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J . Phys. Chem. 1988, 92. 5266-5270
figuration, but bound states exist for the bent configuration. In such a diffuse level the effective radius is quite large, and consequently less electrostriction is expected. The observed slope of -1.36 X lo6 cm3 bar/mol for the Ab',,' line corresponds to an effective radius of about 5 A. The points for 3-MP are above the line here too because the solvent is already constricted around the trapped electron in 3-MP, and thus the magnitude of the volume change from reactants to transition state is expected to be less, as is observed. The entire electrostriction volume of the trapped electron must be recovered to arrive at the transition state. Therefore, the slope of the line through the 3-MP points (dashed) should again be 3.5 X lo5 less than the slope of the solid line through the V,' points. The difference in slopes here is 7.6 X I O 5 cm3 bar/mol, in fair agreement. Diffusion-Controlled Rates. In the case of 3-MP, k , reaches a maximum and after that actually decreases with increase in pressure. A corresponding decrease in the electron mobility, j t , with pressure has been observed in 3-MP,S suggesting that the decrease in k , is due to a diffusion-controlled limit. When the attachment rate constants for pressures from 500 to 2500 bar are fitted to eq 15 along with measured mobility values in 3-MP,Sthe k, = 4rR,D = 4rR,jtkbT/e (15) capture radius R, turns out to be constant at 5.5 f 0.3 A over the temperature range from 70 to 100 'C. At lower temperatures the reaction may be approaching diffusion control. Before reaching a maximum in 3-MP, pressure still has an effect and causes the rate to increase; that is, the reaction is controlled by effects other than diffusion at low pressures. Substitution in eq 15 of corresponding values of k, and mobility gives smaller radii by 1 order of magnitude for 2,2,4-TMP and by 3 orders of magnitude for TMS. Moreover, the dependence of mobility on pressure in these liquids does not correlate with the dependence of k, on pressure. Thus the reaction is not diffusion controlled in these solvents. Detachment Rates. Figure 6 also shows the values of Ab',,', the volume of activation for detachment of an electron from CO,. These volume changes are large and positive and directly proportional to (1/t2)(&/t3P). All the experimental Ab',,' points fall on the same line because here the reactant is C 0 2 - in all three liquids. A least-squares analysis gives an intercept of -3.5 cm3/mol and a slope of 3.15 X lo6 cm3 bar/mol. The slope of this line is seven-tenths of the absolute value of the slope of the AV, line. Thus a large share of the total electrostriction is lost in going from the product COT to the transition state.
Interestingly there is a relation between the volume and entropy of activation for detachment from C02-. The entropy of activation for these detachment reactions is generally equal, but opposite in sign, to the entropy change for the reaction.12 The entropy change for the reaction is approximately -46 cal/(K mol) at 1 bar. This has been associated with changes in the solvation and now can be directly associated with electrostrictive effects. A quantitative relation between volumes and entropies of activation has been noted by Laidler;23as AS* increases, AV also increases. For reactions where ions are disappearing (by recombination), both AS* and AV are large and positive. However the reactions that Laidler refers to are in aqueous solution. Nevertheless the correlation seems to apply to detachment from COT in nonpolar solvents as well. Here the ion COz- is disappearing (by detachment). The difference is that the volume change is much larger in the nonpolar solvent, as noted earlier. Conc1usion Studies of electron reactions occurring in nonpolar liquids often lead to interesting and unexpected findings. The effects of high pressure observed here are dramatic and provide some detailed insight into the mechanism of electron attachment. The volume changes are (to our knowledge) the largest ever reported for a liquid-phase reaction. The overall volume decrease is attributed mainly to concentration of the negative charge on the compact (r = 1.6 A) COT product ion, which constricts the solvent around it. The magnitude of the volume changes scale with the compressibility of the solvent in accord with the classical theory of Drude and Nernst. The large entropy decrease for this reaction is associated with constriction of the solvent. Approximately one-third of the volume decrease occurs between reactants and transition state; the larger volume change occurs between transition state and the product ion. Acknowledgment. We are grateful to H. Schwarz for helpful discussions. This research was carried out at Brookhaven National Laboratory under Contract DE-AC02-76CH00016 with the U S . Department of Energy and supported by its Division of Chemical Sciences, Office of Basic Energy Sciences, and the Japan Society for the Promotion of Sciences under the US.-Japan Cooperative Science Program. Registry No. C02, 124-38-9. (22) Henglein, A. Can. J . Chem. 1977, 55, 21 12. (23) Laidler, K. J. Chemical Kinelics; McGraw-Hill: New York, 1965; p 236ff.
