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Theoretical study of the OH+NO2 reaction: formation of nitric acid and the hydroperoxyl radical
Chemical Physics 231 Ž1998. 39–49
Theoretical study of the OH q NO 2 reaction: formation of nitric acid and the hydroperoxyl radical D. Chakraborty, J. Park, M.C. Lin
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Department of Chemistry, Emory UniÕersity, Atlanta, GA 30322, USA Received 3 December 1997
Abstract The reaction of OH with NO 2 has been studied by high level ab initio molecular orbital and statistical theory calculations. The potential energy surface for the association leading to the formation of HNO 3 by collisional deactivation and the formation of endothermic products, HO 2 and NO via the HOONO intermediate have been computed with a modified Gaussian 2 ŽG2M. method. The rate constants for these two channels have been calculated by means of the canonical variational RRKM approach. The predicted values correlate reasonably well with experimental data for both the forward and reverse processes. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction The reaction of hydroxyl radical with nitrogen dioxide is of considerable practical interest because of the importance of the reaction in both troposphere and stratosphere w1–4x. The reaction is also pivotal to the combustion of nitramine and nitrate ester propellants, typically taking place under high-pressure and high-temperature conditions under which no reliable kinetic data are available through direct laboratory measurements. The OH q NO 2 reaction has been investigated by many laboratories w5–7x. It can take place via two low-energy reaction channels through collisional stabilization and disproportionation, respectively: a
b
ya
qM
OH q NO 2 ° HONO†2 ™ HNO 3 c
d
OH q NO 2 ° HOONO† ™ HO 2 q NO yc
The rate constant for the recombinationrstabilization reaction producing HNO 3 , measured in many studies, can be found in several recent publications and compilations w5–7x. Those for the production of HO 2 q NO via the unstable HOONO intermediate and its reverse process Ža convenient source of OH in atmospheric studies. have been investigated extensively by Howard w8,9x and more recently by Molina and coworkers w10x. These experimental data will be compared with our theoretically predicted results later.
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Corresponding author. E-mail: [email protected].
0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 0 3 3 - 0
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Theoretically, a very detailed potential energy surface ŽPES. of the OH–NO 2 system including the excited triplet intermediates and products has been investigated recently by Sumathi and Peyerimhoff using the density functional ŽDFT. and ab initio molecular orbital ŽMO. methods w11x. Their results and related theoretical and experimental data will be compared with ours for the key species involved in the present study, focusing on the interpretation and correlation of kinetic data obtained over a wide range of experimental ŽT, P . conditions for the two OH q NO 2 reactions occurring in both forward and reverse directions.
2. Computation methods 2.1. Ab initio MO calculations Geometries of the reactants, products and intermediates have been optimized at the hybrid density functional B3LYPr6-311GŽd,p. level of theory, based on Becke 3-grid integration and exchange functional w12–14x with the correlation functional by Lee et al. w15x. Vibrational frequencies employed to characterize stationary points, zero-point energies ŽZPE. and rate constant calculations have also been calculated at this level of theory. The electronic energies of various species were calculated with the recently developed modified Gaussian-2 ŽG2M. method w16x, which approaches high-level results using a series of single-point calculations for basis set size, correlation energy and systematic error corrections. Three versions of the scheme have been suggested by Mebel et al. w16x for varying molecular sizes. For the present system with 4 heavy atoms, the most elaborate and computation-intensive version, G2MŽRCC. was employed. The method is briefly summarized as follows. The scheme calculates the base energy E bas at the MP4r6-311GŽd,p. level of theory and improves it with the following corrections for basis set expansion and electron correlation: D E Ž RCC . s E Ž RCCSD Ž T . r6 y 311G Ž d,p . y E bas , D E Ž q3df2p. s E MP2r6y 311 q G Ž 3df,2p . y E MP2r6y 311G Ž d,p . , D E Ž HLC,RCC,MP2 . s y0.00525nb y 0.00019na The ZPE corrected energy with this scheme in E h is: E Ž G2M Ž RCC, MP2 . s E bas q D E Ž RCC . q D E Ž q3df2p. q D E Ž HLC, RCC, MP2 . q ZPE All calculations were carried out with Gaussian 94 w17x and MOLPRO 94 w18x programs. 2.2. Rate constant calculations 2.2.1. Variational transition state theory (VTST) calculation for the formation of HNO3 Since the reaction path Ža. does not have a well defined transition state ŽTS. because of the absence of reaction barrier, a VTST calculation has to be carried out. According to the canonical variational theory ŽCVT. w19,20x, the rate constant k CV T at T is obtained by maximizing DGŽT, s . with respect to the reaction coordinate s, and the position of the dividing surface associated with the maximum DGŽT, s . is denoted by s a . We applied here the canonical variational method based on the evaluation of the maximum free energy of activation at each temperature along the reaction path. We first scanned the potential energy surface for the approach of OH and ˚ with an interval NO 2 forming HNO 3 . The forming N–O bond distance of HNO 3 was varied from 1.8 to 3.0 A ˚ of 0.1 A, other geometric parameters were optimized for each value of N–O. We calculated twelve optimized ˚ For each structure, we calculated the 3N-7 vibrational geometries for NO distances from 1.8 to 3.0 A. frequencies projected out of the gradient direction. This B3LYP calculated energies at each point along the reaction path was used to evaluate the Morse potential energy function and then scaled by using the scale factor obtained by comparing N–O dissociation energies at G2M and B3LYP levels.
