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J . Phys. Chem. 1990, 94.1482-1481
Conclusions We present the first direct study of the temperature dependence of the self-disproportionation of BrO radicals that does not depend upon the measurement of the absorption cross section. Our results are in excellent agreement with the previous flash photolysis work of Sander and Watson. The slight negative activation energy observed lends support to a mechanism involving a metastable intermediate complex: BrO BrO [BrOOBr*] [BrOOBr*] BrOO Br Br, Oz BrOO Br O2 This is similar to the mechanism that has been proposed in the analogous CIO self-reaction. Although the intermediate species Brz02 and BrOO were not identified, their lifetimes under the experimental conditions are expected to be extremely short due to their weak bond strengths. Direct detection of the product Brz was observed as well, adding further support to this mechanism. Although the branching ratio was not thoroughly investigated in this study, our observations indicate that about 12% of the reaction produces molecular bromine at room temperature, with bromine
+
--
--
+ +
+
atoms being the only other stable bromine-containing product. However, stratospheric chemistry is not sensitive to the branching ratio of the BrO + BrO reaction, since Brz is easily photolyzed to produce two Br atoms; therefore, both channels result in a net production of Br. Channel 1 b does provide a possible means of sequestering bromine in the polar night of the Arctic and Antarctic regions. Data obtained at room temperature and above show no dependence on the source of the BrO radical. However, an unexplained enhancement in the rate coefficient occurs at low temperatures ( T = 253 K) when BrO is generated by the reaction of bromine atoms with ozone. At present, we are unable to explain the observed enhancement; however, it may be due to a Br0.03 adduct formation at lower temperatures or involve vibrationally or spin-orbit excited BrO radicals which are not efficiently quenched at lower temperatures. Acknowledgment. The authors thank J. E. Smith of the National Oceanic and Atmospheric Administration (NOAA) for providing the numerical integration program used in this study. A. A. Turnipseed also thanks the Advanced Study Program of the National Center for Atmospheric Research (NCAR) for providing a graduate research assistanceship.
Collision-Theory Calculations of Rate Constants for Some Atmospheric Radical Reactions over the Temperature Range 10-600 K L. F. Phillips Chemistry Department, University of Canterbury, Christchurch, New Zealand (Received: September 22, 1989; In Final Form: May I , 1990)
Rate constants have been calculated for a number of bimolecular reactions of HOz, OH, H, C10, BrO, SO,O(”),O(’D), NO, and NOz, over the temperature range 10-600 K. For half of the reactions studied so far, calculated capture rates agree with listed experimental rate constants at 300 K to within the stated uncertainties, and calculated temperature coefficients are also consistent with experimental data. Three of the rate constants have not been measured experimentally. For the remaining reactions the calculated value is greater than the measured value and the difference can normally be attributed to the presence of an exit channel barrier, in which case it is possible to predict the form of the temperature dependence to be expected as T tends to zero.
Introduction Experimental rate constant values, of somewhat variable accuracy, are now available for the majority of homogeneous, gas-phase radical reactions that are of interest to modelers of planetary atmospheres.’J However, because of the experimental difficulty of studying many of these reactions, the available values are mostly restricted to a rather narrow range of temperatures near room temperature and their temperature dependences are correspondingly uncertain. The low-temperature range, between about 10 and 200 K,which is particularly difficult experimentally, is also a range of special relevance to the atmospheres of several planets and massive satellites. Rates of radical reactions at the bottom end of this temperature range may be important in relation to processes occurring in interstellar clouds. Most of these reactions lack any significant activation barrier, so that their rate constants outside the range of measurements cannot be predicted simply on the basis of an Arrhenius-type expression. Thus it is ( I ) Atkinson, R.; Baulch, D. L.; Cox, R. A.; Hampson Jr., R. F.: Kerr, J. A.: Troe, J. J. Phys. Chem. Ref Data 1989, 18, 881. (2) DeMore, W. B.;Molina, M. J.; Sander, S.P.; Golden, D. M.; Hampson Jr., R. F.; Kurylo, M. J.; Howard, C. J.; Ravishankara, A. R. Chemical Kinetics and Photochemical Data f o r use in Stratospheric Modeling. Evaluation Number 8; JPL Publication 87-41: California Institute of Technology: Pasadena, CA, 1987.
0022-3654/90/2094-1482$02.50/0
of interest to find a reliable means of predicting the temperature dependence of radical reactions at low temperatures. The present paper gives the results of calculations which yield values of rate constants which are in excellent agreement with roomtemperature experimental data for many reactions, without the use of adjustable parameters, and also agree well with available data at other temperatures. Unlike the exeriments, these calculations are as easy to perform for a temperature of 10 K as for 300 K. Where the results of the calculations are not in agreement with experimental data, the calculated values are invariably larger, and the difference between observed and calculated results can provide an indication of the importance of such factors as exit-channel barriers or the requirements of electronic angular momentum conservation. Also, when there is an exit channel barrier, the calculations can still predict the likely form of the temperature dependence in the low-temperature range. Calculation of ion-molecule reaction rates from the classical rate of crossing the centrifugal barrier in an ion-dipole ionquadrupole + ion-induced dipole potential has been a standard practice for many years.3 Clary4 used analogous quantumscattering calculations of the barrier-crossing rate to obtain rate
+
(3) Su,T.; Bowers, M. T. In Gas Phase Ion Chemistry; Bowers, M. T., Ed.; Academic Press: New York,1979; Vol. 1, p 84. (4) Clary, D. C. Mol. Phys., 1984, 53, 3 .
