J. Phys. Chem. A 2003, 107, 3841-3850
3841
Ab Initio Studies of ClOx Reactions: VI. Theoretical Prediction of Total Rate Constant and Product Branching Probabilities for the HO2 + ClO Reaction Z. F. Xu, R. S. Zhu, and M. C. Lin* Department of Chemistry, Emory UniVersity, Atlanta, Georgia 30322 ReceiVed: September 24, 2002; In Final Form: December 13, 2002
The reaction of HO2 with ClO has been investigated by ab initio molecular orbital and variational transition state theory calculations. The geometric parameters of the reaction system HO2 + ClO were optimized at the B3LYP and BH&HLYP levels of theory with the basis set 6-311+G(3df,2p). Both singlet and triplet potential energy surfaces were predicted by the modified Gaussian 2 (G2M) method. On the singlet surface, the reaction forms two HOOOCl isomers lying below the reactants by 20 kcal/mol. Their stabilization contributes significantly to the observed overall HO2 + ClO rate constant. The predicted high- and low-pressure association rate constants for the 150-600 K range can be represented by k∞ ) 9.04 × 10-17 T1.22 exp(897/T) cm3 molecule-1 s-1 and k0 ) 9.33 × 10-24 T-3.45 exp(472/T) cm6 molecule-2 s-1 for N2 as the third-body. Dissociation of these excited HOOOCl intermediates produces HO + ClOO, HCl + 1O3, HOCl + 1O2, and HO + OClO as minor products via multistep mechanisms. On the triplet surface, formation of HOCl + 3O2 dominates; it occurs via a long-lived O2H‚‚‚OCl complex with 3.3 kcal/mol binding energy. The complex decomposes to give the product pairs with a small (0.1 kcal/mol) barrier. The predicted rate constant can be represented by k(HOCl + 3O2) ) 1.64 × 10-10 T - 0.64 exp(107/T) cm3 molecule-1 s-1 in the temperature range 150-1000 K. The total rate constants predicted for 1-760 Torr N2 pressure exhibit a strong negative temperature dependence below 1000 K. In the 200-400 K range, where most kinetic data have been obtained, the agreement between theory and experiment is excellent. For combustion applications, rate constants for all bimolecular product formation channels have been predicted for the 500-2500 K temperature range.
I. Introduction Both ClO and HO2 radicals are present in the Freon-polluted stratosphere.1 The kinetics and mechanism for their interaction, critical to the prediction of the extent of O3 destruction, have been investigated by many groups.2-14 The reaction of HO2 + ClO may in principle take place by a number of pathways by direct abstraction or by indirect association/decomposition processes involving excited intermediates:
where / denotes excited intermediates. The kinetics of the HO2 + ClO reaction was first investigated by Reimann and Kaufman2 in 1978 using the discharge-flow method at room temperature, and its rate constant was measured to be (3.8 ( 0.1) × 10-12 cm3 molecule-1 s-1 at 298 K. They monitored HO2 with OH-LIF (laser induced fluorescence) following the NO titration reaction, HO2 + NO f OH + NO2, in the presence of an excess amount of ClO generated by the Cl + O3 reaction. Howard and co-workers3 in 1979 employed * To whom correspondence should be addressed. E-mail: chemmcl@ emory.edu.
