Reaction Dynamics of H3+ + CO on an Interpolated Potential Energy

Preliminary ab initio calculations suggest that this reaction is barrierless and should not involve a ...... Erum Gull NazSumitra GodaraManikandan Par...
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J. Phys. Chem. A 2010, 114, 10783–10788

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Reaction Dynamics of H3+ + CO on an Interpolated Potential Energy Surface Hai-Anh Le, Terry J. Frankcombe, and Michael A. Collins* Research School of Chemistry, Australian National UniVersity, ACT 0200 Australia ReceiVed: June 30, 2010; ReVised Manuscript ReceiVed: August 30, 2010

An accurate potential energy surface for H3+ + CO has been constructed by interpolation of ab initio data. The reaction cross sections and thermal rate coefficients for the production of HCO+ and HOC+ have been evaluated using quasiclassical trajectory simulations. Introduction The reaction of H3+ with CO can lead to two isomeric products

H3+ + CO f H2 + HCO+

(1)

H3+ + CO f H2 + HOC+

(2)

and

The relative abundances of the metastable HOC+ and the stable isomer HCO+ in interstellar and circumstellar environments have been the subject of extensive experimental and theoretical study. The less abundant isomer HOC+ is found in the same environments as HCO+, with abundances a factor of 102-104 lower than those of HCO+.1-4 The varying relative abundances are likely connected to the relative importance of different formation mechanisms of HOC+ under different physical conditions. In principle, the HOC+/HCO+ isomers could be interconverted by collision with other species in the interstellar medium.5,6 The most likely species is H2. However, Herbst and Woon7 have shown that the rate for H2 + HOC+ f H2 + HCO+ is very low under the relevant conditions. Recently, the formation of these species by the reaction

H2 + CO+ f H + HCO+ /HOC+

(3)

has been studied by some of us via classical trajectory simulations on an interpolated ab initio potential energy surface.8 In contrast to earlier experimental studies,9-12 it was found that only the stable HCO+ isomer is formed at low energy via reaction 3. The CO molecule is the second most abundant molecule in the interstellar medium after H2. Hence, depending on the relative abundance of H3+ in different interstellar environments, reactions 1 and 2 would be competitive with reaction 3 and might dominate the formation of HOC+. Moreover, because CO and H3+ are both relatively abundant species in interstellar environments, reactions 1 and 2 are also important for modeling the overall chemistry of dark and diffuse clouds, protoplanetary disks, and cold dense clouds.13-15 Reactions 1 and 2 have been studied experimentally,16-21 and the branching fraction of HOC+ formation has been determined * To whom correspondence should be addressed.

to be 6 ( 5% by an indirect measurement.19 Theoretical interest in this system has recently been renewed. Phase space theory calculations suggested branching fractions of 20% at 300 K, falling to 1% at low temperatures.22 Yu23 has performed direct dynamics simulations of these reactions utilizing a weighted average of the Hartree-Fock and Møller-Plesset (MP2) energies to describe the interactions. Yu found the combined reaction rate constant to be smaller than the Langevin value and to have weak temperature dependence, rising approximately linearly from 1.1 × 10-9 cm3 s-1 at 20 K to 1.4 × 10-9 cm3 s-1 at room temperature. With decreasing temperature, the calculated HCO+/HOC+ branching ratio increased from 2.8 (26% HOC+) at room temperature to 11.2 (8% HOC+) at 20 K. Also recently, Klippenstein et al.24 have calculated the rate coefficients for these reactions using a long-range interaction potential and variational transition-state theory based on ab initio calculations. This study included a careful evaluation of the long-range interactions, which are expected to dominate the “capture” of the CO molecule by the H3+ ion. The rates of reactions 1 and 2 were estimated from a statistical calculation. The combined rate coefficient was calculated to be slightly higher than the Langevin value and temperature-dependent, falling from about 2.9 × 10-9 cm3 s-1 at 20 K to 2.2 × 10-9 cm3 s-1 at 300 K. The branching ratio was also found to be temperature-dependent, falling from 4.3 at 20 K to 1.6 at 300 K. In addition, Li et al25 have constructed a reduced (five) dimensional potential energy surface for reactions 1 and 2 using high-level ab initio calculations of the electronic energy, but no dynamics calculations have been reported for this model. Here, we report a full dimensional classical trajectory study of these reactions on a full dimensional PES constructed by interpolation of high-level ab initio data. The rate coefficient and branching ratio are reported. Methods A. Ab Initio Calculations. High-level ab initio calculations of the stationary points on the ground-state H3CO+ PES have been reported previously.7,24,25 To illustrate the variation of the ab initio data with basis set and level of theory, we have examined the relative energies of the products of reactions 1 and 2, relative to the energy of the reactants, using various methods with Dunning-type basis sets, as summarized in Table 1. This table shows that the coupled cluster method with single and double excitations (CCSD) or including triple excitations perturbatively [CCSD(T)] gives close agreement to the complete basis set extrapolated results of ref 24. Fortunately, the CCSD/ aug-cc-pVDZ method agrees with more computationally ex-

