CRITICAL REVIEW OF N, N⁺, N⁺₂, N⁺⁺, And N⁺⁺₂ MAIN PRODUCTION PROCESSES AND REACTIONS OF RELEVANCE TO TITAN'S ATMOSPHERE

A series of studies on the photochemical modeling of Titan's atmospheric chemistry has demonstrated that model predictions were affected by large uncertainties, due to both structural uncertainty (incompleteness of the chemical scheme) and parametric uncertainty (limited precision of physico-chemical parameters) (Carrasco et al. 2007, 2008a, 2008b; Dobrijevic et al. 2008; Hébrard et al. 2006, 2007, 2009, 2012; Plessis et al. 2012). On the structural side, a lot of data are presently missing concerning the reaction rates (1) of heavier species (neutrals and ions) and the associated products (2) of excited states of primary species, (3) of isomers, and (4) of negative ions. On the parametric side, besides the unavoidable experimental uncertainty of measured rate constants, a major source of uncertainty is due to the necessity to extrapolate rate parameters to temperatures representative of Titan's atmosphere. The extrapolation uncertainty for Arrhenius-type laws can amount to several orders of magnitude (Hébrard et al. 2009). Moreover, less than 10% of all rate constants in the models of Titan's neutral chemistry have been measured at the required temperatures (Hébrard et al. 2009). This fraction is even lower for products branching ratios, where in fact only a handful of determinations have been made. In order to alleviate this problem, it is necessary to install a constructive dialog between modelers and experimentalists/theorists, for which the methodology of Key Reactions Improvement (KRI) is an optimal tool.

A key reaction is a reaction for which, at a given stage of a model's development, the reaction parameters need to be known with better accuracy in order to optimally improve the precision of model predictions (Dobrijevic et al. 2010). A list of key reactions can be generated by sensitivity analysis, which requires the implementation of sound uncertainty management in the modeling procedure (Carrasco et al. 2008b; Hébrard et al. 2009). Given these considerations, the outlook might appear hopeless (several hundreds to thousands of reactions, depending on the model), but all the previous studies show that the Pareto principle, or "80/20 rule," is at work here (Juran & Godfrey 1999). It states that roughly 80% of the effects come from 20% of the causes, which means in the present setup that only a small set of reactions is probably responsible for the major part of prediction uncertainty. One can thus expect to improve significantly the precision of the model's predictions through a few, well-targeted, experimental studies on the most influential key reactions. Incidentally, the work by Hébrard et al. (2009) confirms that the updating, in a model, of reactions not identified as key has no or little impact on the precision of model's predictions.

KRI is an iterative procedure, and new key reactions will be identified once the previous ones have been updated in the model. The process can be stopped when the model predictions are deemed precise enough to achieve a specific goal (such as comparison with observations). However, even if one were to loop indefinitely, and because of experimental precision limits, one should not expect to increase the predictions precision beyond a certain threshold: it has been shown for a Titan photochemical model that when all reaction parameters are allotted a very optimistic 10% relative uncertainty, the mole fractions of the heavier species are still predicted with sizeable relative uncertainty (up to 50%; Peng et al. 2010).

Global sensitivity analysis based on Monte Carlo uncertainty propagation has been used for the identification of key reactions in Titan's atmosphere (Carrasco et al. 2008b; Hébrard et al. 2009). This method requires that all uncertain reaction parameters are represented by a probability density function which describes as faithfully as possible the available information (Dobrijevic et al. 2010). Under- or overestimation of the uncertainty of the reactions parameters is counter-productive, because they can significantly bias the sensitivity analysis and produce "false" key reactions. In order to minimize the investment in long and costly studies of low-temperature kinetics, the uncertainty budget has to be as accurate as possible. This adds a significant load to the modeling task, but it is a necessity for the KRI procedure to be efficient.

A few methodological rules should ideally be respected by all actors in the KRI loop (experimentalists, data analysts, database managers, modelers, ...). (1) Experimentalists should provide detailed uncertainty budget, discriminating the systematic and random contributions. (2) The full variance/covariance matrix of the parameters resulting from the fit of a rate law to the experimental data should be published along with the best values of these parameters. This is necessary to derive extrapolation uncertainty (Hébrard et al. 2009); (3) sources of uncertainty coming from independently measured properties should not be mixed. There is a strong case against the use of partial reaction rates when they derive from the product of a global reaction rate and a product branching ratio. Branching ratios require specific probabilistic representations in order to account for their sum-to-one constraint. This intrinsic constraint cannot be preserved at the level of partial reactions (Carrasco & Pernot 2007; Plessis et al. 2010).

As a consequence, in the following, the separation between rate constants and product branching ratios is explicitly preserved. Best estimates of rate constants and product branching ratios, with their uncertainties, are given for all reactions under Titan's atmospheric conditions. Reported uncertainties are the standard relative uncertainties u_x on the reference values x₀ (rate constant or branching ratio). To exclude negative values from the confidence intervals resulting from large relative uncertainties (above 30%), one uses a multiplicative representation: a 67% (1σ) confidence interval (CI) can be estimated as [x₀/(1 + u_x), x₀ × (1 + u_x)] and a (nσ) CI as [x₀/(1 + u_x)ⁿ, x₀ × (1 + u_x)ⁿ].

Uncertainties on ion–molecule reaction branching ratios are almost never given by the authors. We have estimated them to be ±5% for yields higher than 0.1 and to be ±10% for those which are lower. However, the dispersion of the yields measured by different groups is sometimes outside this uncertainty range, due to other factors, for example, the occurrence of secondary reactions which can alter the product branching ratios.

For the implementation of uncertainty management in chemical models from the data provided in the present paper, we invite the reader to refer to Hébrard et al. (2006, 2007, 2009) for reaction rates of neutrals, to Carrasco et al. (Carrasco et al. 2007, 2008a; Carrasco & Pernot 2007) for ion reactions and to Plessis et al. (2010, 2012) for dissociative recombination reactions, and more generally for the treatment of branching ratios.

Some reactive forms of nitrogen have been found to participate in a set of key reactions for Titan's atmospheric chemistry. For neutrals, photolysis of N₂ appears to be an important source of uncertainty at a global level, i.e., having an influence on a large number of species in the upper atmosphere (Hébrard et al. 2009). Recently, Lavvas et al. (2011) have shown that the use of high-resolution N₂ photolysis cross sections has a strong impact on the altitude-dependent photolysis rate. A detailed study on the production of HCN/HNC in Titan's upper atmosphere identified N (²D) as a key reactant, notably through its reaction with CH₄ (Hébrard et al. 2012). For ions, a set of reactions necessary to reproduce the INMS ions mass spectrum at 1200 km during the T5 flyby was identified by Carrasco et al. (2008b). In this restricted set, N⁺ (³P) and N⁺₂ play an important role through their reactions with H₂, CH₄, C₂H₂, and C₂H₄. However, it is certain that other reactions involving reactive forms of nitrogen still require review.

Kinetics:

Recommended value at 300 K: k ⩽ 3 × 10⁻¹⁸ cm³ s⁻¹

The different rate constant data for the N₂ (A³Σ⁺_u) + N₂ reaction can be found in Table 3, which summarizes all published rate constant data for N₂ (A³Σ⁺_u) and N (²D, ²P) reactions. The second and fourth columns indicate the temperature and the experimental method used, respectively.

