30%), c-C₃H + H (30%), and C₃ + H₂ (40%). The C₃ + H₂ exit channel shows a notable exit barrier (Mebel et al. 1998; Park et al. 2006). The products of t-C₃H₂ photodissociation were also derived from Mebel et al. (1998) and Park et al. (2006) and were set to l-C₃H + H (50%) and c-C₃H + H (50%), although the spin-allowed ³C + C₂H₂ exit channel may not be negligible. The absorption cross sections of C₃H and C₃H₂ are given in Figs. A.1, A.2 and A.3.

Appendix A.4: Photolysis of C₃H₃

The lowest energy electronic absorption spectrum of the C₃H₃ radical between 290 and 345 nm shows diffuse bands (Atkinson & Hudgens 1999; Eisfeld 2006; Matsugi et al. 2011), attributed to predissociation in the excited state. This leads to an upper limit of 360.1 kcal mol^-1 for the bond dissociation energy, which corresponds to 346 nm and yields c-C₃H₂ + H. The second (strongest) absorption near 240 nm has been confirmed by Deyerl et al. (1999) by H-atom photofragment yield spectra. The main products after photodissociation at 248 nm are also C₃H₂ + H with a ratio H/H₂ = (97.6/2.4) ± 1.2. We then assumed that C₃H₂ is the only product in the UV wavelength range. Identifying the different C₃H₂ isomers is more delicate. Deyerl et al. (1999) attributed the measured fragments to c-C₃H₂ + H, while an Rice−Ramsperger−Kassel−Marcus (RRKM) analysis (Nguyen et al. 2001b) found t-C₃H₂ + H to be the dominant channel. Goncher et al. (2008) have shown that some c-C₃H₂ is produced. To a first approximation, we estimated the products to be 50% c-C₃H₂ and 50% t-C₃H₂. The absorption cross section of C₃H₃ is given in Fig. A.4.

Appendix A.5: Photolysis of C₃H₄ isomers

The photoabsorption cross sections of CH₃C₂H and CH₂CCH₂ are well known (Ho et al. 1998; Chen et al. 2000). Photolysis studies of these molecules have been performed at 193 nm (Seki & Okabe 1992; Ni et al. 1999) and at 155 nm (Harich et al. 2000a,b). There are some differences. For the CH₂CCH₂ photolysis, the main production channels are H and C₃H₃ (70%) followed by CH₂ + C₂H₂ (20%) with small yields of H₂ + c-C₃H₂ (5%) and H₂ + l-C₃H₂ (5%). For the CH₃C₂H photolysis, the main production channels are also H and C₃H₃ (80%) followed by CH₃ + C₂H (≈7%), CH₂ + C₂H₂ (≈3%) and then H₂ + c-C₃H₂ (5%) and H₂ + l-C₃H₂ (5%). Photodissociation of CH₃C₂H at 193 nm mainly leads to CH₃CC production and not to CH₂CCH (Satyapal & Bersohn 1991; Seki & Okabe 1992).

Appendix A.6: Photolysis of C₃H₅

In Titan’s atmosphere, photodissociation of the allyl radical H₂C=CH-^•CH₂ will be dominated by absorption near 403 nm (Tonokura & Koshi 2000; Matsugi et al. 2011) and by the strongest absorption in the 220−240 nm range (Selby et al. 2008; Nakashima & Yoshihara 1987). The absorption cross section of C₃H₅ is given in Fig. A.5. Photodissociation in the 403 nm band leads to H-atom loss only (Stranges et al. 1998), and mainly to CH₂CCH₂ + H formation (Castiglioni et al. 2006; Szpunar et al. 2002). At 248 nm the H atom loss channel has been found to be equal to 84% with the CH₃ + C₂H₂ channel equal to 16% (corrected to 5% subsequently Stranges et al. 2008). The ratio of CH₂CCH₂ to CH₃C₂H formation in the 240−250 nm region may be estimated from Minsek & Chen (1993) and leads to a ratio between 2:1 and 3:1. RRKM calculations of the ground state dissociation (Stranges et al. 1998) favor CH₃C₂H formation and also lead to 31% of CH₃ + C₂H₂ products at 351 nm in contrast to experimental results. Recent trajectory calculations (Chen et al. 2011) better agree with experimental results and mainly lead to CH₂CCH₂ + H formation. The recommended branching ratios for each absorption band are presented in Table 1.

Appendix A.7: Photolysis of C₃H₆

The photofragmentation of propene (C₃H₆) is complex and wavelength-dependent. Considering the studies of Borrell et al. (1971) at 184 nm, of Lee et al. (2003) at 157 nm as well as the theoretical study of Qu et al. (2010), we considered the product yields to be those given in Table A.1.

Appendix A.8: Photolysis of C₃H₇

For the C₃H₇ photodissociation we considered only absorption in the 220−260 nm range from Adachi & Basco (1981), which leads to C₃H₆ + H (see Fig. A.6).

Appendix A.9: Photolysis of HC₃N

HC₃N photochemistry has been studied between 185 and 254 nm. The main channel seems to be HC₃N^∗∗ metastable product (Clarke & Ferris 1995; Seki et al. 1996; Halpern et al. 1988) with a quantum yield as high as 70% at 193 nm (Seki et al. 1996). The main bimolecular exit channel is H + C₃N formation with a quantum yield of approximately 30% at 193 nm, whereas the C₂H + CN exit channel is very minor (Seki et al. 1996). Recent experimental and ab-initio calculations (Silva et al. 2009) agree well with theoretical work from Luo et al. (2008) and lead to the branching ratios (for bimolecular products only) given in Table A.2. The possible minor production of C₂ + HCN (less than 10%) as well as the production of metastable HC₃N^∗∗ were neglected in this study.

