J. Phys. Chem. 1996, 100, 195-200
195
Predominance of Knockout Reactions at High Energy in Collisions of X + H2 (X ) O(3P), F, Cl, T, and H) Ju-Beom Song and Eric A. Gislason* Department of Chemistry, UniVersity of Illinois at Chicago, 845 W. Taylor, Chicago, Illinois 60607-7061 ReceiVed: July 14, 1995; In Final Form: September 25, 1995X
Quasiclassical trajectory studies have been carried out for the reactions of O(3P), F, Cl, T, and H with H2 over a wide range of relative collision energy. For all five systems at low energy the projectile reacts only with the H atom it hits first (direct reaction), but at high energy the major product channel is the knockout reaction, where the atom hits one H atom but then goes on to react with the other one. This behavior is consistent with the direct interaction with product repulsion model and is attributed to a common feature of the potential energy surfaces, namely, a strong repulsion between the two H atoms after the system makes the rapid transition between the reactant and product regions of the surface. Evidence for the importance of knockout reactions at high energy is also seen in the angular distribution of the products, particularly in the persistence of product molecules scattered into the backward hemisphere.
I. Introduction We have been working to understand the mechanism of reactions such as
O(3P) + H2 f OH + H
(1)
at high energy. For this purpose we have carried out a series of quasiclassical trajectory (QCT) computations1,2 for this and similar reactions. In this work we monitored a number of intramolecular properties during the trajectory in an effort to better understand the reaction mechanism. We have also developed a new, general hard sphere trajectory program2 for studying this type of reaction. This program considers the general collision of A + BC with four possible product channels:
A + BC f A + BC
(2)
f AB + C
(3)
f AC + B
(4)
fA+B+C
(5)
Here A, B, and C are atoms. The last channel is collisioninduced dissociation (CID). The program treats A, B, and C as hard spheres with radii RA, RB, and RC, and assumes that B and C are initially touching. Each hard sphere trajectory commences with A hitting B or C followed by strong interactions between the three atoms which lead to the final velocities of the atoms. From the velocities a set of algorithms is used to select the final product state. The program uses either the sequential impulse model3-7 or the direct interaction with product repulsion (DIPR) procedure8-16 to treat the three-atom interaction and determine the final velocities of A, B, and C. The results of the hard sphere program are then compared with the QCT calculations; similarities and differences give insights into the reaction mechanism. One question which naturally arises in a hard sphere treatment of the A + BC reaction is if A hits atom B first, does it go on to form AB + C or does it react with the other atom to give AC + B? The former case is called a “direct” reaction or X
Abstract published in AdVance ACS Abstracts, December 1, 1995.
0022-3654/96/20100-0195$12.00/0
“abstraction”, whereas the latter is called “knockout”, “insertion”, “substitution”, or “migration”. The same question can be asked in QCT calculations, provided that care is taken to properly define the notion that A “hits” B first or A “hits” C first. Our QCT study2 of reaction 1 on the Johnson-Winter17 surface showed at relative collision energies above 250 kcal/ mol that knockout collisions dominated the reaction. At these higher energies it is very difficult to form stable products AB or AC,7 and the CID channel, reaction 5, is the major product channel. Thus it appears that for some reason the knockout mechanism is more effective in dispersing the collision energy into translational degrees of freedom of the products and allowing a stable diatomic to be formed. In the same paper2 we studied reaction 1 using the hard sphere trajectory program. We determined that the DIPR model predicts that knockout reactions will dominate at high energy. By contrast the SIM predicts that direct and knockout reactions will have equal cross sections at high energies. For this and other reasons we concluded that the DIPR model gives a better description of the mechanism of reaction 1 at high energies. The importance of the knockout mechanism at high energies has been observed in other QCT studies of the reactions of H2 or its isotopic variants with various atoms or ions. These include Muckerman’s study18 of F + HD, the work of Wright et al.19 on T + HD, Malcome-Lawes calculations20 on several isotopic variations of H + H2, and the work of Schechter and Levine21 on H + H2. It was also seen in our recent study of Cl- + H2.22 On the basis of this earlier work and our studies of reaction 1 we decided to carry out QCT calculations on a series of reactions to determine how general is the predominance of the knockout mechanism at high collision energies. In addition to O(3P) + H2 we studied the following reactions:
F + H2 f FH + H
(6)
Cl + H2 f ClH + H
(7)
T + H2 f TH + H
(8)
H + H2 f H2 + H
(9)
The potential energy surface for each of these reactions has a © 1996 American Chemical Society
196 J. Phys. Chem., Vol. 100, No. 1, 1996
Song and Gislason
TABLE 1: Bond Distances at the Linear Transition State for the X + H2 Reactiona atom X
R‡(X-H), Å
r‡(H-H), Å
refs
O F Cl T, H
1.118 1.541 1.398 0.93
0.953 0.760 0.993 0.93
17 24 25 26
a In each case the barrier to reaction is lowest in the linear configuration.
