ABSOLUTE INTEGRAL CROSS SECTIONS AND PRODUCT BRANCHING RATIOS FOR THE VIBRATIONALLY SELECTED ION–MOLECULE REACTIONS: N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄

The ion–molecule reaction of N$_{2}^{+}$ + CH₄ has been the subject of intense studies in the past few decades (Anicich et al. 2004; Gauglhofer & Kevan 1972; Gichuhi & Suits 2011; Gislason et al. 1969; McEwan et al. 1998; Nicolas et al. 2003; Randeniya & Smith 1991; Smith et al. 1978; Tichý et al. 1979; Wyatt et al. 1976). Besides the investigation of chemical reaction dynamics, an important motivation for the study of this reaction is that it represents one of the key initiating ion–molecule reactions for triggering the overall formation and chemical evolution of the atmosphere of Titan, which is the largest moon of Saturn and is recognized as one of the most Earth-like worlds found to date (Anicich et al. 2004; Anicich & McEwan 1997; Carrasco et al. 2008; McEwan et al. 1998; Suits 2009). The atmosphere of Titan is considered to be reminiscent of the primordial atmosphere of Earth (Suits 2009). Because of the implication concerning the origin of life on Earth, modeling and simulation of the chemical composition of Titan are needed for understanding the chemical evolution of its atmosphere (Anicich & McEwan 1997; Carrasco et al. 2008; Suits 2009). The atmospheric composition of Titan is known to consist of N₂ (≈94%), CH₄ (≈4%), and traces of H₂, HCN, C₂H₂, C₂H₄, etc. The ionization of N₂ by electron impact, solar vacuum ultraviolet (VUV), and cosmic rays (McEwan et al. 1998) constitutes the major source of N$_{2}^{+}$. The mission of the Cassini–Huygens spacecraft sent to the Saturn system in 2004 (Owen 2005) has made available enhanced in situ data on the density profiles of ions and neutrals in the atmosphere of Titan, which should allow a more in depth simulation (Atreya 2007; Gu et al. 2009; Imanaka & Smith 2010; Israel et al. 2005; Niemann et al. 2005; Waite et al. 2007), and thus a better understanding of the chemical processes occurring on Titan. Such an effort would demand more detailed laboratory measurements of reaction rate constants or cross sections and product branching ratios for the relevant chemical reactions involved (Suits 2009).

Molecular ions such as N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$), produced by solar VUV and electron impact ionization can be formed in excited vibrational states, and the reactivity of these excited ions can be significantly different from that of the ground vibrational state. For example, the integral cross section of the N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + Ar charge transfer reaction has been shown to be greatly enhanced by vibrational excitation, with the integral cross sections for v⁺ = 1 and 2 to be about 100 and 200 fold greater than that for v⁺ = 0 (Chang et al. 2011, 2012). It is well known that vibrationally excited states of molecular ions in the ground electronic state that formed in this manner usually have long radiative lifetimes in the μs to ms range. For homonuclear diatomic species without a dipole moment, such as N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ ⩾ 1), radiative decay to the ground vibrational state is not possible. Because of the long lifetimes, the reaction for N$_{2}^{+}$ in individual vibrational v⁺-states must be taken into account in a realistic modeling of the observed density profiles of electrons, ions, and neutrals in planetary ionospheres.

To our knowledge, ion–molecule reactions involving vibrationally excited reactant N$_{2}^{+}$ have not been considered in the modeling of ion and neutral density profiles observed in the atmosphere of Titan. The fact that the vibrational dependence of reaction cross sections has been neglected in the modeling of ion and neutral chemical compositions observed in planetary atmospheres, gas comae, and astrochemistry, can be ascribed to the lack of available state-selected cross-sectional data for relevant ion–molecule processes. Ion–neutral reactions generally occur in the temperature range of 300–5000 K in the ionospheres. Thus, for state-selected rate constants or cross sections to be useful for atmospheric modeling, they must be measured down to thermal energies or at center-of-mass collision energies of E_cm ≈ 30–40 meV. For Titan's atmosphere, one needs reaction cross sections (or rate coefficients) at much lower temperatures than 300 K. The demanding requirements for achieving fine control of both kinetic and internal energies for the reactant ions have not been achieved in previous state-selected experiments (Dressler et al. 2006; Ng 1992, 2002). Limited by the achievable kinetic energy resolution, the absolute integral cross sections obtained in previous vibrationally selected studies are limited to E_cm ≈ 0.5–1.0 eV, which is well above thermal energies.

We have recently developed a molecular beam VUV laser pulsed-field ionization-photoion (PFI-PI) source and have successfully coupled this ion source to a double-quadrupole–double-octopole (DQDO) ion guide mass spectrometer for absolute integral cross-sectional measurements of ion–molecule reactions involving rovibrationally selected reactant ions (Chang et al. 2011, 2012; Xu et al. 2012). Employing this unique apparatus, we have obtained rovibrationally selected integral cross sections for the reactions, N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺; N⁺) + Ar → Ar⁺ + N₂ and H₂O⁺(X²B₁; $v_{1}^{+}v_{2}^{+}v_{3}^{+}$; N⁺_Ka+Kc+) + D₂ → H₂DO⁺ + D in the E_cm range from thermal energies to 10.00 eV (Chang et al. 2011, 2012; Xu et al. 2012). The results of these experiments indicate that this ion–molecule reaction apparatus can be equally applicable for absolute cross-sectional measurements of other state-selected ion–molecule reactions involving atomic, diatomic, triatomic, and simple polyatomic ions of relevance to planetary atmospheres. This technical progress of achieving high internal state selectivity and high laboratory kinetic energy (E_lab) resolution for the reactant ion beam presents a unique opportunity for a detailed examination of the kinetic, rotational, and vibrational energy dependencies on reaction cross sections of ion–molecule processes of importance occurring in planetary atmospheres and cometary comae.