There is a considerable scattering of the measured rate constants, due to the experimental challenge of measuring such a slow reaction. Dreyer & Perner (1973), as well as Levron & Phelps (1978) also measured the rate constant for v = 1, but it remains very small. Herron (1999) recommended an upper limit of 3 × 10⁻¹⁸ cm³ s⁻¹, disregarding the values which are above 10⁻¹⁷ cm³ s⁻¹, as Vidaud et al. (1976) used a discharge flow system which does not produce only the N₂ (A³Σ⁺_u) state and Suzuki et al. (1997) corrected later their first measurement (Suzuki et al. 1993a). This very small rate constant demonstrates that the quenching of this excited state by collision with N₂ is not efficient.

Kinetics:

Recommended value at 300 K: k = 3.5 × 10⁻¹⁵ cm³ s⁻¹ (±60%)

The reaction of N₂ (A³Σ⁺_u) with molecular hydrogen has been studied by many groups (see Table 3), but there is no recent study. The rate constant values are in relatively good agreement and the recommended value is the same as the one proposed by Herron (1999), who eliminated the three oldest values. Slanger et al. (1973) measured the temperature dependence of the rate constant as k = 2.2 × 10⁻¹⁰ exp (−3500/T) cm³ s⁻¹ over the 240–370 K temperature range. However for the excited vibrational levels, there are large discrepancies between the measurements made by Hack et al. (1988) and Bohmer & Hack (1989) who observe a level-off of the rate constant value at v = 1 and higher vibrational levels, and measurements of Golde et al. (Golde et al. 1989) who observe a continuous increase of the rate constant from v = 2 and higher vibrational levels. This discrepancy could be due to experimental uncertainties. Bohmer & Hack (1989) observed H atom release, but did not quantify it. It seems likely that the reaction is mainly quenching of the nitrogen excited state, due to the low value of the rate constant, but also produces some dissociation of H₂. This is confirmed by quasi-classical trajectory calculations (Sperlein & Golde 1989), showing that this reaction leads to electronic quenching and vibrational relaxation, but also to dissociative energy transfer with branching ratios which vary with the vibrational level of N₂ (A).

Kinetics:

Recommended value at 300 K: k = 3.0 × 10⁻¹⁵ cm³ s⁻¹ (±60%)

Our recommended rate constant value is the same one recommended by Herron (1999) which is based on the measurements of Slanger et al. (1973). Slanger et al. (1973) measured the temperature dependence of the rate constant as k = 1.3 × 10⁻¹⁰ exp (−3170/T) cm³ s⁻¹ over the 300–360 K temperature range. Several authors measured the rate constant as a function of the vibrational level of N₂ (A³Σ⁺_u) (Clark & Setser 1980; Golde et al. 1989; Piper et al. 1985; Thomas et al. 1983), which can be higher than for v = 0 by a factor of 100 and can be interpreted as vibrational quenching into the vibrational ground state. For v = 0, the products have not been measured. Golde et al. (1989) detected H atom products, but could not quantify this reaction channel.

Kinetics:

Recommended values at 300 K: k = 1.40 × 10⁻¹⁰ cm³ s⁻¹ (±60%) for C₂H₂

k = 1.45 × 10⁻¹⁰ cm³ s⁻¹ (±60%) for C₂D₂.

This reaction has a high rate constant and the different measurements are in rather good agreement (see Table 3). We recommend the most recent rate constant value measured by Umemoto (2007), with an uncertainty that takes into account the scattering of the rate constants measured by other authors. Umemoto also studied the reaction with C₂D₂ which has almost the same rate constant as for C₂H₂. Bohmer & Heck (1991) did not observe any dependence of the rate constant with the vibrational energy of N₂ (A). Both the high rate constant and the absence of vibrational dependence are explained by the fact that, as opposed to reactions with N₂, H₂, and CH₄, this reaction is not mainly quenching of N₂ (A) but produces the dissociation of C₂H₂, as shown by Umemoto et al. (Umemoto 2007).

Products:

Recommended yields: (N₂ + C₂H + H)/(N₂ + C₂ + H₂), 0.52/0.48 for the reaction with C₂H₂

(N₂ + C₂D + D)/(N₂ + C₂ + D₂), 0.33/0.67 for the reaction with C₂D₂.

Umemoto (2007) measured the H atom yield and D atom yield to be equal to 0.52 and 0.33, for the reactions with C₂H₂ and C₂D₂, respectively. They conclude that the presence of an isotope effect in the H/D atom yield suggests that the H/D release competes with the H₂/D₂ molecule release, the latter being favored in the case of C₂D₂. As the rate constant has a high value, the quenching is most probably a negligible channel, compared to the collision-induced C₂H₂ dissociation.

Kinetics:

Recommended values at 300 K: k = 9.7 × 10⁻¹¹ cm³ s¹ (±60%) for C₂H₄

k = 9.3 × 10⁻¹¹ cm³ s⁻¹ (±20%) for C₂D₄.

As for acetylene, this reaction has a high rate constant and the different measurements are in rather good agreement (see Table 3). We recommend the rate constant value of the most recent work by Umemoto (2007), with an uncertainty which takes into account the scattering of the rate constants measured by other authors. Umemoto also studied the reaction with C₂D₄ which has almost the same rate constant as the reaction with C₂H₄. Dreyer & Perner (1973) and Thomas et al. (1987) measured a weak dependence of the rate constant with the vibrational energy of N₂ (A). Similarly to the case of acetylene, both the high rate constant and the quasi-absence of vibrational dependence are explained by the fact that this reaction produces the dissociation of C₂H₄, as shown by Umemoto (2007).

Products:

Recommended yields: (N₂ + C₂H₃ + H)/(N₂ + C₂H₂ + H₂), 0.30/0.70 for the reaction with C₂H₄

(N₂ + C₂D₃ + D)/(N₂ + C₂D₂ + D₂), 0.13/0.87 for the reaction with C₂D₄.

Umemoto (2007) measured the H and D atom yields to be equal to 0.30 and 0.13, respectively. Umemoto also concluded that this isotope effect in the H/D atom yield suggests that the H/D release competes with the H₂/D₂ release, the latter being favored in the case of C₂D₄.

Kinetics:

Recommended value at 300 K: k = 2.3 × 10⁻¹³ cm³ s⁻¹ (±60%)

Our recommended rate constant value is the same as the one recommended by Herron (1999) which is based on the measurements of Slanger et al. (1973), slightly adjusted. It is higher by two orders of magnitude than that for the reaction with methane. Slanger et al. (1973) measured the temperature dependence of the rate constant as k = 1.6 × 10⁻¹⁰ exp (−1980/T) cm³ s⁻¹ over the 300–370 K temperature range. The products are not known, but the value of the rate constant suggests that dissociation of the target molecule is a possible reaction channel in addition to quenching. Several authors (Clark & Setser 1980; Dreyer & Perner 1973) measured the rate constant as a function of the vibrational level of N₂ (A³Σ⁺_u), which can be higher than for v = 0 by a factor of 100 and can be interpreted as vibrational quenching into the vibrational ground state.

Kinetics:

Recommended value at 300 K: k = 1.3 × 10⁻¹² cm³ s⁻¹ (±60%).

The only existing data obtained by Callear & Wood (1971) give a rate constant 1.3 × 10⁻¹² cm³ s⁻¹. The uncertainty can be estimated to be about the same as for the reaction of N₂ (A) with C₂H₄ which is of the same order of magnitude. As for C₂H₆, the products are not known, but the value of the rate constant suggests that, in addition to quenching, the dissociation of the target molecule is a more important channel than in the case of the reaction with C₂H₆.