barrier that is lowest in the linear configuration. In other respects the surfaces for reactions 1 and 6-9 are quite different. II. Theory The QCT calculations were carried out as described in our earlier papers1,2 using the VENUS program developed by Hase and co-workers.23 The potential energy surfaces in most cases were LEPS surfaces, which have been used in the past to study the reactions in question. We recognize that in some cases these are not the most accurate available surfaces, but we have used them for ease of computation. We do not expect any of the conclusions reached in this work for a particular system to be affected significantly by a change in potential energy surface (provided that the surface has a barrier which is lowest in the linear configuration). The LEPS surfaces are as follows: O + H2, Johnson and Winter;17 F + H2, Muckerman24 (surface M5); and Cl + H2, Persky.25 The surface used for T + H2 and H + H2 was the accurate SLTH surface.26 All reactive collisions were separated into two groups: direct reactions, where A hits B first and then forms the product AB, and knockout reactions, where A hits B first but then forms the product AC. In the QCT computations we must define what we mean by A hits B first or A hits C first. The procedure we use for this has been described in our earlier paper.2 For each reaction studied here the potential energy surface has a barrier that is lowest in the linear configuration. At the linear saddle point the bond lengths are denoted R‡(A-B) and r‡(B-C). For each reaction these bond lengths are summarized in Table 1. In the QCT calculations the program monitors the A-B and A-C distances throughout the trajectory. If the A-B distance reaches R‡(A-B) before the A-C distance reaches R‡(A-C), we say A hits B; if the reverse occurs, we say A hits C. (If neither atom-atom distance reaches the critical distance, reaction cannot occur, and the trajectory is ignored.) This allows us to cleanly separate all reactions into direct and knockout types. Standard Monte Carlo sampling procedures were used to select the initial conditions for each trajectory. In most cases 7000 trajectories were run for each reaction at each collision energy. The H2 molecule was in the state V ) 0, J ) 0 in all the calculations. The calculation of the angular distributions was carried out using the Fourier expansion technique developed earlier by us.27 III. Results and Discussion Figure 1 shows the various cross sections for the reaction of O + H2 as a function of relative collision energy E. (A similar figure was given in ref 2.) The total reactive cross section rises rapidly above E ) 10 kcal/mol; the reactivity in this energy range is well explained by several “angular dependent line-ofcenters” models.28,29 All reactions at low energy are direct. The cross section for knockout reactions has a threshold of E ) 70 kcal/mol and rises steadily immediately above that energy. At E ) 104 kcal/mol CID becomes allowed, and its cross section grows rapidly, particularly at the expense of direct reactions. It is clear from inspection of individual trajectories that collisions
Figure 1. Various reactive cross sections for the system O + H2 calculated by the QCT procedure as a function of collision energy. The open circles are the cross sections for direct reactions, where O reacts with the first H atom it hits. The closed circles give the cross sections for knockout reactions, where the O atom hits one H atom but reacts with the other. The total reaction cross sections (direct plus knockout) are shown as ×’s; the ×’s are not shown when they coincide with the direct or the knockout values. The triangles give the cross sections for collision-induced dissociation to give O + H + H. The uncertainty in each cross section is approximately twice the size of the symbol.