As early as 1969, Mahan et al. (Gislason et al. 1969) examined the dynamics of the N$_{2}^{+}$ + CH₄ reaction by the crossed ion–neutral beam method, from which the velocity distribution of the product ion N₂H⁺ formed by H-atom transfer was measured, leading them to propose a stripping reaction model for the reaction process. Using the ion cyclotron resonance technique, Gauglhoffer et al. (Gauglhofer & Kevan 1972) have measured the rate constant for the reaction of N$_{2}^{+}$ + CH₄, which was found to be three times as large as the rate constant predicted by the Langevin–Gioumousis–Stevenson (LGS) model (Stevenson & Schissler 1958). Wyatt et al. (1976) examined the reaction of N$_{2}^{+}$ + CH₄ → N₂H⁺ + CH₃ employing the ion beam-collision chamber method, from which the reaction cross sections as well as the velocity and angular distributions of product N₂H⁺ were measured as a function of kinetic energy. Based on a selected ion flow tube study, Smith and co-workers (Smith et al. 1978) suggested that the N$_{2}^{+}$ + CH₄ reaction was mediated by charge transfer followed by ion fragmentation. In the latter experiment, only product CH$_{3}^{+}$ and CH$_{2}^{+}$ ions were observed with a branching ratio of CH$_{3}^{+}$:CH$_{2}^{+}$ = 0.93:0.07 and no H atom transfer reaction was detectable. A reaction rate constant of 1.0 × 10⁻⁹ cm³ s⁻¹ was determined. In a later paper (Tichý et al. 1979) published by the same group, the CH$_{3}^{+}$:CH$_{2}^{+}$ branching ratio was obtained to be 0.89:0.11 and the rate constant was reported as 1.18 × 10⁻⁹ cm³ s⁻¹. The N$_{2}^{+}$ + CH₄ reaction was also studied by Randeniya & Smith (1991) who employed a free jet flow reactor at very low temperatures (8–15 K), yielding a rate constant of 1.9 (±0.9) × 10⁻⁹ cm³ s⁻¹, which was found to be independent of temperature in the latter temperature range. Furthermore, only two product channels for the formation of CH$_{3}^{+}$ and CH$_{2}^{+}$ with a branching ratio of (0.80 ± 0.10):(0.20 ± 0.10) at 10 K were observed. Employing an ion cyclotron resonance mass spectrometer, Anicich et al. (McEwan et al. 1998) also investigated the N$_{2}^{+}$ + CH₄ reaction, from which three product channels, leading to the formation of CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺, were observed with a branching ratio of 0.80:0.05:0.15, and an integral reaction rate constant of 1.14 × 10⁻⁹ cm³ s⁻¹. Recently, Nicolas et al. (2003) measured the integral and differential cross sections of N$_{2}^{+}$(v⁺ = 0) + CH₄/CD₄ in the E_cm range of 0.1–3.5 eV using a guided-ion beam ion–molecule reaction apparatus. Their results confirm the occurrence of three product channels that produce CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ ions with a branching ratio of 0.86:0.09:0.05, which was found to be independent of collision energies. Secondary reactions involving CH$_{2}^{+}$ and CH$_{3}^{+}$ in the reaction gas cell were observed, and partial corrections on the integral cross sections to the product channels due to secondary reactions were made based on the rate data reported by Anicich & McEwan (1997). However, important secondary reactions, which may affect the integral cross sections and the branch ratio, were ignored in their data analysis. In 2004, V. G. Anicich and co-workers (Anicich et al. 2004) reexamined the reaction of N$_{2}^{+}$ + CH₄, and only two reaction channels leading to the formation of CH$_{3}^{+}$ and CH$_{2}^{+}$ ions were observed. The branching ratio and rate constant were determined as 0.88: 0.12 and 1.00 × 10⁻⁹ cm³ s⁻¹, respectively. More recently, Gichuhi & Suits (2011) examined the low-temperature (≈45 K) primary branching ratio of N$_{2}^{+}$ + CH₄ reaction in a free jet by preparing N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v = 0) via a 2 + 1 resonance-enhanced multiphoton ionization scheme. Only two reaction channels for CH$_{3}^{+}$ and CH$_{2}^{+}$ ions were observed, and a corresponding branch ratio of 0.83:0.17 was reported.

To our knowledge, the reactivity of N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ ⩾ 1) with CH₄ has not been examined previously. Using the newly established VUV laser PFI-PI DQDO ion guide apparatus, we have performed a detailed measurement of the vibrationally selected reaction of N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0, 1, and 2) + CH₄. In this report, we present the vibrationally selected absolute integral cross sections (σ_v+'s) for the formation of product CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ ions as well as the branching ratios, [σ_v+(CH$_{3}^{+}$): σ_v+(CH$_{2}^{+}$): σ_v+(N₂H⁺)]/σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺), for v⁺ = 0, 1, and 2, in the E_cm range of 0.05–10.0 eV, where σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺) = σ_v+(CH$_{3}^{+}$) + σ_v+(CH$_{2}^{+}$) + σ_v+(N₂H⁺).

