8267
J. Phys. Chem. 1991, 95, 8267-8273 of energy release, but they show that the final kinetic energy is quite unlikely to exceed 5000 cm-’. Conclusions We have measured the internal product state distributions of OH from the reaction of H20(104)-) and OD from reaction of HOD(104)) with H atoms and find that in both cases less than 10% of the roughly 9000 cm-’ of available energy appears in internal energy of the product coming from the “old” bond. Analysis of the line shapes in the O D product LIF excitation spectrum places an upper limit of about 5000 cm-I on the translational energy content of the reaction products. The large balance of energy must appear as internal excitation of the H2 product. Depositing this amount of energy into rotation of the H2 product while conserving angular momentum seems unlikely. Theoretical calculations that find more energy in H2vibration than in rotation for the reaction of H 2 0with five quanta of 0-H stretch excitation and 1 eV of relative translational energy support this supposition.’$ Other theoretical work on the reverse reaction correlates both initial H2and OH vibrational excitation with vibration in the H20product. It shows that the reaction indiscriminately distributes the H2 vibrational energy among the water vibrational modes but selectively preserves the OH vibration as 0-H stretching excitation in watere3 The principle of microscopic (15)
Schatz, G. C., private communication.
reversibility requires that these H 2 0 vibrations correlate with vibrationally excited H2 and OH products in the forward reaction. In agreement with this inference, we have found that vibrational excitation initially in the nonreacting bond survives as vibrational excitation in the OH product? These calculations and observations suggest that several quanta excitation of the 0-H stretching vibration in water promotes reaction at the excited bond to produce vibrationally excited H2. In the stripping limit of the reaction, the incident H atom removes an H atom from the vibrationally excited bond to leave behind an unperturbed OH molecule while forming an H2 molecule with an extended bond that begins to vibrate. This picture of energy disposal and our measurements clearly motivate the direct observation of the H2 product. In addition to testing our inferences about the energy content of the “new” bond formed in the reaction, these measurements should reveal the dynamics of state- and bond-selected reaction, and we are preparing experiments to investigate the disposal of energy into the internal degrees-of-freedom of the H2 product.
Acknowledgment. We appreciate discussions with A. B. McCoy and Professor E. L. Sibert about their calculation of the state mixing in HOD. We thank Professor George C. Schatz for several useful discussions of the trajectory calculations and the Division of Chemical Sciences, Office of Basic Energy Sciences, Department of Energy, for their support of this work. Registry No. H, 12385-13-6;H20,7732-18-5;D, 7782-39-0;OH, 3352-57-6.
+
-
A Quasiclassical Trajectory Study of H Cot OH 4- CO: Bulk Reactlon Dynamics and the Effect of van der Waals Precursor Formation Kathleen Kudla and George C. Schatz* Department of Chemistry, Northwestern University, Evanston, Illinois 60208-3113 (Received: January 30, 1991)
-
+
We present the results of a quasiclassical trajectory study of the H + C 0 2 OH CO reaction, with particular emphasis on comparing the bulk reaction dynamics (isolated bimolecular collisions) with results for the van der Waals precursor photoinduced reaction HBr.C02 hu OH CO + Br. All calculations are based on a full-dimensional HCOz potential surface that was derived from ab initio calculations. The T-shaped HBr.C02 system was modeled by adding HBr, BrC, and BrO pair potentials to the HCOl potential. Our cross sections and OH product distributions for the bulk reaction are generally in good agreement with experiment over a wide range of collision energies. The agreement is especially good close to the effective threshold for reaction. The trajectory CO product distributions are in good agreement with recent measurements at 300 K, but there are important differences in the dependence of the distributions on initial rotational temperature. In modeling the van der Waals reaction, we use the experimental geometry for the heavy atoms to define initial conditions, with the orientation of the HBr relative to C 0 2 treated as a variable. We find that reaction occurs efficiently over angular regions in which the H atom is directed into either HOC0 or HC02 wells. Overall energy available to the OH + CO products is about 80% of the bulk value, which is consistent with the major component of the energy distribution that has been inferred from experiment. However, the trajectory calculations indicate that the energy in products is not reduced equally for all degrees of freedom. In particular, OH rotation is not necessarily colder than in the bulk, in contrast to the experimental result. In addition, the energy dependence of the reaction probability is found in the calculations to be stronger in the complexes than in the bulk, while it is about the same in the experimental results.
+
-+
+
I. Introduction The reaction
H + C02 -+OH+ C O (1) has become a benchmark system for studies of chemical reaction dynamics. Early interest in this reaction and its reverse arose because of its importance in combustion and atmospheric chemistry,’ but the surge of recent activity is due to the accessibility of this reaction to time- and/or state-resolved experiments and (1) Miller, J. A.; Kee, R. J.; Westbrook, C. K.Annu. Reu. Phys. Chem. 1990, 41, 345. Weston, Jr.. R. E. J . Chem. Educ. 1988, 65, 1062.