0 1990 American Chemical Society
rhe Journal of Physical Chemistry, Vol. 94, No. 19, I990 7483
T4
reactlon coordinate
Figure 1. Schematic section through the potential energy surface for a complex-formingreaction with no activation barrier. Reactant molecules A and B enter from the left side of the diagram at the energy level indicated by the dotted line and must pass through configurations cor-
responding to the complex AB* and the transition state ABt before forming the products C and D.
constants for neutral reactions of diatomic radicals colliding under the influence of dipole-dipole and dipole-quadrupole potentials, and subsequently extended his calculations to treat other systems, such as the reaction of 0 with OH,5and a number of ion-dipole Clary’s method was applied recently by GrafP to calculate rates of reactions of 0 and C atoms with OH and CH at temperatures appropriate to processes in interstellar clouds. The present calculations use a recently developed computer program for carrying out approximate, quasi-classical trajectory calculations in a potential that, for neutral reactions, can incorporate dipole-dipole, dipole-quadrupole, dipole-induced dipole, qaudrupole-quadrupole, London and Morse or hard-sphere pot e n t i a l ~ . ~The approximations introduced are such that the program runs fairly quickly without resorting to Monte Carlo methods, while retaining sufficient accuracy for comparison with current experimental data. It has been used previously to calculate rate constants for the reaction of BH with NO,lo for the reactions of OOP) with OH, CIO, CH, NO2, and PH3,I1for reactions of O(ID) with 02,C02, H2, and N2,12for a number of ion-molecule reactions of CH3+,I3and for termolecular reactions forming N4+, 04+, N202+,and N2NO+.22Where information about the exitchannel barrier or barriers is available, as in the case of the reaction of BH with NO, the trajectory calculations can be combined with statistical calculations of barrier-crossing rates for the collision complex to give overall rate constants in excellent accord with experiment. In principle, one should make quantum-scattering calculations on an a b initio surface. In practice, the present approach works remarkably well, presumably because molecules are largely classical objects. As noted in ref 9, a Fortran source listing of the program can be obtained from the author by sending a 3.5411. [Macintosh] or 5-in. [PC] floppy disk. For the sake of the discussion which follows, it will be helpful to summarize current ideas concerning the factors that govern the rates of gas-phase radical-radical reactions. These ideas have developed through the efforts of a number of workers, and no particular originality is claimed for them here. The majority of fast ( k > lo-” cm3 molecule-’ s-l) bimolecular reactions of free radicals can be regarded as occurring on a potential surface of the form shown in Figure 1, such that the reaction proceeds through a configuration corresponding to a bound complex, which is separated from the products by a transition state at the top of a low potential barrier. The unimolecular rate constant k ( E ) for ( 5 ) Clary, D. C.; Werner, H.-J. Chem. Phys. Lerr. 1984, 112, 346. (6)Clary, D.C.; Smith, D.; A d a m , N. G. Chem. Phys. Lett. 1985, 119, 320. Clary, D.C.; Henshaw, J. P. Faraduy Discuss. Chem. SOC.1987, 84, 333. Clary, D.C.;Henshaw, J. P. Inr. J. Mars Spectrom. Ion Processes 1987, 80.31. Clary, D.C. J. Phys. Chem. 1988,92, 3173. Clary, D.C. Mol. Phys. 1989, 67, 1099. (7)Dateo, C. E.;Clary, D. C. J . Chem. Phys. 1989, 90, 7216. (8) Graff, M.M. Asrrophys. J . 1989, 339, 239. (9) Phillips, L. F. J . Compur. Chem. 1990, 11, 88. (IO) Phillips, L. F. Chem. Phys. Lerr. 1990, 168,197. ( 1 1 ) Phillips, L. F. Chem. Phys. Lett. 1990, 165, 545. (12) Phillips, L. F. Chem. Phys. Lerr. 1990, 169, 253. (13) Phillips, L. F. J . Phys. Chem. 1990, 94, 5265.
crossing this barrier at a fixed total energy E is given by the usual RRKM formula w(E)/hp(E),where w(E) is the number of states of the transition state between the top of the barrier and the energy level E and p ( E ) is the density of states of the dissociating complex at energy E. A similar expression applies to the rate of dissociation of the complex back to reactants. Because the reactants cross the surface in Figure 1 from left to right a t an energy level well above the minimum dissociation energy of the complex, the intermediate complex is usually too short-lived to be stabilized by collision with the bath gas and the overall reaction rate is independent of pressure. (Nevertheless, the complex is still presumed to live for a time that is long compared with the duration of a rotational period; i.e., the kind of reaction under discussion is not a “direct” reaction.) If, however, the intermediate complex has many internal degrees of vibrational freedom and the configuration corresponding to the top of the potential barrier leading to products represents a relatively “tight” transition state, the complex lifetime may be prolonged sufficiently for a pressure dependence of the overall reaction rate to be observed as, for example, in the case of the reaction of H 0 2 with H02. For a pressure-dependent reaction, the capture rate relates to the high-pressure limit of the bimolecular reaction rate. If the barrier between complex and products is very low, the reaction will proceed to products every time the system enters the potential well of the complex and the rate of reaction will be equal to the rate of capture over the centrifugal barrier in the entrance channel. If, instead, the barrier between complex and products is relatively high, the number of available states above this barrier will be comparable with the number of states above the centrifugal barrier in the entrance channel and a significant fraction of the transient complexes will dissociate to reactants. Thus the capture rate constitutes an upper bound for the reaction rate. At very low temperatures, the number of states above the centrifugal barrier in the entrance channel must become small in comparison with the number of states above the potential barrier leading to products, so the reaction rate must always tend toward the capture rate as the temperature tends to zero. Therefore, a reaction of this sort whose rate is much less than the capture rate at room temperature can be expected to possess a rate constant with a large negative