The present measurement of the absolute integral cross sections for the vibrationally selected N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ reaction was conducted using the VUV laser PFI-PI DQDO apparatus, which has been reported in detail previously (Chang et al. 2011, 2012; Xu et al. 2012). Briefly, the apparatus consists of a tunable VUV laser system, a PFI-PI ion source, and a DQDO ion guide mass spectrometer. Tunable VUV laser radiation is generated by four-wave sum-frequency (2v₁ + v₂) mixing using a Kr pulsed jet as the nonlinear medium, where v₁ and v₂ represent the respective ultraviolet (UV) and visible (VIS) outputs of two dye lasers, which were pumped by the second and third harmonic outputs of one identical Nd:YAG laser operated at 15 Hz. The N₂ molecules were introduced into the photoionization/photoexcitation (PI/PEX) region of the ion source in the form of a supersonic molecular beam traveling along the central axis of the DQDO mass spectrometer. The vibrationally selected N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) PFI-PI ions were prepared by employing a novel electric-field pulsing scheme on the VUV laser PFI-PI ion source for retarding the prompt ions produced by direct VUV photoionization, generating the PFI-PI ions from high-n (n ≈ 100) Rydberg N₂*(n) species formed by VUV excitation of the N₂ molecular beam, and extracting the ions thus produced from the ion source. The control of the timing and magnitudes of the pulsed electric fields applied allows for the preparation of an N$_{2}^{+}$ ion beam with not only high internal state purity and high intensity but also high kinetic energy resolution. The DQDO ion guide mass spectrometer consists of two quadrupole mass spectrometers (QMSs), two radio frequency (rf) octopole ion guides, and reaction gas cells, where the N$_{2}^{+}$ + CH₄ reaction occurs. The reactant QMS is designed for mass selection of reactant ions to enter the first octopole ion guide. Since only N$_{2}^{+}$ PFI-PIs are generated and selected by the PFI-PI scheme in the present experiment, the reactant QMS was operated as an ion lens to guide the reactant N$_{2}^{+}$ PFI-PIs into the reaction gas cell. The pressure of the neutral reactant CH₄ in the gas cell is monitored by an MKS Baratron. The first and second rf-octopole ion guides are designed to join at the middle of the reaction gas cell. While the same rf was applied to both the first and second octopoles to confine and guide all reactant and product ions into the product QMS for detection by the ion detector, different dc voltages could be applied to the first and second octopoles, serving to extract slow product ions from the gas cell, and thus minimizing secondary reactions. The ion detector has the design of a Daley detector except that the photomultiplier tube was replaced by a dual set of microchannel plates. The ion signals passed through an amplifier and a discriminator prior to be measured by a multichannel scalar (MCS).

All cross-sectional data presented in this study are based on at least three independent and reproducible measurements. The standard deviations (generally about 10%) are determined by the reproducibility of the independent measurements. However, the systematic uncertainties for the experimental cross sections presented here are estimated to be 30% (Chang et al. 2011). The N₂ and CH₄ gases used in this experiment have purities of 99.998% and 99.999%, respectively.

Based on the energetic analysis (Lias et al. 1988), four possible exothermic reaction channels leading to the formation of CH$_{4}^{+}$, CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ from the N$_{2}^{+}$ (X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ collisions are shown as reactions (1)–(4):

$$\begin{equation} {\rm N}_2 ^ + \left({X}^2 \Sigma_{\rm g} ^{ + } ;v^ + \,{=}\, 0\right) \,{+}\, {\rm CH}_4 \,{\to}\, {\rm CH}_4 ^ + + {\rm N}_2 \quad \Delta E \,{=}\, {-}3.08\;{\rm eV} \end{equation} \tag{ 1 }$$

$$\begin{equation} \to {\rm CH}_3 ^ + + {\rm N}_2 + {\rm H}\quad \Delta E = - 1.22\;{\rm eV} \end{equation} \tag{ 2 }$$

$$\begin{equation} \to {\rm CH}_2 ^ + + {\rm N}_2 + {\rm H}_2\quad \Delta E = - 0.44\;{\rm eV}\ \, \end{equation} \tag{ 3 }$$

$$\begin{equation} \to {\rm N}_2 {\rm H}^ + + {\rm CH}_3\quad \Delta E = - 2.57\;{\rm eV}. \end{equation} \tag{ 4 }$$

Here, the exothermicities (−ΔE values) for the reactions associated with reactant N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0) are shown in reactions (1)–(4). The exothermicities for these reactions with N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$) prepared in the v⁺ = 1 and two vibrational states are higher by 0.271 and 0.535 eV, respectively (Chang et al. 2012).

Figure 1(a) depicts the mass spectrum for the vibrationally selected N$_{2}^{+}$ (X²Σ$_{\rm g}^{+}$; v⁺ = 0) ion beam at E_cm = 0.30 eV by using the product QMS. Since this spectrum was obtained without CH₄ in the reaction gas cell, only the reactant ions were observed. The two ion peaks observed at m/z = 28 and 29 can thus be assigned as the ¹⁴N¹⁴N⁺ and ¹⁵N¹⁴N⁺ ions, respectively. The ratio of the two ion peaks found in Figure 1(a) is consistent with the natural isotopic distribution of ¹⁴N¹⁴N⁺ and ¹⁵N¹⁴N⁺. When reactant neutral CH₄ was filled into the gas cell at a pressure of 4 × 10⁻⁵ Torr, we recorded the mass spectrum shown in Figure 1(b), in which four ion peaks at m/z = 14, 15, 28, and 29 were identified. The ion peaks at m/z = 14 and 15 can be unambiguously assigned as CH$_{2}^{+}$ and CH$_{3}^{+}$ ions, formed by reactions (3) and (2), respectively. The ion peaks at m/z = 28 must have the major contribution from N$_{2}^{+}$; and the ion peak at m/z = 29 should be contributed by ¹⁵N¹⁴N⁺ and N₂H⁺ formed by the H atom transfer reaction (4). The interference for the detection of product N₂H⁺ by the ¹⁵N¹⁴N⁺ background can be easily removed by subtracting the corresponding ion intensities of the m/z = 29 ions observed with and without the CH₄ reactant gas filled in the gas cell. Another method to eliminate the interference of ¹⁵N¹⁴N⁺ would be to set the reactant QMS to transmit only the ¹⁴N¹⁴N⁺ ions. The mass spectrum of Figure 1(b) clearly shows that CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ are primary product ions of the reaction of N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0) + CH₄. Furthermore, no CH$_{4}^{+}$ ions associated with the charge-transfer reaction mechanism are observed. This latter observation is consistent with the results of all previous experimental investigations (Anicich et al. 2004; Gauglhofer & Kevan 1972; Gichuhi & Suits 2011; Gislason et al. 1969; McEwan et al. 1998; Nicolas et al. 2003; Randeniya & Smith 1991; Smith et al. 1978; Tichý et al. 1979; Wyatt et al. 1976).

