J. Phys. Chem. B 2005, 109, 8431-8438
8431
Direct Dynamics Classical Trajectory Simulations of the O+ + CH4 Reaction at Hyperthermal Energies† Lipeng Sun and George C. Schatz* Department of Chemistry, Northwestern UniVersity, EVanston, Illinois 60208-3113 ReceiVed: October 6, 2004; In Final Form: December 2, 2004
A Born-Oppenheimer direct dynamics simulation of the O+ + CH4 reaction dynamics at hyperthermal energies has been carried out with the PM3 (ground quartet state) Hamiltonian. Calculations were performed at various collision energies ranging from 0.5 to 10 eV with emphasis on high energy collisions where this reaction is relevant to materials erosion studies in low Earth orbit and geosynchronous Earth orbit. Charge transfer to give CH4+ is the dominant channel arising from O+ + CH4 collisions in this energy range, but most of the emphasis in our study is on collisions that lead to reaction. All energetically accessible reaction channels were found, including products containing carbon-oxygen bonds, which is in agreement with the results of recent experiments. After correcting for compensating errors in competing reaction channels, our excitation functions show quantitative agreement with experiment (for which absolute magnitudes of cross sections are available) at high collision energies (several eV). More detailed properties, such as translational and angular distributions, show qualitative agreement. The opacity function reveals a high selectivity for producing OH+ at high impact parameters, CH3+/CH2+/H2O+ at intermediate impact parameters, and H2CO+/HCO+/CO+ at small impact parameters. Angular distributions for CH3+/CH2+/OH+ are forward scattered at high collision energies which implies the importance of direct reaction mechanisms, while reaction complexes play an important role at lower energies, especially for the H2O+ product. Finally, we find that the nominally spinforbidden product CH3+ + OH can be produced by a spin-allowed pathway that involves the formation of the triplet excited product CH3+(a˜3E). This explains why CH3+ can have a high cross section, even at very low collision energies. The results of this work suggest that the PM3 method may be applied directly to the study of O+ reactions with small alkane molecules and polymer surfaces.
I. Introduction In recent years, there has been considerable interest in the reactions of gaseous ions with small organic molecules.1,2 Advances in experimental technologies have enabled the study of very detailed information about the reaction dynamics over a wide range of collision energies and sometimes with quantum state resolution. This in turn has stimulated theoretical and computational studies aimed at understanding the detailed reaction dynamics and kinetics.3 Reactions of ions with the simplest organic molecule CH4 have been studied in a variety of contexts.4-9 Our interest in the hyperthermal energy O+(4S3/2) + CH4 reaction is motivated by interest in the erosion/protection of polymer materials coated on the surfaces of spacecraft in low Earth orbit (LEO) or geosynchronous Earth orbit (GEO). Such surfaces are under constant bombardment by energetic atoms/ molecules, ions, electrons, and various sources of electromagnetic radiation. Among the collision processes, atomic/molecular ions are responsible for space vehicle charging and atmospheric drag. Kinetic energies of these gaseous ions in LEO and GEO range from 1 to 106 eV.10 With such a wide range of collision energies, a large number of reaction channels are energetically accessible, so even though O+ (the most abundant ion in LEO) is much lower in abundance than O, its collisions lead to more significant fragmentation. †
Part of the special issue “George W. Flynn Festschrift”. * To whom correspondence should be addressed.