D. Chakraborty et al.r Chemical Physics 231 (1998) 39–49
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The resulting potential energy function EŽ R . is given by: E Ž R . s De w 1 y ey b Ž RyR e. x
2
˚ y1 and Re s 1.414 A˚ is the equilibrium value of R, i.e., the where De s 50.53 kcalrmol, b s 2.6 A equilibrium N–O bond distance of HNO 3 . Using the Morse potential energy, computed moments of inertia and the vibrational frequencies, we searched for the maximum DG a at various temperatures in the range of 300 to 2000 K. The accurate position of the maximum for each temperature was calculated on the basis of the parabolic fit of the three largest DG values. In the RRKM calculation, we used all the molecular parameters corresponding to the structure with a ˚ have one maximum DG a for each temperature. Since the transition structures of HNO 3 with N–O ) 1.8 A vibrational frequency less than 100 cmy1 , we substituted this mode with the computed reduced moments of inertia corresponding to the free internal rotation. As the DG maxima along the reaction path are located between the calculated structures, the corresponding moments of inertia and vibrational frequencies were obtained by interpolation. 2.2.2. VTST calculation for the reaction HO2 q NO s HOONO The intermediate HOONO formed in the reaction of OH and NO 2 , has three possible rotational isomers due to the rotation along the NO and OO bonds, namely cis–cis Žcc., cis–perpendicular Žcp. and trans–perpendicular Žtp.. Since these rotational isomers are very close in energy, as mentioned by Sumathi and Peyerimhoff w11x, VTST calculation from any one of these rotamers could be considered as a reliable one. Despite our numerous attempts, we were unable to get a reliable PES for the incoming channel, i.e., OH and NO 2 forming HOONO. At the B3LYP level of theory the variational PES obtained at different points along the reaction path was either very scattered or the energy increase monotonically, and cannot be improved by mere energy correction in the frame work of the G2M method. The problem is more multiconfigurational in nature and a more expensive MCSCF calculation along the reaction path might provide a reliable PES. On the other hand, it is known from the experimental work of Molina and coworkers w10x that the reverse channel forming HO 2 and NO is pressure-independent because the reaction occurs via a short-lived intermediate HOONO and our theoretical PES at the G2M level indicates that this channel is endothermic by 7.0 kcalrmol. Thus, the rate constant for the reverse process from HO 2 and NO via the HOONO intermediate is controlled by the initial association reaction and the rate constant for the forward reaction of OH and NO 2 can be effectively obtained by using the principle of microscopic reversibility. Since our work aimed at the correlation between the theoretically predicted and experimental rate constants, the reliability of such approximation can be judged through the agreement between theory and experiment. We performed variational calculations for all three rotational isomers of HOONO for the outgoing channel forming HO 2 and NO. Both the cc and cp rotamers produce multiple imaginary frequencies at some points along the reaction path and have thus not been included in our canonical variational calculation. Instead, we used the potential energy surface for the dissociation of the tp-HOONO isomer. The dissociating NO bond ˚ with the interval of 0.1 A. ˚ Like the reaction path a, all the distance of tp-HOONO was varied from 1.8 to 2.7 A intermediate transition structures were optimized with respect to all other geometric parameters, except the reaction path and the 3N-7 vibrational frequencies projected out of gradient direction were calculated. The B3LYP energy along the reaction path at each point was scaled using the scale factor obtained by comparing the NO bond dissociation energy at the G2M and B3LYP levels of theory. The position of DG a at various temperatures in the range of 300 to 1500 K were then evaluated in the same manner as described in the preceding section using the computed energies, vibrational frequencies and moments of inertia. The RRKM rate constants were then calculated using the molecular parameters corresponding to the maximum DG a at each temperature obtained by the method of interpolation as described above.