10.1021/jp1060182  2010 American Chemical Society Published on Web 09/17/2010

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TABLE 1: Energies (kJ mol-1) of the Products for Reactions 1 and 2, Relative to That of the Reactants CO + H3+ for Various Levels of Ab Initio Calculationa level of ab initio calculation

HCO+ + H2

HOC+ + H2

B3LYP/aug-cc-pVTZ MP2/aug-cc-pVDZ MP2/aug-cc-pVTZ MP2/aug-cc-pVQZ CCSD/aug-cc-pVDZ CCSD/aug-cc-pVTZ CCSD/aug-cc-pVQZ CCSD(T)/aug-cc-pVDZ CCSD(T)/aug-cc-pVTZ CCSD(T)/aug-cc-pVQZ ref 24

-168.4 -176.2 -176.7 -175.8 -169.7 -170.1 -168.9 -169.9 -169.6 -168.4 -169.5

-13.2 -19.3 -16.1 -17.6 -14.0 -17.1 -15.6 -12.2 -13.7 -12.0 -12.5

a The zero-point vibrational energy corrections were calculated at the B3LYP/aug-cc-pVTZ level of theory.

pensive methods to within 2 kJ mol-1. Moreover, the long-range part of the interaction between CO and H3+ is reasonably welldescribed at this level of theory. The CCSD/aug-cc-pVDZ dipole moment of CO is 0.043 au at the experimental bond length, which is in agreement with the experimental value (also 0.043 au)26 and somewhat below the 0.052 au value of ref 24; the CCSD/aug-cc-pVDZ quadrupole moment is -1.03 au, somewhat below the recommended value of -1.46 au;27 and the CCSD/aug-cc-pVDZ polarizability is 12.8 au (R| ) 15.7 au), close to the experimental values28 of 12.1 au (R| ) 15.5 au). Hence, we have constructed a full dimensional PES using this computationally convenient level of theory. B. PES Construction. The PES has been computed as a modified Shepard interpolation over a data set of ab initio points using the Grow methodology.29-33 Briefly, the PES at some molecular configuration Z is given by a weighted average of second-order Taylor series expansions about a set of data points {Z(n)} Ndata

E(Z) )

∑ ∑ w[Z - gOZ(n)]T[Z - gOZ(n)]

(4)

g∈G n)1

Here, T denotes a second-order Taylor series expansion for the energy around each data point, and w is a normalized weight function that is constructed to ensure an interpolation of the ab initio data; g O denotes that the subsequent quantity is changed by an operation of the symmetry group G (here, the complete nuclear permutation group). The PES of eq 4 is correctly invariant to permutation of the three hydrogen atoms. The set of data points in eq 4 is accumulated iteratively in the Grow approach. The initial data set was comprised of about 50 geometries lying on an approximate minimum-energy path linking the reactants (separated by about 10 Å) to the products of reaction 1 via a H2 · · · HCO+ complex and a similar path involving the products of reaction 2. The starting data set defines the starting PES by eq 4. An iterative procedure then builds the set of data points. At each iteration, a small set of 10 classical trajectories was evaluated to simulate reactions 1 and 2 and a sample of molecular configurations obtained from there; the “variance sampling” and “h weight” methods29 have been used at each alternate iteration to select a new data point from these configurations, thus creating a new PES as per eq 4. Until the PES data set grew to 900 points, the small sets of trajectories had initial conditions defined by microcanonical distributions

Figure 1. The probability of HCO+ (×), HOC+ (O), and both products (b) is shown as a function of the number of data points which define the PES. Results are shown for 1000 trajectories, in which initial conditions simulate a thermal (300 K) distribution of reactants, CO + H3+, with an initial maximum impact parameter of 27 au. The error bars represent 95% confidence intervals. The lines are visual aids only.