Absolute Emission Rate of the Reaction between Nitric Oxide and Atomic Oxygen G . R. Bradburn* and H. V. Lilenfeld McDonnell Douglas Research Laboratories, P.O. Box 516, St. Louis, Missouri 63166 (Received: December 17, 1987) The absolute emission rate of the air afterglow reaction has been referenced to the O,('A) emission at 1270 nm. The emission rate constant at 1270 nm was determined to be 6.2 (f1.2) X molecules-' cm3 s-I nm-I. The relative curve from 385 to 1700 nm has also been measured and referenced to the absolute rate at 1270 nm. The results indicate good agreement with the results of previous workers below about 900 nm and show that the IR emission of this reaction is more intense than many previous investigators have thought. Introduction When optical techniques are used to determine absolute emission rate constants for light-emitting gas-phase reactions, it is necessary to calibrate the detection system by referencing it to Some known emitter. Several different calibration Sources have been proposed, including tungsten filament lamps, luminous disks, and other gas-phase reactions, When attempting to reference a 0022-3654/88/2092-5266$01.50/0
gas-phase reaction to a lamp or luminous disk, one must be careful to account for the differences in the geometries of the calibration and reaction sources. One might also have to make corrections for different optical paths if the calibration source cannot be placed inside the reaction vessel. An ideal standard would be a reaction that produced intense, well-dispersed, broad-band emission. The emission intensity of this standard would, of course, need to be
0 1988 American Chemical Society
Nitric Oxide and Atomic Oxygen Reaction
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5267
- -Fontiin at 298 K -...... vqee Golde - - -WmlSey ~
Sutoh
NOmAr
Figure 2. Apparatus used to measure the 0 + NO and O,('A) emission
intensities.
Wavelength (nm)
Figure 1. Absolute rate constants of the 0 + NO reaction versus wavelength as reported by Fontijn, Vanpee (corrected to 298 K using the
results of Clyne and Thrush), Golde, Woolsey, and Sutoh. characterized well in the region of spectral interest. Kaufman'.* found that the intensity of the emission of the 0 N O reaction is broad banded, is proportional to the product [O] [NO], and is independent of the concentration and, apparently, type of gases so that the emission intensity kinetics are of the form
+
Z = k[O] [NO]
(1)
Broida et a1.j later proposed a mechanism to explain these findings but suggested that there should be a slight dependence on the type of gas added. In later work, Clyne and Thrush4 measured a difference in the reaction emission intensity of about 20% when using He and Ar as third bodies. Subsequent to the suggestion by Kaufmann, the 0 N O reaction has been the subject of several investigations5-I3 with the purpose of quantifying the emission intensity of this reaction in the visibile and infrared regions. As a result of these investigations the reaction has been used widely as a calibration standard. The reaction is especially of interest to atmospheric chemists because there are many atmospheric reactions that produce visible or IR emissions. In addition, the 0 + NO reaction has been used to measure atomic oxygen concentrations in the upper a t m ~ s p h e r e . ' ~ Fontijn5g6explained a method for using the 0 N O reaction as a gas-phase calibration reference using the relationship