the LMR (laser magnetic resonance) technique in the temperature range 235-393 K by monitoring both reactants using a discharge flow reactor under low-pressure conditions (P ) 0.83.4 Torr) and obtained the rate constant 3.3 × 10-11 exp (-850/ T) + 4.5 × 10-11 (T/300)-3.7 cm3 molecule-1 s-1. The ClO radical was generated by both Cl + Cl2O and Cl + O3 reactions. At nearly the same time, Leck et al.4 reported their roomtemperature kinetic data, (4.5 ( 0.9) × 10-12 cm3 molecule-1 s-1, on HOCl formation by detecting it mass-spectrometrically in a discharge-flow study. The HO2 radical was produced by both H + O2 + M and Cl + H2O2 reactions, whereas the ClO radical was produced by the reaction of Cl atoms with O3. By using Cl + Cl2O or OClO to generate ClO, they were able to determine the yield of HCl + O3, formed by reaction 2 above, to be less than 2% of HOCl. Cox and co-workers5,6 investigated the reaction with other related processes near ambient T and P conditions by modulated-photolysis of mixtures of H2, O2, Cl2 (or Cl2O), and N2 aided by kinetic modeling and gave rate constant (5.4 ( 4) × 10-12 cm3 molecule-1 s-1 in 19815 and (6.2 ( 1.5) × 10-12 cm3 molecule-1 s-1 in 1986.6 Their results corroborated the finding of Leck et al. on both HOCl and HCl yields. Finkbeiner et al.9 measured the products of the reaction by matrix-isolation/FTIR spectroscopy at a total pressure of 700 Torr and at 210, 240, 270, and 300 K. Their result shows that the HOCl + O2 product channel is a major pathway and the branching ratio of HCl + O3 is 1000 K. For the production of HO + ClOO occurring without a well-defined barrier (see Table 6), canonical variational transition states are located at the O(3)-O(4) separation of 2.1-2.0 Å at 200-800 K and slowly reduced to 1.8 Å above 1200 K. In Figure 7a, the rate constants for the formation of these product pairs, including HCl + O3 (which have been reported experimentally) are compared with those for HOCl + 3O2 and HOOOCl formation at 1 and 400 Torr. Apparently, below room temperature, formation of HOOOCl at 1 Torr pressure is more important than those minor product channels giving O3, 1O2, and ClOO, whose rate constants are pressure-independent. At 400 Torr, the average pressure employed by Nickolaisen et al.,10 HOOOCl formation amounts to about 17% of the abstraction product yield at 200 K and about 1% at 400 K. (c) Formation of HO + OClO and HOCl + 1O2 Via HOOClO. Once they are formed, both HOOClO-1 and HOOClO-2 intermediates fragment readily to these two product pairs. Their rate-limiting step lies in the relatively high barrier for their formation at TS4 (3.6 kcal/mol). Because of this barrier, formation of these products cannot compete with the HOCl + 3O and HOOOCl product channels occurring without barriers. 2 The decomposition of HOOClO-1 to HO + OClO also occurs without a distinct barrier (see Table 6), and its transition states are canonically located at the O(3)-O(4) distance of 1.9 Å below 1500 K and at 1.8 Å above that temperature. The result of ChemRate calculations based on Scheme 3, shown in Figure 7a, indicates that both product channels are comparatively insignificant to the observed HO2 + ClO rate constant as more
Ab Initio Studies of ClOx Reactions
J. Phys. Chem. A, Vol. 107, No. 19, 2003 3849
Figure 7. Plots of predicted rate constants for the HOO + ClO reaction as a function of temperature reciprocal. (a) Rate constants for individual product channels. (b) Branching ratios of individual product channels.
clearly illustrated by the product branching ratio plots presented below. For practical combustion applications, the rate constants for these bimolecular product channels have been evaluated in units of cm3 molecule-1 s-1 for the 500-2500 K temperature range:
k(HOCl + 3O2) ) 1.30 × 10-20 T2.37 exp (-2572/T) k(HOCl + 1O2) ) 1.39 × 10-21 T2.26 exp (226/T) k(HO + ClOO) ) 7.61 × 10-19 T1.80 exp (-1065/T) k(HO + OClO) ) 2.22 × 10-21 T2.32 exp (-2566/T) k(HCl +1O3) ) 7.60 × 10-21 T2.05 exp (-855/T) (d) Product Branching Ratios. The branching ratios for all product channels are shown in Figure 7b as functions of temperature for 1 and 400 Torr N2 pressure. At 1 Torr pressure, the HO2 + ClO reaction occurs exclusively by abstraction producing HOCl + 3O2. This conclusion supports the most recent result of Knight et al.,11 who reported that HOCl was the only product of the reaction and no evidence for HCl + O3 formation was observed in their experiment under 1.1-1.7 Torr pressure conditions. At 400 Torr pressure, the stabilization of HOOOCl becomes significant and competitive with the abstraction channel, amounting to about 15% of the total rate at 200 K and rapidly decreases to less than 4% at room temperature because of the fast increasing back reaction. The potential contribution of HOOOCl formation was first pointed out by Nickolaisen et al.10 as mentioned before. Our results are not consistent with the prediction of Tooley and Anderson13 and the measurement of Finkbeiner et al.9 The
Figure 8. Comparison of the predicted total rate constants with the experimental data. (a) Rate constants in the temperature range from 150 to 2000 K; (b) The close-up of rate constants in the temperature range from 200 to 400 K.