Figure 2. The ratio of the reaction probabilities for the HCO+ and HOC+ products, derived from the data of Figure 1.

of approximately zero-point vibrational energy in CO (0.005 au) and H3+ (0.025 au) with a relative translational energy of 13.13 kJ mol-1 (0.005 au) and zero impact parameter. The integration of trajectories with microcanonical initial conditions was performed with both an in-house program and the Venus trajectory program,34 modified35,36 to employ a PES and associated energy gradients calculated by eq 4. Subsequently, 100 iterations were performed using Venus with trajectories sampled from a canonical distribution at 200 K; then, another 100 iterations were performed with trajectories sampled from a canonical distribution at 300 K. The initial conditions were quasiclassical; vibrational energies of the reactants were selected from a Boltzmann distribution of quantized normal modes, and rotational states were selected from the symmetric rotor thermal distribution. This gave a total set of 1100 data points. Finally, another 142 iterations were performed under microcanonical conditions to ensure the presence of data points with reactant separations of at least 20 Å. Thus, the final data set had Ndata ) 1242. The complete data set and software required for the PES evaluation are given in the Supporting Information. Results All trajectory results reported below were from calculations performed with the modified Venus program. The results from the trajectory simulations are quoted with 95% Wilson score confidence intervals.37 The convergence of the PES as a function of the size of the data set is indicated in Figures 1 and 2. Figure 1 presents the total reaction probability for trajectories with a thermal distribution of initial conditions. The identity of the

Reaction Dynamics of H3+ + CO on an Interpolated PES

J. Phys. Chem. A, Vol. 114, No. 40, 2010 10785 Both Figures 3 and 4 depict fits to the cross sections and rate coefficients, respectively. These lines have been simultaneously fitted to the canonical and microcanonical data as follows. Using the Venus trajectory program with thermal sampling of initial conditions and a maximum impact parameter of bmax, the rate coefficient, at temperature T, is given by

8 [ πµβ ]

1/2

k(T) )

Figure 3. The reaction cross section for HCO+ (×), HOC+ (O), and both products (b) is shown as a function of the relative translational energy of the CO and H3+ reactants. The error bars represent 95% confidence intervals. The lines represent fits to the microcanonical and canonical data (see text).

2 πbmax (Nr /Nt)

(5)

where β ) 1/kBT, kB is the Boltzmann constant, µ is the reduced mass, Nt is the total number of trajectories, and Nr is the number of reactive trajectories. When the value of the maximum impact 2 (Nr/Nt) is indeparameter is sufficiently large, the factor bmax pendent of bmax as the proportion of reactive trajectories 2 .The relation between the rate decreases inversely with bmax coefficient and the cross section can be used to define the thermal cross section

k(T) ) ≡

8 [ πµβ ] 8 [ πµβ ]

∫0∞ σ(E)E exp(-βE) dE

1/2 2 1/2

β

(6)

σ(β)

where the thermal cross section, σ(β), has the dimension of area. Second, we assume that the thermal rate coefficients can be described by a modified Arrhenius form

( ) ()

k(T) ) A +

+

Figure 4. The thermal rate coefficients for HCO (×), HOC (O), and both products (b) are shown as a function of the temperature in canonical trajectory simulations. The error bars represent 95% confidence intervals. The lines represent fits to the microcanonical and canonical data (see text). +

+

product (HCO or HOC ) was determined from the bond lengths in the product asymptotic region. The energy barrier to interconversion of these two isolated isomers is very much higher than the available energy. Figure 2 presents the product branching ratio corresponding to Figure 1. These quantities have clearly converged to within the finite sampling errors (1000 trajectories), indicating that the PES is converged sufficiently well for this dynamical study. Batches of 3000 microcanonical trajectories were calculated over a range of collision energies from about 0.8 to 13.1 kJ mol-1. The resulting cross sections are shown in Figure 3. Cross sections are not reported for energies below 0.8 kJ mol-1, in case the results are adversely affected by interpolation errors in the PES. Using samples of configurations in the reactant valley (CO + H3+), we have found that the interpolated PES can be in absolute error (compared to the correct CCSD/augcc-pVDZ value) by as much as 0.15 kJ mol-1. Such “noise” in the PES might significantly perturb trajectories with very low translational energy. Hence, we do not report cross sections for collision energies below 0.8 kJ mol-1. Batches of 3000 trajectories sampled from a thermal distribution were also calculated with temperatures in the range of 75 to 300 K. The resultant thermal rate coefficients, at temperature T, are shown in Figure 4. Again, no results are reported for temperatures below 75 K, where very low energy collision would be expected to dominate the calculated reaction rate coefficients.