where the intermediate O-H-H bond angle is nearly linear give either direct reaction or, if that product is not stable, CID. By comparison collisions where the intermediate is bent have the additional possibility of knockout reactions. The cross section for direct reactions continues to fall and disappears near E ) 400 kcal/mol. The knockout cross section, on the other hand, peaks at E ) 250 kcal/mol and then slowly declines to zero at E ) 900 kcal/mol. It is also apparent in Figure 1 that the total cross section, i.e., the sum of the reactive and CID cross sections, falls slowly above 100 kcal/mol. This reflects the relatively soft repulsive potential for the O + H2 system. In the hard sphere model the radii are determined from the potential energy surface; the procedure is described in detail in ref 2. The radii decrease with energy because the electron clouds of the atoms are not hard spheres. Our work has shown that all four surfaces considered in this work are remarkably soft, presumably because the H2 molecule has only two electrons. As an example we have fit the O + H2 surface17 in the repulsive region for fixed r(H-H) ) re(H2) and for the O-H-H angle set at 75°. In terms of the O-H distance, ROH, the results are well fit2 by the equation
V(ROH) ) A/ROHn
(10)
with n ) 3.67. The comparable values of n for the other systems are 3.40 for F + H2, 4.47 for Cl + H2, and 2.38 for H + H2. Normally values of n ) 6-12 are expected for repulsive potentials.30 Once the potential has been fit by eq 10, it is straightforward to calculate at high energy the total cross section for reaction plus CID;2,31 the energy dependence is given approximately by E-1/n. Thus the total cross section decreases with energy, and the softer the potential (i.e., the smaller n is), the faster the decrease. The results for F + H2 are shown in Figure 2. The curves are qualitatively similar to those for O + H2, but there are a
Knockout Reactions at High Energy
J. Phys. Chem., Vol. 100, No. 1, 1996 197
Figure 2. Various reactive cross sections for the system F + H2 calculated by the QCT procedure as a function of collision energy. The symbols are explained in the caption for Figure 1. The uncertainty in each cross section is approximately twice the size of the symbol.
Figure 4. Various reactive cross sections for the system T + H2 calculated by the QCT procedure as a function of collision energy. The symbols are explained in the caption for Figure 1. The uncertainty in each cross section is approximately twice the size of the symbol.
Figure 3. Various reactive cross sections for the system Cl + H2 calculated by the QCT procedure as a function of collision energy. The symbols are explained in the caption for Figure 1. The uncertainty in each cross section is approximately twice the size of the symbol.
section (reaction plus CID) is 35% larger at the highest energies. This reflects the fact that the Cl atom is “bigger” than the F atom on the surfaces used in this work. The first three systems have involved atoms which are much heavier than the target H atoms. In Figure 4 we show the results for T + H2. Qualitatively, the results resemble those for the heavier atoms. At low energy all reactions are direct. The threshold for knockout reactions is E ) 50 kcal/mol, and this becomes the predominant mechanism for reaction above E ) 150 kcal/mol. For this system direct reactions do not occur above E ) 300 kcal/mol and the knockout reactions are also gone by E ) 600 kcal/mol. One noticeable difference for T + H2 is that the CID cross section rises rather slowly above the threshold. The total cross section (reaction plus CID) is only 2.5 Å2 at the peak, reflecting the relatively short T-H bond length at the saddle point (see Table 1). This cross section falls very quickly with energy, reflecting the extremely soft potential energy surface for this system.26 Figure 5 gives the results for H + H2. Because the three masses are identical, we had some expectation that the reactivity would be higher than for T + H2 at elevated collision energies. A head-on hard sphere collision of a fast H atom with a stationary H atom should leave the first atom stationary, and this could allow knockout reactions to occur even at very high energies. The reality is that H + H2 is somewhat less reactive than T + H2 at all energies, even though the general features are very similar. We attribute this to the greater importance of recrossing collisions for H + H2. (Recrossing collisions are collisions where the A-B distance reaches R‡(A-B) but reaction does not occur.) To demonstrate this we show in Table 2 the final result of all trajectories at E ) 100 kcal/mol where the X-H distance reaches the transition state distance R‡(XH) given in Table 1. At this energy the CID channel is not open. We see that 15% of the O + H2 and Cl + H2 collisions recross to the reactant region, whereas about 30% of the F + H2 collisions are nonreactive. We attribute the latter result to the fact that the barrier in F + H2 is very early (see Table 1), quite low, and strongly angle-dependent. This point is discussed further in ref 1b. The difference between T + H2 and H + H2 on the same surface is striking, and this difference persists at higher collision energies. Presumably the larger fraction of recrossing collisions for H + H2 is due to the fact that at a
number of differences. First, the barrier to reaction is much lower for F + H2 in the linear configuration as well as at all other A-B-C orientation angles. Thus, the threshold energy for reaction is lower, the direct reactive cross section rises more rapidly with collision energy, and knockout reactions have a lower threshold energy for this system. It is apparent from the data that both knockout reactions and CID occur primarily at the expense of direct reactions as the collision energy increases. As in the case of O + H2, direct reactions do not occur above 400 kcal/mol, whereas knockout reactions continue until E ) 900 kcal/mol. One other important difference is that the total cross section for F + H2 is much bigger than for O + H2. This can be explained by the very large F-H distance at the transition state (see Table 1). We have shown31 that at its peak the total cross section scales nearly as the square of that distance. Figure 3 shows the energy dependence of the cross sections for Cl + H2. Overall, the results are remarkably similar to those for F + H2. Perhaps the biggest difference is that the total cross
198 J. Phys. Chem., Vol. 100, No. 1, 1996
Song and Gislason
Figure 5. Various reactive cross sections for the system H + H2 calculated by the QCT procedure as a function of collision energy. The symbols are explained in the caption for Figure 1. The uncertainty in each cross section is approximately twice the size of the symbol.