0022-36S4/91/2095-8267%02.50/0
to high-quality theoretical studies. References 2-4 review the multitude of experimental studies that have been done on H + C 0 2 , most of which involve collisions of photolytically prepared fast H atoms with thermal C 0 2 followed by detection of the product OH and/or CO, or of the unreacted C02. (2) Flynn, G. W. Science 1989. 246, 1009. (3) Zewail, A. H.Science 1988, 242, 1645. Zewail, A. H.;krnstein, R. B. Chem. Eng. News 1988.66 ( 4 9 , 24. (4) Shin, S.K.;Chen, Y.;Nickolaisen, S.;Sharpe, S.W.; Bcaudet, R.A.; Wittig, C. In Advances in Photochemistry; Volman, D . H.,Ed., submitted for publication. Wittig, C.; Sharpe. S.;Bcaudet, R.A. Ace. Chem. Res. 1988, 21, 341.
0 1991 American Chemical Society
8268 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 1.51
#
HC02+'HOC0
1.0
-
>
. m
0.5
m
0.0
-
0.5
-
-
reaction coordlnate
Figure 1. Schematic of H
+
+
C02 OH CO reaction pathways, showing saddle points and minima based on energies from ref 14.
One especially interesting class of recent experiments has involved the van der Waals clusters HX.C02 (where X = halogen). UV photolysis of these clusters initiates the reaction H X C 0 2 hv OH CO + X (2)
+
+
+
which can be thought of as the intracluster analogue of reaction 1. Two types of experiments have been reported for reaction 2. In the first, due to Wittig and co-workers,ks the product OH vibration/rotation state distributions were measured for both the bulk and complex reactions (Le., reactions 1 and 2). Most of this work has considered the X = Br halogen, but X = CI and I have also been studied. The results indicate that the complex reaction OH produces rotationally colder OH'S than the bulk rea~ti0n.h~ vibrational excitation, which is small, does not change significantly. The efficiency of reaction as a function of photolysis wavelength (Le., as a function of total energy) increases rapidly with decreasing wavelength, with the same functional dependence seen in both bulk and complex reactions starting from the same precursor HXe6 Changing the precursor molecule from HBr to HCI has a significant effect,8 decreasing the reaction efficiency by a factor of 40 a t the same available energy. The structure of the HX.C02 complexes (X = CI, Br) has recently been determined? and it was found that HBr.C02 has the heavy atoms in a T-shaped configuration while HCI.CO2 is linear. It thus appears that the variation in reactivity with halogen atom X is related to cluster structure. The second class of cluster experiments has been done by Bernstein, Zewail, and their collaborators3J0J~on the HI.C02 cluster. In these experiments, picosecond pumpprobe measurements have been able to determine the time scale of reaction (Le., the time between the photolysis pulse and subsequent detection of O H products). The time scale found in these experiments is in the 2-5-ps range with time decreasing as energy increases. Such a long time is consistent with the formation of (5) Buelow, S.; Radhakrishnan, G.; Catanzarite, J.; Wittig, C. J. Chem. Phys. 1985, 83, 444. Radhakrishnan, G.; Buelow, S.; Wittig. C. J . Chem. Phys. 1986, 84. 727. Buelow, S.;Radhakrishnan, G.; Wittig, C. J . Phys. Chem. 1987, 91, 5409. (6) Chen, Y . ;Hoffmann, G . ;Oh, D.; Wittig, C. Chem. Phys. Lett. 1989, 159, 426. (7) Hoffmann, G.; Oh, D.; Chen, Y . ; Engel, Y. M.; Wittig, C. Isr. J . Chem. 1990, 30, 115. Wittig, C.; Engel, Y . M.; Levine, R. D. Chem. Phys. Leu. 1988, 153, 41 I . (8) Shin, S. K.; Chen, Y . ;Oh, D.; Wittig, C. Philos. Trans. R. Soc. London 1990,332, 361. (9) Sharp, S.W.; Zeng, Y . P.; Wittig, C.; Beaudet, R. A. J . Chem. Phys. 1990. 92. 943. (IO)Scherer, N. F.; Khundkar, L. R.; Bernstein, R. B.; Zewail, A. H. J . Chem. Phys. 1987, 87, 1451. ( I I ) Scherer, N . F.; Sipes, C.; Bernstein, R. B.; Zewail, A. H. J . Chem. Phys. 1990, 92, 5239. ~
Kudla and Schatz a long-lived intermediate during reaction. For a number of reasons24,10,11 it has been assumed that the complex being formed is HOCO and that the delay time is just the unimolecular decay lifetime of HOCO. Theoretical studies of reactions 1 and 2 have been concerned with both the potential surfaceI2-l4and the reaction dynamics."17 There have been a number of a b initio studies of the potential surface for reaction l,I2-l4 all of which indicate that the primary reaction pathways are as illustrated in Figure 1. This shows two possible reaction pathways, the lowest of which involves addition of H to 0 over a relatively high barrier (1.1 eV) forming HOCO as an intermediate. Dissociation of HOCO to produce OH + CO occurs without a significant exit channel barrier, and the reaction is endoergic overall by 0.97 eV. The second pathway involves addition of H to C to form the intermediate H C 0 2 and then isomerization of this to HOCO, thereby merging with the first path. The isomerization barrier in the second path is found in the calculations to be higher than the Ha-OCO addition barrier in the first by enough (-0.15 eV) to make only the first path be