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3. Results and discussion 3.1. Potential energy surface Sumathi and Peyerimhoff w11x have recently studied the PES of the OH–NO 2 system in great detail. We focus our study on the part of PES which is relevant to the OH q NO 2 recombination and decomposition processes mentioned above. The optimized geometries of reactants and intermediates for this reaction are shown in Fig. 1; the potential energy surface obtained at the G2M level is drawn in Fig. 2. The relative energies of the reactants and intermediates are compiled in Table 1 and the vibrational frequencies and moments of inertia of all species in Table 2. There are two possible reaction mechanisms for the interaction of OH with NO 2 as shown in Fig. 2. The first channel corresponds to the attachment of oxygen of OH at the N-terminal of NO 2 forming HNO 3 , whose energy at the G2M level of theory is 50.5 kcalrmol lower than the energy of the reactants. The calculated dissociation energy at this level of theory agrees very well between G2 and G2ŽMP2. as shown in Table 1, but is higher by 2.8 kcalrmol than the experimental dissociation energy Ž47.7 kcalrmol. given by the JANAF table w21x. Our G2M-predicted dissociation energy also agrees well with the calculated dissociation energy of 49.3 kcalrmol by Lee at the CCSDŽT.rTZ2P level w22x.
Fig. 1. The optimized geometries of reactants, products and intermediates at the B3LYPr6-311GŽd,p. level of theory.
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Fig. 2. Potential energy profile for the OH q NO 2 reaction based on the G2M calculation.
In the second channel, the reaction takes place by the attachment of oxygen of OH with one of the oxygen atoms of NO 2 forming an HOONO intermediate which in turn dissociates into HO 2 and NO. The HOONO intermediate can exist in three possible conformers with respect to the rotation along the O–O and N–O bond as reported by Sumathi and Peyerimhoff w11x. Our calculations at the B3LYPr6-311GŽd,p. level also reveal that the energies were very close for these three stable minima. The calculated energy of the trans–perpendicular conformer of HOONO is included in Table 1. The calculated energy of this rotamer is lower than the energy of the reactants by 19.3 kcalrmol at the G2M level of theory, whereas the product HO 2 and NO is endothermic by 7.0 kcalrmol.
Table 1 Relative energies Žkcalrmol. of reactants, products and intermediates for the reaction of OH with NO 2 Reaction
B3LYPr6-311GŽd,p.
CCSDŽT.r6-311GŽd,p.
QCID a
G2MŽRCC, MP2.
G2
OH q NO 2 HO 2 q NO HOONO HNO 3
0.0 7.24 y11.2 y44.5
0.0 4.4 y15.6 y47.4
0.0 3.7 y17.6
0.0 7.0 y19.3 y50.5
0.0 8.1b y20.3 b y50.1
a b
QCISDr6-311q q GŽ2df,2pd.rrMP2Ž6-311 q q GŽd,p. level from Ref. w11x. Taken from Ref. w11x.
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Table 2 Calculated harmonic frequencies Žin cmy1 . and moments of inertia Žin au. for all the reactants, products and intermediate at B3LYPr6311GŽd,p. level
y1 y2 y3 y4 y5 y6 y7 y8 y9 Ia Ib Ic a
OH
NO
NO 2
HO 2
HNO 3
HOONO
Expt.a
3702
1989
1706 1399 767
3610 1427 1162
3734 1787 1358 1324 912 777 655 589 481 138.5 149.7 288.2
3748 1823 1407 1014 808 459 358 293 212 33.1 367.9 395.2
3546 1704 1395 960 794 — — — —
3.2 3.2
35.2 35.2
7.5 138.3 145.8
2.9 53.5 56.4
Taken from Ref. w29x for HOONO measured in Ar and N2 matrices.