The dissociation processes of molecular nitrogen are not very well known. The absorption of VUV photons by the N₂ molecule induces dipole-allowed excitation from the ground gerade state to several singlet ungerade states with high energy content. These high-energy states are strongly bound, but can undergo predissociation through the crossing with dissociative triplet states. The photoabsorption spectrum of N₂ consists of very highly structured bands and as the solar spectrum is also highly structured in this spectral region, the correct calculation of atmospheric penetration requires a very high spectral resolution. The first band system of N₂ (Lyman–Birge–Hopfield bands from the ground state ¹Σ⁺_g to the excited ¹Π_g state) is in the region between 8.26 and 12.4 eV, but this transition is forbidden by electric dipole selection rules and the absorption cross sections are very small. Let us note that those bands are nevertheless observed in the airglow emission spectra of Titan (Ajello et al. 2008). The dissociation energy of N₂ is 9.76 eV. In principle, therefore, the forbidden transitions to vibrationally excited levels of the a¹Π_g state can provide enough energy to dissociate the molecule. However, the a¹Π_g state does not correlate with N (⁴S) + N (⁴S) and predissociation via spin–orbit coupling to the ground state of N₂ molecules has never been observed. Absorption of UV light becomes significant only near 12.4 eV and the N₂ spectrum shows a strong banded structure between 12.4 and 18.8 eV and a continuum above 18.8 eV. The first electric dipole allowed and intense transition is toward the b¹Π_u valence state (E < 12.5 eV). This state correlates with N (²D) + N (²D) but the energy necessary to reach the dissociation limit is 14.5 eV. Nonetheless, the b¹Π_u state can undergo predissociation at lower energies via intersystem crossing to the C ³Π_u and C ³'Π_u states, producing N (⁴S) + N (²D) above 12.1 eV (Lewis et al. 2005). Predissociation competes with spontaneous emission, which is indeed observed for most vibrational levels of the b¹Π_u state (Itikawa 2006). Sprengers et al. (2004) measured a predissociation yield of only ∼28% for the v = 1 level of the N₂ b¹Π_u state. Higher valence singlet states populated by allowed transition at higher energy can also undergo predissociation through intersystem crossing (spin–orbit coupling) and can lead to atomic nitrogen in the second electronically excited state ²P above 13.3 eV.

Because of the different reactivity of ground ⁴S and excited ²D and ²P atomic nitrogen and the long radiative lifetime of the ²D and ²P states, it would be quite important to characterize the N₂ predissociation/dissociation yield to quantify the relative concentration of the three states and their role in the atmospheric chemistry of Titan. Unfortunately, the N (²P), N (²D), and N (⁴S) production yields have been measured only for a few specific rovibrational of several electronic states of N₂ by Helm & Cosby (1989) and Walter et al. (1993), not including the b¹Π_u state (the first state accessible by an allowed transition). The observations are sparse and do not allow the derivation of a general model that can describe quantitatively the predissociation/dissociation products of N₂. Nevertheless, some observations of the authors can help in drawing more general conclusions. They have observed that the predissociation of the above-mentioned levels always produces one ground state atom and one excited atom, either in the ²D or ²P states, the energetic limit of the N (²D) + N (²D) channel (14.5 eV) being too high to be reached in their experiments. Remarkably, no dissociation was observed to the ground state N (⁴S) + N (⁴S).

Bakalian (2006) proposed in 2006 a simplified scheme of the N₂ dissociation for modeling the production of hot nitrogen atoms in the Martian thermosphere. More recently, Lavvas et al. (2011), in a work concerning the energy deposition in the upper atmosphere of Titan, summarized most of the recent information on the electronic transitions of N₂. This paper includes detailed calculations of high-resolution photoabsorption and photodissociation cross sections computed using a coupled-channel Schrödinger equation quantum-mechanical model. These authors suggest the following scheme for the N₂ photodissociation:

$$\begin{equation} \hspace{-2pc}{\rm N}_2 + h\nu \to {\rm N}(^2 D) + {\rm N}(^4 S)\quad 12.1\;{\rm eV} < E < 13.9\;{\rm eV} \end{equation} \tag{ 3a }$$

$$\begin{equation} \to {\rm N}(^2 P) + {\rm N}(^4 S)\quad 13.9\;{\rm eV} < E < \;14.5\;{\rm eV} \end{equation} \tag{ 3b }$$

$$\begin{equation} \hspace{-5pc}\to {\rm N}(^2 D) + {\rm N}(^2D)\quad E > 14.5\;{\rm eV}. \end{equation} \tag{ 3c }$$

The choices of energy threshold were dictated by the fact that E = 12.1 eV corresponds to the asymptotic energy of the channel (3a), E = 14.5 eV corresponds to the asymptotic energy of channel (3c), while E = 13.9 eV corresponds to the energy derived by Walter et al. (1993) above which the fragmentation into channel (3b) dominates over that into channel (3a). Nevertheless, this observation was related to the excited states populated in the experiment by Walter et al. (1993) and not the most intense transition to b¹Π_u. Therefore, this scheme might be oversimplified and supplementary high-resolution absolute experimental cross sections complemented by dissociation branching ratios are highly desirable.

In conclusion, it is difficult to recommend a general N₂ photodissociation scheme for the modeling of the atmosphere of Titan because of the fragmentation of the available information, both regarding the predissociation probabilities for all the involved molecular electronic states and their product branching ratios. We suggest using the scheme of Lavvas et al. (2011), until further experimental and theoretical work emerges.

In the upper atmosphere of Titan, N₂ molecules are subject to a significant bombardment by energetic (200 eV) magnetospheric electrons (Strobel & Shemansky 1982) and by lower energy electrons produced both by photoionization processes and by magnetospheric electrons impact creating secondary electrons. Electron impact can induce ionization, dissociative ionization, excitation, and dissociation. A comprehensive review on the processes that follow electron collision with N₂ (including elastic scattering, rotational and vibrational excitation, electronic excitation, dissociation and ionization) is given, and the dependence on the electron energy examined, in (Itikawa 2006). Since there are no selection rules, the collision of N₂ molecules with electrons can populate a plethora of N₂ states, including low-energy triplet states. One important effect is the observation of emission from many excited N₂ states, as well as from its neutral and ion fragments in highly excited atomic levels. The fluorescence yield from the various states depends on the electron energy. The electron-induced dissociation cross section reaches a maximum of 1.2 × 10⁻¹⁶ cm² at 40–100 eV and, at these energies, is comparable to the ionization cross section.

With the present knowledge, it is reasonable to assume that the N₂ dissociation processes by electron impact produce as many N atoms in the ⁴S ground state as in the two ²D and ²P metastable states, with a much higher yield of ²D state compared to ²P state.

N atoms are also formed by dissociative ionization of N₂ by photons or electrons (see Section 5.1 below). The excited electronic states of N⁺₂, at energies higher than 26.3 eV, dissociate mainly into N⁺ (³P) + N (²D) and somewhat into other dissociation channels (Aoto et al. 2006; Nicolas et al. 2003a). So globally it can be estimated that N atoms coming from the N₂ dissociative ionization are mainly in the ⁴S ground state, with less than 10% being in the N (²D) excited state. Nitrogen atoms in the ²D state were also observed following electron impact dissociative ionization when using high electron energies (Van Brunt & Kieffer 1975).