Appendix B: “k_association − ρ” model to determine k₀

Statistical theories allow us to calculate the temperature-dependent low-pressure limiting rate constants k₀(T) (Holbrook et al. 1996) but specific calculations are required for each reaction. Vuitton et al. (2012) performed a master-equation analysis to determine k₀ for various reactions and proposed a general formula (k₀ = 8 × 10^-30 × exp(4.7 × N), where N is the number of adduct carbon atoms) for saturated molecule formation (C₂H₆, C₃H₈, etc.). As stated by Vuitton et al. (2012), this relation, obtained from a fit of their calculations, is valid only if the number of H atoms is equal or close to 2N + 2. For unsaturated molecule formation, the rate constant is lower because of the reduced number of vibrational modes. As many important reactions involve the formation of highly unsaturated species, such as the C₃ + H → C₃H reaction, we propose a new semi-empirical model based in part on a fit of the k₀ calculations from Vuitton et al. (2012) and also on various experimental data for barrierless addition as a function of a power of the vibrational density of states of the adduct, ρ(E₀), with E₀ corresponding to the exothermicity of the addition. ρ(E₀) was calculated using the Whitten-Rabinovitch formula (Whitten & Rabinovitch 1963; Holbrook et al. 1996): $\mathit{\rho }\mathrm{\left(}{\mathit{E}}_{\mathrm{0}}\mathrm{\right)}\mathrm{=}\frac{{\left({\mathit{E}}_{\mathrm{0}}\mathrm{+}\mathit{a}{\mathit{E}}_{\mathit{z}}\right)}^{\mathit{s}\mathrm{-}\mathrm{1}}}{\mathrm{(}\mathit{s}\mathrm{-}\mathrm{1}\mathrm{)}\mathrm{!}{\mathrm{􏽑}}_{\mathit{i}\mathrm{=}\mathrm{1}}^{\mathit{s}}\mathit{h}{\mathit{\nu }}_{\mathit{i}}}\mathit{,}$(B.1)where s is the number of vibrators, E₀ is the enthalpy of addition, E_z is the zero-point vibrational energy, and a is a semi-empirical parameter to account for the level of quantization (a a value ranging between 0.80 and 0.95 is typical), which varies as a function of molecular size and also as a function of the relative E₀/E_z value (Holbrook et al. 1996). The vibrational frequencies are calculated using Gaussian 2009 at the M06/aug-pVTZ level (see Fig. B.1).

Radiative association rate constants, k_r, are complex to calculate accurately (Herbst 1982). k_r values are highly dependent on the size of the system, of the exothermicity of the addition process, and on the radiative emission rate constant, k_IR. For high k_r values, very long adduct lifetimes are required, close to the 1/k_IR value (10^-3 to 10^-2 s), so that radiative associations are important only for large molecule formation. In a similar manner to the molecular association reactions, we performed a fit of the Vuitton et al. (2012) radiative association rate constants with the k_r = k_capture × [k_IR/(k_dissociation + k_IR)] expression, where k_dissociation varies as a function of ρ(E₀) considering similar IR emission probabilities for all adducts.

For a reaction between two chemical species A and B, the temperature dependences of k₀ and k_r can be approximated to T^{−(r_A + r_B + 1)/2}, where r refers to the number of rotational degrees of freedom for a reactant: r = 2 for a linear species and r = 3 for a spherical top (Herbst et al. 2010). As a result and also taking into account the various experimental dependencies of H and CH₃ association reactions with CH₃, NO and O₂ as well as the Vuitton et al. (2012) calculations, we used a T^-1.8 dependence for H reactions and T^-3.5 for CH₃ reactions in the 100−300 K range. The temperature dependence for radiative association is more complex because the radiative rate constants saturate at k_capture if no stabilization by collision occurs.

Our “k_association − ρ” semi-empirical model leads to

• For H addition: k₀ = 1.6 × 10^-31 × (T/300)^-1.8 × ρ^0.9.

• For CH₃ addition: k₀ = 4.0 × 10^-33 × (T/300)^-3.5 × ρ^0.9.

• For radiative association: k_r = 1.0 × 10^-18 × (T/300)^-1.5 × ρ^0.66 × k_capture/(1.0 × 10^-18 × (T/300)^-1.5 × ρ^0.66 + k_capture).

To estimate the association rate constant it is difficult to use a unique formula for all the cases because radiative association must compete with termolecular reaction. For the C₃H_p system, the radiative association rate constants k_r are in general small with respect to k_capture. For barrierless reactions, k_capture = k_∞ and the overall kinetics are described by a modified Troe formula: ${\mathit{k}}_{\mathrm{adduct}}\mathrm{=}\frac{\mathrm{\left(}{\mathit{k}}_{\mathrm{0}}\mathrm{\right[}\mathit{M}\mathrm{]}\mathit{F}\mathrm{+}{\mathit{k}}_{\mathit{r}}\mathrm{)}{\mathit{k}}_{\mathrm{\infty }}}{{\mathit{k}}_{\mathrm{0}}\mathrm{\left[}\mathit{M}\mathrm{\right]}\mathrm{+}{\mathit{k}}_{\mathrm{\infty }}}$(B.2)with $\log \mathrm{\left(}\mathit{F}\mathrm{\right)}\mathrm{=}\frac{\log \mathrm{\left(}{\mathit{F}}_{\mathrm{c}}\mathrm{\right)}}{\mathrm{1}\mathrm{+}{\left[\frac{\log \mathrm{\left(}{\mathit{k}}_{\mathrm{0}}\mathrm{\right[}\mathit{M}\mathrm{]}\mathrm{+}{\mathit{k}}_{\mathrm{capture}}\mathrm{)}}{\mathit{N}}\right]}^{\mathrm{2}}}$, F_c = 0.60 and N = 1. When the radiative association rate constants k_r become comparable to k_∞, it may be more realistic for intermediate pressure behavior to use ${\mathit{k}}_{\mathrm{association}}\mathrm{=}\min \mathrm{(}{\mathit{k}}_{\mathrm{\infty }}\mathit{,}{\mathit{k}}_{\mathit{r}}\mathrm{+}\frac{{\mathit{k}}_{\mathrm{0}}{\mathit{k}}_{\mathrm{\infty }}\mathrm{\left[}\mathit{M}\mathrm{\right]}\mathit{F}}{{\mathit{k}}_{\mathrm{0}}\mathrm{\left[}\mathit{M}\mathrm{\right]}\mathrm{+}{\mathit{k}}_{\mathrm{\infty }}}\mathrm{)}$, but the differences are however much smaller than the uncertainties.

