Exchange and Inelastic OH+ + H Collisions on the Doublet and

Article pubs.acs.org/JPCA

Exchange and Inelastic OH+ + H Collisions on the Doublet and Quartet Electronic States Niyazi Bulut,*,† François Lique,*,‡ and Octavio Roncero*,§ †

Firat University, Department of Physics, 23169 Elazig̃, Turkey LOMC - UMR 6294, CNRS-Université du Havre, 25 rue Philippe Lebon, BP 1123−76 063, Le Havre, France § Instituto de Física Fundamental, CSIC, C/Serrano, 123, 28006 Madrid, Spain ‡

ABSTRACT: The exchange and inelastic state-to-state cross sections for the OH+ + H collisions are computed from wave packet calculations using the doublet and quartet ground electronic potential energy surface (PES) correlating to the open shell reactants, for collision energies in the range of 1 meV to 0.7 eV. The doublet PES presents a deep insertion well, of ≈6 eV, but the exchange reaction has a rather low probability, showing that the mechanism is not statistical. This well is also responsible of a rather high rotational energy transfer, which makes the rigid-rotor approach overestimate the cross section for low Δj transitions and for high collisonal energies. The quartet PES, with a much shallower well, also presents a low exchange reaction cross section, but the inelastic state-to-state cross sections are very well reproduced by rigidrotor calculations. When the electronic partition is used to obtain the total state-to-state cross section, the contribution of the doublet state becomes small, and the resulting total cross sections become close to those obtained for the quartet state. Thus, the total (quartet and doublet) cross sections for this open shell system can be reproduced rather satisfactorily by those obtained with the rigid-rotor approximation on the quartet state. Finally, we compare the new OH+−H cross sections with OH+−He ones recently computed. We found significant differences, especially for transitions with large Δj showing that specific OH+−H calculations had to be performed to accurately analyze the OH+ emission from interstellar molecular clouds.

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INTRODUCTION The launch of the Herschel satellite in 2010 opened a spectral domain hidden by the opacity of the Earth atmosphere. In this spectral region, many lines of light molecular hydrides were observed in different astrophysical regions,1−9 some of them for the first time like, for example, OH+. Hydrides play a central role in molecular astrophysics as significant reservoirs of heavy elements. Indeed, because hydrogen is much more abundant than any other element in the interstellar medium, hydrides are the first molecules to be formed and they constitute therefore sensitive tests of interstellar chemistry networks. In addition, the analysis of their rotational line emissions provides information about the physical conditions in a wide variety of interstellar environments, from hot photodissociation regions (PDR) to cold molecular clouds. In the gas phase, the formation of hydrides is generally initiated by the ion−molecule reactions:10 M + H3+ → MH+ + H 2

and photon-dominated regions (PDR), the reactions with molecular hydrogen M+ + H 2 → MH+ + H

also proceed rapidly. The methylidyne cation (CH+) has been one of the first molecules observed in space by Douglas and Herzberg11 and since then has been detected in many environments8,12−14 and is considered to be ubiquitous throughout the interstellar media. However, in hot environments where H3+ is absent, CH+ must be formed through the reaction in eq 2, which is endothermic by ≈0.374 eV.15 Several sources explaining the extra energy needed have been proposed.16−24 One of these mechanisms proceeds through collisions with vibrationally excited H2 populated by far ultraviolet (FUV) fluorescence.24,25 In addition, recent radiative transfer modeling using the stateto-state formation rate constants for the mechanism of eq 2,26 found that chemical pumping (formation of CH + in

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Special Issue: Dynamics of Molecular Collisions XXV: Fifty Years of Chemical Reaction Dynamics

which are generally rapid (M is an heavy element). These initial steps are followed by a series of hydrogen abstractions to form MHn+. At each stage, dissociative recombination with electrons produces neutral hydrides. At high temperature, e.g., shocks © 2015 American Chemical Society

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Received: June 2, 2015 Revised: July 20, 2015 Published: July 23, 2015 12082