important near the reaction threshold. However, many of the experiments have been done at energies well above threshold, so the second path probably plays a role in what has been measured. Even if this happens, HOCO should still be the longest lived intermediate, and the O H and CO internal-state distributions should reflect the dynamics of HOCO dissociation. In this paper we consider the dynamics of both reactions 1 and 2, based on a global analytical potential surface for H + C02that was derived from ab initio calculations. This surface is a modified version of an earlier many-body expansion surface that was developed by Schatz, Fitzcharles, and Harding.14 This earlier surface was used in studies of both reactions 114 and 2,15 and detailed comparison with experiments available at the time indicated reasonable agreement with some but not all experiments. The best agreement with experiment was for the total reactive cross section and the O H rovibrational distribution, both of which were available at only two energies at that time. The worst agreement was with C02 rotational distributions for nonreactive collisional excitation14 and with the van der Waals complex experiments.Is Much has happened since then which makes it desirable to reconsider the theoretical calculations. Experimental reactive cross sections and OH product state distributions are now available over a wide range of energies6 for both bulk and complex reactions. Also, the C O product distribution has recently been reported.18 In addition, the HBr.C02 structure is now known, and it differs from the linear structure that was used in earlier calculation^.'^ On the theoretical side, the reverse reaction, O H + CO, has recently been the subject of two very detailed ~ t u d i e s ' ~that J ~ have clarified the accuracy of certain parts of the potential surface, especially the H-OCO and OC-OH barriers. The second of these studiesi7 produced the modified version of the Schatz et aI.l4 surface that we use in the present work. The modifications all involve changes in the functional expressions used to define the surface that make the surface and especially its derivatives smoother functions of the internal coordinates. This makes the trajectories numerically better behaved, but it does not change energetic features of the surface significantly. One problem that was not corrected is the strength of coupling between the translational and C 0 2 vibrational coordinates for nonreactive collisions that produce small rotational excitation. It was this problem that was responsible for the poor C 0 2rotational distributions in earlier simulations of the Flynn group experimentsS2 (See refs 14 and (12) Feller, D.; Huyser, E. S.; Borden, W. T.; Davidson, E. R. J . Am. Chem. Soc. 1983, 105, 1459. (13) Aoyagi, M.; Kato, S. J . Chem. Phys. 1988.88, 6409. (14) Schatz, G. C.; Fitzcharles, M. S.; Harding, L. B. Faraday Discuss. Chem. SOC.1987, 84, 359. Schatz, G. C. Reo. Mod. Phys. 1989, 61, 669. (15) Schatz, G. C.; Fitzcharles, M. S. In Selecrioity in Chemical Reactions; Whitehead, J. C., Ed.; Kluwer: Dordrecht, 1988; p 353. (16) Brunning, J.; Derbyshire, D. W.; Smith, I. W. M.; Williams, M. D. J . Chem. SOC.,Faraday Trans. 2 1988,84, 105. (17) Kudla, K.; Schatz, G. C.; Wagner, A. F. J . Chem. Phys., in press. (18) Rice, J. K.; Baronavski, A. P. J . Chem. Phys., in press. Rice, J. K.; Chung, Y . C.; Baronavski, A. P. Chem. Phys. Lett. 1990, 167, 151.
H
+ COz+
OH + CO
6.01
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8269
I
121
I
I
1
'
I
.
1
'
1
'
I
9.
3.0
5
n L
6-
n L
0.01
c
2
n
3.
Y
Y
A
0-3. -6.0 -8.0
-6-
-4.0
0.0
4.0
-8.0
8.0
Figure 2. Contours of HC02 potential surface as a function of the Cartesian coordinates ( X J ) of the H atom, with C02 along the x axis (energy is minimized as described in text). Contours are in 0.27-eV intervals, with zero taken to be H + CO,.
19 for details.) Because this problem has not been fixed, we will not reconsider simulations of this type of experiment. Our modeling of the HBrCO, reaction will be done using a very primitive potential surface for the photoexcited state that simply adds together the interaction of H with Br and of H with CO, as if the Br and CO, were well separated. Only van der Waals interactions are included between the Brand CO,, so we are not allowing for the formation of more complex intermediates like BrCOOH. The idea behind this model is to see whether the experiments can be described without invoking reaction pathways beyond that contained in Figure 1. To summarize the rest of this paper, section 2 provides more details on the potential surfaces plus a brief discussion of dynamics methods, section 3 presents our bulk reaction results while section 4 presents our H B r C 0 , results, and section 5 summarizes our conclusions.
4.0
0.0
8.0
Figure 3. Contours of HBr.C02 potential surface as a function of H atom Cartesian coordinates, with Br-C02 fixed to a T-shape as described in the text. Contours are in 0.4-eV intervals with maximum at 4.2 eV.
