Branching Ratio for O + H3 + Forming OH+ + H2 and H2O+ + H

The gas-phase reaction of O+H3+ has two exothermic product channels: OH+ + H2 and H2O+ + H. In the present study, we analyze experimental data from a merged-beams measurement to derive thermal rate coefficients resolved by product channel for the temperature range from 10 to 1000 K. Published astrochemical models either ignore the second product channel or apply a temperature-independent branching ratio of 70% versus 30% for the formation of OH+ + H2 versus H2O+ + H, respectively, which originates from a single experimental data point measured at 295 K. Our results are consistent with this data point, but show a branching ratio that varies with temperature reaching 58% versus 42% at 10 K. We provide recommended rate coefficients for the two product channels for two cases, one where the initial fine-structure population of the O(3 P J ) reactant is in its J = 2 ground state and the other one where it is in thermal equilibrium.


INTRODUCTION
At the low temperatures typical of diffuse and dense molecular clouds (∼ 10 − 100 K), gas-phase formation of water is dominated by a sequence of exothermic ionneutral reactions (van Dishoeck et al. 2013).Two parallel formation pathways have been identified: One pathway proceeds via the reaction O + H + 3 → OH + + H 2 + 0.66 eV (1a) which is the focus of the present paper.The quoted energies represent the exoergicities of the reactions provided by Milligan & McEwan (2000).The other pathway proceeds via cosmic-ray ionization of O to O + or endothermic charge transfer with H + , produced by cosmic ray ionization of H and H 2 , and the subsequent reaction (Bulut et al. 2015;Kovalenko et al. 2018) Both pathways are followed by the reactions (Tran et al. 2018;Kumar et al. 2018) Dissociative recombination (DR) of electrons with H 3 O + then leads to the formation of H 2 O (Novotný et al. 2010).Two other important ingredients for an accurate gas-phase reaction network for forming water are the DR rate coefficients leading to the destruction of OH + (Amitay et al. 1996;Stroe & Fifirig 2018) and H 2 O + (Rosén et al. 2000;Nkambule et al. 2015).
The various routes of interstellar water chemistry, including reactions (1)-(3), have been reviewed by van Dishoeck et al. (2013van Dishoeck et al. ( , 2021)).The branching ratio for reaction (1b) is particularly important for describing the ortho-to-para ratio of water in interstellar clouds (Faure et al. 2019).Furthermore, the observed abundances of OH + , H 2 O + , and H 3 O + are used to infer the cosmic-ray ionization rate (Hollenbach et al. 2012;Indriolo et al. 2015;Neufeld & Wolfire 2017;Indriolo et al. 2018).At temperatures of ∼ 250 K, endothermic neutral-neutral reactions such as O + H 2 → OH + H become accessi-ble and dominate the gas-phase water formation process (van Dishoeck et al. 2021).This sets an upper limit for the temperature range of interest for reactions (1)-( 3).
In the present paper, we investigate the temperaturedependent thermal rate coefficients and branching ratios for reactions (1a) and (1b).We derive our results from the merged-beams experiment performed by de Ruette et al. (2016).In their work, they derived the thermal rate coefficient for the sum over both product channels, but not those resolved by product channel.We provide the relevant details of the experimental data set in Sec. 2. In Sec. 3 we present our results and compare them to the data available in the literature.Lastly, in Sec. 4 we discuss possible implications of our results on astrochemical models.