3.2. Recombination of OH and NO2 forming HNO3 3.2.1. Effect of pressure The effects of pressure on the recombination reaction of OH and NO 2 are shown in Fig. 3A. The bimolecular recombination rate of OH and NO 2 was calculated at 300–2000 K at varying pressures to compare with the available experimental results. Our calculated high-pressure limit rate constant can be expressed by k `a s 2.4 = 10y1 1 eŽ240r T . cm3r Ž molecule s . At 300 K, k `a s 5.5 = 10y11 cm3rŽmolecule s. which agrees reasonably well with the recent result of Troe and coworkers w23x Ž7.7 = 10y1 1 . and the lower limit set by Tsang and Herron w6x Ž) 4.0 = 10y1 1 . as shown in Fig. 3A. Experimental results with both Ar and N2 as diluent are included in the figure although calculations were made only with Ar as bath gas, using the Lennard–Jones collision parameters assumed by Troe w24x and the average collision energy transfer step-size, - D E ) , reported by Wooldridge et al. w7x. At room temperature, our calculated fall-off curve shows a systematic overestimation in comparison with the available experimental results but can account for the fall-off behavior reasonably well. Such systematic overestimation in the fall of curve can be attributed to several factors: The collision parameters, the energy transfer stepsize and the higher value of N–O bond dissociation energy of HNO 3 at our G2M level of calculation. As a test case, we calculated the fall-off behavior with the experimental dissociation energy and the calculated results show a slightly better agreement with the experimental results. 3.2.2. Effect of temperature The termolecular recombination rate of OH q NO 2 q M forming HNO 3 determined in the temperature range between 300 to 2000 K is shown in Fig. 3B. All the experimental results for this recombination reaction are available for a relatively low temperature range, i.e., - 600 K and at high temperatures, the available experimental results are for the reverse decomposition reaction. Our VRRKM predicted rate constants over the entire temperature range Ž300–2000 K. are aimed at the correlation of the low temperature recombination and high temperature decomposition experimental rate constants. All the RRKM calculations were made using Ar as the bath gas. The high temperature decomposition rate constants were converted to recombination rate constants using the principle of microscopic reversibility. In the RRKM calculations, both the G2M calculated and experimental well depths were used. It is evident from Fig. 3B that at low temperature, our results agree well
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Fig. 3. ŽA. Calculated RRKM rate constants for the OHqNO 2 qAr s HNO 3 qAr reaction as a function of total pressure at 300 K. v, Ref. w23x; (, Ref. w38x; , Ref. w5x; %, Ref. w31x; ^, Ref. w32x; l, Ref. w37x, , this study with Des 50.53; – – –, this study with Des 47.7 kcalrmol. ŽB. Arrhenius plot for the same reaction rate constant comparing the present results with literature data. %, Ref. w30x; B, Ref. w31x; l, Ref. w32x; I, Ref. w5x; , Ref. w34x; (, Ref. w7x; =, Ref. w25x; ^, Ref. w35x; e, Ref. w36x; ', Ref. w26x; , Ref. w37x; \, Ref. w38x; , Ref. w39x, q, Ref. w40x; v Ref. w41x; , this study with Des 50.53; – – –, this study with Des 47.7 kcalrmol.
with the existing experimental results. However, at high temperatures, the calculated and experimental rate constants show some deviation, especially near the fall-off region of the theoretical curve Žat ca. 800 K.. Fig. 3B indicates that for this reaction, which is mainly controlled by collisional deactivation, the calculated rate constants are noticeably dependent on the N–O bond dissociation energy and hence, the calculations based on experimental dissociation energy show a systematic lowering of theoretical rate constants. Both of the calculated curves show a deviation from the experimental results of Harrison et al. w25x near the fall-off region but agree reasonably well with the high temperature observed rate constants of Wooldridge et al. w7x and Glanzer ¨ et al. w26x. Such a deviation of the theoretical results near the fall-off region may be due to the limitation of the canonical variational approach, and it might be possible to improve it by means of a more elaborate theoretical model which includes the conservation of angular momentum w27x. The calculated rate constants for the termolecular recombination reaction and the reverse decomposition reaction in the temperature range 300–2000 K are summarized in Table 3.