+
+
where the specific intensities, Z, and Is, are the actual intensities divided by the concentrations of the rate-determining reactants. He then proceeded to measure the rate constant for emission from 387.5 to 1400.0 nm, the entire range over which he detected Kaufman, F. Proc. R . SOC.London, A 1958, 247, 123. (2) Kaufman, F. J . Chem. Phys. 1958, 28, 352. (3) Broida, H. P.; Schiff, H. I.; Sugden, T. M. Trans. Faraday SOC.1961, (1)
57, 259. (4) Clyne, M. A. A.; Thrush, B. A. Proc. R. SOC.London, A 1962, 269, 404. (5) Fontijn, A.; Meyer, C. B.; Schiff, H. I. J . Chem. Phys. 1964, 40, 64. (6) Fontijn, A.; Schiff, H. I. Chemical Reactions in the Lower and Upper Atmosphere, Proceedings of an International Symposium Arranged by Stanford Research Institute, San Francisco, CA, April 18-20, 1961; Interscience: New York, 1961; p 239. (7) Vanpee, M.; Hill, K. D.; Kineyko, W. R. AIAA J . 1971, 9 , 135. (8) Becker, K. H.; Groth, W.; Thran, D. Chem. Phys. Lett. 1972,15,215. (9) Golde, M. F.; Roche, A. E.; Kaufman, F. J . Chem. Phys. 1973, 59, 3953. (10) Woolsey, G. A,; Lee, P. H.; Slafer, W. D. J . Chem. Phys. 1977, 67, 1220. (1 1) Sutoh, M.; Morioka, Y . ;Nakamura, M. J. Chem. Phys. 1980,72,20. (12) Clyne, M. A. A,; Thrush, B. A. Discuss. Faraday SOC.1962,33, 139. (13) Gulomb, D.; Rosenberg, N. W.; Aharonian, C.; Hill, J. A. F.; Alden, H. L. J . Geophys. Res. 1965, 70, 1155. (14) Badger, R. M.; Wright, A. C.; Whitlock, R. F. J . Chem. Phys. 1965, 43, 4345.
emission. More recent measurement^^^^-^^ indicate that there is much more emission in the IR than measured by Fontijn. However, there is significant scatter in the reported rates of IR emission, as shown in Figure 1, where the results of Vanpee et al.' have been corrected to 298 K by using the work of Clyne and Thrush: as described in ref 7. Thus, while the 0 N O reaction is well established as a calibration reference source in the visible, there continues to be much uncertainty over its application to IR calibrations. Two of the attempts to calibrate the IR emission6*" consisted of calibrations in the visible, where the emission is most intense, followed by extension of the calibration into the IR by use of the relative response of two or more detectors to correct the intensity output of the reaction. A few investigator^^^^-'^ have actually calibrated the reaction in the IR, but there have been large differences in their results. In this work we calibrated the 0 N O reaction rate constant with respect to the 02(lA) emission at 1270 nm by using optical and electron paramagnetic resonance (EPR) detection techniques and a modified form of Fontijn's relationship: k(O+N0,1270nm) = k(O2*)[O2('A)] Z(O+N0,1270nm)(A2 - A,) (3) 1(02*) [OI [NO1 where k(O+NO,1270nm) and Z(O+N0,1270nm) represent the 0 + N O emission rate and intensity at 1270 nm, respectively, k(02*) is the Einstein A coefficient of O2(IA) = 2.6 X lo4 s-l,I4 Z(02*) is the intensity of 02(lA) emission integrated between A, and A*, and A, and A2 are the limits of the 02(lA) emission band.