temperature coefficient (sometimes incorrectly referred to as a “negative activation energy”). It follows that, in general, for any complex-forming reaction with no activation barrier, there is a low-temperature range where the reaction rate is equal to the capture rate and a high-temperature range where the reaction rate is much less than the capture rate. The capture rate that is referred to in the previous paragraph in general is not simply the capture rate that results from the assumption that every collision between reactants takes place with the reactants favorably oriented on the surface of Figure 1. Instead, it is invariably necessary to multiply the raw capture rate by factors smaller than unity to allow for the requirements of collision orientation and electronic degeneracy. Thus, an orientation factor of 0.5 must be applied to the capture rate in a dipole-dipole reaction where collisions with one attractive orientation of the two dipoles can lead to reaction, whereas collisions with the other attractive orientation cannot. An example is the reaction of C10 with NO, where only one of the two attractive orientations can lead to the products CI and NO2. Exceptions arise when complexes with mobile hydrogen atoms are involved-for example, comparison of experimental and calculated rate constants shows that an orientation factor of 1 .O must be used for the reaction of OH with H02, even though one of the attractive orientations of the two dipoles appears to be unfavorable for formation of H 2 0 O2 High mobility of hydrogen atoms in the collision complex is a feature of many reactions; the outstanding example is the reaction of NO with NH2.I4 A different and interesting kind of orientation effect is found for the quadrupole-quadrupole reactions of O(lD) with H2 and N2.I2 In these reactions the quadrupole moment of the atom is free to adjust its sign so as to give an attractive interaction, irrespective of
+
(14)Phillips, L. F. Chem. Phys. Lerr. 1987, 135, 269.
7484 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990
whether the atom is approaching a negative or positive pole of the other quadrupole. For a linear quadrupole, the number of collision orientations corresponding fo end-on attack by the atom is greater than the number of orientations corresponding to broadside attack, assuming all orientations to be equally likely, in the ratio of 55 to 45. Thus, if end-on attack is required, as in the case of the reaction with H2.15the calculated capture rate has to be multiplied by an orientation factor of 0.55. For the reaction with N,, best agreement with the measured rate constant is found when the capture rate is multiplied by 0.45, which can be taken as an indication that a broadside orientation is required. Correction factors for electronic degeneracy are calculated on the assumption that the potential surface of Figure 1 is the lowest potential surface available to the interacting reactant species. (However, exceptions to this rule do occur: Dateo and Clary have calculated potential surfaces for a number of reactions of open-shell species and find that in some cases, such as the reaction of C+ with HC1,7 more than one of the available potential surfaces is attractive and therefore should be able to take part in the reaction. Also noteworthy is the difference, found in the present work, between reactive collisions and physical quenching of O(lD). Physical quenching collisions require a factor of 1/ 5 for electronic degeneracy; reactive collisions apparently do not.) For systems in which electron spin is the only source of degeneracy, the correction factor can be calculated very simply. For example, for the reaction of CN(,Z) with 02(3Z),doublet and quartet surfaces are available and reaction is assumed to occur only on the doublet surface, giving an electronic degeneracy factor of 1/3. For systems in which spin-orbit coupling is unimportant, the array of possible electronic states of a complex of specified symmetry can be deduced by using group theory as described, for example, by Herzberg.I6 For systems in which spin-orbit coupling is important, it is generally necessary to allow for the temperature dependence of the relative populations of different spin-orbit states of the reactants and to use different degeneracy factors for each interacting pair of spin-orbit states. In the present work this has been done by requiring the reaction to occur on a surface which correlates with the lowest 52 state of a linear complex in Hund's case c. This depends on the assumption that the different spinorbit states remain distinct at distances corresponding to the onset of chemical forces. The procedure has been outlined elsewhere for reactions of O(3P) with some radicals in ,II states." For the reaction of a pair of radicals in *II states, assuming the lowest surface to correlate with the lowest ]Z+ (or 0+) state of a linear complex, the resulting degeneracy factors are 1/4 for reactions of 211 species having the same R value and 0 for reaction of 211 species having different R values. An additional factor for dipole orientation may or may not be required for these reactants. The most important source of uncertainty in the present calculations is considered to be the lack of information concerning the magnitude and angle dependence of the London potential between polyatomic collision partners. The expression used for the London potential is
v, =
3ff lff2CIl I2 rvl
+ I,)
(1)
where al and a2 are polarizabilities, II and I , are ionization potentials, and C is an empirical correction factor. For a pair of identical rare-gas atoms, the value of Cis usually stated to be about 2.2. The results of calculations of rate constants for quadrupole-quadrupole reactions of O(lD) with H2, N2, 02,and C 0 2 suggest that C = 1.0 is often appropriate for the angle-averaged dispersion interaction of an atom with a small linear molecule.12 For the interaction of pairs of identical linear molecules, the expressions given by KiharaZ3lead to values of C equal to 0.72, 0.65,0.47,0.31, and 0.20 for F2, D2, O,, N,, and CO,, respectively. On this rather limited basis, the present calculations set C = 1.0 (15) Fitzcharles, M.
S.;Schatz, G. C. J. Phys. Chem. 1986, 90, 3834. (16)Herzberg, G. Molecular Spectra and Molecular Srrucrure, Vol. I l l .
Electronic spectra and electronic structure of polyafomic molecules; Van Nostrand Reinhold: New York, 1966;Chapter 111.