the complex as it is in the gas phase.6 This tells us that at least the short-time dynamics is the same, and there is also support for this from ab initio calculations, in which the full HBPCO, potential has been mapped out for geometries close to the Franck-Condon region. 2o One issue that requires further thought is what sort of interaction we should include between Br and CO, since in contrast to the bulk case this could play some role in OH production. The correct result is that there are many surfaces possible, some attractive and some repulsive. To keep things as simple as possible, we have ignored chemical bonding between Br and CO,, taking the Br...CO, interaction as a sum of Lennard-Jones 6-1 2 potentials. Overall then, our potential for H B r C 0 , is given by V H B ~ C=OV~ H B+ ~ J'HCO~ + VBK + V~fi+ V B ~ (3) where VHco2is the potential described above, and VHB,(R) = Ae-1.681R
11. Theory and Computations Potential Energy Surfaces. The potential surface for H
+ CO, is a global analytical expression in the form of a many-body expansion.14 All the saddle points and minima in Figure 1 are contained in it, and they have the indicated energies. As mentioned in the Introduction, the surface of ref 14 was modified slightly in ref 17, and it is this modified surface that we use for this study. Figure 2 presents a contour plot of this surface as a function of the H atom Cartesian coordinates relative to the CO, center of mass. The energy at each H atom location has been minimized with respect to the CO, bend and stretch coordinates, with the 0-0axis taken to be parallel to the abscissa and all four atoms planar. As a result, all planar stationary points (except the saddle point for dissociation of HOCO into O H + CO) are displayed. The HOCO cis and trans minima give rise to U-shaped contours around each oxygen atom, while the HCO, minimum produces circular contours near the carbon. There is a maximum outside the isomerization pathway between HCO, and HOCO with an energy 2.5 eV (relative to H + COz with CO, at equilibrium). The potential surface for HBrCO, was designed to represent the photoexcited state. If HBr and CO, are initially well separated, then the correct surface would simply be the repulsive HBr excited-state potential plus the HCO, potential described above plus a BrC0, potential that would only be important if Br hits one of the reaction products and in any event would not be involved in the production of OH. We have simply assumed that the same potential can be used when HBr and CO, start out at a geometry that is determined by the ground state of the van der Waals complex. One piece of evidence in support of this is that the measured excitation profile for photodissociation is the same in ~~~
(19) Chawla, G. K.; McBane, G. C.; Houston, Chcm. Phys. 1988.88, 548 1.
-4.0
x (bohr)
x (bohr)
P. L.; Schatz, G. C. J .
VBfi,Bfit,Bc(R)
= 2.32
X
(4)
[[y]"[y] -
(5)
where R stands for the appropriate diatomic coordinate and atomic units are used throughout. Equation 4 was derived from ref 21, while eq 5 was equated to the Ne-Kr potential.2z From ref 21, the parameter A in eq 4 has the value 10.516 au, which makes VHBr = 0.1 182 au = 3.22 eV for R = Re = 2.67ao, the ground-state HBr equilibrium distance. This energy is above the energy supplied in photoexcitation (1.4-2.6 eV) which means that vertical excitation is classically forbidden. This creates a small problem in the classical simulation of photodissociation, as it means that we cannot start the simulation at R = Re. Methods exist to circumvent this problem by starting the HBr distance at values other than Re, but to be realistic in using such methods, we must account for interaction between the H and C 0 2 during the classically forbidden motion between R = Reand the starting position. For a system with many strongly coupled degrees of freedom this is not straightforward. As an alternative we have opted to modify the potential rather than make arbitrary assumptions about motion in the classically forbidden region. Our modification involves adjusting A to make the vertical transition classically allowed. One way to do this which has the additional feature of pinning the initial HBrC0, energy at the sum of the photolysis energy E, plus the CO, zero-point energy is to set
(20) Shin, S. K.; Wittig, C.;Goddard 111, W. A. J . Phys. Chem., in press. (21) Goodeve, C. F.; Taylor, A. W. C. Proc. R. SOC.London 1935, 152,
221.
(22) Parson, J. M.; Schafer. T. P.; Tully, F. P.; Siska, P. E.; Wong, Y.C.;
Lee,Y.T. J . Chem. Phys. 1970, S3, 2123.
8270 The Journal of Physical Chemistry, Vol. 95, No. 21, 1991
Kudla and Schatz
1.50 n
1.251
1
C
.E 0 . 7 5 . 0
* 0.50u)
E
0
0.25. 0.0 1.0
itIIIII 1.5
2.0 2.5 E (eV)
3.0
3.5
Figure 4. Reactive cross section versus translational energy E for H + C02. The X's are the trajectory (QCT) results. Triangles denote zero-point constrained trajectories (QCT + ZPE),and the dotted line represents experimental results from ref 7.
H B r C 0 2 geometry and Va is the H C 0 2 energy for H infinitely far from C o t . The value of A obtained from eq 6 is in the range of 6.0-6.3 au for E, = 2.54 eV. A plot of the VHBr.C02 potential is presented in Figure 3. In this plot we have taken the Br-C distance from the measured ground-state equilibrium geometry (6.844)? and for each H atom location the energy was minimized with respect to the bend and stretch coordinates as in Figure 2. The initial H-Br distance is indicated by the highest energy circle around the Br atom. If we define the C-Br-H angle as 8, then for 8 = 0 (corresponding to H between C and Br) the H is located initially very close to the saddle point for addition into the HC02 well. For 6 30°, the H is located on a line between the Brand the HOC0 minimum, and for 0 45' the H atom is roughly on a line between the Br and the H-OCO addition saddle point. Note how the 2.5-eV maximum that we saw in Figure 2 appears as a "bump" that is encountered for 6 = 30'. Trajectory Calculatiolra The H C02and HBr.C02 dynamics were simulated with a quasiclassical trajectory method that has been described e l ~ e w h e r e . ~Parameters ~ defining the initial conditions are mostly identical with those used previo~sly.'~,'~ However, in the present simulations we studied a much broader range of initial energies (1.35-3.40 eV for H + C02, 1.86-3.40 eV for HBr.CO2). For H + C02,cross sections were calculated by using 2000 trajectories at each energy, with the initial rotational angular momentum fixed at J = 15 (approximately the most probable value for C02at 300 K) and the initial maximum impact parameter b,,, fixed at Sao. Selected calculations were done for other J values as will be discussed. For HBr.C02, two different types of trajectory runs were done. In the first, the C-Br-H angle 8 was fixed, and 500 trajectories were calculated for each value chosen. In the second, the angle 6 was randomly sampled over the range 2.5-25' for which there is significant reactivity. A total of 2000 trajectories were used in this group. The COzwas in both types of calculations taken to be rotationally cold ( J = 0).