Finally, electron–ion recombination of N⁺₂ produces fast N atoms in the ground and metastable states, with a branching ratio which can be estimated to 0.7/0.05/0.25 for N(²D)/N (²P)/N(⁴S) (see Section 4.3.8 below).

3.3.1.1. Reaction N (⁴S) + H

3.3.1.2. Reaction N (⁴S) + CH₂

3.3.1.3. Reaction N (⁴S) + CH₃

3.3.1.4. Reaction N (⁴S) + C₂H₃

3.3.1.5. Reaction N (⁴S) + C₂H₅

3.3.2.1. Reaction N (²D) + N₂

3.3.2.2. Reaction N (²P) + N₂

3.3.2.3. Reaction N (²D) + H₂

3.3.2.4. Reaction N (²P) + H₂

3.3.2.5. Reaction N (²D) + CH₄

Kinetics:

Recommended values at 300 K: k = 4.0 × 10⁻¹² cm³ s⁻¹ (±40%) for CH₄

k = 2.6 × 10⁻¹² cm³ s⁻¹ (±40%) for CD₄.

Since the collisional deactivation of N (²D) by N₂ is a slow process, the reaction of N (²D) with methane has been soon recognized as an important pathway. The rate constant at 298 K recommended by Herron (4.0 × 10⁻¹² cm³ s⁻¹) is the average of the values determined by Fell et al. (1981), Umemoto et al. (1998b) and Takayanagi et al. (1999) (see Table 3). The data by Black et al. (1969) were disregarded as they differ too much with respect to the other measurements. Umemoto et al. (1998b) and Takayanagi et al. (1999) also studied the reaction with CD₄, measuring at 298 K slightly lower rate constants for CD₄ than for CH₄. Takayanagi et al. (1999) also measured the temperature dependence of the rate constant over the range 223–292 K as k = 7.1 × 10⁻¹¹ exp (−750/T) cm³ s⁻¹ and 3.3 × 10⁻¹¹ exp (−700/T) for the reactions with CH₄ and CD₄, respectively.

Products:

Recommended yields: (CH₂NH and/or CH₃N + H)/(NH + CH₃), (0.8 ± 0.2/(0.2 ± 0.1) for CH₄

(CD₂ND and/or CD₃N + D)/(ND + CD₃), (0.8 ± 0.2/(0.2 ± 0.1) for CD₄.

In addition to kinetic data, much work has been done on this system at the level of reaction dynamics experiments and theoretical calculations in recent years. The first hint of the reaction mechanism and primary products came from the ab initio calculations by Kurosaki et al. (1998) of the relevant potential energy surface. According to those calculations, the exothermic channels are:

$$\begin{eqnarray} {\rm N}(^2 {\rm D}) + {\rm CH}_4 (^1 {\rm A}_1) & \to & ({\rm CH}_3 {\rm NH})^{\#}\nonumber\\ &\to & {\rm CH}_2 {\rm NH} + {\rm H} - 3.19\;{\rm eV} \end{eqnarray} \tag{ 3d }$$

$$\begin{equation} \hspace{6pc}\to {\rm CH}_3 {\rm N} + {\rm H} - 0.86\;{\rm eV} \end{equation} \tag{ 3e }$$

$$\begin{equation} \hspace{6pc}\to {\rm CHNH}_2 + {\rm H} - 1.56\;{\rm eV} \end{equation} \tag{ 3f }$$

$$\begin{equation} \hspace{6pc}\to{\rm NH} + {\rm CH}_3 - 1.22\;{\rm eV} \end{equation} \tag{ 3g }$$

$$\begin{equation} \hspace{6pc}\to {\rm NH}_2 + {\rm CH}_2 - 0.41\;{\rm eV} \end{equation} \tag{ 3h }$$

All of these products can be formed after N (²D) has inserted into one of the C-H bonds of methane forming a first intermediate, CH₃NH, which is bound by about 4.43 eV, with respect to the reactants. The insertion mechanism, through a small barrier, has been confirmed by recent ab initio calculations (Ouk et al. 2011). The CH₃NH intermediate can directly dissociate into the products CH₂NH + H (3d), CH₃N + H (3e), and NH + CH₃ (3f), or can rearrange to the isomeric form CH₂NH₂, which is the global minimum of the PES (4.68 eV lower in energy with respect to the reactants). CH₂NH₂ can also fragment and the possible products are essentially CHNH₂ + H (3f), and again CH₂NH + H. A first spectroscopic dynamical study by Umemoto et al. (1997) identified NH (from channel (3g)) and H (from channels (3d–f)) as primary reaction products with an absolute yield of 0.2 ± 0.1 and 0.8 ± 0.2, respectively. Later these authors measured the vibrational population of NH produced in this reaction by a laser induced fluorescence technique. The vibrational distribution was determined to be 10.0 (v = 0); 8.0 ± 1.0 (v = 1); 5.0 ± 0.7 (v = 2); 2.5 ± 0.5 (v = 3), in very good agreement with the theoretical calculations of Pederson et al. (1999) and Honvault & Launay (1999). Casavecchia et al. (Balucani et al. 2009; Casavecchia et al. 2001) have used the crossed molecular beam technique with mass spectrometric detection to investigate which of the three possible CH₃N isomers (CH₂NH, CHNH₂ and CH₃N) is actually produced in conjunction with H. According to the experimental results obtained in a wide range of E_CM collision energies (from about 0.21 to 0.62 eV, it was established that two isomers are actually formed: methylene-imine (CH₂NH) and methyl-nitrene (CH₃N). Notably, the relative branching ratio for the formation of CH₂NH with respect to CH₃N isomers was found to change considerably with E_CM, from 0.6 at E_CM ∼ 0.21 to 0.04 at ∼0.62 eV.

So the assumption that only NH + CH₃ would be the products of the N (²D) + CH₄ reaction is not correct. This reactive channel accounts only for about 20% of the products in the room temperature laboratory experiment and we can assume that the product branching ratios are about the same for the reaction with CD₄. By analyzing the trend of the branching ratio as a function of the available energy (Balucani et al. 2009), we can presume that the yield of NH + CH₃ will be even smaller under the low temperature conditions of Titan's atmosphere. Therefore, the nitrogen chemistry that relies on the dominance of the CH₃ + NH channel in the photochemical models of the atmosphere of Titan should be reconsidered. Furthermore, the crossed molecular beam results suggest that the reaction of N (²D) with CH₄ is an active route for formation of methylene-imine (CH₂NH), a closed-shell molecule containing a new unsaturated CN bond. This reaction demonstrates that C-N bonds can be generated directly by a reaction involving an active form of N₂. An indirect identification of CH₂NH in the atmosphere of Titan has indeed been reported by Vuitton et al. (2006, 2007) and Yelle et al. (2010).

3.3.2.6. Reaction N (²P) + CH₄

3.3.2.7. Reaction N (²D) + C₂H₂

3.3.2.8. Reaction N (²P) + C₂H₂

3.3.2.9. Reaction N (²D) + C₂H₄

3.3.2.10. Reaction N (²P) + C₂H₄

3.3.2.11. Reaction N (²D) + C₂H₆

3.3.2.12. Reaction N (²P) + C₂H₆

3.3.2.13. Reaction N (²D) + C₃H₈

3.3.2.14. Reaction N (²P) + C₃H₈

Kinetics

Recommended value at 300 K: k = 5.0 × 10⁻¹⁰ cm³ s⁻¹ (±25%)

The different rate constant data for the N⁺₂ + N₂ reaction can be found in Table 6, which summarizes all published rate constant data for N⁺₂, N⁺ (³P, ¹D) and N⁺⁺ reactions. The second and fourth columns indicate the temperature or collision energy and the experimental method used, respectively.