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Table 3 Calculated rate constants for the OH and NO 2 recombination-decomposition reaction at various temperatures TrK k wOH q NO 2 q Ar s HNO 3 q Arx k wHNO 3 q Ar s OH q NO 2 q Arx k wOH q NO 2 s HO 2 q NOx k wHO 2 q NO s OH q NO 2 x 300 400 500 600 700 900 1000 1200 1400 1500 2000
1.14 = 10 18 3.35 = 10 17 1.57 = 10 17 8.11 = 10 16 4.71 = 10 16 1.89 = 10 16 1.27 = 10 16 5.83 = 10 15 2.82 = 10 15 2.00 = 10 15 4.10 = 10 14
7.06 = 10y17 5.30 = 10y8 1.09 = 10y2 3.16 = 10 1 8.52 = 10 3 1.14 = 10 7 1.28 = 10 8 3.79 = 10 9 3.74 = 10 10 7.69 = 10 10 8.09 = 10 11
7.43 = 10y16 1.02 = 10y14 4.83 = 10y14 1.16 = 10y13 2.18 = 10y13 4.62 = 10y13 7.68 = 10y13 1.30 = 10y12 2.36 = 10y12 2.66 = 10y12
1.05 = 10y11 8.27 = 10y12 7.11 = 10y12 5.54 = 10y12 4.69 = 10y12 3.48 = 10y12 4.02 = 10y12 3.96 = 10y12 4.87 = 10y12 4.71 = 10y12
Fig. 4. ŽA. Calculated high-temperature Ž700–2000 K. decomposition rate constants for the reaction HNO 3 qAr sOHqNO 2 qAr and comparison with available shock tube data. %, Ref. w7x; ^, Ref. w25x; e, Ref. w35x; , Ref. w36x; Q, Ref. w26x; , this study with Des 50.53; – – –, this study with Des 47.7 kcalrmol. ŽB. Arrhenius plot for the same decomposition reaction in the entire temperature range w300–2000 Kx. Low-temperature experimental results are obtained by converting the corresponding recombination rate constants carry the same symbol as in Fig. 3B. High-temperature shock tube results are the same as in A. Calculated rate constants were obtained by converting the recombination rate constant using equilibrium constant. , Des 50.53; – – –, Des 47.7 kcalrmol.
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3.3. Decomposition of HNO3 The theoretically predicted second order decomposition rates of HNO 3 in the temperature range 700 to 2000 K are shown in Fig. 4A and the correlation of those measured for both directions covering the entire temperature range is shown in Fig. 4B. The calculated recombination rate constants were converted to these decomposition rates using equilibrium constants obtained from the JANAF thermochemical table w21x. It is evident from the figure that the calculated rate constants are in reasonably good agreement with the available high temperature shock tube data for the decomposition reaction. 3.4. Rate constants for the reaction OH q NO2 s HO2 q NO The calculated rate constants for the forward and reverse reactions for this channel are shown in Fig. 5A and B, respectively. Both reactions go through the formation of a short-lived intermediate HOONO as shown in Fig. 2. The rate constants for both directions were measured extensively by Howard w8,9x by means of the laser magnetic resonance technique. Recently, Molina and coworkers reported the rate constants for the reverse reaction forming OH and NO 2 from HO 2 and NO using the turbulent flow technique w10x. Their study indicates that this reaction path is pressure-independent and their rate constant is in agreement with the earlier
Fig. 5. ŽA. Arrhenius plot for OHqNO2 s HO 2 qNO rate constant comparing the present results with literature data. \, Ref. w8,9x; I, Ref. w37x; l, Ref. w42x; , Ref. w43x; (, Ref. w44x; =, Ref. w10x; , this study. ŽB. Arrhenius plot for the reverse reaction HO 2 qNOsOHqNO 2 . ^, Ref. w8,9x; %, Ref. w37x; (, Ref. w44x; l, Ref. w42x; , Ref. w43x; =, Ref. w10x; , this study.