TABLE 2: Summary of Collisions at E ) 100 kcal/mola reaction
direct reaction, %
knockout reaction, %
nonreactive, %
O + H2 F + H2 Cl + H2 T + H2 H + H2
78.6 52.6 71.3 55.1 38.0
5.9 13.2 14.4 16.4 13.2
15.5 34.2 14.3 28.4 48.8
a Percentage of trajectories which end up in the three possible product channels after R reaches R‡ (see Table 1 for values).
given relative energy the H atom is moving 30% faster than the T atom. Therefore, in collisions with H, the target H2 molecule has less time to lengthen to its transition state value (see Table 1). This reduces the cross sections for both reaction and CID. There have been a few other QCT studies of these reactions over a comparably wide energy range. In no cases, however, were the reactive cross sections separated into direct and knockout components. The first study was that of Karplus et al.32 on T + H2 on a different potential energy surface. Their results for reaction and CID are similar to ours, but they continue to observe chemical reaction up to 1700 kcal/mol. MalcolmeLawes has studied the reactions of T + H2 and H + H220 as well as O + H2 and F + H233 up to E ) 250 kcal/mol. He constructed his own potential energy surfaces, and in all cases his reactive cross sections are similar to, but somewhat larger than, our values. Both Bookin et al.34 for F + H2 and Alfassi and Baer35 for O + H2 have used the same potential energy surfaces as we used in this work. As expected the reactive cross sections are very similar over the entire range of energy. The five systems studied here show a remarkable number of similarities. It is instructive to summarize and attempt to explain them. Our earlier work2 on O + H2 using QCT calculations and the hard sphere trajectory program gives some guidance here. First, the total cross section (reaction plus CID) always peaks near E ) 100 kcal/mol, its magnitude there reflects the X-H saddle point distance given in Table 1, and it then falls by as much as a factor of 2 at E ) 900 kcal/mol. This behavior occurs because atoms are not hard spheres, and the fairly rapid falloff reflects the soft repulsive potentials which characterize H2 systems. Second, all of the reactions are direct at low collision energies. This is because there is a barrier to knockout
reactions (typically 60 kcal/mol but lower for F + H2). We have argued2 that this barrier should approximately equal the saddle point energy when the A-B-C angle γ is 120°. (Linear A-B-C corresponds to γ ) 0°.) A larger value of γ would mean the system has moved from an A-B-C to an A-C-B configuration. Third, CID always appears at the energy threshold for this process, and the cross section rises quickly above threshold. Our earlier work2 indicates this occurs because collisions of A + BC with small impact parameters can only give direct reaction (AB + C) or CID; that is, both knockout reactions (AC + B) and recrossing (A + BC) cannot take place. The fourth and most interesting result for the five reactions is that knockout reactions are always favored over direct reactions at high collision energy. To understand this it must be kept in mind that the primary product channel at high energy is CID, and it takes a very special collision to produce a stable product. Our analysis of the O + H2 system2 has identified these collisions. If the initial velocity of the A atom is parallel to the z-axis, reaction is most likely to occur if the BC molecule is directed approximately along the z-axis. For definiteness assume atom A initially approaches the B end of the molecule. During the approach the repulsive force between A and B grows rapidly. At some point the system crosses the hypersurface separating reactants from products, producing a strong repulsion between B and C. Since they are light atoms, they dissociate rapidly. The B atom is propelled backward, whereas the C atom moves rapidly forward in the same direction as the A atom. Thus, only AC is formed. In summary, atom A first approaches atom B closely but then goes on to react with C; this is a knockout reaction. The mechanism described here is very similar to the DIPR model,8-16 which we have shown reproduces many of the scattering features of the O + H2 reaction.2 Real collisions are more complicated because the A-B-C intermediate lives long enough for it to rotate before the energy is released, so product AC molecules appear over a wide range of scattering angles. This point was explored in an earlier paper.36 Nevertheless, the differential cross section is strongly peaked in the forward direction as predicted by the simple DIPR model.2 Experimentally, it is not possible to distinguish product molecules produced in a direct reaction from those made by the knockout mechanism. However, we would expect some confirmation of the reaction