Collisions of N⁺₂ ions (v = 0–4) with N₂ can lead to vibrational deactivation and charge transfer (CT) processes. The formation of N⁺₃, which is endothermic by 4.97 eV, has been studied from thermal energies up to 25 eV energy by Tosi et al. (2001) and has been interpreted as resulting from reactions of the N⁺₂ (⁴Σ⁺_u) quartet state. The symmetric charge transfer reaction has been studied using isotopic labeling, i.e., by measuring the ¹⁵N⁺₂ (v = 0) + ¹⁴N₂ or the ¹⁴N⁺₂ (v = 0) + ¹⁵N₂ reaction. This charge transfer is an efficient process with a rate constant equal to about half the Langevin rate constant (8.3 × 10⁻¹⁰ cm³ s⁻¹). It is hard to predict the value at 150 K, so we recommend the same value as at 300 K with a 70% uncertainty in order to include the maximum Langevin rate value. The recommended rate constant value for N⁺₂ (X, v = 0) at 300 K is 5.0 × 10⁻¹⁰ cm³ s⁻¹, which is the mean value of the literature values (see Table 6). Frost et al. (1994) and Kato et al. (1998) measured the rate constant as a function of the vibrational energy of N⁺₂. Kato et al. explain the observed increase of the rate constant with vibrational energy (about 6.0 × 10⁻¹⁰ (±30%) cm³ s⁻¹ for v = 1–4, instead of 4.0 × 10⁻¹⁰ (±20%) cm³ s⁻¹ for v = 0), as the result of vibrational relaxation in addition to symmetric charge transfer. Vibration and translation inter-conversion processes can occur coincidently with charge transfer during collisions between N⁺₂ and N₂, and several vibrational quanta can efficiently be converted to product kinetic energy during exothermic charge transfer reactions (McAfee et al. 1981; Sohlberg 1999).

Kinetics

Recommended values at 300 K: k = 1.56 × 10⁻⁹ cm³ s⁻¹ (±15%) for H₂ and 1.15 × 10⁻⁹ cm³ s⁻¹ (±20%) for D₂

Recommended values at 150 K: k = 1.3 × 10⁻⁹ cm³ s⁻¹ (±20%) for H₂ and 9.6 × 10⁻¹⁰ cm³ s⁻¹ (±20%) for D₂.

This reaction has been extensively studied over the years. All rate constant measurements at 300 K are in very good agreement (see Table 6) and give a value nearly equal to the Langevin rate (1.56 × 10⁻⁹ cm³ s⁻¹), which is therefore our recommended value. Rowe et al. (1989) and Randeniya & Smith (1991) have measured the rate constant as a function of temperature below 300 K. When temperature decreases, the rate constant goes through a minimum and then increases to reach about 2 × 10⁻⁹ cm³ s⁻¹ at about 8 K (Randeniya & Smith 1991). At 150 K, it is about 1.3 × 10⁻⁹ cm³ s⁻¹, which is our recommended value for Titan's ionosphere. Knott et al. (1995) measured the cross section as a function of collision energy and found two regimes: it follows an E^−0.5_CM law for E_CM = 8–90 meV and an E^−0.33_CM law for E_CM = 90 meV to 2 eV. These authors did not observe a variation of the rate constant with the vibrational level of N⁺₂. Similar behavior is observed at higher collision energies (Henri et al. 1988; Koyano et al. 1987). Isotopic effects have been investigated in guided ion beam experiments (Schultz & Armentrout 1992). These authors found that there is no significant isotopic effect on the rate constant for the reactions of N⁺₂ with H₂, HD, or D₂, which are equal to the Langevin rate within experimental errors. The rate constants decrease from H₂ to HD to D₂, but the ratio of the measured rate constant divided by the Langevin rate remains equal to about 1. In a selected ion flow drift tube (SIFDT) experiment, Schwarzer et al. (1991) observed the same trend in kinetics for the reactions of N⁺₂ with H₂ and D₂. Given the above, the recommended rate constant values are the Langevin rate constants at 300 K for both reactions with H₂ and D₂. At 150 K, the recommended rate constant values are lower. For the reaction with H₂, it is the one measured by Randeniya & Smith (1991) and for the reaction with D₂, it is a value calculated from the one at 300 K, decreased in the same proportion.

Products

Recommended yields at 300 K: (N₂H⁺ + H)/(H⁺₂ + N₂), 0.99/0.01.

Reactive collisions between N⁺₂ and H₂ result either in hydrogen transfer to give N₂H⁺ + H or in charge transfer to give H⁺₂ + N₂, the former channel being strongly favored at 300 K. The hydrogen transfer giving N₂H⁺ + H products has been the subject of extensive experimental investigations. Three of the most recent papers describe guided ion beam experiments (Knott et al. 1995; Schultz & Armentrout 1992; Tosi et al. 1992), while two other experiments focused on the dependence of the reactivity on the N⁺₂ internal state (electronic and vibrational) (de Gouw et al. 1995; Uiterwaal et al. 1995). For ground-state reactants, the reaction proceeds at thermal energies with the rate predicted by the Langevin classical ion–molecule capture theory (1.56 × 10⁻⁹ cm³ s⁻¹). Vibrational excitation of the N⁺₂ appears to have only minor effects on the reaction rates (de Gouw et al. 1995; Knott et al. 1995). As far as the electronic excitation is concerned, the reaction rate for N⁺₂ in the first electronically excited A²Π_u state is 50% lower with respect to the X state (Uiterwaal et al. 1995). This difference in rate is not relevant for Titan, as the A state has a lifetime which is much shorter than the average collision time in Titan's ionosphere. When HD is used as reactant, the production of N₂D⁺ is slightly favored over N₂H⁺, for collision energies below 0.1 eV cm. In particular, at thermal energies the branching ratio is N₂D⁺:N₂H⁺ = 0.52: 0.48 (Schultz & Armentrout 1992), while the formation of N₂H⁺ is favored at energies above 0.1 eV.

The charge transfer process giving H⁺₂ + N₂ products is only a minor product channel (Schultz & Armentrout 1992; Uiterwaal et al. 1995), and has been investigated as a function of the collision energy for ground-state reactants (Schultz & Armentrout 1992), and at thermal energies as a function of the internal state of N⁺₂ (Uiterwaal et al. 1995). The charge transfer cross section is about two orders of magnitude lower than that for the hydrogen abstraction reaction, according to Schultz et al. (Schultz & Armentrout 1992) and one order of magnitude lower, according to Uiterwaal et al. (1995). This small cross section has been explained by the absence of crossing between the potential energy surfaces (Schultz & Armentrout 1992).

Kinetics:

Recommended values at 300 K: k = 1.18 × 10⁻⁹ cm³ s⁻¹ (±15%) for CH₄

k = 1.10 × 10⁻⁹ cm³ s⁻¹ (±20%) for CD₄.