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D. Chakraborty et al.r Chemical Physics 231 (1998) 39–49
determination by Howard w8,9x. The negative temperature-dependency of their result suggests that the reaction proceeds via the formation of an HOONO intermediate. In our RRKM calculation for this channel, the decomposition of the HOONO intermediate to HO 2 and NO as described in the preceding section, was made by using the calculated G2M dissociation energy of 26.3 kcalrmol in the temperature range 300 to 1500 K. The calculated rate constants are summarized in Table 3, corresponding to the high pressure limit show reasonably good agreement with the experimental results. Since the VTST calculation fails to locate any DG maximum below 300 K, our theoretical result is limited to this temperature and cannot account for the lower-temperature observed rates for this reaction. An extrapolation of the theoretical result to low temperature indicates an overestimation in theoretical rate constants in the low-temperature range, although the agreement with the observed rate constants is good at high temperatures. The rate constants for the forward reaction were obtained by converting the calculated rate constants for the reverse reaction of HO 2 and NO using the equilibrium constant. The equilibrium constant is calculated using the thermochemical data available in the literature for all the species. Controversy exists between the reported heats of formation of HO 2 in the literature w8,21,28,33x. The JANAF-value w21x is very low and the calculated equilibrium constants based on the JANAF data agree poorly with the experimental results. To circumvent this problem, we used the heat of formation of 2.5 kcalrmol for HO 2 at 298 K following the recommendation of Howard in the equilibrium constant calculation. Howard’s value has been shown to be in good agreement with the high level ab initio MO result of Bauschlicher w28x. Our predicted heat of formation of HO 2 at the G2M level is 3.3 kcalrmol at 0 K agrees very well with the calculated value of Bauschlicher Ž3.5 kcalrmol at 0 K and 2.8 kcalrmol at 298 K. and also suggests a higher value of heat of formation for HO 2 . All the experimental results for the reverse reaction were then converted to the forward reaction rate for comparison using the calculated equilibrium constants. Fig. 5A shows that our calculated rate constants agree well with the available experimental results, which in turn establishes Howard’s recommendation of the heat of formation for HO 2 . 4. Conclusions In this work, we calculated the rate constants for both channels of the OH q NO 2 reaction using ab initio MO and VRRKM theories. A correlation between the available low and high temperature experimental results for the recombinationrstabilization reaction of OH and NO 2 producing HNO 3 was successfully made using the theoretical rate constants for the temperature range 300 to 2000 K. We believe that such a correlation of the experimental results based on the theoretically predicted rate constants for this channel is reliable throughout that temperature range. The theoretically predicted rate constants for the other channel producing HO 2 q NO via the HOONO intermediate and its reverse process also show reasonably good agreement with the available experimental results. The correlation between the predicted rate constants for the forward and reverse channels for this reaction indicates the poor value of the heat of formation of HO 2 given in JANAF tables and supports the recommendation of Howard and Bauschlicher for the same. Acknowledgements The authors gratefully acknowledge the support of this work by the Caltech MURI project under ONR grant No. N00014-95-1338, Dr. R.S. Miller, program manager. We thank the Cherry L. Emerson Center for Scientific Computation for the use of computing facilities and various programs. References w1x P.J. Crutzen, J.R. Quart, Meteorol. Soc. 96 Ž1970. 320. w2x C.J. Howard, K.M. Evenson, Geophys. Res. Lett. 4 Ž1977. 437.