-
+
111. Results for Bulk Reaction There are three types of information available from experiment for the bulk reaction: the reactive cross secti0n,6*~'OH product and CO product distributions.'* The first two are available as a function of energy over a wide range (1.35-2.54 eV), while the third is only available at one energy (2.3 eV). The CO product distributions have been measured for three C02 rotational temperatures (40, 70, 300 K). Our presentation will consider all of these comparisons with experiment as follows: Reactive Cross Section. Figure 4 presents experimental and theoretical reactive cross sections for H + COz. The experimental results are from ref 6 with the absolute normalization provided (23) Gibson, L. L.; Schatz, G. C. J. Chem. Phys. 1985.83, 3433. (24) Kleinermanns, K.; Wolfrum, J. h e r Chem. 1983, 2, 339. Kleinermanns, K.; Wolfrum, J. Chem. fhys. Lon. 1984, 104, 157. Kleinermanns, K.; Linnebach, E.; Wolfrum, J. J . Phys. Chem. 1985.89, 2525.
Ot,
I
I 30 I I I 60 ' a (degrees)
IH ' ' I 80
Figure 5. Reaction probability (expressed as a percent) for H + C02at 2.54 eV versus angle a between the 0-0 vector and the H to C02 center-of-mass vector. Histograms are normalized such that the unweighted average over a equals the average reaction probability for b , = 5a0 (about 2%).
by ref 24. Two sets of trajectory results are presented, one in which all trajectories producing OH CO products are included (labeled QCT) and one in which trajectories producing OH or CO having less than zero-point energy are omitted (QCT + ZPE). Past studies have generally shown2' that zero-point constrained trajectories provide more realistic results, so we will assume that our QCT ZPE results are more accurate. Figure 1 shows that there is, in fact, a substantial difference between QCT and QCT + ZPE, especially close to the reaction threshold. The threshold, according to Figure 1, is determined by the H-OCO barrier, and if zeropoint energy is preserved in going from H C02to H-OCO, then this threshold should occur at a translational energy of 1.10 eV. Any violation of the zero-point constraint by classical mechanics would tend to make the QCT or QCT + ZPE threshold energies lower, but what Figure 4 indicates is that the threshold energy is actually a little higher, closer to 1.2 eV. This is probably due to the significant distortion of the C 0 2 needed to reach the transition state (0-C-0angle is 158'). The experimental results are in excellent agreement with QCT ZPE close to threshold. Above 2.0 eV, however, the measured cross section rises quickly to a value at 2.54 eV that is even above QCT. The QCT + ZPE, by contrast, rises more slowly at first, with a quicker rise seen only at 3.4 eV. One possible reason for the quicker rise in the measured cross section is that a second reaction pathway opens up at lower energy in the experiment than in the calculations. A good candidate would be reaction through the HCO, intermediate, but our trajectories do not indicate significant structure in the cross section as a result of this process as we now show. At 2.54 eV we have tagged each reactive trajectory according to its impact parameter b and the angle a between the 0-0 vector and the C02 center of mass to H vector. The distribution of b values obtained from this is relatively uninteresting, basically a flat function for b's between 0 and 3 . 8 and ~ ~ then zero for larger b. However, the a distribution, shown in Figure 5 , is more interesting, as it shows significant variation in reactivity. In particular, the reaction probability is largest for 20' Ia I30°, corresponding to H-OCO attack at angles that are close to the transition-state value of a (-20'). Attack from angles close to linear is disfavored, and so is attack from larger a's (30-70'). Reactivity peaks again at 70-80°, corresponding to near-perpendicular attack. This second peak is clearly due to the HCO2 pathway, so what Figure 5 shows is that reaction by this path is significant at 2.54 eV, accounting for about 1/3 of the cross section. A similar analysis a t 3.40 eV (not shown) gives qualitatively the same result but with the H C 0 2 path contribution now somewhat larger than H-OCO. Thus, the H C 0 2 path increases
+
+
+
+
(25) Truhlar, D. G. J . fhys. Chem. 1979,83, 188. Miller, J. A. J . Chem. Phys. 1981, 74, 5120. Nyman, G.; Davidsson, J. J . Chem. Phys. 1990, 92, 2415.