Appendix C: Comments on selected reactions

These reactions were identified as the key reactions following our global sensitivity analysis (see Sect. 5). For each reaction, we recommend a value for its rate constant and its uncertainty factors along with a justification for these recommendations. $\begin{array}{ccc}\frac{\mathrm{Reaction}}{\mathrm{Rateconstant} \mathit{k} {\mathit{F}}_{\mathrm{0}} \mathit{g}}& & \end{array}$F₀ is the uncertainty in the rate constant k(T) at T = 300 K and g is the “uncertainty-extrapolating” coefficient defined for use with F₀ to obtain the rate constant uncertainty F(T) at different temperatures following the expression adapted from KIDA (Wakelam et al. 2012). k_∞(T) and k_r(T) are expressed in cm³ molecule^-1 s^-1 and k₀(T) in cm⁶ molecule^-2 s^-1.

All following ΔH_R were calculated using $\mathrm{\Delta }{\mathit{H}}_{\mathrm{f}}^{\mathrm{298}}$ taken from Baulch et al. (2005) except for

$\mathrm{\Delta }{\mathit{H}}_{\mathrm{f}}^{\mathrm{298}}$(C₃(X${}^{\mathrm{1}}\mathrm{\Sigma }^{\mathrm{+}}$)) = 830 ± 10 kJ mol^-1(Gingerich et al. 1994)

$\mathrm{\Delta }{\mathit{H}}_{\mathrm{f}}^{\mathrm{298}}$(c-C₃H(X²B₂)) = 715 ± 8 kJ mol^-1(Costes et al. 2009)

$\mathrm{\Delta }{\mathit{H}}_{\mathrm{f}}^{\mathrm{298}}$(l-C₃H(X²A’)) = 728 ± 8 kJ mol^-1(Costes et al. 2009)

$\mathrm{\Delta }{\mathit{H}}_{\mathrm{f}}^{\mathrm{298}}$(c-C₃H₂(X¹B₁)) = 497 ± 4 kJ mol^-1(Vazquez et al. 2009)

$\mathrm{\Delta }{\mathit{H}}_{\mathrm{f}}^{\mathrm{298}}$(t-C₃H₂(X³B)) = 543 ± 8 kJ mol^-1(Aguilera-Iparraguirre et al. 2008)

$\mathrm{\Delta }{\mathit{H}}_{\mathrm{f}}^{\mathrm{298}}$(l-C₃H₂(X¹A₁)) = 557 ± 4 kJ mol^-1(Vazquez et al. 2009)

$\mathrm{\Delta }{\mathit{H}}_{\mathrm{f}}^{\mathrm{298}}$(C₃H₃(X²B₁)) = 352 ± 4 kJ mol^-1(Vazquez et al. 2009).

Appendix C.1: H + CH₃

$\begin{array}{ccc}\mathrm{2}\mathrm{H}\mathrm{+}\mathrm{2}\mathrm{C}{\mathrm{H}}_{\mathrm{3}}\mathrm{\to }\mathrm{1}\mathrm{C}{\mathrm{H}}_{\mathrm{4}}\mathrm{(}\mathrm{+}\mathrm{h}\mathit{\nu }\mathrm{)} \mathrm{\Delta }\mathit{H}r\mathrm{(}\mathrm{298}\mathrm{K}\mathrm{)}\mathrm{=}\mathrm{-}\mathrm{439}\hspace{0.17em}\mathrm{kJ}\hspace{0.17em}\mathrm{mol}-1& & \end{array}$

Brouard et al. (1989) have performed a detailed experimental study of this reaction. Forst (1991) performed RRKM calculations scaled to the experimental data in the 300−1000 K range, leading to the expressions k₀(T) = 2.63 × 10^-28 × (T/300)^-2.98 × exp−635/T cm⁶ molecule^-2 s^-1 for He as the bath gas with k_∞(T) = 4.57 × 10^-10 × (T/300)^-0.20 cm³ molecule^-1 s^-1. The k₀ expression seems reliable, but only above 300 K. Baulch et al. (1994) proposed k₀(T) = 6.20 × 10^-29 × (T/300)^-1.80 cm⁶ molecule^-2 s^-1 with He as the bath gas in the 300−1000 K range and k_∞(T) = 3.5 × 10^-10 cm³ molecule^-1 s^-1. Smith (2003) performed RRKM simulations in the 65−300 K range, leading to k₀(T) = 5.1 × 10^-29 × (T/300)^-1.06 × exp(+ 17/T) cm⁶ molecule^-2 s^-1 (F_c = 0.56) in He and k_∞(T) = 3.5 × 10^-10 × (T/300)^-0.09 × exp(+ 12/T) cm³ molecule^-1 s^-1. Vuitton et al. (2012) have performed new calculations between 50 and 300 K. There is a relatively good agreement between the calculations (Baulch et al. 1994; Smith 2003; Vuitton et al. 2012) and the experimental data (Brouard et al. 1989), even if the results of Vuitton et al. (2012) seem to be slightly overestimated. However, is not possible to fit the entire temperature and pressure range with only one expression, and the results of Vuitton et al. (2012) are likely to be the more precise ones at low temperature and low density. We recommend their values with k₀ scaled to the available experimental data at 300 K using the Troe expression in N₂ with F_c = 0.60, N = 1. The radiative association rate constant given by Vuitton et al. (2012) at 150 K, k_r(150 H) = 2.8 × 10^-16 cm³ molecule^-1 s^-1, agrees relatively well with Smith (1989), who used a similar methodology, that led to a value of 7.0 × 10^-16 cm³ molecule^-1 s^-1 without tunneling. $\begin{array}{ccc}\frac{\mathrm{2}\mathrm{H}\mathrm{+}{\mathrm{2}}^{}\mathrm{C}{\mathrm{H}}_{\mathrm{3}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.2: H + C₃

$\begin{array}{ccc}\mathrm{2}\mathrm{H}\mathrm{+}\mathrm{1}{\mathrm{C}}_{\mathrm{3}}\mathrm{\to }\mathrm{c}\mathrm{-}\mathrm{2}{\mathrm{C}}_{\mathrm{3}}\mathrm{H}\mathrm{(}\mathrm{+}\mathrm{h}\mathit{\nu }\mathrm{)}& & \mathrm{\Delta }\mathit{H}r\mathrm{(}\mathrm{298}\mathit{K}\mathrm{)}\mathrm{=}\mathrm{-}\mathrm{333}\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}\\ \mathrm{\to }\mathrm{l}\mathrm{-}\mathrm{2}{\mathrm{C}}_{\mathrm{3}}\mathrm{H}\mathrm{(}\mathrm{+}\mathrm{h}\mathit{\nu }\mathrm{)}& & \mathrm{\Delta }{\mathit{H}}_{\mathit{r}}\mathrm{(}\mathrm{298}\mathit{K}\mathrm{)}\mathrm{=}\mathrm{-}\mathrm{320}\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}\mathit{.}\end{array}$