However, knowledge of alkane molecule reactions involving O+(4S3/2) is very limited. An early experiment measured the product branching ratios for the O+ + CH4 thermal reaction. Only charge transfer and CH3+ + OH hydride abstraction were observed, with their branching ratio being 5.5:1 approximately.11,12 Recently, we performed ab initio electronic structure calculations to investigate the stationary points and intrinsic reaction coordinates (IRCs) for the primary and secondary reactions on their ground state potential energy surfaces (PESs).13 By inspecting the PES, we found that the O+ + CH4 collision proceeds with a long range charge transfer process followed by a large number of chemical reactions, most of which are highly exothermic and have energy barriers lower than the reactants. The low energy transition states and high exothermicity imply that reaction should be very efficient. All the C-O bond formation reaction channels (HCO+, H2CO+, CH3O+, CO+, etc.) are more exothermic than the CH3 + OH+ hydride abstraction pathway in which only the C-H bond breaks. This is of particular interest to the erosion process in LEO since the formation of a C-O bond provides a pathway that can lead to the production of volatile oxygen-containing species containing carbon such as CO and CO2. Our previous theory work was published jointly with experimental results for O+ + CH4,13 in which a guided-ion-beam apparatus was used to measure absolute cross sections for collision energies ranging from nearthermal to 15 eV. The appearance of oxygenated products in the experiments supports our theoretical predictions; however
10.1021/jp0454568 CCC: $30.25 © 2005 American Chemical Society Published on Web 02/12/2005
8432 J. Phys. Chem. B, Vol. 109, No. 17, 2005 theory was not used to calculate cross sections or product distributions. Recently, there has been much theoretical interest in collisions of O(3P) with small hydrocarbons and with alkane thiol selfassembled monolayers (SAMs) on Au(111) surfaces, as model systems for LEO erosion by atomic oxygen.14-20 These studies have demonstrated that triplet oxygen is capable of undergoing addition reactions to hydrocarbons at hyperthermal energies and that the reaction mechanisms seen in O + alkane gas phase collisions are largely preserved in the corresponding O + SAM system. These studies of atomic oxygen chemistry have not yet considered the importance of ion-surface collisions on erosion mechanisms. However new measurements have just been published which provide useful data for addressing the role of O+ in LEO erosion. Dressler and co-workers carried out experimental studies of the reaction of O+ with CH4, C2H6, C3H8, and C4H10.13,21 In addition, collisions of O+ with alkane thiol SAMs have been reported.22 A general picture provided by these experiments is that charge transfer takes place as the O+ approaches the molecule or surface, followed by various chemical reactions; however the mechanisms of the reactions are not known. In the work reported here, we performed direct dynamics classical trajectory simulations of O+ + CH4 collisions with the PM3 semiempirical Hamiltonian on its lowest quartet potential energy surface. By using O+ + CH4 as a benchmark system, the goal of our paper is to understand the microscopic reaction mechanisms and dynamics, thereby testing the usefulness of direct dynamics/PM3 trajectories as a general and practical method for the study of O+ collisions in more complex environments. The PM3 approach is of course a much lower level method than we used earlier to characterize stationary point properties, but this level of theory is practical for trajectory applications, and it may be adequate for a hyperthermal energy study like this where high accuracy is not essential. In addition, we find that PM3 is more robust than higher level methods with respect to convergence of the self-consistent field equations, making it much easier to use. One issue that will be of particular interest in this study is whether the dynamics is well described using just the ground state potential surface, as there are many surfaces accessible after charge transfer, and it is unknown if internal conversion to the ground state is fast on the time scale of reaction. Another issue is whether we can describe the results using spinconserving dynamics (the reagent quartet state in this case) as there was indication in our earlier work that certain products must be produced by spin-forbidden mechanisms. What we show here is that despite the many limitations of PM3 with ground-state-only dynamics, and ignoring spinforbidden pathways, the results from this work are in many respects very similar to those found in experiment, with the agreement being especially good at high energies and for product channels that are summed over collective families of products rather for specific products. Although charge transfer to give CH4+ is the dominant product in this system, the primary emphasis in this work is on smaller impact parameter collisions that lead to chemical reaction. For these collisions, we show that direct dynamics using PM3 provides much insight into the reaction mechanisms. The paper is structured as follows: in section II, the computational details are provided; in section III, the results are described; and section IV summarizes the conclusions.