H + Cot -+ OH + CO
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8271
H + COSvs HBr.C02
TABLE I: Reactivity 8 d Energy Parti1.86 eV
react ivityb (EoH)'
(Eco)' (&I)'
(Em)' (UOH )
(NOH )
(E%)'
(ah)' ( uco ) (Jco)
(q0)'
(Gk)' (E,) / ( EldB
2.54 eV
2.09 eV
B
V'
0.9 0.46 0.24 0.49 1.18 0.13 8 0.20 0.26 0.08 18 0.09 0.15
0.02 0.45 0.13 0.48 1.06 -0.37 13 0.42 0.03 -0.19
B 1.1 0.45 0.43 0.57 1.46 0.04 9 0.24 0.21 0.67 20 0.13 0.30
I5 0.05 0.08 0.90
3.40 eV
V
B
V
B
V
0.35 0.45 0.24 0.53 1.22 -0.13
1 .o 0.59 0.58 0.70 1.87 0.17
1.o 0.56 0.38 0.66 1.60 0.02 11 0.36 0.20 0.54 18 0.1 1 0.27 0.86
1.3 1.04 0.86 0.85 2.75 0.78 13 0.54 0.50 2.02 26 0.21 0.65
5.4 0.92 0.64 0.76 2.32 0.60 14 0.50 0.42 1.43 20 0.14 0.50 0.84
IO
IO
0.3 1 0.14 0.18 13 0.06 0.18 0.84
0.33 0.26 1.06 24 0.18 0.40
#Only one reactive trajectory was found (out of 2000) so the results given are not statistically significant. bRatioQCT of reactive cross section (for bulk) or reaction probability (van der Waals) to that at 2.54 eV. CAllenergies are in eV. 2000
5000 4000
1500v
3000
'E
'E
1000-
fi-2000
h
>
Q v
0 ;
1000 0
1.0
1.5
2.0
2.5
3.0
500-
i.0
3.5
E (eV)
Figwe 6. Average OH rotational energy (E&) versus E, showing QCT (X's),
QCT + ZPE (circles), and experimental (triangles) results.
the cross section, but not dramatically. OH Product-State Distribution. The trajectory calculations usually produce a small enough number of reactive trajectories (-50) that only low order moments of the vibrational and rotational distributions are statistically meaningful, so our analysis will be restricted to this type of information. This is actually not a serious limitation, as the experimental distributions can be fit accurately with functions that use only the zeroth and first moments as parameters. Table I summarizes a number of features of the final-state distributions for the H COz reaction (labeled B for 'bulk") at four energies in the range 1.86-3.40 eV. (The HBr.COZ results labeled V in the table will be discussed later.) The O H information in the table includes the average total internal energy ( E O H ) (including zero-point energy), its vibrational and rotational components, (l&) and and the average vibration and rotation quantum numbers ( ~ 0and ~ (NOH). ) The OH rotational quantum number N was calculated from our results by using the method of Clary and Connor.26 Figure 6 presents a plot of E& versus E, including both QCT and QCT + ZPE results. (Only the former are in Table I, but the difference according to Figure 6 is small at most energies.) Also included in Figure 6 are measured OH average rotational energies from ref 8b. These agree well with the QCT + ZPE results, especially for E 5 2 eV. At the high energy limit of the experimental results, the QCT + ZPE rotational distributionsare noticeably hotter than experiment. Table 1 indicates that OH vibration is generally quite cold, though increasing rapidly above 2.54 eV. The experimental vibrational distribution has been reported at 1.86 and 2.54 eV. At 1.86 eV, the measured ( D O H ) is 0.06,24while the QCT value is
+
(eH),
(26) Clary, D.C.; Connor, J. N. L.; Southall, W.J. E.J . Chem. Phys.
1986,81, 2620.
I
1.5
2.0 2.5 E (eV)
3.0
3.5
Figure 7. Average CO rotational energy (Em) versus E, showing QCT (X's) and QCT + ZPE (circles) results.
+
0.1 and the QCT ZPE value is 0.4. At 2.54 eV, a lower bound of 0.3 was measured5 for (uOH), while our results at that energy are 0.2 (QCT) and 0.5 (QCT + ZPE). CO Product-State Distribution. Table I and Figure 7 present CO final-state information analogous to that just discussed for OH. Except at the lowest energy in Table I, the average total energy going to CO is about the same as to OH, but the partitioning between CO vibration and rotation is somewhat different, with vibration being favored, Le., (E-!'-!) > (Go). Note that the average vibrational quantum number ( uco) rises more rapidly with energy than the average rotational quantum number (Jm). It was noted in ref 14 that the QCT values of ( D O H ) , (uco), (NOH),and (Jco) are close to values obtained from microcanonical statistical theory. The present results are, within statistical error, identical with the older results at the two energies where the old and new results overlap, but with the more extensive results that we now have, it is possible to notice features that are different. For example, classical statistical theory predicts that (G&) = =( SA=)(E&, but Table I indicates that this is not generally true, especially at higher energies. Recently, Rice and Bar0navsk.P have measured the CO product distribution from H + C 0 2 at 2.3 eV, including a detailed comparison between results at different C 0 2 rotational temperatures Trot.Table I1 presents a number of comparisons between their results and ours. For Tm = 300 K, most results are in reasonable agreement, including the CO(o= l)/CO(u=O) ratio, ( Jc0), and (S&(,(OCO)) (with experiment lying somewhere between QCT and QCT + ZPE). However, at lower Tmt(we considered Tr,,, = 0, while the experiment studied Trot= 40 and 70 K), there are important differences. We find that vibrational excitation decreases slightly and rotational excitation increases slightly as Tm decreases, while the experiment finds that vibrational excitation increases substantially and rotational excitation decreases substantially. At this point we have no explanation for this significant
(ak)
8272 The Journal of Physical Chemistry, Vol. 95, No. 21, I991 TABLE 11: CO Product-State Energy Partitioning ( E = 2.3 eV)
theorlP OCT
CO(ti=1)/CO(u=O)
0.8 0.9
0.19 0.19
0.10
0.06
0.09
0.09
0.08 0.08
0.1 1 0.1 1
0.04
(Jco)
0.9 22 21
tic0
=0 =1
* 0.2 *
1.0 0.2 0.65 0.06 0.51 0.05 11 1 20 1
0.7
UCO
exatb
1.8
1.4 I .4 1.1 1.1 17 16
(Uco)
(G(uco)), eV
OCT + ZPE
(>0.07)
OThe top value for each entry is for Tmt= 0 K, and the bottom value is for Tm = 300 K. *The top value is for Tmt= 70 K, and the bottom value is for Tm(= 300 K. Results from ref 18.