+
+
Experiment Materials. In this work, all gases were used without further purification. The oxygen was Matheson UHP grade, 99.98% pure; the nitrogen was 99.99% pure; the Ar, which was used as a carrier for the discharge gases, was 99.99% pure; the N O was Matheson C.P. grade, 99.0% pure. Enough nitrogen-containing impurities were present in the oxygen that a faint glow was always visible when a discharge in O2was running. Efforts were made to correct for this background intensity as described in a later section. Apparatus. The apparatus employed in this work and shown schematically in Figure 2 consisted of a quartz flow tube (2.25-cm i.d.) with a movable Pyrex injector and a side arm connected to a microwave discharge cavity. For absolute rate-constant measurements, the observation region was a minimum of 15 cm downstream of the mixing region, and fiber optic bundles 0.64 cm in diameter by 1.2 m long were used to collect the emitted light upstream and downstream of the EPR cavity. For relative emission rate measurements, the monochromator entrance slit was placed directly against the flow tube. The emitted light was dispersed with a Jarrell-Ash 0.25-m monochromator with a 590 groove/mm grating blazed at 1000 nm for IR signals, or an 1180 groove/nm grating blazed at 600 nm for visible signals. A 200-Hz chopper was mounted between the monochromator and the optical detectors for noise and background discrimination. To obtain the relative emission over the range 350-1650 nm, we used four distinct optical systems: (1) from 350 to 800 nm, a Hammamatsu R636 PMT detector with no filters; (2) from 540 to 880 nm, a Hammamatsu R636 PMT detector and a Corning 3484 colored glass filter to block second order; (3) from 750 to 1300 nm, a liquid-nitrogen-cooled North Coast Model EO-8 17
5268
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
intrinsic germanium detector with no filter; (4) from 1200 to 1650 nm, the cooled intrinsic germanium detector with a Corning 2550 colored glass filter. An Eppley Laboratory, Inc., Model 30A/T24/13 standard of spectral radiance calibrated from 225 to 2400 nm was used as a source for determining the relative response of the detection systems. This tungsten ribbon lamp was operated at 38.00 A supplied by a Hewlett-Packard Model 6261 B dc power supply. Signals from the optical detectors were passed directly to an Ithaco/Dynatrac Model 391A lock-in amplifier. The output of this instrument was then passed to a Digital Equipment Corp. PDP 11-23 Minc computer, which also controlled the scan of the monochromators. EPR data were also recorded by this computer, so it was not normally possible to make the optical and EPR measurements simultaneously. Instead, the EPR measurements were taken between optical spectra. Preliminary data analysis was also performed on this computer. Absolute concentrations of the radical species involved in the measurement (O(3P)and OZ(lA))were measured during passage of the flow through the cavity of an EPR spectrometer. This technique has been described in detail e l s e ~ h e r e . ' ~ , ' ~ The system was pumped by a 150 dm3/s Roots Model 2507 RGS blower backed by a 140 dm3/s Stokes Model 412 Microvac mechanical pump. A gate valve was used to throttle the vacuum and adjust the pressure for a given experiment with fixed gas flows. Because the O3 N O reaction also emits in the region of interest, we used two different 0-atom sources to ensure that the ozone reaction was not a significant contributor to our results. The first source was a simple discharge in a mixture of O2 in Ar, and the second source was a discharge in N2 followed by addition of excess NO. The nitrogen atoms produced in the discharge reacted with the N O added downstream to form 0 atoms."
Bradburn and Lilenfeld 1 .o
800
loo0 1200 1400 Wavelength (nm)
I
1600
1800 2000
Figure 3. Relative reaction rate as measured by this work and previous work by Vanpee, Golde, and Sutoh.