Sun and Schatz TABLE 1: Relative Energies for Reactants and Products on the Ground State Quartet Potential Energy Surfacea chemical species O+
+ CH4 O + CH4+ CH3O+ + H CH3 + OH+ CH3+ + H + O CH2+ + H2 + O H2CO+ + 2H H2O+ + CH2 HCO+ + 3H HC-OH+ + 2H CH3+(3E) + OH
PM3
MP2/6-311++G(3df,3pd)b
exptc
0.0 -0.57 (-0.90) -2.70 (-3.08) -1.03 (-1.24) 1.18 (0.76) 0.69 (0.15) -1.45 (-2.09) -1.96 (-2.20) -0.33 (-1.20) -1.24 (-1.79) 0.41 (0.22)
0.0 -0.58 (-0.75) -1.64 (-1.96) -0.12 (-0.33) 1.22 (0.85) 2.28 (1.78) -0.51 (-1.08) -0.90 (-1.14) 0.04 (-0.81) -0.65 (-0.60) 0.29 (-0.01)
0.0 -1.01 -2.25 -0.51 0.75 1.56 -1.23 -1.28 -0.08 -0.76
a Energies are in eV. Numbers in parentheses are zero point corrected. Results from ref 13, where the smaller basis set is used for geometry optimization and the larger one for a single point energy calculation. c The energy for charge transfer is derived from the adiabatic ionization potentials of CH4 (ref 23) and O(3P) (ref 26). The rest of the energies are obtained from refs 24 and 26. b
II. Computational Details II.A. PM3 Potential Energy Surface. In our previous calculations,13 stationary points and IRCs for the following 10 chemical reaction channels were investigated for the quartet potential energy surface.
O+ + CH4 f [O---CH4]+ f CH3O+ + H
(1)
f H2CO+ + 2H
(2)
f OH+ + CH3
(3)
f H2O+ + CH2
(4)
f CH3+ + H + O
(5)
f CH2+ + H2 + O
(6)
CH3O+ f H2CO+ + H
(7)
CH3O+ f H2C-OH+
(8)
H2CO+ f HCO+ + H
(9)
H2CO+ f HC-OH+
(10)
Previous ab initio calculations show that the first six reactions are the primary reactions. Among those, the first four reactions are exothermic with low energy barriers. Reactions 7-10 are secondary unimolecular dissociation/isomerization channels. All of these chemical channels involve an initial charge transfer step to give O + CH4+, and charge transfer is the primary product overall in O+ + CH4 collisions, so processes 1-10 are only associated with small impact parameters where the oxygen and methane interact strongly enough to produce rearrangement. Table 1 presents ab initio, PM3, and experimental energies for the products in reactions 1-10. The ab initio calculations reported in ref 13 were carried out at HF, B3LYP, MP2, and CCSD(T) levels of theory with the basis sets ranging from 6-31G* to Aug-cc-pVTZ. Both MP2/6-311++G(3df,3pd) and CCSD(T)/aug-cc-pVTZ//MP2/6-311++G(3df,3pd) results for the reaction energies are in overall good agreement with experiment.13 Therefore, our previous ab initio (MP2) results in Table 1 provide a useful calibration for the PM3 energies for these reactions.13
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Figure 1. Diagram showing the primary reaction channels. The charge transfer channel is not shown. The same labeling for reaction intermediates (CP) and transition states (TS) as in ref 13 is used. Energies are in eV, with the top number for each structure giving the PM3 zero point corrected energy and the bottom the MP2 zero point corrected energy. The zero energy reference is O+ + CH4.
As shown in Table 1, PM3 overestimates the reaction exoergicity for the above reaction channels. A similar trend was found earlier in studies of the O(3P) + CH4 reaction mechanisms.17 The largest difference between PM3 and experiment is for channel 6, O+ + CH4 f CH2+ + H2 + O, where the PM3 method gives a dissociation barrier that is 1.4 eV too low. As a result, on the PM3 PES, channel 6 is energetically more favorable than channel 5. Since CH3+ is one of the major products from O+ + CH4 reaction, this error in PM3 may severely affect the CH3+/CH2+ branching ratio even though the PM3 energy for CH4+ f CH3+ + H dissociation is in very good agreement with experiment. This point provides incentive for studying the sum of CH2+ and CH3+ products, so we will consider this possibility later on. The CH3+ + H + O product arises from a dissociative charge transfer (DCT) mechanism; however Table 1 shows that CH3+ can also be produced as an excited triplet through the product CH3+(a˜3E) + OH (X2Π) and that this is a lower energy pathway for producing CH3+ than is DCT. Later we will examine the importance of this pathway. Of course there is an even lower energy pathway that leads to ground state CH3+(X ˜ 1A′1) + 2 OH(X Π); however this is spin-forbidden and is not included in the present study. Reaction paths for the different products are depicted in Figure 1 and Figure 2, including PM3 and MP2 energies for several stationary points. We have also compared PM3 and MP2 geometries and vibrational frequencies (not included in Figures 1 and 2), and we find reasonable agreement. For example, the PM3 and MP2 calculated equilibrium structures (excluding QTS2 and QCP3 in Figure 1) have a mean absolute deviation in bond lengths of 0.082 Å and 7.9° for the bond angles. In addition, there is a 4% difference on average between the PM3 and MP2 calculated frequencies. For collisions at high energies (e.g., 5 eV) for the [O‚CH4]+ system, stationary point properties such as harmonic vibrational frequencies and equilibrium structures are not expected to play a critical role. Therefore we focus on the reaction energetics in the following discussion. The results in Figure 1 show that PM3 makes errors in the energies of intermediates, here relative to the MP2 energies, that are comparable to the errors in Table 1. Most of the reaction paths are the same as found using MP2 calculations, with the initial ion-dipole complex (QCP1) evolving to several products
Figure 2. Same as Figure 1, but diagram for the (a) CH3O+ (M ) methoxy ion) and (b) H2CO+ (F ) formaldehyde ion) isomerization (I) and dissociation (D).