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The use of a low gas cell pressure (4 × 10⁻⁵ Torr) of reactant CH₄ was intended to minimize secondary reactions involving products CH$_{3}^{+}$ and CH$_{2}^{+}$ with CH₄ in the reaction gas cell. Nevertheless, secondary reactions of CH$_{3}^{+}$ and CH$_{2}^{+}$ according to reactions (5)–(7) are still found to occur.

$$\begin{equation} {\rm CH}_3 ^ + + {\rm CH}_4 \to {\rm C}_2 {\rm H}_5 ^ + + {\rm H}_2 \quad \Delta E = {-}1.21\;{\rm eV}\ \, \end{equation} \tag{ 5 }$$

$$\begin{equation} {\rm CH}_2 ^ + + {\rm CH}_4 \to {\rm C}_2 {\rm H}_5 ^ + + {\rm H}\quad \Delta E = {-}1.98\;{\rm eV} \end{equation} \tag{ 6 }$$

$$\begin{equation} \quad\qquad\qquad\to {\rm C}_2 {\rm H}_4 ^ + + {\rm H}_2\quad \Delta E = {-}2.54\;{\rm eV}.\ \ \end{equation} \tag{ 7 }$$

Previous studies have shown that these exothermic reactions, possibly proceeding with a complex formation mechanism at thermal energies, have very high reaction rate constants. Anicich & McEwan (1997) have shown that C₂H$_{4}^{+}$ can be formed efficiently by the reaction between CH$_{2}^{+}$ and CH₄ and thus, the observed m/z = 28 ion peak should include the contribution from C₂H$_{4}^{+}$ ions. As shown below, the formation of slow C₂H$_{4}^{+}$ ions by this secondary reaction (7) can be distinguished by the time-of-flight (TOF) method. The minor ion peak appearing at m/z = 29 is also expected to have an attribution by secondary C₂H$_{5}^{+}$ ions produced by reactions (5) and (6) (Anicich & McEwan 1997). Secondary C₂H$_{5}^{+}$ ions can also be distinguished from primary N₂H⁺ ions by the TOF method as illustrated below.

The occurrence of secondary reactions (5)–(7) has the effect of reducing the apparent cross sections for the formation of CH$_{2}^{+}$ and CH$_{3}^{+}$, and increasing those for N₂H⁺ if proper corrections for secondary reactions are not made. In order to determine accurate integral cross sections and branching ratios for the formation of CH$_{2}^{+}$, CH$_{3}^{+}$, and N₂H⁺, we have examined the secondary reactions of CH$_{2}^{+}$ and CH$_{3}^{+}$ in detail. At similar experimental conditions, Nicolas et al. have verified the occurrence of secondary reactions between CH₃⁺ (CH$_{2}^{+}$) and CH₄ to form C₂H$_{5}^{+}$ by using deuterated methane CD₄ as the neutral reactant gas (Nicolas et al. 2003). Since the reaction mechanisms for the formation of N₂H⁺ and C₂H$_{5}^{+}$ ions are different, they are produced with different velocity distributions. This allows N₂H⁺ and C₂H$_{5}^{+}$ to be separated and detected by the TOF method. The N₂H⁺ ions are known to be formed by the reaction of N$_{2}^{+}$ + CH₄ via a direct H-stripping mechanism. Due to the significantly lighter mass of H atoms compared to that of N$_{2}^{+}$ ions, the velocities of the N₂H⁺ ions are expected to be similar to those of N$_{2}^{+}$ ions. According to the charge transfer mechanism for the reaction of N$_{2}^{+}$ + CH₄, CH$_{3}^{+}$ and CH$_{2}^{+}$ are fragments of excited CH$_{4}^{+\ast}$ formed by charge transfer collisions of N$_{2}^{+}$ and CH₄. Considering that the charge transfer CH$_{4}^{+\ast}$ ions are formed mostly at thermal energies, the velocities of secondary C₂H$_{4}^{+}$ and C₂H$_{5}^{+}$ ions produced by secondary reactions of CH$_{3}^{+}$ and CH$_{2}^{+}$ fragments from CH$_{4}^{+\ast}$ are also expected to be slow. This expectation can be verified by TOF measurements of the mass 28 (mass 29) ions resulting from the N$_{2}^{+}$ (X²Σ$_{\rm g}^{+}$; v⁺) + CH₄ reaction by using the MCS and setting the product QMS at m/z = 28 (m/z = 29).