The kinetics of this reaction has been extensively studied (see Table 6). The latest determinations at 300 K are all in good agreement, and are satisfyingly represented by the value (1.14 × 10⁻⁹ cm³ s⁻¹ (±15%)) in the compilation of McEwan & Anicich (2007). Moreover, this value is very equal within experimental uncertainties to the Langevin rate (1.18 × 10⁻⁹ cm³ s⁻¹), which is reasonable for such a reaction. It is thus our recommended value.

Rowe et al. (1989) and Randeniya & Smith (1991) studied this reaction at low temperatures, 70 and 8–15 K, respectively. In spite of a slight increase of the rate constant at low temperatures, 1.20 × 10⁻⁹ at 70 K and 1.90 × 10⁻⁹ at 8–15 K, the difference with the value of the rate constant at 300 K is not significant. The rate constant seems effectively unchanged over the temperature range 8–300 K, so the recommended value is the same at 300 K and 150 K. The study of Nicolas et al. (2003b) shows, however, a substantial increase of the rate constant with collision energy, and in the thesis report of Nicolas (2002), a variation of less than 20% in the rate constant is observed with vibrational energy (v = 0–4). A small isotopic effect has been observed by Nicolas et al. (2003b), who measured, in the 0.1–3 eV E_CM range, rate constants equal to (1.53–2.83) × 10⁻⁹ cm³ s⁻¹ and (1.43–1.64) × 10⁻⁹ for the reaction with CH₄ and CD₄, respectively, as expected for the Langevin rates, because the reaction relative mass and the polarization are not the same for CH₄ and CD₄. The Langevin rate for the reaction with CD₄ is 1.10 × 10⁻⁹ cm³ s⁻¹, calculated with the polarization of CD₄ which is lower by 0.034 than the one from CH₄ according to Bell (1942) and Wong et al. (1991). So the recommended rate constant values at 300 K and 150 K for the reaction with CD₄ are the Langevin rates, which are independent of temperature.

Products

Recommended yields at 300 K and 150 K:

(CH⁺₃ + H + N₂)/(CH⁺₂ + H₂ + N₂)/(N₂H⁺ + CH₃), 0.86/0.09/0.05 for CH₄

(CD⁺₃+ D + N₂)/(CD⁺₂+ D₂ + N₂)/(N₂D⁺+ CD₃), 0.88/0.07/0.05 for CD₄.

Table 7 summarizes the product branching ratio data for the N⁺₂ + CH₄ reaction.

All studies are in agreement concerning the identity of the dissociative charge transfer products, CH⁺₂ and CH⁺₃, with CH⁺₃ formation being the major channel. The nondissociative charge transfer product CH⁺₄ is not observed (less than 0.2% in the study of Nicolas et al. (2003b) because a large amount of internal energy is transferred to the primary CH⁺₄ product which then dissociates. However, there is an important disagreement concerning the production of N₂H⁺. Only three studies relate its formation (McEwan et al. 1998; Nicolas et al. 2003b; C. Alcaraz et al., unpublished). Note that an older work of Harrison & Myher (Harrison & Myher 1967; Li & Harrison 1978) studied specifically this reaction channel. They found a partial rate constant of 2.3 × 10⁻¹⁰ cm³ s⁻¹ for the production of N₂D⁺ in the reaction with CD₄, but underline it only represents 2% maximum of the products. Their results are not directly comparable with other values in the literature, but do confirm the production of this ion. The detection of N₂H⁺ is difficult because there is a mass overlap with the secondary product C₂H⁺₅ (from the reaction CH⁺₃ + CH₄) and the natural isotope of N⁺₂, ¹⁴N¹⁵N⁺. In their work, Nicolas et al. (2003b) studied very precisely, at collision energies between 0.1 and 3 eV, the production of N₂H⁺ and N₂D⁺ in the reactions of N⁺₂ with CH₄ and CD₄, respectively. Their time of flight analysis allowed them to unambiguously distinguish between N₂H⁺ and C₂H⁺₅, and the uncertainty of their determination is very small. The measurements of Nicolas et al. (2003b) were confirmed in unpublished experiments of some of the authors of the present paper (C. Alcaraz et al., unpublished). The measured branching ratios are almost constant with collision energy. So it is reasonable to expect the same values at 300 K. C. Alcaraz et al. (unpublished) also studied the variation of the branching ratios with vibrational energy of N⁺₂ (X²Σ⁺_g, v = 0, 4)). The effect is very weak, 2%–3% for the main product CH⁺₃. Recently, Gichuhi et al. (Gichuhi & Suits 2011) measured the branching ratio of this reaction at 45 ± 5 K. Their mass resolution was not sufficient to distinguish N₂H⁺ from the intense N⁺₂ parent ion peak. But for the two other products, their branching ratio is very close to the measurements made at 300 K, in good agreement with the previous measurements of Randeniya & Smith. (1991) at even lower temperatures (8–15 K). In conclusion, the product branching ratio of this reaction seems to be constant as a function of temperature and vibrational excitation of N⁺₂ parent ions within experimental uncertainties. Our recommended yields are the values from Nicolas et al. (2003b).

Kinetics

Recommended value: k = 4.15 × 10⁻¹⁰ cm³ s⁻¹ (±25%)

All published rate constant data are shown in Table 6. The study of Dreyer et al. (Dreyer & Perner 1971) involves quite particular conditions, such as a high pressure of N₂ (about 40 Torr, and up to 160 Torr). The results of Anicich et al. (2004) have also been obtained at rather high pressure in order to detect the products of multiple successive reactions and not only the primary products. We thus recommend an average value (k = 4.15 × 10⁻¹⁰ cm³ s⁻¹⁾) for the two other experimental determinations at ∼300 K (k = 4.15 × 10⁻¹⁰ cm³ s⁻¹⁾. This value is significantly smaller than the Langevin rate (1.16 × 10⁻⁹ cm³ s⁻¹). It can be explained by the fact that it is mainly a nonresonant charge transfer reaction (see below). Nicolas et al. (Nicolas 2002) measured a lower rate constant at E_CM = 0.08 eV (928 K), which indicates that most probably the rate constant decreases with temperature, as expected such a nonresonant charge transfer. This decrease is compatible with the typical variation of the cross section with collision energy for such reactions, i.e., proportional to E^−1/2_CM. Using this expression, the reaction cross section value extrapolated down to 150 K is 39.6 Ų, giving a rate constant of 1.03 × 10⁻⁹ cm³ s⁻¹ at 150 K. This should be checked experimentally, but until then, we recommend a rate constant value of 1.0 × 10⁻⁹ cm³ s⁻¹ at 150 K, with an uncertainty of 50% which includes the value at 300 K.

Products

Recommended yields: (C₂H⁺₂ + N₂)/(N₂H⁺ + C₂H), 0.94/0.06.

Table 8 summarizes the product branching ratio data of the N⁺₂ + C₂H₂ reaction.

C₂H⁺₂ is the only significant product observed by Nicolas (2002), which is in agreement with Anicich et al. (2004), Warneck (1972) and with the recent work at low temperature (45 ± 5 K) of Gichuhi et al (Gichuhi & Suits 2011). The disagreement with the study of McEwan et al. (1998) is assumed by Anicich et al. (2004) to be due to the presence of impurities in the instrument, so these results are disregarded. The erroneous old branching values are still present in the compilation of McEwan & Anicich (2007), probably due to an error. The N₂H⁺ product observed by Nicolas (2002) is a very minor product and was probably not detected in other studies, due to experimental difficulties. In conclusion, we recommend the branching ratios measured by Nicolas (2002). They should be nearly identical at 150 K.