over transition states that are below the QCP1 energy. Since these energies are all well below the available energy in the collisions, we expect that the indicated products should be formed even at low energies, with the exception of CH3+ + H + O and CH2+ + H2 + O, both of which are endoergic by less than 1 eV. The large overestimation of many of the reaction exothermicities makes the PM3 model invalid for low energy (below 1 eV) O+ + CH4 collisions. Figure 2 presents reaction paths and energies for unimolecular processes associated with the H2CO+ and CH3O+ products that are produced in the primary reaction. Here we find that the PM3 energies are in good agreement with MP2 results. As mentioned earlier, we chose the PM3 method for this study because it is much quicker to use for trajectory calculations than density functional theory or MP2, it provides accuracy that could be adequate at hyperthermal collisions, and it is less susceptible than density functional methods or MP2 methods to selfconsistent field (SCF) convergence problems. We note that the PM3 method with specific reaction parameters (SRPs) can be used as an improvement to the PM3 Hamiltonian. However, for a complex reaction system with multiple reaction channels a large number of very high level ab initio calculations have to be done for different molecular configurations along the IRCs to fit the SRPs. In addition, it is often necessary to introduce analytical potential energy functions for further potential energy corrections. This is not practical for a system with many reaction pathways; however excellent work has been done by Yan et. al. for the O(3P) + ethane reaction.20 Another alternative to PM3 is the MSINDO method that Troya, Schatz, and co-workers have extensively used to describe the reaction of neutral oxygen with saturated hydrocarbons.15-18 In that work it was found that MSINDO had more realistic estimates of high energy barriers to reaction, so since the neutral oxygen reactions are all activated, this led to more accurate MSINDO results than PM3 when compared to results of more accurate methods such as density functional theory. However
8434 J. Phys. Chem. B, Vol. 109, No. 17, 2005 for the reactions of O+ with hydrocarbons, we find that PM3 gives somewhat more accurate energetics than MSINDO (for example, the mean absolute deviation between MSINDO and MP2 for the stationary points in Figures 1 and 2 is 0.86 eV while the corresponding PM3-MP2 deviation is 0.45 eV), so we have chosen to use PM3 rather than MSINDO. II.B. Direct Dynamics Simulations. With increased speed of computers, direct dynamics simulations, in which the electronic structure calculations are performed “on the fly” during integration of classical trajectories, has been widely used for chemical dynamics simulations. In the work reported here, we used the PM3 direct dynamics algorithm directly coded in the GAMESS software package.26 A quasiclassical sampling method was used for selecting trajectory initial conditions with a center-of-mass relative translational energy ranging from 0.5 to 12 eV. The impact parameter b is randomly selected according to b ) bmax(ξ)1/2 , where ξ is a random number ranging from 0 to 1 and bmax is selected to be 4 Å which is large enough that there are no chemical reactions at larger impact parameters. The trajectory integration uses the standard leapfrog algorithm in the DRC subroutine of the GAMESS program.26 The trajectory integration step-size is chosen to be 0.1 fs. The maximum energy change during each trajectory (due to errors in energy conservation) is less than 1 kcal/mol with this step size. For trajectories which show evidence for reaction, the trajectory is integrated for 500 fs. Otherwise it is stopped with a center-of-mass separation of 10 Å. For all the results reported, spin contamination is found to be small (change in 〈S2〉 is less than 5%). A total of 3000 trajectories were calculated at 0.5 eV and 5000 for higher collision energies. III. Results III.A. Reaction Products. Before we present