angular range found in Figure 8 is quite narrow, it should be adequate to take the angular weighting factor to be a constant within this range. In our calculations we considered angles between 2.5’ and 25’. Table I summarizes the results of calculations that we did at four energies (labeled V in the table). There are two types of information included: product energy partitioning analogous to the bulk results that we presented in section I11 and the normalized reaction probability (labeled “reactivity”). The latter is defined for the complex to be the ratio of the fraction of reactive trajectories at energy E to the fraction at 2.54 eV. The corresponding bulk result is similarly defined by using ratios of reactive cross sections. Table I indicates that the complex reactivity rises more quickly with energy than the bulk. In fact, between 2.09 and 3.40 eV, the complex reactivity increases by a factor of 15 while the bulk increases by 20%. In addition, our complex results have an apparent threshold a t 1.86 eV, while the bulk threshold energy is much lower (1.2 eV). This difference between the energy dependence of the bulk and complex reactivity does not agree with experiments (which indicate the same energy dependence for bulk and complex6)). Our results are, however, consistent with the idea that there should be a higher effective barrier to reaction in the complex, as reaction is forced to occur through pathways well away from the minimum-energy path. In fact, it can be argued that in order for the bulk and complex reactivities to be the same, the H atom angles of approach must be similar to those in the bulk. This would only be possible for the complex if the excited-state dynamics is different from what we have assumed. Now consider the product energy partitioning in Table I. The row labeled (Eto,)gives the total energy available to the OH CO products. For the bulk reaction this is strictly related by energy conservation to the initial energy. For the complex reaction, some of the energy available to the products can go to the Br atom, so the energy going to O H + CO is determined by the dissociation dynamics. The bottom row in Table I gives the ratio of the complex to bulk total energies. What we see from this ratio is that O H + CO receives 80-90% of the available energy, implying that Br must get 10-20%. This percentage is much larger than would be expected if only the H-Br repulsive interaction and masses determine the Br energy (roughly a 1% ratio expected). The percentage is, however, somewhat smaller than would be determined by a repulsive interaction between Br and rigid H C 0 2 (36% ratio). The ratio of OH + C O energies just discussed has never been measured directly, but there is evidence from the experiments that the value we obtain, 80-90%, is characteristic of most of the OH + CO’s that are produced. This was the conclusion of a recent analysis by Wittig and co-workers’ in which the measured OH rotational distribution for HBr.C02 was fit by superimposing bulk results at two different total energies, one about 80% of the available energy (at 2.54 eV) and the other about 20%. The 80% part is responsible for about 70% of the total products formed. There is no evidence in our results for the low-energy component. Wittig and co-workers point out that this component may arise from higher than binary clusters or other sources that would not be included in our model. Let us now consider partitioning of the O H + CO product energy into vibration and rotation. Table I indicates that the van der Waals vibrational and rotational energies are very much like their bulk counterparts, but reduced in magnitude. The OH vibrational energy is similarly reduced, but the OH rotational is essentially unchanged at m a t energies. energy as well as (NOH) These results for OH are not in accord with observations, where O H rotation is colder and OH vibration is unchanged in the complex compared to the OH + CO Formation Time Distribution. To gain insight conceming the product energy partitioning that we have just noted, we have examined lifetime distributions for reactive trajectories. Table I11 shows the result, where we have specifically monitored the time between photoexcitation of HBr.C02 and production of OH + CO separated by 12ao. What Table I11 shows is that there
+
0 ~
0
Kudla and Schatz
5
10
15 20 25 0 (degrees)
30 35
Figure 8. Reaction probability (expressed as a percent) for HBr.C02 versus C-Br-H angle B at 2.54 eV.
difference between theory and experiment. Changing the C02 rotational temperature in the 0-300 K range changes the energy and angular momentum of the HOCO intermediate by rather modest amounts, so the small changes in CO distributions that we calculate seem reasonable.