Phillips TABLE I: Capture Rate Constants k , for H 0 2 + O('P,), with Q o = 1.07, 0.54, and 0.0 X lo-%esu cm2 for J = 2, 1, and 0, Respectively, and the Thermally Averaged Rate Constant, k,,' T/K k,( 1.07) kJ0.54) k,(O.O) k,,,. IO 40.0 29.8 15.5 6.68 20 39.3 29.9 17.4 6.54 30 39.3 30.3 18.6 6.55 50 39.8 31.1 20.2 6.62 75 40.3 31.9 21.7 6.66 100 40.8 32.5 22.7 6.69 150 41.5 33.6 24.3 6.71 200 42.1 34.4 25.5 6.72 250 42.5 35.1 26.5 6.74 300 42.9 35.1 27.3 6.77 350 43.2 36.2 28.0 6.79 43.7 36.7 400 28.6 6.85 500 44.1 37.3 29.6 6.89 600 44.5 37.9 30.4 6.95 'Units of k , lo-" cm3 molecule-' s-l. Listed rate constant and uncertainty factor at 300 K, 5.9 X IO-" (1.2);kT = 3 X IO-" exp(200 i loo/?"). Data: p(H0,) = 2.09 D, a ( H 0 2 )= 2.0 X lo-,' cm3 (est); a ( 0 ) = 0.802 X cm3; Morse (re, De, we) estimated (1.2 A, 100 kJ, 900 cm-I); London potential factor C = 0.50.
for collisions of an atom with a diatomic species, C = 0.5 for collision of two diatomic species or of an atom with a triatomic species, C = 0.33 for a diatomic and a triatomic species or an atom and a four-atom species, and C = 0.20 for two triatomic species. For a collision of two strong dipoles, the choice of Cis not critical. For O H H02, for example, the difference between rate constants calculated for C = 0 and for C = 1 amounts to only 20% of the larger (C = 1) value at 300 K, falling to 15% at 10 K. For the reaction of H with H 0 2 , on the other hand, where there is only a weak dipole-induced dipole interaction with the same radial dependence as the London potential, the difference between results for C = 0 and C = 1 amounts to a factor of 4.7 at 300 K, falling to 1.9 at 10 K. Thus the absolute accuracy of the rate constant values given by these calculations can be expected to vary with the relative strengths of the electrostatic and London interactions, and the degree of agreement between the calculated results and experimental data may provide an indication of the correctness or otherwise of this approach to estimating dispersion forces.
+
Results and Discussion I . Reactions of H 0 2 . Table I shows capture rates k, (rate constants for crossing the centrifugal barrier in the long-range dipole-quadrupole dipole-induced dipole Morse + London potential) for the reaction of O(3PJ) with HO,. Data used in the calculations are listed at the bottom of the table. The Morse parameters, which are chosen arbitrarily, have little effect on the calculated rates provided the well depth is greater than about 50 kJ/mol and we is not too small. The listed value of the rate constant for this reaction at 300 K is 5.9 X 10-I' cm3 molecule-I s-l, with an uncertainty of a factor of 1.2 and a small, negative temperature coefficient. The effective quadrupole m ~ m e n t * , ~ ~ * ~ * of O(3PJ) interacting with the positive end of a dipole is 1.07 X esu cm2 for J = 2, 0.54 X esu cm2 for J = 1, and zero for J = 0, and capture rates k, have been calculated for each of these values. The last column of Table I contains values of k,,, the thermal average of k , over the populations of 'P, levels, multiplied by a factor of 1/6, which comprises a factor of 1/3 for the fraction of doublet states of the O H 0 2 complex and a factor of 1/2 for the possibility of the 0 atom being attracted by the wrong end of the H 0 , dipole. The calculated rate constant at 300 K agrees with the experimental value to within the stated limits of error; however, the small, negative temperature coefficient is not reproduced. Table I1 contains k,,, values calculated for the reaction of O H with H 0 2 , and k , and k,,,, values for reaction of H with HOz. The reaction of OH with H 0 2 is predominantly a dipole-dipole
+
+
(17) Gentfy, W. R.; Giese, C. F. J. Chem. Phys. 1977, 67. 2 3 5 5 . (18) Buckingham. A . D. Adu. Chem. Phys. 1967, 12, 107.