Figure 2 depicts the TOF spectrum of mass 29 ions resulting from the N$_{2}^{+}$ (X²Σ$_{\rm g}^{+}$; v⁺ = 2) + CH₄ reaction at E_cm = 0.5 eV. The prominent sharp ion peak appearing at about 150 μs is assigned to N₂H⁺/¹⁵N¹⁴N⁺ ions. As pointed out above, the interference of ¹⁵N¹⁴N⁺ in the measurement of product N₂H⁺ can be easily corrected by taking the difference between the mass 29 ion intensities observed with and without the reactant CH₄ gas filled in the reaction gas cell. The broad ion TOF peak observed at 260 μs with a long tail extending to about 1000 μs is attributed to C₂H$_{5}^{+}$ ions produced by the secondary reactions (5) and (6). Based on this assignment, the intensity of C₂H$_{5}^{+}$ ions can be measured by summing all the ion counts of the broad peak covering the region of 260–1000 μs for a fixed accumulation time of the TOF spectrum.

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The measured TOF spectrum for the mass 28 ions resulting from the N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0) + CH₄ reaction at E_cm = 0.5 eV as shown in Figure 3(b) reveals a sharp peak at about 150 μs and a broad peak at around 300 μs with a long tail extending up to more than 1000 μs. As a comparison, we have recorded the TOF spectrum (Figure 3(a)) by shutting off the neutral reactant CH₄ gas from entering the reaction gas cell. As expected, the latter TOF spectrum shows a single sharp peak for reactant N$_{2}^{+}$ appearing at 150 μs with nearly no ion counts at TOFs longer than 200 μs. Thus, the sharp peak at 150 μs and the broad peak at 300 μs can be ascribed to unreacted N$_{2}^{+}$ ions and secondary C₂H$_{4}^{+}$ ions, respectively. The seeming weakness of this broad peak for C₂H$_{4}^{+}$ compared to that for C₂H$_{5}^{+}$ in Figure 2 is due to the significantly shorter time (30 s) used in the accumulation of the spectrum of Figure 3(b) compared to the accumulation time (300 s) for the spectrum of Figure 2. Nevertheless, the observation of the broad peak for C₂H$_{4}^{+}$ can be taken as support for the occurrence of reaction (7) in the reaction gas cell.

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In order to make the proper corrections of secondary reactions in the determination of the absolute integral cross sections, we need to partition the measured C₂H$_{5}^{+}$ intensity to contributions from the CH$_{3}^{+}$ + CH₄ and CH$_{2}^{+}$ + CH₄ reactions. Here, we have adopted the argument from Nicolas et al. (2003) by assigning the relative contributions from these reactions according to the ratio of their known thermal rate constants, k(CH$_{3}^{+}$) and k(CH$_{2}^{+}$), which are reasonably well determined to be =1.1 × 10⁻⁹ cm³ s⁻¹ and 3.9 × 10⁻⁹ cm³ s⁻¹, respectively. The application of this approach here is based on the crude assumption that the ratio k(CH$_{3}^{+}$)/k(CH$_{2}^{+}$) is constant for CH$_{3}^{+}$ and CH$_{2}^{+}$ formed in the N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ reactions at the E_cm range of interest in the present experiment. In Nicolas et al. (2003), the authors assumed that the CH$_{2}^{+}$ + CH₄ reaction only produced C₂H$_{5}^{+}$ and the production of C₂H$_{4}^{+}$ was not included in their consideration. The branching ratio for reactions (6) and (7) at thermal energies was determined to be 0.3:0.7 by Anicich & McEwan (1997), indicating that more CH$_{2}^{+}$ ions undergo reaction (7) to generate C₂H$_{4}^{+}$ ion than producing C₂H$_{5}^{+}$ by reaction (6). Combining the measured intensities of C₂H$_{5}^{+}$, the rate constant ratio k(CH$_{3}^{+}$)/k(CH$_{2}^{+}$), and the branching ratio for secondary reactions (6) and (7), we have been able to determine the proportions of primary CH$_{3}^{+}$ and CH$_{2}^{+}$ ions that have undergone secondary reactions (5)–(7). These corrections, together with the intensities of the CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ ions measured directly, are used for the determination of the σ_v+(CH$_{3}^{+}$), σ_v+(CH$_{2}^{+}$), and σ_v+(N₂H⁺) values and their branching ratios, [σ_v+(CH$_{3}^{+}$):σ_v+(CH$_{2}^{+}$):σ_v+(N₂H⁺)]/σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺), for v⁺ = 0, 1, and 2.

Instead of using the branching ratio of 0.3:0.7 determined by Anicich & McEwan (1997) to estimate the intensity of C₂H$_{4}^{+}$ relative to the measured C₂H$_{5}^{+}$ intensity, the intensity of C₂H$_{4}^{+}$ can be measured directly by the TOF method as shown in the spectrum of Figure 3(b). However, due to the overwhelming intensity of the N$_{2}^{+}$ TOF peak, the broad peak assigned to C₂H$_{4}^{+}$ was found to overlap with the tail of the reactant N$_{2}^{+}$ peak for the N$_{2}^{+}$ + CH₄ reaction occurring at E_cm < 0.50 eV. Since this introduces an error in the measurement of the C₂H$_{4}^{+}$, we have decided to use the above scheme of relying on the branching ratio for reactions (6) and (7) to estimate the contribution of the C₂H$_{4}^{+}$ intensity. We have compared the branching ratios deduced by the two approaches at E_cm = 0.50 and 1.00 eV and found that the observed discrepancies are within the assigned uncertainty (10%–15%) for the branching ratio measurements.