DOI: 10.1021/acs.jpca.5b05246 J. Phys. Chem. A 2015, 119, 12082−12089

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The Journal of Physical Chemistry A

the two electronic states with those obtained from rigid rotor (hence, purely inelastic) results. The paper is then organized as follows. Computational Details describes the methods used, and the convergence details. In Results and Discussion, we discuss the results obtained for exchange and inelastic processes on the two electronic doublet and quartet states, considered here. Finally, in Conclusions, some conclusions are extracted.

rovibrationnally excited states) can explain the increase of the line fluxes of high-j lines of CH+. Another particularly interesting diatomic hydride is OH+, which initiates the oxygen chemistry and is considered a waterbuilding molecule. This system has been detected for the first time only very recently, because of the opacity of the Earth atmosphere. Until now, only a few rotational transitions among low rotational levels have been observed in interstellar and circumstellar environements.4,27−36 These observations were generally performed in hot PDRs, dominated by infrared and UV transitions. Because OH+ is very reactive and rapidly destroyed after its formation, its rotational populations may be also assumed to be driven by the chemical state-to-state pumping mechanism of eq 2, as it was for CH+. In a recent work37 the state-to-state cross sections for the chemical pumping mechanism of eq 2 were calculated and introduced into radiative transfer models to simulate the rotational emission of OH+ from PDR’s. In addition, the radiative Einstein coefficients for infrared (OH+(3Σ− ← 3Σ−)) and UV (OH+(3Π ← 3Σ−)) transitions were calculated together with the inelastic collisional rates for OH+(3Σ−)−He collisions. These last values were scaled to get a rough estimate of the rate coefficients for the collisions of OH+(3Σ−) with H and H2. Surprisingly, it was found that the inelastic rates dominate over the chemical pumping ones for determining the emission from low rotational states of OH+(3Σ−). For higher rotational states, chemical pumping may dominate, as occurs for CH+. Unfortunately, for OH+(3Σ−) there are no observations available for intermediate and high excited rotational states. Such a conclusion clearly indicates that the two processes, inelastic and reactive, compete in determining the rotational populations of OH+ and that both have then to be calculated accurately for modeling of the physical conditions and the abundance of OH+ in the different astrophysical environments. In particular, it was found that the excitation of the first rotational levels is primarily driven by inelastic collisions with electrons and atomic hydrogen. In many cases the inelastic rate coefficients with H and H2 used in these astrophysical models are scaled from those obtained with the He collisional partner.37 However, this approximation may be too crude for the OH+−H collisional system and may need to be checked.38 First, in OH+ + H collisions, in addition to the inelastic process, there is a reactive channel corresponding to the exchange of hydrogen that may affect strongly to the inelastic rates, making the commonly used rigid-rotor approximation fail. Second, in the case of open shell hydrides like OH+(3Σ−), there are several electronic states, each one having different rate coefficients. Third, the OH+ + H collisions can be reactive (the endothermicity being ≃0.5 eV), leading to a competition between inelastic and reactive processes at high energies. The aim of this work is to calculate state-to-state cross sections for the inelastic and exchange processes in OH+(3Σ−,v0 ,j0 ) + H ↔ H + OH+(3Σ−,vf ,jf )

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COMPUTATIONAL DETAILS Potential Energy Surfaces. In this work, we use the PES of the ground quartet and doublet electronic states of the H2O+ ́ system, which were previously calculated by Martinez et al.39 40 and Paniagua et al., respectively. These two PESs correlate to the two H + OH+(3Σ−) channels corresponding to inelastic and exchange. The third rearrangement channel, correlates to the products O+(4S) + H2 and O(3P) + H2, both of which are considerably higher in energy, at ≈0.5 and 2 eV above the inelastic threshold, respectively. In the present calculations we shall calculate the cross sections up to 0.75 eV. Therefore, this third channel be energetically accessible only in the case of the quartet PES. However, its contribution is very small. For the quadruplet, the reaction probability is less than 5% for collision energies higher than 0.5 eV and J = 0. For the doublet, the O(3P) + H2+ threshold is at higher energies. These two reactive channels are negligible at low temperatures and are not of interest in this work.” The topologies of the two PESs are very different, as shown in the minimum energy path (MEP) obtained for fixed H−O− H angles, joining the inelastic and exchange channels, in Figure 1.

Figure 1. MEPs of the quartet (red) and doublet (blue) PES of OH+ (3Σ−) + H obtained at frozen H−O−H angles Θ, indicated in each panel. Distances are in au, and eneries, in eV.