T TR

γ

exp

B T

(7)

Then, by inverse Laplace transform, the microcanonical cross section has the corresponding form

σ(E) ) aH(E + c)

(E + c)γ+1/2 Γ(γ + 3/2)E

(8)

where H is the Heaviside function, Γ is the gamma function, a ) A(πµ/8)1/2(kBTR)γ, and c ) kBB. Moreover, the thermal cross section has the form (from eqs 6 and 7)

σ(β) ) aβ-γ+1/2 exp(cβ)

(9)

The variables a, c, and γ are fitted by minimizing a penalty function measuring deviations of σ(E) and σ(β) from the corresponding trajectory data (cf. Figures 3 and 4). Each energy and temperature at which a cross section is known contributes equally to the penalty function. For each energy and temperature, the square of the difference between the analytic fit cross section (eqs 8 and 9) and the trajectory results is added to the cost function, with an additional penalty of 100 times the square of the extent to which the fitted function lies outside of the calculated confidence intervals. The penalty function was minimized using the simulated annealing procedure implemented by Goffe et al.38 The accuracy of the fitting shown in Figures 3 and 4 indicates that the microcanonical and canonical trajectory simulations are mutually consistent and reasonably described by the simple form adopted in eq 7. The optimized parameters are shown in Table 2. Finally, Figures 5 and 6 present the branching ratio for reactions 1 and 2 as a function of energy and temperature,

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TABLE 2: Optimized Values for the Parameters Which Define the Rate Coefficients and Cross Sections in Equations 6 and 7 product parameter -9

3 -1

A (× 10 cm s ) B (K) γ a (au) c (× 10-6 au)

HCO

+

1.827 ( 0.075 -13.9 ( 3.5 -0.034 ( 0.041 416 ( 17 -44 ( 11

HOC+

HCO+ + HOC+

1.192 ( 0.048 -12.9 ( 6.9 0.0014 ( 0.053 272 ( 11 -41 ( 22

3.008 ( 0.048 -12.3 ( 2.5 -0.0034 ( 0.0216 686 ( 11 -39 ( 8

respectively. Figure 5 shows that the branching ratio, counting all trajectories, is roughly constant at about 1.6 at over the lower energies studied, rising to near 2 at the highest energies. Figure 6 indicates that the thermal branching ratio is around 1.4-1.5 over the whole temperature range. At these temperatures, the rate coefficients are dominated by reaction at the lower end of the collision energies shown in Figure 5. Discussion The total reaction cross sections and rate coefficients for reactions 1 and 2 combined are expected to depend on the longrange capture of the CO molecule by the H3+ ion. Figure 7 presents the combined reaction probabilities as a function of the impact parameter (opacity function) for collisions at one energy. This probability is roughly constant at about 0.8 for small impact parameters and then declines to 0 at around 7 Å. The Langevin model, which considers only the ion-induced dipole interaction, predicts unit reaction probability at small impact parameters and a critical impact parameter beyond which the probability is 0. Clearly, the critical Langevin impact parameter coincides quite well with the value at which the reaction probability begins to fall. However, there is a significantly large tail in the reaction probability for impact parameters

Figure 5. The ratio of the cross sections of Figure 3 (reaction 1/reaction 2) is shown as a function of the collision energy, (b) for all trajectories and (O) for trajectories which lead to at least zero-point vibrational energy in the products.

Figure 6. The ratio of the thermal rate coefficients of Figure 4 (reaction 1/reaction 2) is shown as a function of the temperature.