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 1485
Atmospheric Radical Reactions TABLE 11: Calculated Values of k,,, for Reaction of OH with HOB and of k , (Morse and Hard Sphere) and k , for the H + HO, Reaction"
TIK IO 20 30 50 75
IO0 150 200 250 300 350 400 500 600
k..,. (OH)
k.(H, Morse)
k.(H, h-s)
24.0 18.4 16.7 15.0 13.8 12.9 11.7 10.8 10.2 9.75 9.38 9.10 8.68 8.41
50.3 55.8 59.0 62.7 65.3 66.9 69.4 68.9 69.2 67.4 65.5 63.7 59.8 56.2
50.3 56.2 59.9 64.5 64.9 65.9 65.7 63.8 57.0 54.3 50.9 48.4 43.9 35.9
k,,.(H) 12.6 14.0 14.9 15.9 16.3 16.6 16.9 16.6 15.8 15.2 14.6 14.0 13.0 11.5
"Units of k , IO-'' cm3 molecule-' s-I. Listed rate constants and uncertainty factors2at 300 K: OH + H02, 1.0 X (1.2); H + HO,, 8.1 X IO-'' (1.3). ktvalues: 4.6 X IO-'' exp(230 f 2O0/T) and 8.1 X IO-Il exp(0 & 200/T). Data: H02 as in Table I; p(OH) = 1.67 D; cm3;a(H) = 0.667 X IO-*' cm3; Morse (re,De, a(OH) = 1.14 X w e ) est = ( 1.25 A, IO0 kJ, I500 cm-I) for OH; ( I . 1 A, 200 kJ, 3500 cm-I) for H; London potential factor C = 0.33 (OH), 0.50 (H). reaction, with smaller contributions from the dipole-induced dipole, Morse, and London potentials. A constant factor of 1/4 was used to convert k, to krate,this factor arising solely from electron spin. One would expect to require an additional factor of 1 / 2 for dipole orientation, but for the circumstance that the distinct orientations involve hydrogen atoms which, as discussed in the Introduction, are expected to be extremely mobile in the intermediate complex at energies above its dissociation limit. The value calculated at 300 K is in very good agreement with the listed cm3 molecule-' s-I, and its temperature value, namely 1 .O X dependence is also consistent with the evaluations. It is noteworthy that the listed values, which are larger by a factor of 1.5 at 300 K than those recommended by earlier evaluations, are consistent with current models of stratospheric ozone p h o t ~ h e m i s t r y l ~ whereas the earlier values are not. Collisions of H with H 0 2 involve a dipoleinduced dipole potential and London potential at long range (both varying with l/#) with a strong or weak Morse-type interaction at short range. Here it is assumed that collisions of H with the oxygen end of the dipole involve a short-range Morse potential, while collisions with the hydrogen end of the dipole involve an essentially hard-sphere potential. The mean of the two values of k,, with a factor of 1/4 for electron spin, gives k,,,. The value of k,,, at 300 K is larger than the experimental value by more than the stated uncertainty factor of 1.3, but this degree of agreement is probably acceptable in view of the high sensitivity of the results to the value of the London potential factor C. The calculated temperature dependence is consistent with experiment.2 This calculation appears to overestimate the rate of reaction to form H2 + 02,two different experimental estimates giving fractional contributions of 0.69 and 0.87 for reaction via the channel leading to OH OH,2 whereas the present calculation gives this fraction as 0.55. This suggests the possible presence of a small barrier in the reaction channel leading to H2 0,; a barrier of only 1.44 kJ/mol in the entrance channel is sufficient to change the fraction giving OH + OH to 0.69 and reduce k,,, to 1.2 X cm3 molecule-' s-I at 300 K. According to the data of Table 11, the rate constant for reaction of H with H 0 2 is predicted to pass through a small maximum near T = I50 K;the experimental rate constant is independent of temperature. If a 1.44 kJ/mol barier is located in the entrance channel for production of H2 + 02,the rate constant falls off more rapidly at low temperatures. A barrier in the corresponding exit channel has the opposite effect. Table Ill contains calculated k,,, values for the dipole-dipole reactions of H 0 2 with NO, HOz, and CIO. The fact that the
+
+
(19) Nataranjan, M . Geophys. Res. Len.1989, 16, 473.
10 20 30 50 75
IO0 150 200 250 300 350 400 500 600
2.80 2.43 2.42 2.46 2.49 2.47 2.39 2.30 2.26 2.22 2.18 2.16 2.12 2.12
9.90 7.67 6.99 6.34 5.95 5.74 5.43 5.23 5.06 4.93 4.84 4.77 4.67 4.59
18.8 15.1 13.8 12.6 11.7 11.2 10.8 10.6 10.6 10.6 10.6 10.5 10.4 10.2
"Capture rate times 0.125 (NO and H02) or 0.375 (CIO). Units of k: IO-" cm3 molecule-' s-I. Listed rate constants at 300 K: H02 NO, 8.3 X (1.2); H02 + HO,, 1.7 X IO-'* (1.3); H02 + CIO, 5.0 X (1.4). kT formulas: 3.7 X exp(240 f 80/T), 2.3 X IO-" exp(700 + 250 - 700/T). Data: HO, exp(600 f 200/T), 4.8 X as in Table I; p(N0) = 0.16 D, p(CI0) = 1.24 D; a ( N 0 ) = 1.68 X esu IO-'' cm3;a(CI0) = 3.1 X cm3 (est); Q(N0) = -1.23 X cm2; Morse (re, De, we) est = (1.3 A, 100 kJ mol, 900 cm-I) for NO, (1.2 A, 100 kJ/mol, 700 cm-I) for H02, (1.3 , 180 kJ/mol, 900 cm-I) for CIO; London potential factor C = 0.33 (NO, CIO), 0.20 (HO,).