The doublet PES presents a very deep insertion well, ≈6 eV deep, at Θ = 120°, but extending over a wide angular interval, [30, 180°]. For shorter angles the exchange reaction presents a relatively high barrier. The deep well makes us think that the dynamics on this surface may be dominated by resonances, which may be observed in the dynamics of the exchange reaction. The quartet PES shows a different behavior. There is a relatively high barrier between the two rearrangement channels

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on the doublet and quartet ground electronic states. For this purpose we have performed quantum time-dependent wave packet (WP) calculations considering the inelastic and exchange processes simultaneously. In the calculations, we have used recent potential energy surfaces (PES) calculated for the quartet39 and doublet40 electronic states. Then, we compare the cross section for the exchange and inelastic processes for 12083


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The Journal of Physical Chemistry A for nearly all angles, except for a narrow region around Θ = 20° where there is no barrier but a shallow well. In this PES, there is also a well of ≈0.5 eV at both sides of the barrier separating the inelastic and exchange channels. This may also indicate that for this surface there will be resonances due to these two wells, but they are not expected to mediate the exchange reaction, in contrast to the doublet case. The important differences between the two PES indicate that the reaction mechanisms are going to be rather different, forcing us to analyze the convergence of the dynamical calculations separately as discussed below. We also anticipate that the collisional excitation on both PES will be different. Wave Packet Calculations. The state-to-state cross sections for the inelastic and exchange processes are calculated using the usual partial wave expansion: π 1 σv0j → vf j (Ec) = 2 0 f k 2j + 1

Jmax

∑ ∑ J = 0 Ω 0, Ω f

Table 1. Parameters Used in the Wave Packet Calculations in Reactant Jacobi Coordinatesa rmin, rmax, Nr rabs, Ar Rmin, Rmax, NR Rabs, AR Nγ R0, E0, ΔE R′∞ Vcut Elcut Ωmax Ω′max

doublet 0.001, 25,512 15, 2 2 × 10−6 0.001, 32, 620 22, 2 × 10−6 200 in [0, π/2] 21, 0.3, 0.12 12 4.3 5 19 25

a

The function used for the absoprtion has the form X − Xabs n ⎤ ⎡ f (X ) = exp⎣⎢− AX ⎦⎥ for X > Xabs and f(X) = 1 elsewhere, b with X ≡ R and r, with n = 4 and b = 2. Distances are in Å and energies in eV.

(

(2J + 1)PvJ0j Ω0 → vf j Ω f (Ec) 0

quartet 0.01, 36, 360 16, 2 × 10−6 0.01, 56, 512 36, 2 × 10−6 160 in [0, π/2] 34, 0.3, 0.12 11 4.3 5 15 25

f

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where J is the total angular momentum quantum number, and Ω0, Ωf are the projections of the total angular momentum on the reactant and product body-fixed z-axis, respectively. (v0, j0) and (vf, jf) denote the initial and final vibrational and rotational quantum numbers of the diatomic fragments. k2 = 2μrEc/ℏ2 is the square of the wave vector for a collision energy Ec, and PJv0j0Ω0 → vfjfΩf(Ec) are the transition probabilities, i.e., the square of the corresponding S-matrix elements. In all the calculations, the fine structure splitting of the OH+ was neglected. However, collisional data between fine structure levels of OH+ levels can be obtained using approximate posttreatment as described in Faure and Lique41 The calculations for each partial wave J are done with a time dependent WP method, using a modified Chebyshev integrator.42−48 The WP is represented in reactant Jacobi coordinates in a body-fixed frame. At each iteration, a transformation to exchange products Jacobi coordinates is performed to analyze the final flux on different OH+(vf, jf) channels, using the method described by Gómez-Carrasco and Roncero.49 The calculations are performed using the MADWAVE3 program.50 The parameters used in the propagation are listed in Table 1, being different for the two PESs used. To get reliable results at moderately low kinetic energies, a careful convergence analysis has been done. The main sources of errors in iterative time dependent propagations are longlived resonances and low kinetic energies, both requiring long propagations on dense grids extending over large intervals to get energy resolution. At low kinetic energies, particular attention has to payed to the absorption at the edges of the grids to avoid undesired reflections. To avoid this, small exponential factors are used in the absorbing function that are applied on long absorption regions, sometimes longer than the interaction region we are interested in. To check the quality, the outgoing flux on all the accessible channels are summed. This sum has to be one and indicates when a propagation can be stopped. Thus, for total angular momentum J = 0, the propagation in the quartet state required 81 000 iterations, so that the total flux is 1 ± 1% for energies E > 0.03 eV. In the interval 0.01−0.03 eV this error increases up to 4%, and below these energies, errors are even larger. The doublet case is particularly difficult, because the presence of such a deep well makes necessary the use of denser radial and angular grids and hence the absorption region had to be