Kinetics

Recommended value at 300 K: k = 1.30 × 10⁻⁹ cm³ s⁻¹ (±15%)

The disagreement between the determinations of Anicich et al. (2004, 7.10 × 10⁻¹⁰ cm³ s⁻¹) and McEwan et al. (1998, 1.30 × 10⁻⁹ cm³ s⁻¹) which are the only published rate constant data for this reaction, is not explained by the authors (see Table 6). However, the experimental conditions are substantially different, with a higher pressure in the case of Anicich et al. (2004) inducing secondary reactions. The inherent uncertainty in this higher pressure procedure being more significant, we recommend the rate constant determined by McEwan et al. (1998), as in the recent compilation of McEwan & Anicich (2007). This value is equal to the Langevin rate (1.29 × 10⁻⁹ cm³ s⁻¹) within experimental errors. As the Langevin rate does not depend on temperature, the value will be the same at 150 K.

Products

Recommended yields: (C₂H⁺₃ + H + N₂)/(C₂H⁺₂ + H₂ + N₂)/(N₂H⁺ + C₂H₃), 0.67/0.23/0.10.

Table 9 summarizes the product branching ratio data for the N⁺₂ + C₂H₄ reaction.

In the study of McEwan et al. (1998), C₂D₄ was used in addition to C₂H₄. They could conclude that the direct charge transfer product fragmented into C₂H⁺₃ + H and C₂H⁺₂ + H₂, as for the study of Gichuhi et al. (Gichuhi & Suits 2011) at 45 ± 5 K. The chemical products HCNH⁺ and HCN⁺, observed by McEwan et al. (1998), which would result from an N₂ triple bond breaking, are, however, very unlikely to be produced in this reaction, which is confirmed by the results of Anicich et al. (2004), who did not detected them. The production of N₂H⁺, observed by McEwan et al. (1998) was not confirmed in the work of Anicich et al. (2004). Nevertheless, the production of this ion cannot be definitively excluded. That is, N₂H⁺ signals could have been masked in the work of Anicich et al. (2004), as a mass overlap with ¹⁴N¹⁵N⁺ complicates this ion's detection. Gichuhi et al. (Gichuhi & Suits 2011) could also not have detected N₂H⁺ product ions, due to a lack of mass resolution. We thus recommend the branching ratios measured at low temperature by Gichuhi et al. (Gichuhi & Suits 2011), normalized to 100%, after adding 10% of N₂H⁺ ions, i.e., C₂H⁺₃/C₂H⁺₂/N₂H⁺ yields being equal to 0.67/0.23/0.10.

Kinetics

Recommended value at 300 K: k = 1.30 × 10⁻⁹ cm³ s⁻¹ (±30%) with C₂H₆

k = 1.25 × 10⁻⁹ cm³ s⁻¹ (±30%) with C₂D₆.

The three different rate constant measurements made at 298 K for this reaction (see Table 6) are in good agreement and very close to the Langevin rate (1.30 × 10⁻⁹ cm³ s⁻¹), so this is our recommended value. As the Langevin rate is independent of temperature, we recommend the same value at 150 K. Nicolas et al. (2002) measured a lower value at E_CM = 0.1 eV for the N⁺₂ + C₂D₆ reaction. It seems to indicate a small isotope effect, as expected for the Langevin rate. So we recommend the Langevin rates for both reactions.

Products

Recommended yields: C₂H⁺₅/C₂H⁺₄/C₂H⁺₃/C₂H⁺₂/CH⁺₃/CH⁺₄, 0.14/0.27/0.32/0.18/0.08/0.01.

For clarity, the neutrals associated with the ions are not indicated in this paragraph due to a too high number of product channels. However, they are reported in Table 17 which summarizes our recommended values for all ion–molecule reactions. Table 10 summarizes the product branching ratio data for the N⁺₂ + C₂H₆ reaction.

The results of Praxmarer et al. (1998) and those of Nicolas (Nicolas 2002) are in good agreement for the products C₂H⁺₅, C₂H⁺₄, and C₂H⁺₃, even though the experiments of Nicolas were not performed at thermal energy (∼0.04 eV), but at E_CM = 0.1 eV. CH⁺₃ was not detected in the experiments of Praxmarer et al. (1998) because of their lower sensitivity, and C₂H⁺₂ was not detected in those of Nicolas because of a mass overlap between C₂D⁺₂ and N⁺₂. So the main product ions are the result of dissociative charge transfer, as expected. Both experiments suggest that the branching ratios do not depend much on collision energy and are not sensitive to an isotope effect when using C₂H₂ or C₂D₂. The HCNH⁺ product detected by McEwan et al. (1998) is very unlikely to be produced directly by the reaction as for the N⁺₂ with C₂H₄ reaction. In conclusion, we recommend branching ratio values which combine the results from the studies of Praxmarer et al. (1998) and Nicolas (2002), i.e., 0.14/0.27/0.32/0.18/0.08/0.01 for C₂H⁺₅/C₂H⁺₄/C₂H⁺₃/C₂H⁺₂/CH⁺₃/CH⁺₄, as well as for the reaction with deuterated ethane. In the experimental study of Nicolas (2002), cross sections were observed to be almost constant with the variation of the photon energy which produces N⁺₂ reactant ions. This indicates that the reaction does not depend much on the vibrational energy of N⁺₂ ions.

Kinetics

Recommended value at 300 K: k = 1.30 × 10⁻⁹ cm³ s⁻¹ (±30%)

There is only one experimental study of this reaction (Praxmarer et al. 1998). This value is close to the Langevin rate (1.42 × 10⁻⁹ cm³ s⁻¹), so it will be about the same value at 150 K.

Products

Recommended yields C₃H⁺₅/C₂H⁺₅/C₂H⁺₄/C₂H⁺₃, 0.13/0.30/0.17/0.40.

For clarity, the neutrals associated with the ions are not indicated in this paragraph due to a too high number of product channels. However, they are reported in Table 17 which summarizes our recommended values for all ion–molecule reactions. Products of this reaction have been measured by only one group (Praxmarer et al. 1998). They have observed only dissociative charge transfer products with branching ratios C₃H⁺₅/C₂H⁺₅/C₂H⁺₄/C₂H⁺₃ equal to 0.13/0.30/0.17/0.40.

Further studies would be required to confirm this experimental study.

Kinetics

Recommended value: k (N⁺₂, v = 0) = 2.2 × 10⁻⁷ (T_e/300)^−0.39 cm³ s⁻¹ (±25%).

The dissociative recombination of N⁺₂ has been extensively studied, both experimentally (Canosa et al. 1991; Cunningham & Hobson 1972; Geoghegan et al. 1991; Kasner 1967; Kella et al. 1996; Mahdavi et al. 1971; Mehr & Biondi 1969; Mul & McGowan 1979; Noren et al. 1989; Oddone et al. 1997; Peterson et al. 1998; Queffelec et al. 1985; Sheehan & St. Maurice 2004; Zipf 1980) and theoretically (Guberman 1991, 2003, 2012; Guberman et al. 1993). The interest in the reaction arises because of its involvement in Earth's atmosphere photochemistry (Fox & Dalgarno 1985; Torr & Torr 1979), and more generally in the chemistry of terrestrial planet ionospheres (Fox 1992, 1993; Fox et al. 1993). All the previous studies on the N⁺₂ recombination process are summarized in the review papers on ion dissociative recombination reactions by Florescu-Mitchell & Mitchell (Florescu-Mitchell & Mitchell 2006) and more recently by Johnsen (2011). This recombination process is usually very exothermic and therefore tends to be an important source of kinetically and internally excited fragments which contribute to heating. Furthermore, the energetic nascent products may have enough energy to escape the atmosphere. As a consequence, the dissociative recombination of N⁺₂ for example, may contribute to ¹⁵N/¹⁴N isotope enrichment at Titan (Lammer et al. 2000).