There is no bimolecular exit channel for this reaction. Mebel & Kaiser (2002) performed ab initio calculations that showed no barrier at the CCSD(T)/6-311+G(3df,2p)//B3LYP/6-311G(d,p) level. Because this reaction is a very important sink for C₃, we also performed DFT (M06-2X/aug-cc-pVTZ) calculations, which showed no barrier, and ab-initio calculations (MRCI+Q/aug-cc-pVTZ), that showed a very small barrier (1 kJ mol^-1) for this reaction. Therefore we recommend a slightly lower value for k_∞ than k_capture to take into account the possible presence of an activation barrier. (Mebel & Kaiser 2002) also showed that the isomerization barrier between both C₃H isomers is considerably lower than the entrance valley. Therefore we considered to a first approximation an equal production of both isomers for termolecular reaction and also for radiative association. We estimated k₀ and k_r using our “k_association − ρ” semi-empirical model. We also performed RRKM calculations in the same way for the two reactions H + C₃ → C₃H and the well-known H + CH₃ → CH₄, and obtained k₀(H + C₃) = 2.5 k₀(H + CH₃), in good agreement with our “k_association − ρ” semi-empirical model.

$\begin{array}{ccc}\frac{\mathrm{2}\mathrm{H}\mathrm{+}{\mathrm{1}}^{}{\mathrm{C}}_{\mathrm{3}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

With 50% of c-C₃H and 50% of l-C₃H production.

Appendix C.3: H + C₃H

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}& & \end{array}$

These reactions have been studied theoretically in great detail during studies of the ³C + C₂H₂ and ¹C + C₂H₂ reactions (Mebel et al. 2007; Takayanagi 2006; Takahashi & Yamashita 1996; Park et al. 2006). They have no barrier on the singlet surface and on one of the triplet surfaces, which leads to various ^1,3C₃H₂ isomers. The main exit channel leads to C₃ + H₂ formation on the singlet surface with a notable barrier on the exit channel located only −10 kJ mol^-1 below the reactants. Recent calculations coupled with low-temperature experiments (Costes et al. 2009) indicate that the exit channel C(³P) + C₂H₂ might be thermoneutral or even slightly exothermic with respect to H + l-C₃H. Nevertheless, once the cyclic ³C₃H₂ intermediate has been formed, both exit channels H + c-C₃H and C + C₂H₂ can be reached without barrier; the former being lower in energy. As a result, the formation of C(³P) + C₂H₂ products is likely to be very low, whilst isomerization to H + c-C₃H is also likely to be low with respect to C₃ + H₂ formation given the lower exit barriers. As shown experimentally (Costes et al. 2009; Bergeat & Loison 2001) and theoretically (Mebel et al. 2007), intersystem crossing is efficient enough to quickly convert ³C₃H₂ into ¹C₃H₂. The electronic degeneracy factor is then high and the rate constant should be close to the capture rate constant. Taking into consideration the various uncertainties the global rate constant for H + c-C₃H and H + l-C₃H reactions is estimated to be equal to 2.0 × 10^-10 cm³ molecule^-1 s^-1. Stabilization of the c-C₃H₂ adduct (we neglect the other l,t-C₃H₂ adducts) may play a non-negligible role at high pressure because the complex has a long lifetime (Park et al. 2006). Because there is one bimolecular exit channel, we considered that these association reactions had rates close to the H + C₃ one, neglecting the possibility of radiative stabilization through electronic emission.

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}\mathrm{c}\mathit{,}\mathrm{l}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}\mathrm{H}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.4: H + t-C₃H₂

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}& & \end{array}$

The reaction ²H + t-³C₃H₂ can proceed through direct abstraction or through addition. Ab initio calculations (Nguyen et al. 2001a; Goulay et al. 2009; Harding et al. 2007; Vereecken et al. 1998) showed no barrier for addition, which leads to an excited C₃H₃^∗∗ adduct. Subsequent evolution of C₃H₃^∗∗ leads either to stabilization at high pressure or to H + c-C₃H₂. The l-C₃H + H₂ exit channel is thermodynamically accessible but involves a high exit barrier (40 kJ mol^-1) above the exit level and close to the entrance channel. The stabilization cannot be neglected because the only exit channel (c-C₃H₂ + H) is not very exothermic and involves a complex rearrangement, which leads to a long C₃H₃ adduct lifetime. We neglected however the ²H + l-¹C₃H₂ →²H + t-³C₃H₂ reaction as well as the C₃H + H₂ production from the adduct and also the direct C₃H + H₂ formation. The ²H + t-³C₃H₂ reagents correlate with doublet and quadruplet states but the products ²H + 1,c−C₃H₂ only correlate with doublet states. There is then a 2/6 = 1/3 electronic degeneracy factor for this reaction, but not for the ²H + l-¹C₃H₂ reaction. Harding et al. (2007) performed variable reaction coordinate transition state theory calculations (VRC-TST) that led to a high value for k_{H + t − C3H2 → C3H3} = 4.42 × 10^-10 × (T/298)^0.22 × exp(+ 43.7/T) cm³ molecule^-1 s^-1. Because there is one bimolecular exit channel, we considered that the association reactions were similar to those of H + C₃, neglecting the possibility of radiative stabilization through electronic emission.