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reduced to make the calculations feasible. Also, because the doublet PES presents more long-lived resonances, the propagation were longer, arriving up to 220 000 iterations. In this case the error on the total flux is larger than for the quartet, becoming 3−5% at some resonances for E > 0.1 eV and less than 10% for energies in the interval 0.01−0.1 eV. The largest source of error arises from the elastic channel. When real wave packet dynamics is used, the initial wave packet is a superposition of two complex Gaussian functions, one ingoing and the second outgoing, so that its sum is real. The only contribution of interest to extract the reaction probabilities is that coming from the ingoing component and has to be separated from the outgoing one. Using relatively broad energy distributions, this is difficult for low energies, because the fast components of the ingoing wave packet reach the slow components of the outgoing wave packet, producing an interference responsible for an important part of the error of the total flux at low energies. We have also performed time-independent close cloupling calculations using hyperspherical coordinates as implemented in the ABC code,51 to check the accuracy of these calculations, using the parameters of Table 2 and for J = 0. The state-to-state Table 2. Parameters Used in the ABC Time-Independent Calculations for Partial Waves J = 0 (All Parameters in Angstroms) hypershperical maximal radius, rmax no. of grid points in r no. of basis functions energy interval maximum rotational quantum no., jmax energy for basis cut/eV, emax

quartet

doublet

30.0 500 1290 0.0004 35 4.0

30.0 600 1856 0.0004 35 5.0

reaction probabilities obtained for J = 0 are compared in Figures 2 and 3 for the quartet and doublet states, respectively. For the quartet state, the low energy regions for low rotational excitation are shown. The agreement between WP and ABC results clearly improves with increasing energy and rotational excitation. For low energy some disagreement is found at some narrow resonances, but taking into account that the energy 12084


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Figure 2. Inelastic (left panels) and exchange (right panels) reaction probabilities obtained for J = 0 for the OH+ (v0 = 0, j0 = 0) + H collisions on the quartet state, as a function of collision energy, Ec, in eV, and different final rotational states. Blue lines correspond to WP calculations, and points, to ABC calculations.

Figure 3. Same as in Figure 2 but for the doublet electronic state. In this case, the ABC results are plotted with red lines for clarity.

value was well converged, as checked with a larger number of Ω’s for J = 30 and 40. However, for the doublet it was not possible to consider higher Ωmax because the calculations became extremely long. The sum in eq 4 needs to be done up to Jmax = 110 to get convergence for the inelastic term in the whole collision energy interval considered, up to Ec = 0.75 eV. The exchange probabilities become zero for J > 60, because the effective rotational barrier appears at shorter distances leading to higher barriers. The calculation of all partial waves in eq 4 is computationally very demanding. For this reason we have calculated the probabilities PvJ0j0Ω0→vf,jf,Ωf (Ec) for some selected J’s. The probabilities for intermediate J values are obtained by an interpolation based on the J-shifting approximation, as described previously.26,37 The probabilities directly obtained by WP calculations are those for J = 0, 1, 5, 10, 15, 20, 25, 30, 40, 50, ..., 110. The procedure is applied to exchange and inelastic probabilities.