Figure 7. The total probability of reactions 1 and 2 is shown as a function of the impact parameter for a collision energy of 13.13 kJ mol-1. The error bars indicate the uncertainly due to the finite sample of trajectories (95% confidence intervals). The arrow indicates the critical impact parameter expected from the Langevin model.

above the Langevin critical value. This is not surprising as there are additional long-range attractive forces between the reactants, particularly ion-dipole and ion-quadrupole interactions.24 The fact that the reaction probability at small impact parameters is only about 0.8 suggests that steric hindrance plays a role, preventing reaction even if the CO molecule is captured by the H3+ ion. Across the range of energies shown in Figure 3, the opacity function is essentially similar to that in Figure 7, except that the value of the impact parameter where the tail commences increases as the energy decreases. In light of the tail seen in Figure 7, it is not surprising that the total reaction cross section and thermal rate coefficients are higher than the Langevin values. At 300 K, the total reaction rate coefficient is about 2.97 ( 0.15 × 10-9 cm3 s-1, compared to the Langevin prediction of 1.96 × 10-9 cm3 s-1. The trajectory simulation gives a somewhat larger rate coefficient at 300 K than that estimated in ref 24 (about 2.21 × 10-9 cm3 s-1) and a substantially larger rate coefficient than that calculated in ref 23 (1.42 × 10-9 cm3 s-1). It is clear from Figure 4 that the thermal rate coefficients for both reactions 1 and 2 are roughly constant from 300 down to 75 K. The work in ref 24, which relies substantially on transition-state theory (TST), predicted a rise in the rate coefficients with decreasing temperature. On the other hand, the molecular dynamics study of Yu23 predicted an approximately linear decrease in the rate coefficients with decreasing temperature. Experimental results16-20,39-42 for the combined reactions 1 and 2 are quite scattered at or slightly below the Langevin prediction, near 2 × 10-9 cm3 s-1. The scarce available data below 300 K does not indicate any temperature dependence for the rate coefficient. Here, we do not observe any significant variation of the rate coefficient with temperature. However, the PES reported here is subject to interpolation error. Although this error is small in relation to the energy range of the PES (as indicated in Table 1, this is on the order of 200 kJ mol-1), it is large enough to cast doubt on the reliability of trajectory simulations well below 100 K. Figure 6 shows that the relative magnitude of the thermal rate coefficients for reactions 1 and 2 is roughly constant at around 1.5. This observation is in reasonable agreement with a value of about 1.6 in ref 24 at 300 K but does not show a rise in the branching ratio with decreasing temperature, as calculated in ref 24. Our calculations for the branching ratio are substantially smaller than the results of ref 23, which give a value near 2.8 at 300 K, rising to near 10 below 50 K. There is no single obvious reason for the differences between the results obtained here and those in the two very recent

Reaction Dynamics of H3+ + CO on an Interpolated PES calculations, refs 24 and 23. Both this work and that in ref 23 employ classical trajectories to evaluate the reaction dynamics. This work is based on an apparently converged Shepard interpolation of the PES at the CCSD/aug-cc-pVDZ level of ab initio theory, while ref 23 employs a combination of MP2 and Hartree-Fock calculations with a cc-pVTZ basis set. According to the analysis of ref 24, differences in reactivity at either end of CO are dominated by the magnitude of the CO dipole moment. The combined Hartree-Fock and MP2 method of ref 23 leads to a substantial error in the CO dipole moment; MP2/ cc-pVTZ gives 0.127 au, HF/cc-pVTZ gives -0.092 au, while the weighted average gives 0.061 au, compared to the experimental value of 0.043 au. This method gives a reasonable value for the quadrupole moment, -1.007 au, but underestimates the polarizability, giving R ) 11.2 au. Both the long-range capture cross sections and branching ratios would be affected by inaccuracies in the dipole moment and polarizability. Both this work and that in ref 24 appear to rely on very similar longrange potential energy surfaces, though direct comparison of the PESs over the whole range of relevant molecular configurations is impossible as only a restricted part of the PES is employed in the TST calculation. The branching analysis in ref 24 depends on a reduced dimensionality molecular dynamics approach43 that gives qualitatively the same branching as the ratio of the TST rates for H3+ approaching either end of the CO fragment. Here, a simple classical trajectory approach has been employed that does not discern between trajectories that conserve zero-point energy in the products and those that do not. The problem of nonconservation of zero-point vibrational energy is well-known in classical trajectory studies of chemical dynamics. Figure 5 also shows values of the product branching ratio where only trajectories which lead to at least the (harmonic) zero-point vibrational energy in the H2 and HCO+/HOC+ products are counted. Clearly, this estimate of the branching ratio is higher than that from all trajectories. This probably reflects the fact that the total vibrational energy available to HOC+ is much less than that available to HCO+. It is not clear which set of values in Figure 5 is the better estimate of the branching ratio, but the variation between the two sets provides some indication of the uncertainties inherent in a classical trajectory estimate of this quantity. However, it may be relevant to note that neither set of values in Figure 5 indicates any significant energy dependence in the branching ratio. Classical trajectories do not “conserve zero-point energy” any time. Even before a collision with CO, the initial vibrational mode energies in H3+ are subject to intramolecular vibrational energy redistribution (IVR). Hence, the distribution of vibrational energy in H3+ when it collides with CO does not necessarily correspond closely to the initial distribution. However, in this system, we have evaluated trajectories with both microcanonical and quasi-classical (energy allocated to individual normal modes) initial conditions and found no statistically significant difference in the cross sections. This suggests that IVR in the reactants is not a complicating factor in this system. Importantly, a global PES is reported herein, so that estimates of the rate coefficients and branching ratio may be evaluated using alternative dynamics methods. The results reported here may be directly relevant to interstellar chemistry at temperatures above about 75 K. However, one must remember that quantum effects have been completely ignored here. Given that a proton transfer determines the rate, quantum effects may be significant. Nonetheless, we find, in qualitative agreement with ref 24, that the overall rate coefficient