IV. Results for HBr.C02 Orientation Dependence of Reactivity. In our simulations of HBr.C02, we first consider the variation in reactivity with the C-Br-H angle 0. Figure 8 presents the results of our simulations at 2.54 eV using the potential surface described in eqs 3-6. The ordinate in this case is just the probability of producing OH + CO products for trajectories starting from the T-shaped complex, with t9 fixed and C02sampled with zero-point energy in defining initial conditions. The figure indicates that reactivity is significant for angles in the 0-28’ range. From Figure 3 one can infer that this range corresponds to shooting the H toward either the HCO, or HOCO wells, but in contrast to Figure 5, there is little or no dip in reactivity for angles between the two minima where the H atom sees a more repulsive potential. The reactivity decreases rapidly for angles much larger than 25’, going to zero by 28’. This means that, for larger angles, the H atom flies away from the complex, without significant attractive interactions with the COP For 0 close to zero the probability is also reduced, implying that H does not react when shot directly at carbon. The average reaction probability for 2.5’ I t9 I 25O is 3 2 , which is comparable to the probability found (Figure 5 ) for the bulk reaction. Orientation-AveragedResults. Now that we have determined what range of 0’s leads to reaction, we can consider averaging over t9 to generate ensemble-averaged results. In this averaging, we do nor weight by any factor that describes the ground-state probability density (such as would be described by a FranckCondon factor). Obviously such a weight factor is extremely important to determining the overall reaction probability, but since there are no experimental measurements of this probability, its value is not something we can evaluate. In addition, since the
H
+ CO2
+
OH + C O
The Journal of Physical Chemistry, Vol. 95, No. 21, 1991 8213
TABLE III: OH + CO Formation Time Distribution (from HBPCO, at 2.54 eV) 1, ps probability 1, ps probability t, ps probability 0.07 0.12 0.17 0.22
0.0 0.0 0.0
0.27 0.31 0.36 0.41
0.15
0.35 0.20 0.12 0.10
0.46 0.51 0.56 0.61
0.05 0.03 0.0 0.0
is an induction period of about 0.2 ps wherein no O H + C O is produced, followed by a peak in production at about 0.3 ps, followed by decay of the distribution at longer times. The average product formation time is 0.3 ps. This is long enough for the intermediate HOCO to vibrate about four periods in the lowest frequency mode, so one expects that the OH + C O product distributions will tend to be statistical though not completely. This is consistent with the product energy partitioning in Table I. Statistical distributions give average energies that scale with the total internal energy. Our results follow this behavior for all degrees of freedom except OH rotation. This degree of freedom is highly excited in the initially formed HOCO and apparently does not have enough time to relax. One reason why O H rotation can retain its initial excitation is that the surface we have used has a very low out-of-plane bend frequency ( 140 cm-I) at the HO-CO saddle point.17 This feature was found to provide a serious source of error (making the transition state too loose) in studies of the OH + CO reaction,I7 and it could also be a problem for H C02. We will consider this point in future studies that will be based on a surface currently being developed that corrects this problem.27 The average product formation time that we have calculated is close to the HOCO lifetime (compared a t the same total energies) that was found in recent studies of the OH + CO reaction on the same potential surface.I7 This is, of course, not surprising, as the lifetime of a complex should not depend on how it is formed if it is truly statistical. The present complexes are not fully statistical but apparently close enough. The study of OH CO also included comparisons of lifetimes with those measured by Scherer et al." What was found is that the trajectory lifetimes are consistently factors of 5-6 smaller than experiment. This difference is important to the OH + C O final-state distributions, as longer lived complexes should be more statistical. More statistical behavior would lead to colder OH rotations, in better accord with experiment. Thus, this could be a second reason for the error in the present results. Preliminary results from a model quantum study of OH + C02*do, in fact, N
+
+
(27) Harding, L. B. Private communication. (28) Schatz, G. C. Faraday Discuss. Chem. Soc., in
press.
show that classical mechanics consistently underestimates the HOCO lifetimes by factors that are consistent with the discrepancy found in ref 17.
V. Conclusions The overall conclusion of this study is that we can describe most features of the H C02 reaction quite well, but there remain serious problems with regard to the H B r C 0 2 van der Waals precursor reactions. With regard to the bulk reaction, both the absolute cross section and its energy dependence are described accurately, especially near the reaction threshold. We have presented strong evidence for the participation of a second reaction path at high energy involving transient HC02 formation. The OH product rotational and vibrational distributions are also in good agreement with experiment. The CO distributions agree with experiment at 300 K, but the dependence of these distributions on initial C02 rotational temperature is quite different. We have no explanation for these differences, but the physical basis for our results is understandable, so either our model is wrong or the experiment is not being correctly interpreted. In our studies of HBr.C02, we found that there is a significant difference in the amount of energy that the OH + CO fragments get in comparison with the bulk reaction, amounting to 10-20'37 of the energy available to the bulk. This difference arises because the Br pushes against more than just the H atom in photodissociation, though less than the entire HC02fragment. The reduction in energy available to the OH + CO agrees well with what has been inferred from measurements. However, this reduction does not translate equally to all product degrees of freedom. In particular, OH rotation is not colder in the simulations, in contrast to experiments. This could be due to a problem with the OH-CO transition-state properties on our surface (a point which is supported by new potential surface calculation^^^), but we also found that the OH + CO formation times are too short to completely equilibrate energies (a problem that is apparently due to quantum effects2*). These times disagree with recent picosecond studies, so one possibility is that if the trajectory lifetime were longer, more complete equilibration of the product degrees of freedom would occur and the reduction in total energy would translate into a reduction in OH rotational energy.
+
Acknowledgment. This research was supported by NSF Grant CHE-9016490. We thank Richard Bernstein, Curt Wittig, Jane Rice, George Flynn, Ahmed Zewail, and their groups for numerous discussions and preprints. Registry No. H (atomic), 12385-13-6; C02, 124-38-9; HBr, 1003510-6.