1.5
[NO] = 2.1 x lo1' 0 0 [NO] = 4.5 x lo1' - - 0.87 * X -26.7 _ _ _ 1.06* X -3 1.9
I
/
d /
/
I
+
I I
Results The experiment was performed in two parts. First we determined the relative emission curve for the 0 N O reaction over the wavelength ranges (-350 to -1700 nm) of the detection systems used. Second, we determined the absolute rate constant for the 0 NO reaction relative to the 02(lA) emission at 1270 nm and used this value to calibrate the relative emission curve. Relative Emission Curve. The first step in determining the relative emission curve was to record the spectrum of the 0 N O reaction over the range of the measurements. To do this, we excited a microwave discharge in a mixture of Ar and O2 to produce oxygen atoms. Nitric oxide was added to the flow downstream of the microwave discharge to produce the characteristic "air afterglow" emission. The appropriate detection system was then positioned against the flow tube. The pressure in the flow tube was adjusted by throttling the vacuum pump to optimize the signal for maximum intensity with minimum gradient down the flow tube. Relative curves were measured in the pressure range 0.05-0.26 kPa and were equivalent within the accuracy of these measurements. Even at the highest pressures the reaction zone was at least 50 cm in length. Next, the detection system sensitivities were determined by recording spectra of a calibrated standard lamp with a tungsten ribbon filament. Both lamp and flame spectra were taken with the same optics with the exception that when the lamp spectra were recorded, a 0.3-cm-thick quartz flat was inserted between the lamp and the detector. The flat was used to simulate the absorption of light by the flow tube walls when the flame spectra were obtained. Since only the relative lamp output was important in this work, it was not necessary to make a geometry correction. When all the spectra were recorded, the relative emission rate curve was determined. In doing this, appropriate background spectra were subtracted from both the flame and lamp curves. Then the lamp characteristics were removed from the lamp spectra by dividing the spectra by the emission rate for the lamp as determined from a blackbody function fit to the lamp calibration
+
+
+
I
0'51
(15) Westenberg, A. A,; deHaas, N. J . Chem. Phys. 1964, 40, 3087. (16) Westenberg, A. A. Prog. React. K i m . 1973, 7, 23.
4 5 i 19 5
/
"/ / ,
I
/
/ ,
31 0
30 0
In
32 0
33 0
P I
Figure 4. In I(O+N0,1270nm versus In [O], [O] varied by changing the microwave power. The lines represent least-squaresfits to the data.
curve provided by the supplier. This procedure gave the relative sensitivity of the detection system with respect to wavelength. The 0 + N O reaction spectra were then divided by the system sensitivity curves to obtain the relative reaction rate. These spectra were combined for the different detection systems to give the relative reaction rate from 350 to 1700 nm as shown in Figure 3. Figure 3 also shows the results obtained by three other investigators who performed calibrations in the IR. The results of this work, Vanpee et al.,' and Sutoh et a]." have been normalized to the intensity at the peak. The work of Golde et aL9 was normalized to match this work at 1550 nm. As can be seen, our work agrees very well with the results of Vanpee et al. and of Golde et al. However, the IR portion of the curve of Sutoh et al. falls significantly below our results in the IR on a relative curve. The reaction order with respect to oxygen atoms was determined by plotting the log of the 0 N O emission intensity as a function of the log of the oxygen-atom concentrations when all flows were kept constant ( [ O ]was varied by changing the microwave discharge power). The results of this determination at two different N O concentrations are shown in Figure 4. These data were fit to a line with a slope of 1.0 within experimental error, indicating first-order dependence on [0]. A subsequent experiment was performed in which the N O flow was varied. For these data, the log of the intensity, normalized to the oxygen-atom concentration, was plotted against log [NO] as shown in Figure 5. The slope was again found to be 1 within experimental error, thus demonstrating that the reaction responsible for the emission is indeed first order in [NO]. Determination of Absolute Emission Rate Constant. The absolute emission rate was calibrated in the IR against the radiative emission of the 0 2 ( l A ) line at 1270 nm. For this measurement the detection system was modified to include the fiber optic. Emission spectra were recorded from about 1220 to 1320
+
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5269
Nitric Oxide and Atomic Oxygen Reaction -30.0 ~
1.1 ' X -69.4
-30.2
..........