After making the corrections due to secondary reactions, the vibrationally selected absolute integral cross sections, σ_v+(CH$_{3}^{+}$), σ_v+(CH$_{2}^{+}$), and σ_v+(N₂H⁺) determined in the v⁺ range of 0–2 and the E_cm range of 0.05–10.00 eV are plotted in Figures 4(a)–(c), respectively, to illustrate the vibrational and E_cm effects. For all E_cm values examined in the present study, the absolute integral reaction cross sections for the formation of CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ at a given E_cm are in the order: σ_v+(CH$_{3}^{+}$) > σ_v+(CH$_{2}^{+}$) > σ_v+(N₂H⁺), v⁺ = 0, 1, and 2. The integral cross sections of all three product channels are found to increase as E_cm is decreased. This trend is consistent with the exothermic nature of these reactions and the prediction of the LGS model (Stevenson & Schissler 1958). We note that the E_cm dependences for σ_v+(CH$_{3}^{+}$) and σ_v+(CH$_{2}^{+}$), v⁺ = 0–2, at E_cm = 0.30–10.00 eV are similar. This observation is consistent with the previous suggestion that the formation of CH$_{3}^{+}$ and CH$_{2}^{+}$ is governed by a common dissociative charge transfer mechanism.

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As shown in Figures 4(a)–(c), complicated vibrational dependences are observed by comparing the σ_v+(CH$_{3}^{+}$), σ_v+(CH$_{2}^{+}$), and σ_v+(N₂H⁺) values obtained for v⁺ = 0, 1, and 2. In the E_cm range of 0.05–0.40 eV, the vibrationally selected absolute integral cross sections are found to be on the order of σ₀ > σ₂ > σ₁ for the formation of CH$_{3}^{+}$ and N₂H⁺. The σ₁(CH$_{3}^{+}$) [σ₁(N₂H⁺)] is ≈25% (≈40%) lower than σ₀(CH$_{3}^{+}$) [σ₀(N₂H⁺)]. That is, the N$_{2}^{+}$ (X²Σ$_{\rm g}^{+}$) + CH₄ collisions to produce CH$_{3}^{+}$ and N₂H⁺ are significantly inhibited by vibrational excitation of N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$) at E_cm = 0.05–0.40 eV. However, for the formation of CH$_{2}^{+}$ in this E_cm region, the σ_v+ values for v⁺ = 0, 1, and 2 are found to be nearly identical after taking into account the experimental uncertainties. Assuming that the formation of CH$_{3}^{+}$ and CH$_{2}^{+}$ at low E_cm values is mediated by the dissociative charge transfer mechanism as suggested by previous studies, the formation of excited CH$_{4}^{+}$* by charge transfer collisions of N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$) + CH₄ should reflect the vibrational energy resonance of N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$) and CH$_{4}^{+}$. The subsequent dissociation of excited CH$_{4}^{+}$* to form CH$_{3}^{+}$ + H is likely to proceed via a loose transition state, which mostly involves stretching an H···CH$_{3}^{+}$ bond and is expected to have no potential energy barrier. Thus, the charge transfer mechanism can partially account for the observed vibrational dependences for σ_v+(CH$_{3}^{+}$). In the case of the formation of CH$_{2}^{+}$ + H₂ from CH$_{4}^{+}$*, the H₂ elimination is likely involved in a tight transition state associated with a potential energy barrier, which could wash out the vibrational energy effect for reaction (3).

In the region of E_cm = 0.50–1.00 eV, no vibrational effects are discernible for reactions (2)–(4), after taking into account the experimental uncertainties of about 10%. When E_cm is increased from 2.00 to 10.00 eV, a clear vibrational inhibition effect can be observed with σ₀ > σ₁ > σ₂ for all three product channels, revealing the rich dynamics for this reaction system resulting from the nonadiabatic coupling involving the kinetic and vibrational motions of the N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ reaction system. In order to understand the experimental observations, rigorous dynamical calculations based on the accurate potential surfaces of the N$_{2}^{+}$ (X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ reaction system are needed.

To further illustrate the vibrational excitation on the overall reactivity of the N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ collisions, we have taken the sum of the absolute integral cross sections for all product channels σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺), v⁺ = 0, 1, and 2, and have plotted them as a function of E_cm in Figure 5. These plots show similar trends on both kinetic and vibrational energy dependences for individual reaction channels shown in Figures 4(a)–(c). Although all previous cross sections and thermal rate constants (k_T) for the N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$) + CH₄ reaction available in the literature were concerned only with N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$) in the v⁺ = 0 ground state, we have included these results in Figure 4 for comparison with the present study. Here, the k_T values were converted into absolute integral cross section (σ₀) by using the relation σ₀ = k_T(μ/2E_cm)^1/2, where μ is the reduced mass of N$_{2}^{+}$ and CH₄. The predictions based on the LGS model (Stevenson & Schissler 1958) are also depicted in Figure 5. The significantly smaller LGS predictions for the integral cross sections have been noted in previous studies (Nicolas et al. 2003), indicating that for the N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ reaction system, the interaction between N$_{2}^{+}$ and CH₄ cannot be adequately described by the LGS model which only assumes the charge-induced dipole interaction. As shown in Figure 5, while the profile for the σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺) curve of Figure 5 obtained in the present study is in agreement with that reported by Nicolas and co-workers, the absolute cross-sectional values of this experiment are about 70% larger than that reported (Nicolas et al. 2003). We note that the absolute cross sections reported by Nicolas et al. were determined by calibrating their N$_{2}^{+}$ (X²Σ$_{\rm g}^{+}$; v⁺ = 0) + Ar charge transfer cross sections with those measured by Schultz & Armentrout (1991). Considering that the uncertainties for individual absolute integral cross-sectional measurements by using the guided ion beam technique are ≈30%, the accumulated uncertainty for the absolute integral cross sections thus obtained by Nicolas et al. (2003) could be more than 30%. In our cross-sectional measurements, the ion lenses were carefully tuned to maximize the product ion transmission such that the sum of the product ion signals is close to the attenuation of the reactant H₂O⁺ ion beam signal.