details of our calculations, a few qualitative statements about our results are useful. In agreement with experiment,13 the PM3 trajectories show that all 10 of the possible products (eqs 1-10) are produced, including important contributions from oxygenated carbon containing species. In agreement with Figure 1, only CH3+ and CH2+ have a nonzero threshold energy. These ions are produced (in part) by the collision induced dissociation (or more rigorously, DCT) reactions CH4+ f CH3+ + H and CH4+ f CH2+ + H2. These are competitive processes, so the low threshold energy for producing CH4+ f CH2+ + H2 leads to overestimation of its cross section and reduces that for CH4+ f CH3+ + H. Therefore, in making comparisons with experiment, we will combine the CH2+ and CH3+ channels together. A similar issue arises for reactions that lead to the H2CO+, HCO+, and CO+ ions. Here we find that a large amount of the available energy can be deposited into the internal degrees of freedom of the primary product ion CH3O+ leading to its efficient dissociation to give H2CO+, HCO+, and CO+. As a result, the CH3O+ cation radical is completely negligible when the collision energy is higher than 0.5 eV. The branching fraction to give H2CO+ is also small, being only 6% at 0.5 eV and less than 1% above 8 eV. The HC-OH+ isomer of H2CO+ is also observed with a population of about 50% of H2CO+. The H2O+ cation is the main product at low energies, but it becomes much less important at higher energies. Its decline is not balanced by a rise in the OH+ cross section (instead the latter decreases slowly with energy over the whole range of energies studied), and we find (described later) that there are mechanisms for H2O+ formation that are not connected to OH+ formation. As a result H2O+ and OH+ will not be grouped together in making comparisons with experiment.
Sun and Schatz
Figure 3. Opacity functions at (a) 5 eV and (b) 10 eV collision energy.
III.B. Opacity Function. The opacity functions for major reaction channels are shown in Figure 3 for 5 and 10 eV trajectories. Here we have summed the opacities for similar families of products, for reasons just described. The figure shows that at small impact parameters, the dominant process is HCO+/ H2CO+. (No CH3O+ survives at these energies.) CO+, which we have separately plotted in this figure, has a similar impact parameter dependence. This is consistent with our conclusion that this product arises from decay of HCO+/H2CO+. However the reactivity to CO+/HCO+/H2CO+ decreases dramatically for b larger than 1.25 Å, indicating that direct impact of the incoming O with the carbon atom in methane is needed for these reactions to occur. The large impact parameter for OH+ implies a spectatorstripping mechanism for this reaction, and we have verified that the product translational energies are consistent with this model. The C-O distance in the prereaction complex QCP1 is about 2.6 Å, which is almost identical to the peak position in Figure 3 for the OH+ + CH3 channel. Unlike the two opacity functions described above which are confined either to small impact parameters or to large impact parameters only, the CH3+/CH2+ curve is relatively broad with a peak at b ) 1.6 Å. This is interesting since if the CH3+ cation is mainly produced from the DCT mechanism (channel 5), there should have been a more significant peak at smaller impact parameters. A detailed analysis of the trajectories shows that CH3+ in its 3E electronic state is the major source of CH3+ in this simulation, which means that the reaction mechanism leading to CH3+ involves CH3+ + OH formation instead of DCT. To further understand the contribution of the CH3+ excited state and the relationship of the CH3+ and CH2+ reaction channels, the opacity functions of the CH3+ and CH2+ channels are plotted independently in Figure 4. Here we find that the overall shapes of the CH3+ and CH2+ opacity functions are very
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Figure 4. Opacity functions for CH3+/CH2+ product channels at 5 eV.