J. Phys. Chem. A, Vol. 114, No. 40, 2010 10787 is larger than the Langevin value. This implies that H3+ is destroyed by CO, which is a relatively abundant species in dark interstellar clouds, at a higher rate than would be predicted by the Langevin model. Both isomers, HCO+ and HOC+, are produced with comparable yields. By contrast, we previously found that only HCO+ was produced in the collision of CO+ with H2. Herbst and Woon have shown that the isomerization of HCO+ to HOC+ is slow. This result is based on high-level ab initio calculations of the PES for collision of HOC+ with H2 (the dominant species present) and a phase-space approach to the rate coefficient rather than an exact quantum calculation. The energetics for isomerization in this system are similar to that in Kr + HOC+.45 A classical trajectory study of that system showed that the cross section for isomerization was small (several Å2), implying a low rate coefficient. Isomerization of HOC+ in collisions (with Kr or H2 and probably with any other species) involves a relatively complicated path or sequence of geometry changes, rendering the process unlikely. Hence, the conclusions of the phase-space calculation for HOC+ isomerization7 by collision with H2 is likely to be robust. However, it should be noted that conversion of HOC+ to HCO+ by collision with CO, that is

COH+ + C′O′ f CO + HC′O′+

(10)

is possible. Preliminary ab initio calculations suggest that this reaction is barrierless and should not involve a complicated reaction pathway. Hence, we might expect the relative abundances of HCO+ and HOC+ in a particular interstellar environment to depend strongly on the product of the concentrations of CO+ and H2, compared to the product of the concentrations of CO and H3+. However, the density and concentrations of different molecular species not only vary from one interstellar environment to another but may be spatially inhomogeneous even within a single interstellar gas cloud. Complex models of the transport and chemistry are required to understand the abundances of species in such clouds.44 The rate coefficients reported herein are necessary for such models. Acknowledgment. This work was supported with computational resources from the National Computing Infrastructure National Facility at the Australian National University. Supporting Information Available: Data files and Fortran programs required to evaluate the PES and the Cartesian energy gradient. A README file contains an explanation of the individual files supplied. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Fuente, A.; Rodriguez-Franco, A.; Garcia-Burillo, S.; MartinPintado, J.; Black, J. H. Astron. Astrophys. 2003, 466, 899. (2) Apponi, A. J.; Ziurys, L. M. Astrophys. J. 1997, 481, 800. (3) Liszt, H.; Lucas, R.; Black, J. H. Astron. Astrophys. 2004, 428, 118. (4) Fuente, A.; Garcia-Burillo, S.; Gerin, M.; Teyssier, D.; Usero, A.; Rizzo, J. R.; Vicente, P. d. Astrophys. J. 2005, 619, L155. (5) Chalk, A. J.; Radom, L. J. Am. Chem. Soc. 1997, 119, 7573. (6) Moyano, G. E.; Jones, S. A.; Collins, M. A. J. Chem. Phys. 2006, 124, 124318. (7) Herbst, E.; Woon, D. E. Astrophys. J. 1996, 463, L113. (8) Ramazani, S.; Frankcombe, T. J.; Andersson, S.; Collins, M. A. J. Chem. Phys. 2009, 130, 244302. (9) Freeman, C. G.; Knight, J. S.; Love, J. G.; McEwan, M. J. Int. J. Mass Spectrom. Ion Processes 1987, 80, 255.

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