As already mentioned in the previous section, in the DC mode we have measured absolute values of the cross sections as a function of the collision energy E_CM at two selected photon energies: E_phot = 13.78 eV (no vibrational excitation of the CO2+ cation) and E_phot = 16.48 eV (some excitation to high vibrational levels). The main reaction products observed are due to the CT and deuterium-atom-transfer channels (1) and (2), respectively:

Also, small amounts of CD3+, and minimal amounts of CD₃CO2+ are detected and attributed to the following channels (3), (4) and (5):

Using literature values (taken from NIST Chemistry Webbook¹, with the exception of some products as specified in the following) for the standard enthalpies of formations (Δ_fH°) of reagents and products we can assess that both channels (1) and (2) are exothermic, while channels (3) and (4) are endothermic. In particular, the CT channel (1) has a reaction enthalpy Δ_rH° = −1.17 eV, while Δ_rH° for (2) is equal to −1.26 eV, assuming that HOCO⁺ has the structure of the hydroxyformyl cation (Holmes et al., 2006). The production of CD3+ can derive either from D⁻ transfer process (3) or from dissociative CT (4). In the former case, the DOCO radical might be formed in association with the methyl cation, and the overall process is calculated to be endothermic by about 0.56 eV, using the heat of formation of HOCO as reported in Francisco et al. (2010). In the latter case, the methyl cation derives from dissociation of the CT product and the process is endothermic by about 0.61 eV.

The CD₃CO2+ formation can be due to D loss from the ion-molecule adduct CO2+-CD₄ (reaction 5). We can attempt to estimate the reaction enthalpy of (5) assuming that CD₃CO2+ has the structure of the methoxycarbonyl cation [an average value for its heat of formation Δ_fH°(CH₃OCO⁺) is 5.57±0.19 eV, as reported in Holmes et al., 2006] to get Δ_rH° = −1.10 eV. We note in passing that the adduct CO2+-CD₄ was not observed, as expected, as the CD₄ pressure in the scattering cell used throughout the experiments (about 2 × 10⁻⁴ mbar) was too low to allow for secondary collisions for its stabilization.

Cross sections for products CD4+, DOCO⁺ and CD3+ as well as CD5+ (from secondary reactions of the primary CD4+ and DOCO⁺ products) measured as a function of the collision energy when the reagent CO2+ ion is in its ground vibrational state (i.e., at E_phot = 13.78 eV) are reported in Figure 2, while results for E_phot = 16.48 eV are shown in Figure 3. The cross section for CD5+ was measured to correct the absolute value of the cross section for reactions (1) and (2) due to product ion losses via the highly efficient secondary reactions operative at the deuterated methane pressures used:

with k = 1.1 × 10⁻⁹ cm³·molecule⁻¹·sec⁻¹ for reaction (6) (Anicich, 2003) and k = 7.2 × 10⁻¹⁰ cm³·molecule⁻¹·sec⁻¹ for reaction (7) (Anicich, 2003). The measured CD5+ yields have been redistributed among the CD4+ and DOCO⁺ products on the basis of the CD4+/DOCO⁺ yield ratio (that changes with collision energy from ~2 at low energies up to ~7 at high energies) and of the different rate coefficients for reactions (6) and (7). In Figures 2, 3 the uncorrected and corrected cross sections for CD4+ are labeled as “CD4+” and “CD4+ corr” respectively, and the same notation is used for DOCO⁺.

The sudden increase in the cross section shown for CD4+ and CD5+ products at E_CM ~ 0.3 eV (clearly visible in the data of Figure 2, but also present in the data of Figure 3) is an instrumental effect due to a decrease in the collection efficiency for “slow” products. In particular, when product ions are produced at very low velocities in the lab frame, they have a chance to move backwards in the 1st octopole (O1) in the opposite direction from the parent ions, and they then face the last electrode before this octopole, L3, which is set to a potential of −0.4 V. As these ions are produced in O1, their fate depends on their initial kinetic energy and the relative values of the O1 and L3 potentials. At high collision energies, the mean potential of O1 is very low (negative values) and all product ions going back in O1 are reflected on L3 and later detected. At low collision energies, the O1 potential can be higher than that of L3, and backward product ions can be lost, accounting for the step in the product yield observed below collision energies of ~0.3 eV. To correct for such effect, we have rescaled the data measured at E_CM ≤ 0.3 eV by a fixed multiplication factor, chosen equal to 1.12 to match the data measured at E_CM < 0.3 eV with those measured at higher collision energy. Implicit in this way of rescaling data is the assumption that the number of product ions lost at low collision energy is independent on the collision energy. The corrected data (reported only for CD4+ cross sections corrected for the presence of secondary reactions leading to CD5+) are shown as dashed lines in Figures 2, 3.