grids used are not the same, the agreement is found to be excellent. The only exception occurs for the elastic channels, showing a larger error by the interference commented above. This disagreement does not affect the results discussed below because we are interested only in the inelastic cross sections. The convergence in the case of the doublet is more difficult because of the very deep well. In this case, the interference problem in the elastic channel is larger because the use of a denser grid makes it impractical to start the propagation at a longer distance, as done for the quartet state. WP and ABC calculations make use of different coordinates, which makes it even more difficult to reproduce the resonances exactly, corresponding to highly excited quasi-bound states. Assuming a larger error in the WP calculations, the ABC calculations also present some convergence problems, because the well depth of the triatomic system is larger than the dissociation energy of OH+, and hence the number of channels correlating to OH+ products is insufficient to warranty convergence over all the energy range. Nevertheless, the overall agreement between WP and ABC calculations is considered to be satisfactory. We also reiterate that the purely elastic cross sections are not the object of the present paper. For J > 0, the maximum number of helicities, Ω, included in the calculations are Ωmax = max(J, 15) for the quartet and Ωmax = max(J, 19) for the doublet. In the case of the quartet this

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RESULTS AND DISCUSSION On the Statistical Behavior. The reaction probabilities obtained for the two electronic states show many sharp peaks associated with resonances. In particular, the doublet case shows a marked high density of very narrow resonances, which may let us think that the reaction is mediated by resonances and that the mechanism may be statistical. If so, the dynamics

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The Journal of Physical Chemistry A would lose the memory of the initial state and the two equivalent asymptotes, inelastic and exchange, would be equally populated, the exchange probability being 1/2. This is by far not the situation here, as can be seen in Figure 4 where the total

Figure 4. Reactive hydrogen exchange probability for total angular momentum J = 0, and H + OH+ (v0 = 0,j0 = 0) → HO+ (vf, jf) + H summing over all final vf, jf channels, for the doublet electronic state, considering three different masses for the oxygen atom: mO = 16 (blue), mO = 4 (red), and mO = 1(black).

Figure 5. State-to-state integral cross section for the H + OH+ (v0 = 0, j0) → OH+ (vf = 0, jf) + H in the quartet state for j0 = 0 (top) and j0 = 1 (bottom). Each panel corresponds to a final rotational state of OH+ (vf, jf) arising in the inelastic (red) and exchange (blue) rearrangement channels. The black line corresponds to the inelastic cross section calculated in the rigid rotor approach as explained in the text.

exchange probability is shown in blue, with mO = 16. This exchange probability is less than 10% nearly in all the energy interval considered, and only at very low energies, below 0.01 eV, may reach values close to 0.5. The statistical mechanism would occur when the density of states is larger than their natural widths,52 provided that the collisional complex lives long enough to allow the energy transfer among all the modes of the system. Therefore, the characteristic lifetime depends on the strength of the couplings among the modes, and this ratio depends on different factors, such as collision energy, masses, etc. For example, as collision energy increases, the widths of the resonances become broader and the process become more direct, reducing the statistical character and hence the exchange probability, as shown in Figure 4. If the mismatch between the masses involved increases, the energy transfer becomes less efficient. In the present case the oxygen atom is much heavier than the hydrogen atoms. Reducing artificially the oxygen mass, to the values of mO = 4 and 1, makes that the exchange probability increases gradually, as shown in Figure 4. Thus, maximizing the energy transfer also favors the exchange probability and the statistical character of the reaction mechanism. Another factor is the number of rearrangement channels. In this case the O(3P) + H2+ channel is energetically closed. If this channel would be open, the density of states would increase and, more importantly, the anharmonicity would increase significantly, introducing a larger coupling among the vibrational modes. This is the situation of CH+ + H where the exchange probability is much higher.53 State-to-State Cross Sections. The state-to-state integral cross sections (ICS) for the H + OH+(v0 = 0, j0) collisions in the quartet states are shown in Figure 5 for j0 = 0 and j0 = 1, for different final rotational states of OH+ arising in the inelastic and the exchange mechanisms. Only results for vf = 0 are shown, because the vf = 1 channel opens at Ec ≈ 0.4 eV and it is nearly negligible.