former suggested that the direct hydrogen abstraction channel should dominate at high temperatures, whereas the indirect elimination from the cyclic HOOClO intermediate would dominate at lower temperatures. The latter reported a branching ratio for the HCl + O3 product channel up to as high as 5% at low temperatures according to their experimental measurement, inconsistent with our prediction and the observation of Knight et al.11 as alluded to above. (e) Total Rate Constant. The Arrhenius plots of predicted total rate constants at 1, 400, and 760 Torr pressures for HO2 + ClO are compared with all existing experimental data in Figure 8. The predicted values lie within the scatter of experimental data with correct temperature dependence. Below room temperature, the total rate constant increases with pressure, attributable to the P-dependent contribution from HOOOCl formation. At 1 Torr pressure, the abstraction process accounts for nearly 100% of the observed rate as concluded above. The predicted value agrees closer with the results reported by Knight et al.11 obtained at 1.1-1.7 Torr pressure with He as a carrier gas, k(T) ) (7.1 ( 0.4) × 10-12 exp[(-16 ( 17)/T] cm3 molecule-1 s-1. At 400 Torr N2 pressure, the predicted total rate constant agrees closely with those of Nicklaisen et al.,10 k(T) ) 2.84 × 10-12 exp[(312 ( 60)/T] cm3 molecule-1 s-1. Our results also agree well with the data of Stimple et al.3 and Cattell and Cox.6 The values obtained by Reimann and
3850 J. Phys. Chem. A, Vol. 107, No. 19, 2003 Kaufman,2 Leck et al.,4 and Burrows and Cox5 are, however, somewhat lower than the predicted value. The predicted total rate constants can be expressed in units of cm3 molecule-1 s-1 by the following equations for the temperature range 150-1000 K:
k(T) ) 1.97 × 10-10 T-0.66 exp(100/T) at 1 Torr k(T) ) 3.66 × 10-11 T-0.45 exp(270/T) at 400 Torr k(T) ) 3.52 × 10-11 T-0.45 exp(288/T) at 760 Torr. IV. Conclusions The kinetics and mechanism for the HO2 + ClO reaction system have been investigated at the G2M level of theory in conjunction with VTST and RRKM rate constant calculations. On the singlet PES, the reaction takes place via two isomers of HOOOCl which lie 20.3 kcal/mol below the reactants. At temperatures below 500 K, the collisional stabilization of HOOOCl accounts significantly for the observed rate constant and the formation of higher-barrier products such as HCl + O3, HOCl + 1O2, and HO + ClOO/OClO cannot compete with HOOOCl formation at P > 1 Torr. On the triplet PES, the direct abstraction reaction producing HOCl + 3O2 is the overall most favorable channel; this highly exothermic (∆H ) -45.2 kcal/ mol) process occurs via a O2H‚‚‚OCl complex, with a 3.3 kcal/ mol binding energy and a 0.1 kcal/mol decomposition barrier leading to product formation. The theoretically predicted total rate constants at 200 K < T < 400 K and 1-760 Torr pressure agrees satisfactorily with existing experimental data, exhibiting a strong negative temperature dependence below 1000 K. On account of the reasonable stability of the HOOOCl intermediate at low temperatures (T < 250 K), its photochemistry in the lower stratosphere might affect the O3-destruction process to some extent. Acknowledgment. This work is sponsored by the Office of Naval Research under Contract No. N00014-02-1-0133, Dr. J. Goldwasser program manager. References and Notes (1) Wayne, R. P. Chemistry of Atmospheres, 2nd ed.; Clarendon Press: Oxford, U.K., 1991. (2) Reimann, B.; Kaufman, F. J. Chem. Phys. 1978, 69, 2925. (3) Stimpfle, R. M.; Perry, R. A.; Howard, C. J. J. Chem. Phys. 1979, 71, 5183. (4) Leck, T. J.; Cook, J.-E. L.; Birks, J. W. J. Chem. Phys. 1980, 72, 2364. (5) Burrows, J.; Cox, R. A. J. Chem. Soc., Faraday Trans. 1 1981, 77, 2465. (6) Cattell, F. C.; Cox, R. A. J. Chem. Soc., Faraday Trans. 2. 1986, 82, 1413. (7) Leu, M.-T. Geophys. Res. Lett. 1980, 7, 173. (8) Kou, Y.-P.; Ju, S.-S.; Lee, Y.-P. J. Chin. Chem. Soc. 1987, 34, 161. (9) Finkbeiner, M.; Crowley, J. N.; Horie, O.; Mueller, R.; Moortgat, G. K.; Crutzen, P. J. J. Phys. Chem. 1995, 99, 16264. (10) Nickolaisen, S. L.; Roehl, C. M.; Blakeley, L. K.; Friedl, R. R.; Francisco, J. S.; Liu, R.; Sander, S. P. J. Phys. Chem. A 2000, 104, 308.
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