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}\mathrm{t}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{2}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.5: H + l-C₃H₂

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}& & \end{array}$

This reaction can also proceed through direct abstraction or addition. We neglected direct C₃H + H₂ production from H atom abstraction. Ab initio calculations (Nguyen et al. 2001a; Goulay et al. 2009; Vereecken et al. 1998) showed no barrier for addition, which leads to ${\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{3}}^{\mathrm{\ast }\mathrm{\ast }}$. The subsequent evolution of ${\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{3}}^{\mathrm{\ast }\mathrm{\ast }}$ leads either to stabilization at high pressure or to H + c-C₃H₂, neglecting the ²H + l-¹C₃H₂ → ²H + t-³C₃H₂ reaction and the C₃H + H₂ production. The ²H + l-¹C₃H₂ reagents correlate with doublet states, as the ²H + c-¹C₃H₂ products do. As a result, there is no electronic degeneracy factor for this reaction, which leads to a very high total rate constant. However, the potential curve is likely to be less attractive than the potential energy curve for the ²H + t-³C₃H₂ reaction, a reaction between two open shell radical species. As a result, the variational TS (Georgievskii & Klippenstein 2005) should occur at high energy, slowing down the corresponding rate constant. Taking into account the higher electronic degeneracy factor for l-C₃H₂, we recommend using the same value for both reactions, with a global rate constant equal to 4.0 × 10^-10 cm³ molecule^-1 s^-1. Because there is one bimolecular exit channel we considered that the association reactions are similar to the H + C₃ ones, neglecting the possibility of radiative stabilization through electronic emission.

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}\mathrm{l}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{2}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.6: H + c-C₃H₂

$\begin{array}{ccc}\begin{array}{c}\\ & \end{array}& & \end{array}$

The only exothermic reaction is association. There are several ab initio calculations (Nguyen et al. 2001a; Goulay et al. 2009; Vereecken et al. 1998) on the H + c-C₃H₂ reactions (related to unimolecular dissociation of the propargyl radical and the CH + C₂H₂ reaction). All calculations lead to the absence of a barrier, or a very small one (0.4 kJ mol^-1), which will have a minor effect in the 150−200 K range and lead to relatively high value for addition rate constant in this temperature range, fixed at 2.0 × 10^-10 cm³ molecule^-1 s^-1. We estimated k₀ and k_r using our “k_association − ρ” semi-empirical model, neglecting the possibility of radiative stabilization through electronic emission.

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}\mathrm{c}\mathrm{-}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{2}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.7: H + C₃H₃

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \end{array}& & \end{array}$

The only possible reaction is the association found to happen without a barrier with k_∞(T) = 2.88 × 10^-10 × (T/300)^0.15 × exp(+ 46.30/T) cm³ molecule^-1 s^-1 (Harding et al. 2007; Miller & Klippenstein 2003). The high-pressure limit should be reached at relatively low pressures compared with the H + C₃H₅ reaction (Hanning-Lee & Pilling 1992) (no clear pressure-dependence between 98 and 400 Torr). Branching ratio calculations have been performed by Miller & Klippenstein (2003), leading to 25% of allene and 75% of methylacetylene, but the calculations have been performed only above 500 K and the rate was found to be pressure-dependent. We estimated k₀ and k_r using our “k_association − ρ” semi-empirical model, neglecting the possibility of radiative stabilization through electronic emission.

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{3}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

We estimated the branching ratios to be 80% of CH₃C₂H and 20% of CH₂CCH₂ below 300 K.

Appendix C.8: H + C₃H₄

$\begin{array}{ccc}\begin{array}{c}\\ & \\ & \end{array}& & \end{array}$

The rate constant values for the H + methylacetylene (CH₃C₂H) and H + allene (CH₂CCH₂) reactions were taken from various experimental measurements, particularly from Whytock et al. (1976) and Faravelli et al. (2000) for H + CH₃C₂H and from Wagner & Zellner (1972) and Aleksandrov et al. (1980) for H + CH₂CCH₂. We also used the recent theoretical work by Miller et al. (2008). The CH₃ + C₂H₂ production channel is always very minor and was neglected. We also neglected H + CH₂CCH₂ → H + CH₃C₂H because it is a minor channel and CH₃C₂H reacts mainly with H atoms to produce the C₃H₅ radical. We recommend to use the experimental k_∞(T) values and the calculated k₀ and k_r values (Vuitton et al. 2012) for the H + CH₃C₂H and H + CH₂CCH₂ reactions.

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{4}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.9: H + C₃H₅

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \end{array}& & \end{array}$

There are three C₃H₅ isomers: H₂C=CH-^•CH₂ (allyl), H₃C-^•C=CH₂ and H₃C-CH=^•CH, the allyl being by far the most stable one and the only isomer considered here. There is one experimental determination of the rate constant for this reaction by Hanning-Lee & Pilling (1992). They measured the room temperature rate constants at four pressures in the range 98−400 Torr, which showed no clear pressure-dependence in this range with the mean rate constant equal to (2.8 ± 1.0) × 10^-10 cm³ molecule^-1 s^-1. Calculations based on the Troe factorization method confirm that this reaction is near its high-pressure limit under their experimental conditions. Theoretical results (Qu et al. 2010; Zhao et al. 2007) clearly show that there are no bimolecular exit channels. These calculations agree well with Zhao et al. (2007) for the roaming channel (leading to C₂H₂ + CH₄) with the TS calculated to be at +11 kJ mol^-1 with respect to the reactant energies. The high-pressure rate constants have been determined theoretically (Harding et al. 2007), leading to a good agreement with experiments (Hanning-Lee & Pilling 1992). The C₂H₃ + CH₃ exit channel is endothermic. Davis et al. (1999a) proposed a global kinetic mechanism for propene pyrolysis that does not fully agree with the ab initio calculations. There are no bimolecular exit channels, which leads to a high rate constant for the association reaction. We estimated k₀ and k_r using our “k_association − ρ” semi-empirical model, neglecting the possibility of radiative stabilization through electronic emission.

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{5}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.10: H + C₃H₆

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}& & \end{array}$

There have been various experimental measurements over a wide temperature range (Tsang 1991; Seakins et al. 1993). The H atom can add at two positions, which leads to i,n−²C₄H₇ formation (Galland et al. 2003). The n-²C₃H₇ isomer can evolve towards CH₃ + C₂H₄, which is a pressure-dependent channel, but the bimolecular exit channels do not compete with i-C₃H₇ formation but only with n-C₃H₇ formation. In this study we considered only one C₃H₇ isomer. Because the main pathway of this reaction in the low-pressure limit of the addition is dominated by i-C₃H₇ production, the rate constant should be close to the low-pressure-limiting rate constant k₀ of the H + C₃H₄ reaction (Vuitton et al. 2012).