The exchange cross section is about 10−20 times lower than the inelastic one for all the final jf. This inelastic/exchange ratio decreases with the decreasing of collision energy, because the exchange cross section decreases more rapidly with increasing enegy than the inelastic one. Inelastic ICSs dominate for two reasons. First the transition probabilities for each partial wave are larger for the inelastic processes than for the exchange, as shown for J = 0 in Figure 2. Second, the number of partial waves needed to get convergence is much higher for the inelastic process. Thus, it is needed to sum up to J = 110 in the inelastic case for Ec ≈ 0.75 eV, whereas the exchange process become closed for J > 60. On the basis of this dominance, we have also performed calculations of the inelastic process alone, within the rigid-rotor (RR) time independent approach (i.e., fixing the internuclear distance of the OH+ reactant). In the rigid rotor calculations, the standard time-independent coupled scattering equations were solved using the MOLSCAT code.54 The integration parameters were chosen to ensure convergence of the cross sections. In particular, a large number of closed channels had to be incorporated in the calculations because of the large well depth in the OH+−H PES. The rotational energy levels of the OH+ molecule were computed with the use of experimental spectroscopic constants of Horani.55 We used a total energy grid with a small steps to correctly describe the resonances (shape and Feshbach) that may appear in the cross sections at low and intermediate energies. The agreement between the rigid rotor results and the inelastic cross section is good. This agreement improves when one considers the sum of inelastic and exchange probabilities. This indicates not only that the exchange process is negligible but also that the anisotropy introduced by the exchange channel has a minor effect on the inelastic process for this 12086


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rotational energy redistribution would be statistical, the ICS would increase proportionally to 2jf + 1 simply as a consequence on the increase of the accessible final states. However, this is not the case, and only for jf < 2 is the increase significant. For jf > 2 the ICS is nearly constant as a function of jf, until a final cutoff due to energy restrictions. This low Δj propensity demonstrate that the presence of the deep well do not introduce enough anisotropy to induce large rotational transitions, because for high j the energy difference between adjacent rotational states increases quadratically with j. This fact also explains why the reaction is nonstatistical for the doublet state on spite of the deep insertion well for this reaction. This well is not completely reproduced in the RR approach, producing an underestimation of the ro-vibrational excitation. As a consequence, the transition to OH+ rotational levels closer to the initial one are overestimated. The state-to-state cross sections for the OH+(3Σ−, v0 = 0, j0 = 0) + H(2S) → OH+(3Σ−, vf = 0, jf = 0) + H(2S) for the two electronic states, doublet and quartet, are compared in Figure 8.

quartet state. These results are encouraging and demonstrate that, in this case, this approach is very well suited to calculate state-to-state inelastic cross sections. The state-to-state cross sections obtained for the doublet state, in Figure 6, show that the exchange becomes more

Figure 6. Same as Figure 5 but only for j0 = 0 in the doublet electronic state.

important than for the quartet, especially at higher energy. This is attributed to the deep insertion well appearing in the doublet state, which connects the two rearrangement channels. The exchange cross section is about 1 order of magnitude lower than the inelastic one, except close to the threshold for the Δj = 1 channel, for which exchange and inelastic processes present very similar cross sections. This fact may also justify the RR approach, as in the case of the quartet. The comparison made in Figure 6 clearly shows that the RR approach yields qualitative good behavior when compared to the exact calculations, but that it overestimates small Δj transitions and high collisional energy cross sections. Thus, for Δj = 1, the RR results are larger by a factor of ≈5, whereas for Δj = 2 this factor reduces to 3. This factor reduces for larger Δj, for which the agreement between RR and WP results is good at low energies, below Ec ≈ 0.2−0.3 eV. At higher energies, the deviation between the two sets of data stands between a factor of 2 and a factor of 5 depending on the transitions. To further analyze this fact, the state-to-state inelastic cross sections for some fixed energy as a function of final rotational states of OH+(vf = 0, jf) fragments are shown in Figure 7. If the

Figure 8. State-to-state ICS, summed over inelastic and exchange channels, for H + OH+ (v0 = 0, j0 = 0) → OH+ (vf = 0, jf) + H for the doublet (red) and quartet (blue) states.

For Δj = 1, ICS for the quartet is considerably larger, because in this electronic state this channel dominates. For higher Δj = 2 and 3, the cross sections obtained for the two electronic states are very similar, whereas for Δj > 4 the ICS for the doublet is larger by a factor of ≈2−3. The electronic partition function is 2/6 for the doublet and 4/6 for the quartet. Using these factors, the sum of the two electronic state-to-state cross sections are also shown in Figure 8. It is found that the sum of ICS’s is rather well approximated by that of the quartet. Therefore, it may be thought that the state-to-state OH+(3Σ−, v0 = 0, j0 = 0) + H(2S) → OH+(3Σ−, vf = 0, jf = 0) + H(2S) rate coefficients may be approximated by those obtained in the RR approach only for the quartet.