+
6,
experimental rate constants for these reactions are all smaller than IO-'' cm3 molecule-' s-' suggests that they are probably not going to be in good agreement with the calculated capture rates, and this expectation is borne out in practice. For all of these reactions the calculated value is considerably greater than the experimental value at 300 K;nevertheless the comparison is instructive. For the reactions of H 0 2 with NO and H 0 2 , the capture rate constant k, was divided by factors of 4 for electron spin and 2 for orientation. The reaction with C10 has to occur on a triplet potential energy surface to give ground-state HOC1 and O2 as products, so the divisors in this case are 4/3 and 2. The difference between k,,,, and the experimental rate constant amounts to a factor of 2.7 for the H 0 2 NO reaction a t 300 K. The most likely explanation for this discrepancy is the presence of a significant barrier in the exit channel between the HOONO collision complex and the products OH NO2, at an energy below the level of the reactants H 0 2 NO. On the basis of the arguments outlined in the Introduction we can predict that the rate constant for reaction of H 0 2with NO should increase monotonically with decreasing temperature and become equal to kmk,as given in Table 111, at temperatures of the order of 50 K or below. Experimentally the rate constant has a fairly strong negative temperature coefficient near room temperature. For the reaction of HOz with H 0 2the calculated value of k,,, exceeds the experimental low-pressure limiting rate by a factor of 29. As the observed pressure dependence of the rate constant implies, this reaction is well-known to involve an intermediate H402 complex, with a free-energy barrier in the exit channel leading to H202and 02.Thus the temperature dependence of this rate constant should be qualitatively the same as predicted for HO2 + NO, the high-pressure limiting value of the rate constant rising to approach the calculated values of k,, at very low temperatures. Experimentally, there is a strong negative temperature dependence of the rate constant near room temperature. For the reaction of H02 with C10, the calculated rate constant exceeds the experimental value by a factor of 21 at 300 K. This reaction is unusual in that it is required to occur on a triplet surface if the products are to be in their electronic ground states, and it is forbidden for the products HOC1 and O2to the extent that the electronic orbital angular momentum quantum number L is a good quantum number. If the factor of 21 arose solely from this forbidden character, the temperature dependence would be the same as that of k,,,, in Table 111. However, it seems more likely that an exit channel barrier is involved, in which case a large negative temperature coefficient would be expected. Experi-
+
+
+
7486 The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 TABLE IV: Capture Rate Constants k, Calculated for BrO + O(jP,), with Oxygen Quadruple Moments and Polarizability as in Table I. and Thermallv Averaaed Rate Constant k-,.a T/K k,( 1.07) kJ0.54) kJO.0) kmte 24.4 3.42 34.2 28.6 IO 30.9 3.65 36.5 32.7 20 36.3 35.2 3.89 30 38.9 40.3 4.33 50 43.1 41.7 42.0 4.74 75 46.7 45.0 48.8 46.4 42.8 IO0 5.01 42.1 5.24 50.2 46.8 150 41.4 5.29 50.3 46.2 200 40.5 5.27 250 49.8 45.5 44.9 39.9 5.24 300 49.3 39.4 5.22 48.8 44.3 3 50 43.8 39.2 5.21 400 48.3 43.1 38.6 5.23 500 47.5 38.6 5.30 600 47.0 42.8 'Units of k: IO-" cm3 molecule-' 5-l. Listed rate constant and uncertainty factor at 300 K: 3.0 X lo-" (3); kT = 3 X IO-" exp(0 f 250/T). Data: p(Br0) = 1.61 D; a ( B r 0 ) (est) = 4.1 X cm3; Morse (re, De, we) est = (1.45 A, 200 kJ/mol, 600 cm-I); London potential factor C = l .O; other data as in Table I.
TABLE V Values of k,,,/lO-" cm3 molecule-' s-l for Reactions of Diatomic Radicalso kkkkkT/K (BrO+NO) (BrO+OH) (BrO+ClO) (CIO+NO) (CIO+OH) 5.77 2.46 12.5 IO 2.50 13.8 20 2.45 12.5 5.20 2.45 11.0 30 2.49 14.4 4.93 2.51 10.3 50 2.55 9.99 4.61 2.59 8.84 75 2.52 8.39 4.41 2.56 7.48 7.27 4.29 2.46 6.53 100 2.45 5.93 4.07 2.24 5.12 150 2.32 200 2.23 5.16 3.86 2.05 4.35 4.69 3.67 1.91 3.89 250 2.16 3.56 3.50 1.81 300 2.12 4.35 4.09 3.35 I .73 3.39 350 2.07 3.24 1.67 3.26 2.03 3.91 400 500 1.96 ' 3.62 3.04 1.57 3.07 600 1.90 3.43 2.92 1S O 2.97 'Listed rate constants and uncertainty factors at 300 K: BrO + NO, 2.1 IO-" (1.15); BrO + OH, 1.0 X IO-" (5); BrO + CIO, 1.3 X IO-" (2); CIO + NO, 1.7 X IO-" (1.15); CIO + OH, 1.7 X to-" (1.5); kT(BrO + NO) = 8.8 X lo-" exp(260 f 130/7"), kT(BrO + OH) unlisted, kT(Br0 + CIO) = 1.3 X IO-" exp(0 f 250/T), kT(C1O+ NO) = 6.4 X exp(290 i 100/7"), k,(C10 + OH) = 1.1 X lo-" exp(l20 i 1 5 0 / n . Data: Morse (re, De, u,)est = (1.45 A, 80 kJ/mol, 600 cm-I) for BrONO, (1.45 A, 160 kJ/mol, 600 cm-I) for BrOOH, (1.45 A, 180 kJ/mol, 700 cm-l) for BrOCIO, (1.3 A), 80 kJ/mol, 600 cm-I) for CIONO, ( I .3 A, 180 kJ/mol, 900 cm-l) for CIOOH; London potential factor C = 0.50; other data as in earlier tables. X
mentally, there is a quite strong negative temperature dependence. 2. Reactions of CIO, BrO, OH, and SO. Results for the reaction of O(3P) with CIO and CH, for which the present calculations give values in excellent agreement with experiment, and for the reaction of O(3P)with OH, for which the calculated rate constant is too large by a factor of 1.6 at 300 K, have been described elsewhere." The difficulty with 0 + OH has been discussed by Markovic et aIs2Oin terms of an additional barrier in the entrance channel, a feature that is difficult to treat with the present model. Table IV shows calculated capture rates for the reaction of O(3P,) with BrO, and values of k,,,, calculated with allowance for electronic degeneracy as in ref 1 1. Agreement with experiment at 300 K is well within the stated factor of 3 uncertainty, and the absence of any marked temperature dependence is consistent with the evaluations. Table V contains calculated rate constant values for radicalradical reactions of BrO with NO, OH, and CIO, and of CIO with NO and OH. Electronic degeneracy factors were calculated as described in the Introduction. Except for the reaction of CIO with (20) Markovic, N.; Nyman, G.; Nordholm, S. Chem. Phys. Lett. 1989, 159. 435.