Considering only one C₃H₇ isomer:

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{6}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Considering i-C₃H₇ and n-C₃H₇ isomers:

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{6}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ \\ & & \\ & & \\ \\ & & \\ \\ & & \end{array}}& & \end{array}$

Appendix C.11: H + C₃H₇

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}& & \end{array}$

To a first approximation we considered only one C₃H₇ isomer. This system is very similar to that of H + C₂H₅ (Baulch et al. 2005). Direct H atom abstraction may happen without a barrier but is considered to be a minor channel compared with the H + C₂H₅ reaction (Camilleri et al. 1974). Therefore the rate constant is estimated to be equal to 3.0 × 10^-12 cm³ molecule^-1 s^-1 and independent of temperature (Tsang 1991). There is very likely no barrier for the addition leading to propane. The various exit channels have been calculated by Zhu et al. (2004), showing a high barrier for the H₂ + C₃H₆ exit channel but no barrier for the CH₃ + C₂H₅ exit channel. New calculations (Sivaramakrishnan et al. 2011) show an accessible tight TS for CH₄ + C₂H₄ formation (roaming channel). The various calculations led us to conclude that the main exit channel at low pressure is the formation of CH₃ + C₂H₅. The total rate constants (excluding direct H atom abstraction) have been calculated by Harding et al. (2005), leading to k_{(H + C3H6))} = 9.68 × 10^-11 × (T/300)^0.22 cm³ molecule^-1 s^-1. Because there is one bimolecular exit channel without an exit barrier and with high exothermicity, the addition rate constant at low pressure will be low. The k₀, value for the H + C₃H₇ → C₃H₈ reaction is taken from Teng & Jones (1972).

$\begin{array}{ccc}\frac{\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{7}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.12: C + C₂H₂

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \end{array}& & \end{array}$

A considerable amount of work has been performed on this reaction; see for example Costes et al. (2009) and the references therein. The carbon atom in its triplet electronic state can add either to a single carbon of the acetylene molecule to form triplet t-C₃H₂, or to the triple bond to produce triplet c-C₃H₂, both additions occurring without a barrier. The exit channels on the triplet surface lead to c-C₃H + H and l-C₃H + H. Because these channels are not very exothermic, the lifetime of the triplet adduct is long enough (Guadagnini et al. 1998; Mebel et al. 2007) to allow intersystem crossing to the singlet surface and then production of C₃ + H₂, which is the main exit channel below 300 K (85% between 150 and 200 K, Costes et al. 2009). As a result of this exit channel, the pressure dependence of the rate constants should be weak for P < 100 Torr (Guadagnini et al. 1998) and C₃H₂ stabilisation should not occur.

$\begin{array}{ccc}\frac{\mathrm{C}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{2}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.13: C + C₂H₄

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \end{array}& & \end{array}$

The rate constant for this reaction has been measured in the 15−300 K range by various groups (Haider & Husain 1993a,b; Chastaing et al. 1999, 2001; Bergeat & Loison 2001). The recommended value is an average of the room temperature rate with the temperature dependence of the Chastaing et al. (2001) experiment. The H atom branching ratio has been determined at 300 K (Bergeat & Loison 2001) to be equal to 0.92 ± 0.04 and co-products and other branching ratios have been determined using ab initio calculations (Le et al. 2001). Adduct stabilization is negligible.

$\begin{array}{ccc}\frac{\mathrm{C}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{4}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.14: CH + C₂H₂

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}& & \end{array}$

The reaction kinetics of CH with C₂H₂ has been widely studied (Butler et al. 1981; Berman et al. 1982; Canosa et al. 1997; Thiesemann et al. 1997) for temperatures ranging from 23 K (Canosa et al. 1997) to 710 K (Thiesemann et al. 1997). The experimental temperature dependence of the total rate constant is given by the expression 1.59 × 10^-9 × T^-0.233 × exp(−16/T) cm³ molecule^-1 s^-1 between 23 K and 295 K, suggesting that this reaction proceeds without a barrier. The absence of any pressure dependence for the rate constant shows that stabilization is not competitive with dissociation of the intermediates. There have been five experimental branching ratio determinations for the CH + C₂H₂ reaction (Boullart et al. 1996; McKee et al. 2003; Goulay et al. 2009; Loison & Bergeat 2009; Maksyutenko et al. 2010) in addition to various theoretical studies (Walch 1995; Vereecken et al. 1998; Vereecken & Peeters 1999; Guadagnini et al. 1998; Nguyen et al. 2001b; Mebel et al. 2007; Goulay et al. 2009). The ab-initio/RRKM calculations give scattered results on this system (Vereecken & Peeters 1999; Mebel et al. 2007; Goulay et al. 2009). A review of the various studies is given by Maksyutenko et al. (2010). There is a general agreement for a branching ratio of 91 ± 4% for H atom production and 9 ± 2% for H₂ production. The co-product isomers of the H atom have been determined by Maksyutenko et al. (2010) in a single collision experiment but at relatively high collisional energy (16.8 kJ mol^-1): 31 ± 5% of c-C₃H₂ + H and 60 ± 5% of t-C₃H₂/l-C₃H₂ + H and by Goulay et al. (2009): 90% of c-C₃H₂ + H in a slow-flow reactor at 4 Torr and 293 K. The apparent disagreement may be explained by H-atom-assisted isomerization of the nascent C₃H₂ product to the cyclic c-C₃H₂ isomer through l,t−C₃H₂ + H → C₃H₃ → c-C₃H₂ + H (Mebel et al. 2007; Goulay et al. 2009). Considering that the branching ratio does not depend on the collision energy, we can reasonably use the value of Maksyutenko et al. (2010). Given the scatter of the various RRKM calculations, we considered that only t-C₃H₂ is formed in the t-C₃H₂/l-C₃H₂ + H pathway.