shifting from primarily direct at low energies to knockout at high energies to show up in the differential cross section I(θ) sin θ plotted as a function of energy. All of the systems considered here have PESs with barriers to reaction which are lowest in the linear configuration. It is well-known for reactions of this type that the differential cross section peaks in the backward direction at low collision energies.37 This is to be expected for direct reactionssthe O-H-H intermediate is nearly linear, the product atom recoils forward, and the product molecule appears in the back hemisphere. At higher energies the picture is quite different. Now knockout reactions are allowed, any O-H-H intermediate angle γ can give reaction, and in principle all center of mass productscattering angles θ are allowed. In practice, however, most product molecules which would appear in the back hemisphere have too much internal energy, and CID results. Thus, the products appear primarily in the forward hemisphere for both direct and knockout reactions. This is observed in our calculations for O + H2 presented in Figure 6. An inspection of individual trajectories shows that the direct scattering seen at 300 kcal/mol occurs via a “stripping” mechanism. The O-H-H intermediate angle γ at the transition state (R ) R‡) is always close to 90°, so little impulse is given to the departing H atom
Knockout Reactions at High Energy
J. Phys. Chem., Vol. 100, No. 1, 1996 199 H2,24 and Cl + H2.25 But, the calculations for T + H2 and H + H2 were done on the accurate SLTH surface,26 and both systems showed the same behavior. One can easily imagine reactive systems where the DIPR model should not work as well. For example, we41 have studied the reaction of He with H2+, where there is also a sharp distinction between the reactant and product regions. However, this reaction is endothermic, and, in addition, the repulsive forces between the products are almost nonexistent. In summary, we expect the behavior observed in this paper will occur only if there is a strong repulsion between atoms B and C after the system makes the transition between the reactant and product regions of the surface. Acknowledgment. The authors have enjoyed many useful discussions with M. Sizun. References and Notes
Figure 6. The reduced angular distribution, proportional to I(θ) sin θ, plotted against the reduced center of mass scattering angle θ/π. The integral under each curve is one. The distribution for direct reactions is shown as a dotted curve and for knockout reactions as a dashed curve, and the properly weighted total distribution is shown as a solid curve. The relative collision energies (top to bottom) are 300, 158, 70, and 20 kcal/mol. In the bottom two panels all reactions are direct.
by the OH product. Stripping reactions are known to be characterized by a very narrow angular distribution peaked in the forward direction and by a rapid falloff of the reactive cross section at high energies.38 Both features are seen in the direct reaction of O + H2. By comparison, products formed by the knockout mechanism at high energies are also forward peaked, but the angular distribution is much broader, and products are seen at angles larger than θ ) 90°. This behavior persists at even higher energies. For example, I(θ) sin θ at E ) 500 kcal/mol (not shown) is entirely due to knockout scattering and is forward peaked, but products are still observed for θ >90°. Experimental measurements of the angular distribution at high energies have not been made for the O + H2 reaction or the other systems considered here. However, measurements have been made for a number of ion-molecule reactions such as Ar+ + H239 and N2+ + H2.40 In both cases I(θ) sin θ is strongly peaked in the forward direction, and this is attributed to a stripping mechanism. However, even at the highest energies studied (∼250 kcal/mol), reactive scattering is also seen in the backward hemisphere. To date there is no satisfactory explanation for these backwardscattered products. On the basis of our calculations we would argue that the persistence of wide angle scattering at large collision energies is strong, albeit indirect, evidence for the importance of knockout reactions for these ion-molecule systems. Similarly, we would expect that experimental measurements of I(θ) sin θ for O + H2 would show the same features, confirming the importance of knockout reactions for this reaction and the other reactions studied in this paper. In our opinion, the DIPR model describes well the reactions of all five systems studied here at high energy. It might be tempting to attribute this behavior to special properties of the LEPS potential surfaces used in this work for O + H2,17 F +
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