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CONCLUSIONS In this work we have computed the H + OH+(v0 = 0, j0 = 0) → OH+(vf = 0, jf) + H state-to-state cross sections, considering the inelastic and exchange rearrangement channels on two adiabatic electronic states, the quartet and doublet, whose PES were ́ et al.39 and Paniagua et al.,40 previously calculated by Martinez respectively. The competition between exchange and inelastic processes was taken into account by using a wave packet method. It is found that the exchange channel is negligible compared to the purely inelastic one. On the basis of this fact, it is found that the rigid rotor approach can lead to rather good results as

Figure 7. State-to-state ICS as a funtion of final rotational state, jf, for several collisional energies, summed over inelastic and exchange channels, for H + OH+ (v0 = 0, j0 = 0) → OH+ (vf = 0, jf) + H for the doublet state. 12087



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compared to the exact WP ones but only for the quartet electronic state. For the doublet state the RR approach overestimate the low Δj transitions because it is not able to describe correctly all the anisotropy due to the very deep insertion well of this electronic state. The state-to-state cross sections obtained by summing the results obtained with the WP method for the two electronic states can be reasonably described by the RR results obtained on the quartet state alone. On the basis of this result, it is concluded that the RR method can be used to obtain the rates from other initial ji values, which are very difficult to be obtained with the more exact WP method because they are very demanding computationally. However, this finding is not expected to be general, and for other systems the validity of the RR approach should be addressed. Finally, it is interesting to compare the OH+−H and OH+− He cross sections. Indeed, as mentioned in the Introduction, collisional data with the H (or H2) collisional partner can be estimated from collisional data with the He collisional partner assuming that the cross sections of both systems are the same and by just correcting the reduced mass that appear in the boltzmann average of the cross sections to compute the collisional rate coefficients.38 In Figure 9 we show the OH+−H and OH+−He cross sections from the ground rotational state. The OH+−He are

Article

AUTHOR INFORMATION

Corresponding Authors

*N. Bulut. E-mail: [email protected]. *F. Lique. E-mail: [email protected]. *O. Roncero. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge the support of Ministerio de Economiá e Innovación (Spain), for grants CSD2009-00038, FIS201129596-C02, and FIS2014-52172-C2, TUBITAK (Turkey), Project No. TBAG-112T827, the Agence Nationale de la Recherche (France), contract ANR-12-BS05-0011-01. O.R. and N.B. also acknowledge CSIC for a travelling grant I-LINK0775. The calculations have been performed in the parallel facilities at CESGA computing center, through ICTS grants, which are acknowledged.

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REFERENCES

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Figure 9. State-to-state cross sections for H + OH+ (v0 = 0, j0 = 0) → H + OH+ (vf = 0, jf) (solid line) and He + OH+ (v0 = 0, j0 = 0) → He + OH+ (vf = 0, jf) (dashed line) collisions. The H + OH+ (v0 = 0, j0 = 0) → H + OH+ (vf = 0, jf) are those averaged with the electronic partition for the doublet and for the quartet.

those of ref 37 summed over the fine and hyperfine structure. As one can see, the agreement between the two sets of cross sections is good for small Δj. For transition with larger Δj, significant differences appear. The differences can be explained by the relatively weak well depth of the OH+−He that does not favor transitions with large Δj. From this comparison, we can see that OH+−He collisional data can hardly be a template for OH+−H ones. This fully justify the necessity of computing real OH+−H data. As mentioned in the Introduction, in the interstellar medium, the main excitation and de-excitation pathways are primarily driven by inelastic collisions with electrons and atomic hydrogen. This molecule is an essential ion precursor for oxygen chemistry, and we expect that these new data will significantly help in the accurate interpretation of OH+ emission spectra from interstellar molecular clouds. 12088


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Exchange and Inelastic OH+ + H Collisions on the Doublet and

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