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A. Thompson, R.W. Stewart, J. Geophys. Res. 96 Ž1991. 13089. H.S. Johnston, Annu. Rev. Phys. Chem. 43 Ž1992. 1. N.M. Donahue, M.K. Dubey, R. Mohrschladt, K.L. Demerjian, J.G. Anderson, J. Geophys. Res. 102 Ž1997. 6159. W. Tsang, J.T. Herron, J. Phys. Chem. Ref. Data 20 Ž1991. 609. M.S. Woolridge, R.K. Hanson, C.T. Bowman, in: R. Brun, L.Z. Dumitrescu ŽEds.., Shockwaves at Marseille II, Springer-Verlag, Berlin, 1995, p. 83. C.J. Howard, J. Am. Chem. Soc. 102 Ž1980. 6937. C.J. Howard, J. Chem. Phys. 71 Ž1979. 2352. J.V. Seeley, R.F. Medas, M.J. Elrod, M.J. Molina, J. Phys. Chem. 100 Ž1996. 4026. R. Sumathi, S.D. Peyerimhoff, J. Chem. Phys. 107 Ž1997. 1872. A.D. Becke, J. Chem. Phys. 98 Ž1993. 5648. A.D. Becke, J. Chem. Phys. 96 Ž1992. 2155. A.D. Becke, J. Chem. Phys. 97 Ž1992. 9173. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 Ž1988. 785. A.M. Mebel, K. Morokuma, M.C. Lin, J. Chem. Phys. 103 Ž1995. 7414. M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham, V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, D.J. DeFrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez, J.A. Pople, GAUSSIAN 94, Revision D. 3, Gaussian Inc., Pittsburgh, PA, 1995. H.-J. Werner, P.J. Knowles, MOLPRO 94, University of Sussex, Falmer, Brighton, 1994. B.C. Garrett, D.G. Truhlar, J. Chem. Phys. 70 Ž1979. 1593. C.-C. Hsu, A.M. Mebel, M.C. Lin, J. Chem. Phys. 105 Ž1996. 2346. M.W. Chase Jr., C.A. Davles, J.R. Downey Jr., D.J. Frurip, R.A. McDonald, A.N. Syverud, JANAF thermochemical tables, J. Phys. Chem. Ref. Data 14 ŽSuppl. 1. Ž1985. 1. T.J. Lee, J. Phys. Chem. 99 Ž1995. 1943. R. Forster, M. Frost, D. Fulle, H.F. Hamann, H. Hippler, A. Schlepegrell, J. Troe, J. Chem. Phys. 103 Ž1995. 2949. J. Troe, J. Chem. Phys. 66 Ž1977. 4758. H. Harrison, H.S. Johnston, E.R. Hardwick, J. Am. Chem. Soc. 84 Ž1962. 2478. K. Glanzer, J. Troe, Ber. Bunsenges. Phys. Chem. 78 Ž1974. 71. ¨ S.J. Klippenstein, J. Chem. Phys. 96 Ž1992. 367. C.W. Bauschlicher Jr., H. Partridge, Chem. Phys. Lett. 208 Ž1993. 241. B.M. Cheng, J.W. Lee, Y.P. Lee, J. Phys. Chem. 95 Ž1991. 2814. J.P. Burrows, T.J. Wallington, R.P. Wayne, J. Chem. Soc., Faraday Trans. 79 Ž1983. 111. P.H. Wine, N.M. Kreutter, A.R. Ravishankara, J. Phys. Chem. 83 Ž1979. 3191. C. Anastasi, I.W.M. Smith, J. Chem. Soc., Faraday Trans. 2 72 Ž1976. 1459. G.W. Harris, R.P. Wayne, J. Chem. Soc., Faraday Trans. 1 71 Ž1975. 610. J.G. Anderson, J.J. Margitan, F. Kaufman, J. Chem. Phys. 60 Ž1974. 3310. Y.M. Gershenzon, A.P. Dement’ev, A.B. Nalbandyan, Dokl. Phys. Chem. 210 Ž1973. 403. V.Y. Basevich, S.M. Kogarko, Bull. Acad. Sci. USSR 27 Ž1979. 1988. R. Atkinson, D.L. Baulch, R.A. Cox, R.A. Hampson, J.A. Kerr, J. Troe, J. Phys. Chem. Ref. Data 18 Ž1989. 881. J.S. Robertshaw, I.W.M. Smith, J. Phys. Chem. 86 Ž1982. 785. L.G. Anderson, J. Phys. Chem. 84 Ž1980. 2152. R. Atkinson, R.A. Perry, J.N. Pitts, J. Chem. Phys. 65 Ž1976. 306. C.J. Howard, K.M. Evanson, J. Chem. Phys. 61 Ž1974. 1943. A.A. Jemi-Alade, B.A. Thrush, J. Chem. Soc., Faraday Trans. 86 Ž1990. 3355. B.A. Thrush, J.P.T. Wilkinson, Chem. Phys. Lett. 81 Ž1981. 1. W. Hack, A.W. Preuss, F. Temps, H.-Gg. Wagner, K. Hoyermann, Int. J. Chem. Kinet. 12 Ž1980. 851.
Theoretical study of the OH q NO 2 reaction: formation of nitric acid and the hydroperoxyl radical D. Chakraborty, J. Park, M.C. Lin
)
Department of Chemistry, Emory UniÕersity, Atlanta, GA 30322, USA Received 3 December 1997
Abstract The reaction of OH with NO 2 has been studied by high level ab initio molecular orbital and statistical theory calculations. The potential energy surface for the association leading to the formation of HNO 3 by collisional deactivation and the formation of endothermic products, HO 2 and NO via the HOONO intermediate have been computed with a modified Gaussian 2 ŽG2M. method. The rate constants for these two channels have been calculated by means of the canonical variational RRKM approach. The predicted values correlate reasonably well with experimental data for both the forward and reverse processes. q 1998 Elsevier Science B.V. All rights reserved.
1. Introduction The reaction of hydroxyl radical with nitrogen dioxide is of considerable practical interest because of the importance of the reaction in both troposphere and stratosphere w1–4x. The reaction is also pivotal to the combustion of nitramine and nitrate ester propellants, typically taking place under high-pressure and high-temperature conditions under which no reliable kinetic data are available through direct laboratory measurements. The OH q NO 2 reaction has been investigated by many laboratories w5–7x. It can take place via two low-energy reaction channels through collisional stabilization and disproportionation, respectively: a
b
ya
qM
OH q NO 2 ° HONO†2 ™ HNO 3 c
d
OH q NO 2 ° HOONO† ™ HO 2 q NO yc
The rate constant for the recombinationrstabilization reaction producing HNO 3 , measured in many studies, can be found in several recent publications and compilations w5–7x. Those for the production of HO 2 q NO via the unstable HOONO intermediate and its reverse process Ža convenient source of OH in atmospheric studies. have been investigated extensively by Howard w8,9x and more recently by Molina and coworkers w10x. These experimental data will be compared with our theoretically predicted results later.