EXPERIMENTAL DATA
In the merged-beams experiment of de Ruette et al. ( 2016), a beam of atomic oxygen was overlapped with a beam of H + 3 at a well-defined relative collision energy.The product ions, either OH + or H 2 O + , were counted, normalized to the intensities of the two parent beams and the interaction volume, and corrected for transmittance and detection efficiencies.The particle densities in the interaction volume were low enough to exclude the formation of H 2 O + by sequential collisions.
From the data, absolute cross sections as a function of the relative collision energy, E r , were derived for each product channel individually.The range of E r was 3.5 meV to 15.5 eV and 3.5 meV to 130 meV for the OH + and H 2 O + products, respectively.At values of E r higher than the ones investigated, the individual cross sections were smaller than the detection sensitivity of the experiment.
The data for each product channel was parameterized by the fit function Here, x = {OH + , H 2 O + } refers to reactions (1a) and (1b), respectively, σ x is in units of cm 2 , and E r is in eV.
The ∼ E −2/3 r scaling in the limit of E r → 0 reflects the effect of the long-range charge-quadrupole interaction between the H + 3 ion and the oxygen atom, as was discussed by Klippenstein et al. (2010).The fit parameters are given in Tab. 1.The total uncertainty of the cross sections was given by the fitting uncertainty and the relative systematic uncertainty of 13%, both summed in quadrature.
Considering the astrochemical motivation of this study and the range of measured collision energies, we derived translational rate coefficients, k tr x (T ), in the temperature range of T = 10 − 1000 K by convoluting each cross section times the relative collision velocity, σ x (E r ) × v r , with a Maxwell-Boltzmann distribution.
The uncertainties of the rate coefficients were propagated from the total uncertainties of the cross sections.Furthermore, we define the branching ratios, f x (T ), as the relative yields, The uncertainty of f x (T ) is solely affected by statistical fluctuations, while the systematic uncertainty cancels out.In the considered temperature range, the relative uncertainties of f OH + and f H2O + range from 3 to 5% and 5 to 12%, respectively, while the absolute magnitude of the uncertainty is identical for both branching ratios.
To understand the relation between k tr x (T ) and the thermal rate coefficient, k x (T ), we will discuss the role of the internal excitation of the two reactants in Secs.2.1 and 2.2, respectively.

The H +
3 reactant The merged-beams experiment of de Ruette et al. ( 2016) was performed with an internally excited H + 3 beam.Most of the possible influences of this internal excitation on the measured merged-beams rate coefficient were discussed in their publication.In the experiment, the internal temperature of the H + 3 ions was estimated to be T int ≈ 2500 − 3000 K.In Hillenbrand et al. (2019), we performed a more detailed analysis of the H + 3 internal temperature and its dependency on the H 2 pressure in the ion source.From these results we confirmed that the H 2 pressure applied in the measurements of de Ruette et al. ( 2016) corresponds consistently to the previously estimated internal temperature.Here, we discuss an additional aspect of the H + 3 internal temperature that was not considered in de Ruette et al. (2016).
For comparison, the exothermic reaction of C + H + 2 → CH + + H was studied in Hillenbrand et al. (2020).In that reaction, a low-lying endoergic reaction channel forming C + + H + H is energetically accessible at zero translational energy, provided that the internal excitation of the H + 2 reactant is sufficiently high.We found that this considerably reduced the measured mergedbeams rate coefficient for all translational energies investigated.
For the reaction studied here, the lowest endoergic channel is (de Ruette et al. 2016) We can estimate the fraction of H + 3 ions, whose internal energy is above this threshold, E int > E th = 1.77 eV, for a given internal temperature of T int by integrating the Boltzmann distribution over the internal energy, Based on the partition function provided by Kylänpää & Rantala (2011), T int = 2500 and 3000 K correspond to mean internal energies of E int = 0.64 and 0.86 eV, where 6% to 13% of the H + 3 ions have an internal energy above E th , respectively.A part of this fraction can potentially form OH + H + 2 , even at the lowest measured translational energies.As a worst-case scenario, we can assume that all reactions of H + 3 ions with E int > E th do not contribute to reactions (1a) or (1b).This would mean that the cross sections and rate coefficients reported by de Ruette et al. ( 2016) need to be scaled up by a factor 1.06 to 1.15.This scaling lies well within the total experimental uncertainty limits.Moreover, it affects both channels in the same direction and therefore does not affect the branching ratios.