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Branching ratios for the three reaction channels (reactions (2)–(4), [σ_v+(CH$_{3}^{+}$):σ_v+(CH$_{2}^{+}$):σ_v+(N₂H⁺)]/σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺) for v⁺ = 0, 1, and 2, determined in the E_cm range of 0.05–10.00 eV are summarized in Table 1. As shown in the table, after taking into account the experimental uncertainties, the branching ratios for the three channels are found to be independent of E_cm and the v⁺ state of reactant N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$) for v⁺ = 0–2 and E_cm = 0.05–9.00 eV. The branching ratios for v⁺ = 0 determined at E_cm = 0.05 eV are [σ₀(CH$_{3}^{+}$):σ₀(CH$_{2}^{+}$):σ₀(N₂H⁺)]/σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺) = 0.68 ± 0.05:0.26 ± 0.04:0.06 ± 0.01, which are quite different with previous (Anicich et al. 2004; Gichuhi & Suits 2011; McEwan et al. 1998; Nicolas et al. 2003; Randeniya & Smith 1991; Smith et al. 1978; Tichý et al. 1979) measurements. These ratios remain nearly the same until E_cm is increased to 9.00 eV. When E_cm is further increased to 10.00 eV, a branching ratio of 0.58 ± 0.05:0.34 ± 0.04:0.08 ± 0.01 is observed, indicating that the relative intensity for product CH$_{3}^{+}$ decreases while those for both products CH$_{2}^{+}$ and N₂H⁺ become more important as E_cm is increased from 9:00 to 10.00 eV. As pointed out above, the variation and E_cm dependences of the branching ratios [σ_v+(CH$_{3}^{+}$):σ_v+(CH$_{2}^{+}$):σ_v+(N₂H⁺)]/σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺) for v⁺ = 1 and 2 are essentially the same as those presented above for v⁺ = 0.

Table 1. Branching Ratios for the Formation of CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ from the Vibrationally Selected Reaction N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ Determined in the E_cm Range 0.05–10.00 eV^a,b

	v+ = 0			v+ = 1			v+ = 2
Ecm	CH$_{3}^{+}$	CH$_{2}^{+}$	N2H+	CH$_{3}^{+}$	CH$_{2}^{+}$	N2H+	CH$_{3}^{+}$	CH$_{2}^{+}$	N2H+
(eV)
0.05	0.68	0.26	0.06	0.66	0.29	0.05	0.68	0.26	0.06
0.10	0.70	0.24	0.06	0.68	0.27	0.05	0.69	0.26	0.05
0.20	0.68	0.26	0.06	0.67	0.28	0.04	0.69	0.27	0.04
0.30	0.68	0.27	0.05	0.65	0.30	0.05	0.66	0.30	0.04
0.40	0.67	0.28	0.05	0.65	0.32	0.03	0.67	0.29	0.04
0.50	0.65	0.30	0.05	0.63	0.33	0.04	0.66	0.30	0.03
0.60	0.66	0.30	0.04	0.64	0.33	0.03	0.67	0.30	0.03
0.70	0.65	0.31	0.04	0.64	0.33	0.03	0.67	0.30	0.03
0.80	0.65	0.31	0.04	0.64	0.33	0.03	0.65	0.32	0.03
0.90	0.63	0.33	0.04	0.63	0.33	0.04	0.65	0.31	0.04
1.00	0.64	0.32	0.04	0.66	0.31	0.03	0.65	0.32	0.03
2.00	0.64	0.32	0.04	0.63	0.34	0.03	0.65	0.32	0.03
3.00	0.63	0.33	0.04	0.63	0.34	0.03	0.65	0.31	0.04
4.00	0.63	0.32	0.05	0.63	0.33	0.04	0.65	0.31	0.04
5.00	0.66	0.29	0.05	0.64	0.33	0.03	0.62	0.33	0.05
6.00	0.64	0.30	0.06	0.63	0.32	0.05	0.62	0.34	0.04
7.00	0.64	0.29	0.07	0.62	0.33	0.05	0.63	0.31	0.06
8.00	0.63	0.30	0.07	0.66	0.28	0.06	0.63	0.31	0.06
9.00	0.59	0.33	0.08	0.55	0.37	0.08	0.53	0.40	0.07
10.00	0.58	0.34	0.08	0.56	0.35	0.09	0.57	0.33	0.10

Notes. ^aThese branching ratios have been corrected for secondary reactions involving product CH$_{3}^{+}$ and CH$_{2}^{+}$ ions from the N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ reactions. ^bThe standard deviations are measures of the reproducibility from independent measurements. The estimated branch-ratio uncertainties for CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ branches are 5%, 4%, and 1%, respectively.