Vanpee at 298 K Golde
-30.4
/ c
-30.6
P,b
.-e. =
-30.8
-31.0 -31.2
O
ii
..
o'&l
/
-3 1.4 -31.6
34.5
/
35.0
800
ldoo 1200 1400 1$00 Wavelength (nm)
1800
2 1 m
Figure 7. Absolute reaction rate as measured in the IR, this work, Golde, and Vanpee (corrected to 298 K by using the results of Clyne and
Thrush4). 35.5 In [NO]
36.0
36.5
Figure 5. In (I(O+N0,1270nm)/[O] versus In [NO]. The line represents a least-squares fit to the data. 0.007
Qoo
--'5
14 x lo-"
1-
$ -
A
lol 12
8
0,mscharge
0 0,+Armscharge 0 N, +Ardischarge
h
CL
4
i 0.001 -
_ _ _ -3.6~10-~*X+7.6~10-~
02 0.4 06 08 Mole fraction of N, or 0,in the flow
10
Figure 8. Absolute rate as a function of fraction of discharge flow that is active gas.
we then calibrated the entire 0 + NO emission curve from 350 to 1700 nm as shown in Figure 7 . Also shown in Figure 7 for comparison purposes are the results of Vanpee et al.' and of Golde et al.,9 whose results are closest to ours. Our results indicate that the IR emission from the 0 NO reaction is stronger relative to the visible emission than most of the previous workers would indicate. Our measure of the absolute rate constant in the IR is in good agreement with the results of Golde et al. and of Vanpee et al., who also performed their calibrations in the IR. The mechanism proposed by Broida et. aL3 suggests that the apparent rate constant should depend on the nature of the third body, M, in the reaction 0 + NO + M. These effects have been measured for some third bodies4 and are on the order of 10-20%. In this work where three different third bodies were used (02, N2, and Ar), we saw no significant difference in the value of k(O+ N0,1270nm) between the cases when the third body was N2 or Ar. However, when the third body was 02,the measured rate at 1270 nm was about 50% greater than with a discharge in a mixture of N2 or O2 in Ar. We did not make an effort to identify the exact cause for this difference, but in view of the results of Sutoh et al." it seems likely that the excess emission is caused by the reaction of O3with NO and not by the effect of the third body on the reaction rate. As seen in Figure 8, where we plot the apparent absolute rate constant for the 0 NO reaction as a function of O2or N2mole fraction, our results indicate that this effect can be more pronounced than the 10% effect seen by Sutoh. The results at O2mole fraction greater than 0.8 are anomalously high and have a large scatter. The large scatter supports the supposition that the anomalous emission is related to O3density since we would expect the O3 density to vary under differing experimental conditions, Le., ozone is formed by the reaction of atomic oxygen with molecular oxygen and will vary as a function of reaction time. Examination of the data in Figure 8 suggests a trend of increasing apparent rate constant with decreasing O2 or N2 mole fraction. Analysis of the data in those cases where pure O2 was not used, however, showed no statistically significant dependence
+
+
J . Phys. Chem. 1988, 92, 5270-5272
5270
TABLE I: Results of Applying Calibration at 1270 nm to Relative Curve A, 0 NO emission X 1020, A, 0 NO emission X lozo, nm cm3 (molecule s nm)-' nm cm3 (molecule s nm)-'
+
380 385 390 395 400 425 450 475 500 525 550 575 600 625 650 700 750 800
+
0.0 0.2 0.3 0.5 0.6 2.2 4.9 7.9 11 14 17 18 19 20 20 19 17 15
850 900 950 000 050 100
150 200 250 1300 1350 1400 1450 1500 1550 1600 1650 1700
14 12 12 10 9.1 8.3 7.5
6.8 6.3 5.7 5.3 5.0 4.4 3.8 3.5 3. I 2.6 2.5
on O2 or N2 mole fraction; we therefore averaged these data to determine the absolute rate constant.