Phillips TABLE VI: Values of k, Calculated for the Reactions SO + OH, SO + (30,and SO + NO2' T/K k(SO+OH) k(SO+CIO) k(SO+NO,) IO 19.7 8.62 3.19 20 16.9 7.23 3.34 30 15.6 6.70 3.50 13.5 6.18 50 3.57 75 11.9 5.83 3.59 100 10.9 5.65 3.68 150 5.47 9.72 3.99 200 5.39 9.05 4.18 250 5.34 8.67 4.33 300 5.26 8.39 4.46 350 5.20 8.18 4.56 400 5.13 8.03 4.66 4.98 500 7.83 4.79 600 4.86 7.66 4.89 'Electronic degeneracy factors as described in text. Units of k: lo-" cm3 molecule-l s-l. Listed rate constants (uncertainty factors)2 at 300 K: SO + OH, 8.6 X lo-" (2); SO + CIO, 2.8 X IO-" (1.3); SO NO1, 1.4 X lo-" (1.2). kT formulas: SO OH, not listed; SO CIO, 2.8 X IO-" exp(0 f 50/T); SO + NOz, 1.4 X IO-" exp(0 f 50/T). Data: p ( S 0 ) = 1.55 D; p(N02) = 0.209 D; p ( C 0 ) = 0.122 D; a ( S 0 ) = 3.0 X cm3 (est); a ( N 0 2 )= 2.8 X cm3; Morse (re, De, w e ) est = (1.3 A, 180 kJ/mol, 900 cm-I) for SOOH, SOOCI,and SONO,; London potential factor C = 0.50; other data as in earlier tables.
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BrO, there is an additional factor 1/2 due to the requirement that the correct ends of the dipoles should meet in the collision. For BrO + C10 both orientations are acceptable, and this model leads to equal branching ratios for the channels forming Br + OClO and Br + C1+ 02,in accord with the evaluation of ref 2. Recently Poulet et aL2I have reported a slightly lower and evidently much more accurate value of the rate constant at 300 K (( 1.13 f 0.15) X lo-" cm3 molecule-' s-I) and have measured branching rations of 0.43 f 0.1 for the Br OClO channel and 0.12 f 0.04 for a channel leading to BrCl + 02.These last products are presumed to arise from a square transition state whose formation would appear to require a collision of BrO and CIO with the dipoles in a repulsive orientation. For three of the reactions in Table V the calculated values at 300 K agree with the evaluations to within the stated uncertainty factors. For CIO + OH and CIO + BrO the difference between theory and experiment is greater than the stated uncertainty and is in the right direction to be due to an exit-channel barrier. Table VI contains calculated values of k,, for reactions of SO with OH, CIO, and NO2. The result for reaction of SO with OH agrees with the experimental value at 300 K to well within the stated uncertainty. For SO + CIO and SO + NOz the difference is outside the limits of error and again is in the right direction to be the consequence of an exit-channel barrier. No temperature dependence is listed for SO + OH. For the other reactions the experimental temperature dependence is close to zero, which appears to be inconsistent with the postulated presence of exitchannel barriers for the SO NO2 and SO + CIO reactions. 3. Reactions ofO(ID). Table VI1 shows rate constants calculated for reactions of O('D) with HCl, HF, NH3, and H 2 0 . These calculations used the quadrupole moment Q for O('D) calculated by Gentry and Giese,17with a factor of 0.5 arising from the use by the present computer program of angular factors that correspond to Buckingham's definition of the quadrupole moesu cm2 for Q, the ment.'* This gives a value of f 1 . 0 7 X sign being chosen to correspond to an attractive dipole-quadrupole interaction. For these reactions k,,,, is obtained by multiplying the capture rate by a factor of 0.5, on the assumption that reaction occurs with only one end of the dipole. Agreement between experimental and calculated values at 300 K is seen to be excellent for H 2 0 and NH,, tolerable for HF, and just outside the limits
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(21) Poulet, G.; Lancor, 1. T.LeBras, G. J . Phys. Chem. 1990, 94, 278. (22) Phillips, L. F. J . Chem. Phys. 1990. 92, 6523. (23) Kihara, T.Infermolecular Forces; Wiley: New York, 1978; p 104.