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The branching ratios for CH$_{3}^{+}$:CH$_{2}^{+}$ and CH$_{3}^{+}$:CH$_{2}^{+}$:N₂H⁺ in the temperature range from 10 to 300 K have been measured in seven previous experiments employing different experimental techniques (Anicich et al. 2004; Gichuhi & Suits 2011; McEwan et al. 1998; Nicolas et al. 2003; Randeniya & Smith 1991; Smith et al. 1978; Tichý et al. 1979). Among these experiments, all have reported the observation of CH$_{3}^{+}$ and CH$_{2}^{+}$ as the major products, but only two have reported the detection of the N₂H⁺ product channel. The branching ratios for CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ obtained in previous measurements (Anicich et al. 2004; Gichuhi & Suits 2011; McEwan et al. 1998; Nicolas et al. 2003; Randeniya & Smith 1991; Smith et al. 1978; Tichý et al. 1979) were found to be in the ranges of 80%–93%, 5%–20%, and 5%–15%, respectively, indicating that CH$_{3}^{+}$ is the major primary product ion. After making the correction for secondary reactions of CH$_{3}^{+}$ and CH$_{2}^{+}$ using the procedures outlined above, we have determined the branching ratios as [σ₀(CH$_{3}^{+}$):σ₀(CH$_{2}^{+}$): σ₀(N₂H⁺)]/σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺) = 0.68 ± 0.05:0.26 ± 0.04:0.06 ± 0.01 at E_cm = 0.05 eV. Since CH$_{2}^{+}$ is more reactive than CH$_{3}^{+}$ toward CH₄, the net effect of making the correction for secondary reactions of CH$_{3}^{+}$ and CH$_{2}^{+}$ is enhancing the branching ratio for CH$_{2}^{+}$ and correspondingly suppressing that for CH$_{3}^{+}$. If we only made the correction for reactions (5) and (6), i.e., for the formation of C₂H$_{5}^{+}$, but not C₂H$_{4}^{+}$, as was done by Nicolas et al. (2003), we obtained the branching ratios as [σ₀(CH$_{3}^{+}$):σ₀(CH$_{2}^{+}$) and σ₀(N₂H⁺)]/σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺) = 0.75 ± 0.05:0.19 ± 0.04:0.06 ± 0.02 at E_cm = 0.05 eV, which are also included in Table 2. These partially corrected values are consistent with those reported by Nicolas et al. (2003) and Gichuhi & Suits (2011), and their co-workers, respectively.

Table 2. Comparison of the Branch Ratios for the Formation of CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ from the N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0) + CH₄ reaction determined in the temperature (T) range 10–380 K

Reference	CH$_{3}^{+}$	CH$_{2}^{+}$	N2H+	T (K)
This worka	0.65 ± 0.05	0.26 ± 0.04	0.06 ± 0.01
				380b
	(0.75 ± 0.05	(0.19 ± 0.04)	(0.06 ± 0.02)
Smith et al. 1978	0.93	0.07	0	298
Tichý et al. 1979	0.89	0.11	0	298
Randeniya & Smith 1991	0.80 ± 0.10	0.20 ± 0.10	0	10
McEwan et al. 1998	0.80	0.05	0.15	298
Nicolas et al. 2003	0.86	0.09	0.05	298
Anicich et al. 2004	0.88	0.12	0	298
Gichuhi & Suits 2011	0.83 ± 0.02	0.17 ± 0.02	0	45 ± 5

Notes. ^aThe branching ratios obtained at E_cm = 0.05 eV, which corresponds to T ≈ 380 K. These branching ratios have been corrected for secondary reactions of CH$_{3}^{+}$ + CH₄ and CH$_{2}^{+}$ + CH₄, leading to the production of C₂H$_{5}^{+}$ and C₂H$_{4}^{+}$. The values in parentheses were obtained without the correction for the production of C₂H$_{4}^{+}$ from the secondary reaction of CH$_{2}^{+}$ + CH₄. See the text. ^bThe temperature of 380 K is converted from E_cm = 0.05 eV.

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Laser-based VUV–PFI-PI technique was employed to prepare reactant N$_{2}^{+}$ ions in single-vibrational quantum states with high-purity, high-intensity, and high kinetic resolution, allowing the experimental investigations of the vibrationally selected ion–molecule reaction N$_{2}^{+}$(X²Σ$_{\rm g}^{+}$; v⁺ = 0–2) + CH₄ in a wide E_cm range from 0.05 to 10.00 eV. Three product channels, which lead to the respective formations of CH$_{3}^{+}$, CH$_{2}^{+}$, and N₂H⁺ ions, are observed. The σ_v+ values for these product channels are found to exhibit complicated vibrational dependences and vibrational inhibition for the N$_{2}^{+}$ + CH₄ reaction is clearly evident. The σ₀(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺) values determined in the present study are larger than those reported in the guided ion beam study (Nicolas et al. 2003) and the predictions based on the LGS model (Stevenson & Schissler 1958). After correcting for the secondary reactions involving CH$_{3}^{+}$ and CH$_{2}^{+}$, the branching ratios for the three primary product channels [σ_v+(CH$_{3}^{+}$):σ_v+(CH$_{2}^{+}$):σ_v+(N₂H⁺)]/σ_v+(CH$_{3}^{+}$ + CH$_{2}^{+}$ + N₂H⁺) determined here are different from those reported available in the literature. The lack of vibrational and kinetic energy dependences observed here are consistent with the result of previous study (Nicolas et al. 2003). Rigorous theoretical treatments are needed to fully understand all the phenomena observed. The branching ratios obtained in this study should be useful for the modeling of ion and neutral densities in the atmosphere of Titan. The cross-sectional data obtained in the present work should be useful for benchmarking theoretical predictions for ion–neutral collision dynamics.

This work was supported by the NASA Planetary Atmospheres Program Grant No. 07-PATM07-0012. The construction of the DQDO apparatus used in this study was financed by the U.S. Department of Energy–Basic Energy Sciences (DE-FG02-02ER15306).