Sensitivity Analyses Pressure Variations. The flow tube was operated at relatively high pressures, 0.054.66 kPa, by throttling the flow downstream of the measurement ports, thus reducing the pressure drop. The pressure was measured 12 cm upstream of the EPR cavity center. In some cases it was also measured downstream of the EPR cavity with differences of less than 5% from upstream of the EPR cavity to downstream (a distance of about 25 cm); thus pressure was not considered to be a major source of error. 0-Atom Recombination. We used a Varian Model 917500-14 E-line EPR spectrometer to determine [O]at the position of interest and upstream and downstream optical measurements with a linear fit to determine 0 + NO emission intensities at the EPR
cavity center. Typically, upstream and downstream intensity measurements differed by less than 25%. Wall Effects. Because we could actually measure [ O ]and [ 0 2 ( ' A ) ] , we could ignore wall recombination. Because the radiative lifetime of NO2* is small (4.4 X s") compared to the diffusion times to the wall at the pressures we worked with, no attempt was made to correct for wall quenching of NO2*. Experimental Measurements. The values of [ O ] ,[02('A)], and [NO] can each be determined to about 5%, and the intensities can be measured to about 5% as well. This results in an overall estimated error of about 25%, not including the error in the value of the Einstein A coefficient of 02('A). The latter value has been estimated to be about 15%.14 An additional 10% error can be applied to our results below 850 nm because of the noise in the relative curves in the region of overlap of the detection systems, where both systems have a relatively low response.
Conclusions Calibration of the 0 + N O emission by referencing it to the Einstein A coefficient of O,('A) yields an emission rate constant of 6.2 (fl.1.2) X molecules-' cm3 s-' nm-' at 1270 nm. The stated error represents the 95% confidence limits of the statistical errors. Other sources of error result in larger overall error. Our results are in excellent agreement with Vanpee et al. and with Golde et a1.-workers who have also calibrated in the IR. The calibration at 1270 nm has been applied to the relative curve and the results are shown in Figure 7 and tabulated in Table I for ease of application. Acknowledgment. This research was conducted under the McDonnell Douglas Independent Research and Development Program. Registry No. NO, 10102-43-9; 0, 17778-80-2.
(17) Myers, G. H.; Silver, D. M.; Kaufman, K. J . Chem. Phys. 1966,44, 718.
Atom-Exchange Reactions In Collisions of Noble-Gas Atoms and Dimers Nancy S. Gettys, Lionel M. Raff, and Donald L. Thompson* Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078 (Received: December 28, 1987)
Classical trajectories have been used to calculate angular distributions and reaction cross sections for atom exchange in collisions of Xe + Ar,, Kr + Ar,, and Kr + Xe,. The potential energy surfaces are simple pairwise-additive Morse functions with parameters based on empirical results. The computed results are in good agreement with the molecular beam results of Worsnop et al. ( J . Phys. Chem. 1986, 90, 5121) except for the case of Xe + Ar,, where the scattering data obtained from the trajectories suggest that the simple pairwise potential is not sufficiently repulsive.
Introduction One of the major uses of classical trajectories has been the calculation of reactive scattering for comparisons with crossed molecular beams results. A serious obstacle and the cause of disagreements between theory and experiment is often inaccuracy in the potential energy surfaces used in the trajectory calculations. This is the case even for the atom-diatomic molecule reactions for which most of the studies have been done. The crossed beams experiments by Worsnop et al.' on exchange reactions between noble-gas atoms and dimers provide an opportunity to compare (1) Worsnop, D. R.; Buelow, S. J.; Herschbach, D. R. J . Phys. Chem. 1981, 85, 3024.
0022-3654/88/2092-5270$01.50/0
experiment and theory for systems for which the potential energy surfaces are not of seriously questionable accuracy. Previous studies have suggested that the potential energy surfaces for these systems can be represented by simple pairwise additive functions.2 Extensive empirical information has been reported for the rare gases, and this can be used directly to obtain the simple potentials. In view of this, a few years ago we carried out some classical trajectory ~ t u d i e s ~for- ~Ar + Ar2, Ne2, ArKr, Kr + NeAr, Kr (2) See, for example: Howard, R. E.; Roberts, R, E.; DelleDonne, M. J . J . Chem. Phys. 1976, 65, 3067. (3) Thompson, D. L.; Raff, L. M. J . Chem. Phys. 1982, 76, 301. (4) Raff, L. M.; Thompson, D. L. J . Chem. Phys. 1982, 77, 6065.
0 1988 American Chemical Society