From an experimental point of view, two classes of studies have been carried out: those measuring directly the rate constant k (Canosa et al. 1991; Cunningham & Hobson 1972; Geoghegan et al. 1991; Kasner 1967; Mahdavi et al. 1971; Mehr & Biondi 1969; Zipf 1980) and those which determined cross sections as a function of the relative energy of the N⁺₂ ions and electrons (Kella et al. 1996; Mul & McGowan 1979; Noren et al. 1989; Oddone et al. 1997; Peterson et al. 1998; Sheehan & St. Maurice 2004). The latter were then able to derive a rate constant by averaging the cross section over a Maxwellian energy distribution. Three main aspects had to be considered: the electron temperature (T_e) dependence of k, the role of the vibrational state of the ions and finally the state of the nitrogen atoms formed through this process.

Two extensive determinations of the direct electron temperature dependence of k are available in the literature. In 1969, Mehr & Biondi (1969) studied the dissociative recombination of N⁺₂ (v = 0) within the temperature range 300 K ⩽ T_e ⩽ 5000 K using an afterglow apparatus, then in 1972, Cunningham & Hobson (1972) studied this process in a reduced temperature range, 700–2700 K, using a shock tube experiment. Both experiments were in good agreement with each other and led to a temperature dependence of k (T_e) ∼ T⁻ⁿ_e (with n = 0.39 or 0.37, respectively). All other rate constant determinations were carried out at T_e = 300 K (Canosa et al. 1991; Geoghegan et al. 1991; Mahdavi et al. 1971) or within a reduced temperature range (Kasner 1967). Interestingly, more recent studies from Peterson et al. (1998) and Sheehan & St. Maurice (2004) who measured cross sections using merged beam techniques led to the same electron temperature dependence of k (k(T_e) ∼ T^−0.39_e) for T_e < 1200 K (Sheehan & St. Maurice 2004), but for a population of ions in several vibrational states among which the ground state accounted for about 50%. This observation suggests that the vibrational excitation of the ions has probably little influence on the electron temperature dependence below 1200 K. It is worth indicating however that recent merged beam experiments demonstrated that the electron temperature dependence may be non-monotonic. Thus, the authors proposed a power law such as k (T_e) ∼ T^−0.56_e for 1200 K ⩽ T_e ⩽ 4000 K indicating that vibrationally excited ions present a steeper temperature dependence within the range 1200–4000 K, which is of interest for the ionosphere of Titan at altitudes greater than 1600 km (Keller et al. 1992; Wahlund et al. 2005). No uncertainty is given with respect to the power-law exponent, but an error of 20% seems reasonable. A theoretical work by Guberman (2003) concluded that the electron temperature dependence is slightly different according to the temperature range. For the ground state v = 0, he proposed three different power laws: T^−0.20_e for 200 K ⩽ T_e ⩽ 400 K; T^−0.35_e for 700 K ⩽ T_e ⩽ 900 K; and T^−0.50_e for 1800 ⩽ T_e ⩽ 2000 K (Guberman 2003; S. L. Guberman 2006, private communication). His set of results however is in good agreement with the global single temperature dependence T^−0.39_e found experimentally and recommended by Sheehan & St. Maurice (2004) for the v = 0 state. Very recently, Guberman (2012) revisited this reaction including for the first time in calculations both major and minor dissociative routes for the v = 0 state. He was able to derive from his calculation a rate coefficient for the N⁺₂ ground vibrational level in the temperature range 100–3000 K which was well fitted by the following expression: (2.2 ± ^+0.2_−0.4) × 10⁻⁷ × (T_e/300)^−0.40 cm³ s⁻¹, in perfect agreement with the previous recommendation for the temperature dependence. Guberman, however, points out in his paper that an improved representation of k (N⁺₂, v = 0) can be obtained by separating the temperature range into two sub-ranges: k (N⁺₂, v = 0) = 2.2 × 10⁻⁷ (T_e/300)^−0.22 cm³ s⁻¹ for 100 K ⩽ T_e ⩽ 600 K and k (N⁺₂, v = 0) = 1.1 × 10⁻⁷ (T_e/1800)^−0.51 cm³ s⁻¹ for 600 K ⩽ T_e ⩽ 3000 K.

Considering now the absolute rate constant k, analysis of the literature shows that several experiments (Canosa et al. 1991; Cunningham & Hobson 1972; Geoghegan et al. 1991; Mehr & Biondi 1969) dealt with N⁺₂ (v = 0) ions. At 300 K, a rate constant of 2.2 × 10⁻⁷ cm³ s⁻¹ matches all these studies (Sheehan & St. Maurice 2004) with a typical 25% uncertainty. Therefore, it seems reasonable to recommend the following expression for the rate constant for the dissociative recombination of the ground state:

$$\begin{equation*} k({\rm N}_{2}^{+}, \nu = 0) = (2.2\pm 0.5)\times 10^{-7}(T_{\rm e}/300)^{-(0.39\pm 0.08)}\, {\rm cm}^{3}\, {\rm s}^{-1}. \end{equation*}$$

Finally, it is also worth mentioning that the dissociative recombination of ¹⁵N¹⁴N⁺ (v = 0) has been found to be rather similar to that of ¹⁴N⁺₂ (v = 0). The only available work is a quantum-theoretical calculation from Guberman (2003) who indicated that at room temperature the rate constant is 2.6 × 10⁻⁷ cm³ s⁻¹ and at 1000 K 1.6 × 10⁻⁷ cm³ s⁻¹.

For ions in vibrational excited states, however, there are no experiments that allow clear conclusions, because ions are formed in a mixture of different vibrational states (Peterson et al. 1998; Sheehan & St. Maurice 2004; Zipf 1980). In 1980, Zipf (1980) made a study in which he identified the v = 0, 1, and 2 levels by laser-induced fluorescence and reported rate constants at 300 K, which were increasing with the excitation level. However, it was recognised later that his experiment reflected the effective recombination for N⁺₂ ions with a vibrational temperature near 1500 K. Reanalysis of this work by Bates & Mitchell (1991) led to the qualitative conclusion that, at 300 K, the rate constant for the dissociative recombination of N⁺₂ (v = 1, 2) should be much smaller than for the ground state. From a theoretical point of view, work is presently in progress (Guberman 2012). It is worth mentioning however that in the ionosphere of Titan, vibrational excited N⁺₂ ions should be quenched prior dissociative recombination by collisions with N₂. The rate constant for the N⁺₂ (X, v) vibrational relaxation can be estimated to be efficient and equal to a few 10⁻¹⁰ cm³ s⁻¹ (see the above discussion about the N⁺₂ reaction with N₂). Although it is about three orders of magnitude less than the dissociative recombination rate constant, the relative abundance of electrons with respect to N₂ in the ionosphere of Titan is too small (∼1 ppm) to favor this latter process.