$\begin{array}{ccc}\frac{\mathrm{CH}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{2}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.15: CH + C₂H₄

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \end{array}& & \end{array}$

The reaction kinetics of CH with C₂H₄ has been widely studied (Butler et al. 1981; Berman et al. 1982; Canosa et al. 1997; Thiesemann et al. 1997, 2001) for temperatures ranging from 23 K (Canosa et al. 1997) to 726 K (Thiesemann et al. 2001). There are three experimental branching ratio determinations for the CH + C₂H₄ reaction (McKee et al. 2003; Goulay et al. 2009; Loison & Bergeat 2009) and also theoretical studies (Gosavi et al. 1985; Wang & Huang 1998) as well as coupled ab initio/RRKM studies of this reaction (McKee et al. 2003) or studies on the evolution of the excited allyl radical C₃H₅ (Davis et al. 1999b; Stranges et al. 2008), which is thought to be the main reaction intermediate. The experimental temperature dependence of the global rate constant of the CH + C₂H₄ reaction, 7.74 × 10^-9 × T^-0.546 × exp(−29.6/T) cm³ molecule^-1 s^-1 between 23 K and 295 K, suggests that this reaction proceeds without a barrier. There is a good agreement with the various experimental results as well as with the ab initio/RRKM calculations, leading to 70 ± 8% of CH₂CCH₂ + H, 30 ± 8% of CH₃C₂H + H.

$\begin{array}{ccc}\frac{\mathrm{CH}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{4}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.16: ¹CH₂ + C₂H₂

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \end{array}& & \end{array}$

This reaction has been studied experimentally between 195 and 798 K by Gannon et al. (2010a,b). They measured the H atom branching ratio between 298 and 398 K and calculated that adduct stabilization was negligible below 100 Torr. Because there are no models to describe the H atom production increase between 195 K and 298 K and because the rate constant is almost constant in the 195−300 K range, we recommend to use the 195 K value in the 150−200 K range. $\begin{array}{ccc}\frac{\mathrm{1}\mathrm{C}{\mathrm{H}}_{\mathrm{2}}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{2}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.17: ¹CH₂ + C₂H₄

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \end{array}& & \end{array}$

This reaction has been studied experimentally at low pressure (1 Torr) between 195 and 798 K by Gannon et al. (2010a,b). They measured the H atom branching ratio between 298 and 398 K but calculated neither adduct stabilization, nor the exit channels. An earlier experiment by Canosa-Mas et al. (1985) showed that cyclopropane formation is the main exit channel at 400 Torr. The first step of this reaction is likely to be cyclopropane formation resulting from the addition of ¹CH₂ to the double bond (with 427 kJ mol^-1 in internal energy), so much more than the cyclopropane isomerization barrier toward propene equal to 276 ± 10 kJ mol^-1 (Dubnikova & Lifshitz 1998) or propene formation resulting in ¹CH₂ insertion into one C-H bond (with 460 kJ mol^-1 in internal energy). The bi-radical H₂C^•-CH₂-^•CH₂ formation is either endothermic or is only a local minimum. Because the formation of allyl H₂C = CH-^•CH₂ + H is exothermic (−91 kJ mol^-1) without an exit barrier (Harding et al. 2007), this will be the main exit channel at low pressure, and adduct stabilization plays a role only at high pressure (Canosa-Mas et al. 1985). Because there are no models to describe the H atom production increase between 195 K and 298 K and the rate constant is almost constant in the 195−300 K range, we recommend to use the 195 K values in the 150−200 K range. We also neglected adduct stabilization.

$\begin{array}{ccc}\frac{\mathrm{1}\mathrm{C}{\mathrm{H}}_{\mathrm{2}}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{4}}\mathrm{\to }{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{5}}\mathrm{+}\mathrm{H}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.18: CH₃ + CH₃

$\begin{array}{ccc}\mathrm{2}\mathrm{C}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}\mathrm{2}\mathrm{C}{\mathrm{H}}_{\mathrm{3}}\mathrm{\to }\mathrm{1}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{6}}& & \mathrm{\Delta }\mathit{H}r\mathrm{(}\mathrm{298}\mathrm{K}\mathrm{)}\mathrm{=}\mathrm{-}\mathrm{377}\mathrm{kJ}\hspace{0.17em}\mathrm{mo}{\mathrm{l}}^{-1}\mathit{.}\end{array}$

This reaction has been widely studied (Slagle et al. 1988; Cody et al. 2002, 2003). Wang et al. (2003) have fitted various experimental data between 202 and 900 K, leading to k₀(T) = 1.14 × 10^-25 × (T/300)^-3.75 × exp(−494/T) cm⁶ molecule^-2 s^-1 and k_∞(T) = 7.4 × 10^-11 × (T/300)^-0.69 × exp(−88/T) cm³ molecule^-1 s^-1. The k₀ value at low temperature from the fit is not precise due to the lack of experimental data; the measured rate constants at 155 K are already approaching the high pressure limit. Smith (2003) performed RRKM simulations in the 65−300 K range, that led to k₀(T) = 8.3 × 10^-26 × (T/300)^-4.28 × exp(−131/T) cm⁶ molecule^-2 s^-1 (F_c = 0.3) with H₂ bath gas (k₀(N₂) = 0.7 × k₀(H₂)Smith 2003) and k_∞(T) = 8.1 × 10^-11 × (T/300)^-0.262 × exp (−37/T) cm³ molecule^-1 s^-1. Vuitton et al. (2012) have performed new calculations between 50 and 300 K, but their results are slightly overestimated with regard to the available experimental data. However, it is not possible to fit the entire temperature and pressure range with only one expression, and the results of Vuitton et al. (2012) are likely to be the most precise at low temperature and low density. We recommend their values with k₀ scaled to fit the experimental data (using Troe expression in N₂ with F_c = 0.60, N = 1).

$\begin{array}{ccc}\frac{\mathrm{C}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}\mathrm{C}{\mathrm{H}}_{\mathrm{3}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.19: CH₃ + C₂H₃

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \end{array}& & \end{array}$

There is no barrier on the singlet surface, leading to the C₃H₆ adduct (Thorn et al. 2000; Qu et al. 2010), and this reaction has been studied experimentally by Fahr et al. (1999), Thorn et al. (2000) and Stoliarov et al. (2000) between 1 and 200 Torr. The H atom abstraction reaction by CH₃ is likely to be a separate channel with a rate constant that has been measured on several previous occasions (Fahr et al. 1999; Stoliarov et al. 2000). The C₃H₆ adduct can lead to C₃H₅ + H formation, which means that adduct stabilization and bimolecular product formation compete. The results of Stoliarov et al. (2000) and Fahr et al. (1999) as a function of pressure lead to lower k₀ values than k_{0,CH3 + CH3 → C2H6}(T). We estimate k_{0,CH3 + C2H3 → C3H6}(T) = 0.1 × k_{0,CH3 + CH3 → C2H6}(T). The open-exit channels from the adduct also prevent efficient radiative association, therefore we neglected radiative association in this case.