The Journal of Physical Chemistry, Vol. 94, No. 19, 1990 I481
Atmospheric Radical Reactions TABLE VII: Calculated Rate Constants for Reaction of O('D) with HCI.. HF.. NHI. -. and H,W T/K k(HCI) k(HF) k(NH3) k(H20) IO 18.9 26.8 22.6 26.6 20.6 23.1 20 18.1 25.7 25.0 20.0 22.2 30 18.0 23.6 19.8 21.9 50 18.4 23.7 19.9 21.9 75 18.4 22.0 23.9 20.0 100 20.2 20.7 22.3 24.6 150 21.4 25.1 21.4 22.6 200 22.1 25.2 22.1 23.0 250 22.6 25.4 22.9 23.4 300 22.8 25.5 23.6 23.8 350 23.0 24.2 24.2 23.2 25.6 400 25.0 25.5 25.4 500 23.4 25.5 26.3 25.8 600 23.7
TABLE VIII: Calculated Rate Constants for Reaction of O(lD) witb N,O, - . HCN,. NO,,_.and CloO T/K k(N20) k(HCN) k(NO2) k(C10) IO 17.7 25.7 9.29 16.2 20 19.3 25.3 9.87 16.8 30 20.4 25.3 10.3 17.2 50 21.8 25.5 11.1 18.1 75 23.0 25.9 11.9 19.0 100 23.9 26.2 12.7 19.9 150 25.0 26.5 13.9 21.3 200 26.7 25.5 14.3 22.2 250 25.7 26.8 15.4 22.9 300 25.8 26.9 15.9 23.4 350 25.8 27.0 16.3 23.6 400 25.8 27.2 16.5 23.7 500 25.7 27.4 16.7 23.8 600 25.8 27.8 16.8 23.9
"Units of k: IO-" cm3 molecule-l s-l. Listed rate constants (un(1.2); HF, 1.4 X certainty factors) at 300 K: HCI, 1.5 X (2.0); NH,, 2.5 X (1.3); H,O, 2.2 X (1.2); all kT = exp(0 f 100/7'). Data: p(HC1) = 1.08 D; p(HF) = 1.83 D; p(NH,) = 1.47 D; p ( H 2 0 ) = 1.84 D; a(HC1) = 2.63 X cm3;a(HF) = 0.83 X cm3; a(NH3) = 2.26 X IO-,' cm3;a ( H 2 0 ) = 1.44 X cm3;Morse (re, De, w e ) = ( I .3 A, 200 kJ/mol, 900 cm-I) for all; London potential factors C = 1.0 (HCI, HF), 0.5 (H,O), 0.33 (NH,); other data as in earlier tables.
'Units of k: lo-" cm3 molecule-l s-l. Listed rate constant and uncertainty factor2for N20: 1.16 X (1.3); temperature coefficient exp(0 f lOO/T). Other experimental values not listed. Data: p(N,O) = 0.166 D; p(HCN) = 2.98 D; p(N0,) = 0.29 D; a(N,O) = 3.00 X cm3;a(HCN) = 2.56 X cm'; a(N0,) = 2.8 X cm3; Q ( N 2 0 ) = -3.0 X esu cm2; Q(HCN) = +2.6 X esu cm2; Morse parameters (re,De, we) = (1.3 A, 258 kJ/mol, 1000 cm-') CIO; (1.3 A, 200 kJ/mol, 900 cm-') for others; London potential factors C = 0.50 (N20, NO2, HCN), 1.0 (CIO); other data as in earlier tables.
of error for HCI. The calculated rate constants are almost independent of temperature, in agreement with the evaluations. It is interesting that division by a factor of 5 for O(lD) state degeneracy in a C,field would clearly be wrong for these reactive collisions of O(lD), whereas division by 5 was essential for agreement with experiment in the case of purely physical quenching reactions of O(lD).12 This implies that a much closer approach of the reactants is required for physical quenching than for the reactive collisions of Tables VI1 and VIII. Table VI11 shows the results of similar calculations for reactions of O(lD) with N 2 0 , HCN, NO2, and C10. The values of k,,,, correspond to half the capture rate, as in Table VII, except for N20,where k,,, was set equal to the capture rate. For N 2 0 the experimental results imply that reaction can occur at both ends of the dipole, the listed rate constant at 300 K being 4.9 X lo-" cm3 molecule-l s-l for production of N, 02,and 6.7 X lo-" for production of N O NO, with an uncertainty factor of 1.3. The sum of the experimental values is less than the calculated value by a factor of 2, which implies the presence of barriers in both exit channels, the different rates for the two channels being interpreted as a consequence of the two barriers being of different heights. Experimental values are not listed for the reactions with HCN, NO2, and CIO. For these reactions the calculated rate may be taken as a firm upper limit for the true rate constant, with a high degree of probability that the calculated rate is close to the true rate.
the present paper. Reference 12 gives similar results for quadrupole-quadrupole reactions of O(lD) with 02,COz, Hz, and N2, all of which are in fair to excellent accord with experiment. Together with the previous results for reactions of O(3P)with OH, CIO,CH, and N02,11 and for the reaction of BH with NO, where the effect of the exit barrier was calculated explicitly,I0this makes a total of 32 bimolecular reactions investigated. For 15 of the 32 reactions the experimental rate constant and the calculated capture rate agree to within the experimental error; in 3 cases an experimental value is not available. For the remaining 14 reactions the experimental value is less than the calculated rate and, except for the reaction of H with H 0 2 , where the calculated rate constant is too sensitive to the value of the London potential factor C and, apparently, for the reaction of 0 with OH, the difference can reasonably be attributed to the presence of an exit-channel barrier. Thus, in cases where there is no experimental data, one may confidently assume that the present calculation procedure will provide a firm upper limit for the reaction rate. If it can be shown, e.g., by ab initio calculations, that no secondary barriers are present, current experience suggests that the capture rate and the experimental rate constant for a dipole-diple reaction can be expected to agree to within about 15% at 300 K. For such small systems as these, the determination of energies and other relevant properties for barriers, bound complexes, and transition states is well within the compass of current a b initio calculations, so it is to be expected that useful predictions of rate constants and temperature coefficients for the slower reactions will soon be available. However, the calculations are not necessarily restricted to reactions of small molecules. When the experimental rate constant is significantly less than the calculated value at 300 K and ab initio data are not available, it is still possible to make a qualitative prediction of the temperature dependence of the rate constant, on the basis of the conclusion that the experimental rate constant and the calculated capture rate should become equal at very low temperatures.
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Conclusions
It appears that many radical-radical reactions occur at rates that are equal to the collision rate multiplied by simple factors for orientation and electronic degeneracy. With a few exceptions, the reactions considered here were selected on the basis of having rate constants greater than lo-" cm3 molecule-' s-I, and the exceptions are the ones that give poorest agreement with the calculated rate constants. Results for 23 reactions are given in
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