The O 3 P J reactant
In de Ruette et al. (2016), the atomic oxygen beam was generated through laser detachment of an oxygen anion beam (O'Connor et al. 2015b).The resulting oxygen atoms were in the 3 P J ground term and the fine structure levels were populated according to their multiplicity, with fractional populations being 5/9, 3/9, and 1/9 for J = 2, 1, and 0, respectively.This statistical population was verified at the few percent level in the experiment of Génévriez et al. (2018).
For O( 3 P J ), J = 2 represents the ground level, while the J = 1 and the J = 0 levels are excited by E 1 = 19.6 meV and E 0 = 28.1 meV, respectively (Lique et al. 2018).The three fine-structure levels comprise a total of nine magnetic sublevels.As first pointed out by Gentry & Giese (1977), only the three sublevels corresponding to J = 2 with M J = ±1 or M J = 0 correlate to the reactive 3 Σ potential energy surface (PES).The other six sublevels all correlate with the nonreactive 3 Π PES (Gentry & Giese 1977;Bettens et al. 1999;Klippenstein et al. 2010).Since both product channels only proceed on the 3 Σ PES, the branching ratio of the product channels is independent of the initial fine-structure population.This aspect was overlooked by de Ruette et al. ( 2016) and prevented them from deriving thermal rate coefficients for the individual product channels.
Two astrochemical scenarios for the fine-structure level population may be of interest: Either only the J = 2 ground level is populated or the fine-structure level populations are in thermal equilibrium.Which of the two cases is applicable actually depends on the particle density.According to Lique et al. (2018), atomic oxygen is thermalized only at H or H 2 densities on the order of 10 6 − 10 7 cm −3 .
The conversion of the measured translational rate coefficients into thermal rate coefficients assuming a statistical population of the fine-structure levels in the merged-beams experiment and a thermal population in the astrochemical environment is (de Ruette et al. 2016) Here, k B is the Boltzmann constant.For the scenario of a pure O( 3 P 2 ) reactant, the relation reduces to k x (T ) = k tr x (T )×9/5.As discussed above, the rate coefficients for O( 3 P 1 ) and O( 3 P 0 ) reactants are zero for both scenarios.

Summed over both product channels
The thermal rate coefficient summed over both product channels, assuming a thermal population of the O 3 P J fine-structure levels, has been discussed in detail by de Ruette et al. (2016).The temperature dependency of the thermal rate coefficient is mainly formed by the effect of the long-range charge-quadrupole interaction [see Eq. ( 4)], and the effect of the fine-structure population [see Eq. ( 8)].The results were compared to two published experimental data points, both measured at room temperature: Fehsenfeld (1976)  Thermal rate coefficient for the OH + + H2 channel (upper bold data) and the H2O + + H channel (lower fine data).Shown are: our results by the red solid lines, with the gray area indicating the total experimental uncertainty at one standard deviation; the results of Milligan & McEwan (2000) by the circular data points (shifted slightly in temperature for clarity); and the data implemented in the astrochemical models listed in Sec.3.2 by the green dashed lines.
flowing afterglow technique to measure the thermal rate coefficient summed over both product channels, and Milligan & McEwan (2000) applied a combined flowing afterglow/selected flow tube technique to measure thermal rate coefficients resolved by product channel.Both methods are such that the translational temperature and the internal temperature of both reactants were in thermal equilibrium.The results of de Ruette et al. (2016) were in good agreement with the measurement of Fehsenfeld (1976) and in reasonable agreement with the measurements of Milligan & McEwan (2000).Furthermore, the theoretical rate coefficients of Bettens et al. (1999) and Klippenstein et al. (2010) had the same temperature dependency as the result of de Ruette et al. ( 2016), but were overall a factor of about 1.5 higher.Following the discussion of Sec.2.1 it is unlikely that such a discrepancy was caused by the internal excitation of the H + 3 beam in the experiment.

Resolved by product channel
The thermal rate coefficient resolved by product channel, derived from the data of de Ruette et al. (2016), are shown in Fig. 1.Considering the mutual uncertainties, they agree reasonably well with the measurement of Milligan & McEwan (2000) at 295 K. Astrochemical models such as UMIST (McElroy et al. 2013), KIDA (Wakelam et al. 2015), and UGAN (Hily-Blant et al. 2018) implemented channel resolved rate coefficients using the total reaction rate coefficient of Klippenstein et al. (2010), the branching ratio from Milligan & McEwan (2000), Figure 2. Branching ratio expressed as relative yield for the two product channels.Shown are: our results by the red solid line, with the gray area indicating the total experimental uncertainty at one standard deviation; the results of Milligan & McEwan (2000) by the circular data point; the results of Bettens et al. (1999) by the blue dotted line; and the ratio implemented in the astrochemical models listed in Sec.3.2 by the green dashed line.
and assumed the ratio to be temperature-independent.Our results are generally lower than the rates implemented in the models.Of particular note is the factor 1.7 difference at 10 K for the OH + + H 2 channel.