similar and they both show a peak at b ) 1.6 Å. Formation of CH3+(3E) is dominant for all but low impact parameters. The ratio of CH3+(3E) to CH3+(1A′) is about 2:1 at 5 eV. PM3 calculations (Table 1) indicate that CH3+(3E) + OH(2Π) is 0.22 eV higher in energy than the O+ + CH4 asymptote while MP2 gives -0.01 eV, and the experimental result is likely lower still as the MP2 result overestimates the difference in vertical ionization energies of CH3 to give the a˜3E and X ˜ 1A′1 states of CH3+ by about 0.3 eV compared to experiment.27 Thus we conclude that the PM3 branching to give CH3+(3E) is probably underestimated at low collision energies, and indeed it is possible that this mechanism may be more important than the spin-forbidden doublet state mechanism for producing CH3+ that previously was assumed to be dominant.13 Other CH3+ product channels may involve CH3O+ dissociation to CH3+ + O and direct reaction to give CH3+(X ˜ 1A′1) + OH (4∑-) followed by decay of the weakly bound OH(4∑-) to O(3P) + H. The classical trajectory simulations have observed these pathways. However, as shown in Figure 4, contribution from these channels is very small and never exceeds 10%. The small peak at b ) 0.4 Å is related to the DCT mechanism. Our simulations show that at larger impact parameters, e.g., b > 1.0 Å, CH3O+ f CH3+ + O unimolecular dissociation has a non-negligible contribution. The unimolecular dissociation of CH3O+ is fast for this channel, and indeed it often dissociates within one C-O vibration period. At a collision energy of 10 eV, the CH2+/CH3+ opacity function gets narrower and the peak position is reduced slightly by 0.3 Å. The reaction probability is increased about 9% at b ) 1.3 Å, while the H2CO+/HCO+/CO+ reaction probability is reduced by about 7%. A similar correlation between CH2+/CH3+ and H2CO+/HCO+/CO+ also happens at smaller impact parameters but is a much smaller effect. The large correlation happens within a narrow range of impact parameters from 1.3 to 1.6 Å, and this leads to an increase of the CH3+/CH2+ peak at 1.6 Å. III.C. Excitation Functions. One observable that can be compared with experiment is the reaction cross section. In Figure 5a, the excitation function for two major products, i.e., CH3+ and CH2+, is compared with experimental results. Error bars for the experiments are not available; however they are typically (30%. The analogous comparisons for H2CO+, HCO+, and CO+ products are shown in Figure 5b. For all these channels, the calculated excitation function has a similar shape to the experimental curves especially for high collision energies. This
Figure 5. Excitation functions for the O+ + CH4 reaction system. Solid lines (s) are experimental results from ref 13. Dashed lines (- - -) are simulation results. Results for the CH2+ and CH3+ products are in panel a. Results for the H2CO+, HCO+, and CO+ products are in panel b. Panel c shows the summed cross sections for CH2+/CH3+ and for CO+, HCO+, and H2CO+ as well as unsummed cross sections for OH+ and H2O+.
indicates that the PM3 PES is qualitatively correct for these reaction channels. However, there is a large difference in the magnitude of the cross sections between the simulation and experiment for these products. Indeed, the simulation overestimates the cross section for CH2+ and underestimates it for CH3+. Figure 5c shows a comparison of the summed cross sections (CH3+ + CH2+) with experiment, and here we see much better agreement, indeed excellent agreement at 10 eV. Figure 5c also shows the sum of H2CO+, HCO+, and CO+ crosses, and we see that there is again very good agreement between theory and experiment, except at very low energies. In this case the branching ratios for HCO+, H2CO+, and CO+ are 1:0.09:0.16 at 5 eV, so the excitation function does not differ much from that for HCO+ itself. These ratios are in rough agreement with experiment at this energy (1:0.08:0.10).
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Figure 6. Energy partitioning for the CH3 + OH+ (s) and CH3+ + OH (- - -) products: (a) relative translation; (b) CH3/CH3+ vibration and rotation; (c) OH+/OH rotation; (d) OH+/OH vibration.