$\begin{array}{ccc}\frac{\mathrm{C}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{3}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \\ \end{array}}& & \end{array}$

Appendix C.20: CH₃ + C₂H₅

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \end{array}& & \end{array}$

We recommend the Vuitton et al. (2012) values scaled to the Troe formula with F_c = 0.60 and N = 1. We adopted the Baulch et al. (1992) value for the H atom abstraction channel by CH₃.

$\begin{array}{ccc}\frac{\mathrm{C}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}{\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{5}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.21: CH₃ + C₃H₃

$\begin{array}{ccc}\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}& & \end{array}$

The H atom abstraction channel by CH₃ is very likely to have a barrier in the entrance valley, because the C-H bond strength in C₃H₃ is high. Adduct formation occurs without a barrier with k_∞(T) = 6.8 × 10^-11 × exp(+ 130/T) cm³ molecule^-1 s^-1 (Knyazev & Slagle 2001). Fahr & Nayak (2000) studied this reaction at room temperature at 50 Torr using laser photolysis of the precursors, GC/MS product analysis, and kinetic modelling. They identified the main products as approximately 60% of 1-butyne and 40% of 1,2-butadiene, which shows that at 50 Torr adduct stabilization is the main channel. Lee et al. (2003) found that the H₂CC + C₂H₄ product channel is accessible through a TS localized 22 kJ mol^-1 below the reactants, leading to these bimolecular products at low pressure. Lee et al. (2003) also found that the other bimolecular exit channels involve TSs located above the entrance level. We estimated k₀ and k_r using our “k_association − ρ” semi-empirical model, k₀ and k_r being then divided by 100 to take into account the open bimolecular exit channel. The H₂CC produced should isomerize quickly to C₂H₂.

$\begin{array}{ccc}\frac{\mathrm{C}{\mathrm{H}}_{\mathrm{3}}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{3}}}{\begin{array}{c}\\ & & \\ & & \\ & & \\ & & \\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.22: C₂H + C₃

$\begin{array}{ccc}& & \mathrm{2}{\mathrm{C}}_{\mathrm{2}}\mathrm{H}\mathrm{\left(}\mathrm{2}\mathrm{\Pi }\mathrm{\right)}\mathrm{+}\mathrm{1}{\mathrm{C}}_{\mathrm{3}}\mathrm{\left(}\mathrm{1}{\mathrm{\Sigma }}_{\mathrm{g}}^{\mathrm{+}}\mathrm{\right)}\mathrm{\to }\mathrm{2}\mathrm{H}\mathrm{\left(}\mathrm{2}\mathrm{S}\mathrm{\right)}\mathrm{+}\mathrm{1}{\mathrm{C}}_{\mathrm{5}}\mathrm{\left(}\mathrm{1}{\mathrm{\Sigma }}_{\mathrm{g}}^{\mathrm{+}}\mathrm{\right)}\\ & & \mathrm{\Delta }\mathit{H}r\mathrm{(}\mathrm{298}\mathrm{K}\mathrm{)}\mathrm{=}\mathrm{-}\mathrm{87}\mathrm{kJ}\mathrm{mol}-1\mathit{.}\end{array}$

The C₂H radical is highly reactive, particularly with unsaturated hydrocarbons (Chastaing et al. 1998). There is therefore little doubt that the C₂H + C₃ → H + C₅ reaction has no barrier in the entrance valley. In the C_s geometry; the reactants correlate with 2(A′ + A′′) ⊗ 1A′ = 2A′ + 2A′′ states and the products correlate with 2A′⊗ 1A′ = 2A′ states, i.e., there is an electronic degeneracy factor of $\frac{\mathrm{1}}{\mathrm{2}}$. Applying classical capture theory (Georgievskii & Klippenstein 2005) and considering only the isotropic dispersion term for long-range interaction, the capture rate constant is close to 6 × 10^-10 cm³ molecule^-1 s^-1 at 300 K, leading to a rate constant value of 3 × 10^-10 cm³ molecule^-1 s^-1 taking into account the electronic degeneracy. This value is close to the rate constant of C₂H + alkene reactions (Chastaing et al. 1998). Considering the small variation of the rate constant for these reactions, we recommend a constant value in the 150−300 K range.

$\begin{array}{ccc}\frac{{\mathrm{C}}_{\mathrm{2}}\mathrm{H}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}}{\begin{array}{c}\\ & & \\ & & \end{array}}& & \end{array}$

Appendix C.23: N(²D) + C₃

$\begin{array}{ccc}& & \mathrm{N}\mathrm{\left(}\mathrm{2}\mathrm{D}\mathrm{\right)}\mathrm{+}\mathrm{1}{\mathrm{C}}_{\mathrm{3}}\mathrm{\left(}\mathrm{1}{\mathrm{\Sigma }}_{\mathrm{g}}^{\mathrm{+}}\mathrm{\right)}\mathrm{\to }\mathrm{2}\mathrm{CN}\mathrm{\left(}2\mathrm{\Sigma }+\mathrm{\right)}\mathrm{+}\mathrm{1}{\mathrm{C}}_{\mathrm{2}}\mathrm{\left(}\mathrm{1}{\mathrm{\Sigma }}_{\mathrm{g}}^{\mathrm{+}}\mathrm{\right)}\\ & & \mathrm{\Delta }\mathit{H}r\mathrm{(}\mathrm{298}\mathrm{K}\mathrm{)}\mathrm{=}\mathrm{-}\mathrm{260}\mathrm{kJ}\mathrm{mol}-1\mathit{.}\end{array}$

There are no measurements of this reaction, but we considered the N(²D) + C₃ reaction to be slightly faster than the N(²D) + C₂H₂ reaction. N(²D) reactions with closed-shell molecules, for which only scattered information exists, are particularly important for modeling Titan’s atmosphere and need to be studied in more detail.

$\begin{array}{ccc}\frac{\mathrm{N}{\mathrm{(}}^{\mathrm{2}}\mathrm{D}\mathrm{)}\mathrm{+}{\mathrm{C}}_{\mathrm{3}}}{\begin{array}{c}\\ & & \\ & & \end{array}}& & \end{array}$

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