Branching ratio
The branching ratio defined in Eq. ( 5) is plotted in Fig. 2. For the H 2 O + + H product channel the branching ratio derived from our results ranges from (42 ± 3)% at 10 K down to (22±3)% at 1000 K.At 295 K, our result of (33±2)% is consistent with the value of (30±9)% measured by Milligan & McEwan (2000).Up to now, those astrochemical models that considered the branching ratio assumed it to be 30% independent of the temperature, based on the measurement of Milligan & McEwan (2000).
The branching ratio calculated by Bettens et al. (1999) was (5.6 ± 1.6)% for the H 2 O + + H product channel, and thus does not agree at all with either set of experimental results.For the analog reaction of C + H + 3 , we found a similar discrepancy between our experimental results in O'Connor et al. (2015a) and the theoretical results of Bettens & Collins (1998, 2001).These findings may suggest a shortcoming of the classical trajectory simulations and the PES used.The good agreement for the branching ratio for O + H + 3 from the experimental results of Milligan & McEwan (2000) and our results in de Ruette et al. (2016), which used two different experimental methods with differing systematics, and for C + H + 3 from Savić et al. (2005) and ours in O'Connor et al. (2015a), which also used two different experimen- tal methods with differing systematics, suggest that the discrepancy is not an experimental issue.

Recommended rate coefficients
We used the Arrhenius-Kooij formula, to parameterize our results for the two product channels in the temperature range of 10 to 1000 K for implementation into astrochemical models.The fit parameters, α, β, and γ, are shown in Tab. 2 for the two cases of the O( 3 P J ) level population discussed in Sec.2.2 and the two product channels.The fits describe our results to better than 5% for reaction (1a) and to better than 10% for reaction (1b).
Resolved by the nuclear-spin states, reactions (1a) and (1b) read where p-signifies para and o-signifies ortho.In reactions ( 10) and ( 11), the numbers given in squared brackets represent the statistical factors resulting from the nuclear-spin selection rules (Oka 2004).In nuclear-spin state resolved astrochemical networks, the rate coefficients are typically scaled by multiplying the parameters α with the statistical factor while the parameters β and γ are considered to be independent of the spin states (Majumdar et al. 2017;Hily-Blant et al. 2018).
This approach is justified for reactions where the exoergicity does not differ significantly between different spin-resolved product channels.The same approach can be applied to our results given in Tab. 2 and the resulting nuclear-spin-resolved rate coefficients can be implemented into models studying the ortho-to-para ratio of gas-phase formed water (Faure et al. 2019).

ASTROCHEMICAL IMPLICATIONS
In de Ruette et al. ( 2016), the derived thermal rate coefficient summed over both product channels was implemented into the KIDA model (Wakelam et al. 2015), and potential implications were studied for the predicted abundances of H 3 O + , H 2 O, and other molecules downstream the reaction chain.Here, we briefly discuss the relevance of the O + H + 3 branching ratio along the following simplified reaction chain: For typical astrochemical environments, the H 2 density is high enough such that the H 2 O + formation through the intermediate step of OH + formation proceeds with an effective rate coefficient comparable to the direct formation pathway.In this case, including the branching ratio decreases the predicted OH + abundance, but not the H 2 O + abundance nor subsequent products along the reaction chain, such as H 3 O + and, prominently, H 2 O.However, in those scenarios where the destruction of OH + by DR plays a significant role, direct formation of H 2 O + presents a bypass with respect to the OH + destruction by DR, and thus may enhance the abundance of H 2 O + and its subsequent reaction products.reactants, but we find that this has no significant effect on the derived rate coefficients.
Up to now, the general understanding for the branching ratio of these reactions relied solely on the fixed temperature measurement of Milligan & McEwan (2000) at 295 K.At that temperature, we found a branching ratio that is consistent with the one implemented in commonly used astrochemical models, but we find an enhanced yield for the H 2 O + + H product channel towards lower temperatures.Our results underline the impor-tance of including both product channels into reliable models.
This research was supported, in part, by the NSF Division of Astronomical Sciences Astronomy and Astrophysics Grants program under AST-2002461.X. U. is a Senior Research Associate of the Fonds de la Recherche Scientifique-FNRS.
Figure1.Thermal rate coefficient for the OH + + H2 channel (upper bold data) and the H2O + + H channel (lower fine data).Shown are: our results by the red solid lines, with the gray area indicating the total experimental uncertainty at one standard deviation; the results ofMilligan & McEwan (2000) by the circular data points (shifted slightly in temperature for clarity); and the data implemented in the astrochemical models listed in Sec.3.2 by the green dashed lines.
experimental data of de Ruette et al. (2016), we have derived temperature-dependent thermal rate coefficients for reactions (1a) and (1b).The experimental data were measured with internally excited H + 3