Excellent agreement between theory and experiment is also seen in Figure 5c for the H2O+ ion, including the significant drop with energy (factor of 10 in going from 1 to 10 eV) that occurs as H2O+ loses out to CH2+/CH3+ formation (as endothermic processes that lead to the latter open up). For the OH+ ion, the measured cross section also includes contributions from CH5+ ions (produced by secondary reactions)13 so the comparison with experiment in Figure 5c for that species is not meaningful. What we see is that the OH+ cross section decreases slowly with energy, as would be expected for a stripping mechanism. The good agreement between experiment and calculations confirms that the PM3 model is a valid approach for the qualitative description of the dynamics of O+ + CH4 at high collision energies. For quantitative results, we see that summing the cross sections for competing mechanisms leads to better agreement with experiment. III.D. Product Energy and Angular Distributions. Ionmolecule reactions at low energy often involve the formation of an ion-dipole complex in which the collision energy is repartitioned among different internal degrees of freedom. However direct reaction will become progressively more important as collision energy increases. This changing of the reaction mechanisms affects energy partitioning and angular distributions, so this information provides additional insight into the collision dynamics. To study these quantities, in Figure 6 we have plotted the partitioning between translational and internal energies for the CH3 + OH+ and CH3+ + OH products, while in Figure 7 we show angular distributions for several of the products. Although the CH3 + OH+ and CH3+ + OH products are nominally related by a simple charge transfer process, we have already seen that these can have different mechanisms due to the participation of excited electronic states. Indeed the opacity functions for both reactions have peaks at large impact parameters, but CH3+ +
Figure 7. Angular distribution expressed as normalized differential cross section (DCS, (1/σ)(dσ/d(cos(k‚k′)) for selected product channels: (a) DCS at 0.5 eV collision energy; (b) DCS at 5 eV collision energy.
OH, which can be thought of as a hydride abstraction channel, requires closer impact than CH3 + OH+, which is a hydrogen abstraction product. Figure 6 shows that for both channels, most of the available energy is partitioned into relative translation at high collision
Direct Dynamics Classical Trajectory Simulations energy. This is consistent with the spectator-stripping model, and it matches the higher energy experimental results as well.13 The fractions become somewhat constant with energy above 5 eV for the more exoergic CH3 + OH+ channel, but for CH3+ + OH, product translational energy continues to rise with collision energy. The CH3+ + OH channel receives less translational energy but picks up more CH3+ internal and OH rotational energies than the CH3 + OH+ channel. This is consistent with the fact that the CH3+ + OH product channel requires smaller impact collisions. There is much more internal excitation in the CH3+ cation than in CH3, and OH rotation is generally higher than OH+ rotation, but OH vibration closely matches OH+ vibration. For the H2CO+ products, we find that over 85% of the total available energy is transferred to the H2CO+ internal degrees of freedom at 2 eV and 54% at Ecoll ) 5 eV. Dissociation of H2CO+ to HCO+ is the major source of the HCO+ cation, so not surprisingly we find that over 50% of the total available energy is partitioned to internal energy of HCO+. These results are again consistent with experiment.13 In Figure 7, the angular distribution is defined in terms of the normalized differential cross section (DCS, (1/σ)(dσ/d(cos(k‚k′)), where σ is the integral cross section and k and k′ are the initial and final unit vectors of velocity) as a function of the scattering angle cos(k‚k′). Figure 7 shows angular distributions that are consistent with the expected transition from longlived complex formation to direct reaction as collision energy is increased. Indeed Figure 7a shows broad angular distributions for the H2O+/CH3+/OH+ products at Ecoll ) 0.5 eV, while Figure 7b shows mostly forward scattering for these products at 5.0 eV. However it should be noted that none of the angular distributions in Figure 7a show forward-backward symmetry. Instead, scattering of CH3+/OH+ is more forward while H2O+ scattering is more backward. The more forward scattering of CH3+/OH+ is due to the fact that the intermediate complex is not long-lived, and the reaction dynamics even at low energies is associated with high impact parameters. The backward scattering of H2O+ arises because this product often comes from double hydrogen abstraction trajectories that involve smaller impact parameters (Figure 3) and dynamics that is complex mediated. The complex mediated dynamics of the H2O+ product is in agreement the observed experimental velocity distributions. We have omitted H2O+ in Figure 7b because this is a negligible product at this energy. However we have added CH2+ and HCO+, and we find that the former is very much like CH3+ and OH+, with a strongly forward peak, while HCO+ shows a nearly isotropic distribution. The strong forward peaks for OH+/ CH3+ are consistent with the laboratory velocity distribution observed in the experiment.13 The HCO+ angular distribution is consistent with the formation of an intermediate complex whose lifetime is long enough compared to its rotational period. Indeed, we find from the trajectory simulations that, at a collision energy of 5 eV, the H2CO+/HCOH+ intermediate has a lifetime of up to 400 fs before it decomposes to HCO+, while that for the CH3O+ cation radical is much shorter (