According to the above-mentioned thermochemistry, the formation of CD3+ via either (3) or (4) is endothermic and the cross-section for its formation, when CO2+ is generated with no vibrational excitation (see green diamonds in Figure 2), shows the expected threshold behavior, with an appearance energy compatible with the endothermicity. Above threshold, the cross section increases accordingly with collision energy. The small amount of signal observed below the threshold is an artifact due to the tail of the very intense mass peak at 20 m/z (CD4+). Data measured at E_phot = 16.48 eV show non-negligible cross sections even at low E_CM, thus indicating that vibrational excitation of the CO2+ cation can promote the endothermic channel.

At E_phot = 13.78 eV and at the CD₄ pressure used, the yield of CD₃CO2+ was below the detection limit, while at E_phot = 16.48 eV it was possible to measure a cross section for this very minor channel (data for CD₃CO2+ in Figure 3 are multiplied by 300 to be able to show them in the same scale of the other products).

In Table 2 results at the two photon energies are summarized by reporting the branching ratios (BRs) for the observed product channels and the energy-dependent rate constants. BR for the i-th channel have been calculated from the absolute cross sections according to the expression:

The energy-dependent total rate constants k_tot(E_ave) have been estimated using the expression k_tot(E_ave) = 〈V〉 · σ_tot, were σ_tot is the total reaction cross section (i.e., ∑σ_i), as measured in this work (see data in Figures 3, 4) and < v> is the average relative velocity that can be estimated from the collision energy E_CM (see Ervin and Armentrout, 1985 and Nicolas et al., 2002 for a more detailed treatment). While the total rate constants do not change (within the error bars) when increasing the amount of internal excitation of the CO2+ cation (compare the values at different photon energies but same E_ave), a slight change in the BRs is observed when increasing the collision energy, which favors the production of CD4+ (and CD3+) over that of DOCO⁺.

Interestingly, our results for the branching ratios (see Table 2) show reaction (1) to be the dominant channel at all the explored collision energies, in net disagreement with some of the existing values for the branching ratios (see Table 1). As already mentioned, in fact, in the literature there is a spread of the branching ratios for reaction (1) and (2) ranging from 1:0 (Durup-Ferguson et al., 1983) to 0.6:0.4 (Smith et al., 1978), to 0.5:0.5 (Copp et al., 1982), to 0.28:0.72 (Tsuji et al., 1994) and 0.25:0.75 (Huntress et al., 1980), and finally to 0:1 (Harrison and Myher, 1967; Rakshit and Warneck, 1980). We provide here some explanations for the differences observed between our experiment and previous ones:

1. In addition to working with CD₄, in our experiment we perform a mass selection of the parent ion before reaction. In this way, we eliminate the contribution due to the ¹³CO2+ parent ion that appears at the same m/z as the HOCO⁺ product (from residual not fully deuterated methane) and represents ~1% of the parent ion intensity. Additionally, our experimental procedure consists in measuring both parent and product ion yields first with the target gas in the collision cell, secondly with the target gas in the chamber. In this way, we correct for any contribution of “impurities” coming from the source at the same mass as the product (namely ¹³CO2+/HOCO⁺). In one of the earlier papers (Tsuji et al., 1994), the experiment is performed without parent ion mass selection, and no correction for ¹³CO2+ is mentioned. Hence the claimed HOCO⁺ branching ratio (0.72) is most likely overestimated. In Durup-Ferguson et al. (1983), the parent ion mass selection is performed, although no indication is given about the mass resolution. In Rakshit and Warneck (1980), a mixing of CO2+, CO₂CO2+ and H₂O⁺ parent ions are used. The values from Huntress et al. (1980) are given without any experimental details, for which a reference is given to an earlier paper (Huntress, 1977) where the ICR set-up is described. However, the earlier paper does not contain data for the title reaction, and it is impossible to infer whether and how the ¹³CO2+ contribution was taken into account.

2. In our experiment, we keep the target gas pressure as low as possible to limit the number of secondary reactions. Some of the earlier works (Harrison and Myher, 1967; Kasper and Franklin, 1972; Tsuji et al., 1994) have a pressure in the reaction cell higher than ours by a factor 30-50, with about the same cell length. Such differences may lead to underestimating the BR for CH4+ if secondary reactions are not adequately accounted for (as done in our study).

3. In our experiment, we use a pure target gas, while some of the earlier works perform mass spectrometry studies in mixtures of gases. If some CO₂ is present in the region where CH4+ products are generated by the CO2+ + CH₄ reaction, the CH4+ will be easily consumed by the efficient reaction CH4+ + CO₂ → HOCO⁺ + CH₃ (k = 1.2 × 10⁻⁹ cm³·molecule⁻¹·s⁻¹) that will produce HOCO⁺, leading to a negative bias in the CH4+/HOCO⁺ ratio. This is an issue in Rakshit and Warneck (1980) as highlighted by Copp et al. (1982), where CO₂ is present in the reaction cell, as well as in Ryan and Harland (1974), where mixing of CH4 and CO₂ occurs in the reaction region, in Tsuji et al. (1994), Harrison and Myher (1967) and Kasper and Franklin (1972).

4. In our experiments we mass select ionic products. Hence we can directly give BRs among different channels. In some of the flow/drift tube experiments, the reaction rate constants are measured by observing the decline of the primary ion signal upon addition of the neutral gas. For instance, in Durup-Ferguson et al. (1983) no mention is made about the mass detection of products, as if the authors have assumed the exclusive formation of CH4+ via non-dissociative CT, not considering the possibility that HOCO⁺ might be produced.

In the TPEPICO mode, we recorded cross sections for the reaction of CO2+ ions in the (0,0,0) ground state and in two vibrationally excited states: (0,1,0) with one quantum of bending vibration and [(1,0,0) + (0,0,1)] corresponding to a combination of the symmetric and antisymmetric stretching vibration. Cross sections were measured for products CD4+, DOCO⁺ and CD3+ as well as CD5+ (from secondary reactions of the primary CD4+ products, see above). The ion yield for product CD₃CO2+ was too low to be detectable in coincidence. For most of the other products, reactive cross sections were measured at two different collision energies E_CM = 0.17 ± 0.02 eV and 1.34 ± 0.01 eV and results are shown in Figures 4, 5. Despite the larger uncertainties (due to the low S/N ratio in the coincidence mode) cross section measurements are consistent with results obtained in the DC mode. In particular, when converting cross sections reported in Figure 4 for CO2+ at low collision energy and in the (0,0,0) ground state we obtain the following BRs: CD4+ (0.75 ± 0.25), DOCO⁺ (0.25 ± 0.11) and CD3+ (0.00 ± 0.03), entirely consistent, within the error bars, with the data obtained in the DC mode (see Table 2, second column from the left).

In addition, the TPEPICO results confirm that cross sections for the exothermic CT (1) and deuterium-atom-transfer (2) channels change very little with increasing vibrational excitation, and the increase is more evident in data taken at high collision energy (Figure 5). Cross sections for the endothermic channel leading to CD3+ increase with collision energy but they do not seem to depend strongly on the internal excitation of the ionic parent, at least for the low internal excitations here explored (i.e., maximum one quantum of vibrational excitation).

The observed small dependence of reactions (1) and (2) from CO2+ vibrational excitation requires some consideration. First of all, we note that our result is in agreement with a previous study (Durup-Ferguson et al., 1983) in which a drift tube technique is used, and the dependence of the reaction rate constant on the internal energy of the ions is examined by varying the mass of the buffer gas. Despite the limitations of the technique compared to our truly state-selection method, in Durup-Ferguson et al. (1983) the non-dissociative CT giving CH4+ plus CO₂ is found to occur at near the collision rate and to have little energy dependence and no measurable vibrational dependence.

We also note that, differently from the CH₄ case, vibrational excitation of CO2+ ions was found to enhance the CT reaction probability with O₂ (Durup-Ferguson et al., 1983; Ferguson et al., 1992; Viggiano and Morris, 1996; Nicolas et al., 2002). To rationalize such results, it should be considered that the two systems present several differences:

The inefficiency of the CT with O₂ is attributed to the non-resonant character of the reaction, i.e., to the fact that Franck-Condon factors for O₂ ionization at the ionization potential of CO₂ (13.78 eV) are close to zero (see for instance Wacks, 1964). On the other hand, it is known that for CH₄ the Franck-Condon factors are low at the ionization threshold and increase reaching a maximum in the region 13.5–14.5 eV (see for instance Stockbauer and Inghram, 1971). Thus, while in the CH₄ case CT can occur efficiently at long range via the direct mechanism previously described, for O₂ it should involve the formation of a collision complex. As tentatively explained and demonstrated in Ferguson et al. (1992), in the O₂ case a small amount in the stretching excitation of CO2+ can lead to an increase in the CT probability. Hence, CH₄ and O₂ are quite different reaction systems, and in the latter case, the effect of CO2+ excitation could be more pronounced than for a reaction already at the Langevin limit (as in CH₄).

More generally, the dynamics of CT processes is regulated by crossings among entrance and exit potential energy surfaces. When such crossings are occurring at distances for which the probability of electron transfer from one adiabatic PES to the other is unfavorable, the CT cross section will be very small even for exothermic processes (according to the Landau-Zener model for CT probability). The fact that increasing the vibrational excitation of the cation does not increase the CT cross section can be related to the fact that the crossing probability does not change much when increasing the vibrational excitation of CO2+, even though the exothermicity increases. Unfortunately, modeling the dynamics occurring on a CO2+- CH₄ multidimensional potential energy surface which includes vibrational excitation of CH₄ is not an easy task, and it is beyond the scope of our paper. We hope that our results will stimulate theoreticians and experts in ab-initio calculations to use this system as a test bench for theory.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.