)
Corresponding author. E-mail: [email protected].
0301-0104r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 0 1 - 0 1 0 4 Ž 9 8 . 0 0 0 3 3 - 0
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Theoretically, a very detailed potential energy surface ŽPES. of the OH–NO 2 system including the excited triplet intermediates and products has been investigated recently by Sumathi and Peyerimhoff using the density functional ŽDFT. and ab initio molecular orbital ŽMO. methods w11x. Their results and related theoretical and experimental data will be compared with ours for the key species involved in the present study, focusing on the interpretation and correlation of kinetic data obtained over a wide range of experimental ŽT, P . conditions for the two OH q NO 2 reactions occurring in both forward and reverse directions.
2. Computation methods 2.1. Ab initio MO calculations Geometries of the reactants, products and intermediates have been optimized at the hybrid density functional B3LYPr6-311GŽd,p. level of theory, based on Becke 3-grid integration and exchange functional w12–14x with the correlation functional by Lee et al. w15x. Vibrational frequencies employed to characterize stationary points, zero-point energies ŽZPE. and rate constant calculations have also been calculated at this level of theory. The electronic energies of various species were calculated with the recently developed modified Gaussian-2 ŽG2M. method w16x, which approaches high-level results using a series of single-point calculations for basis set size, correlation energy and systematic error corrections. Three versions of the scheme have been suggested by Mebel et al. w16x for varying molecular sizes. For the present system with 4 heavy atoms, the most elaborate and computation-intensive version, G2MŽRCC. was employed. The method is briefly summarized as follows. The scheme calculates the base energy E bas at the MP4r6-311GŽd,p. level of theory and improves it with the following corrections for basis set expansion and electron correlation: D E Ž RCC . s E Ž RCCSD Ž T . r6 y 311G Ž d,p . y E bas , D E Ž q3df2p. s E MP2r6y 311 q G Ž 3df,2p . y E MP2r6y 311G Ž d,p . , D E Ž HLC,RCC,MP2 . s y0.00525nb y 0.00019na The ZPE corrected energy with this scheme in E h is: E Ž G2M Ž RCC, MP2 . s E bas q D E Ž RCC . q D E Ž q3df2p. q D E Ž HLC, RCC, MP2 . q ZPE All calculations were carried out with Gaussian 94 w17x and MOLPRO 94 w18x programs. 2.2. Rate constant calculations 2.2.1. Variational transition state theory (VTST) calculation for the formation of HNO3 Since the reaction path Ža. does not have a well defined transition state ŽTS. because of the absence of reaction barrier, a VTST calculation has to be carried out. According to the canonical variational theory ŽCVT. w19,20x, the rate constant k CV T at T is obtained by maximizing DGŽT, s . with respect to the reaction coordinate s, and the position of the dividing surface associated with the maximum DGŽT, s . is denoted by s a . We applied here the canonical variational method based on the evaluation of the maximum free energy of activation at each temperature along the reaction path. We first scanned the potential energy surface for the approach of OH and ˚ with an interval NO 2 forming HNO 3 . The forming N–O bond distance of HNO 3 was varied from 1.8 to 3.0 A ˚ of 0.1 A, other geometric parameters were optimized for each value of N–O. We calculated twelve optimized ˚ For each structure, we calculated the 3N-7 vibrational geometries for NO distances from 1.8 to 3.0 A. frequencies projected out of the gradient direction. This B3LYP calculated energies at each point along the reaction path was used to evaluate the Morse potential energy function and then scaled by using the scale factor obtained by comparing N–O dissociation energies at G2M and B3LYP levels.
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The resulting potential energy function EŽ R . is given by: E Ž R . s De w 1 y ey b Ž RyR e. x
2
˚ y1 and Re s 1.414 A˚ is the equilibrium value of R, i.e., the where De s 50.53 kcalrmol, b s 2.6 A equilibrium N–O bond distance of HNO 3 . Using the Morse potential energy, computed moments of inertia and the vibrational frequencies, we searched for the maximum DG a at various temperatures in the range of 300 to 2000 K. The accurate position of the maximum for each temperature was calculated on the basis of the parabolic fit of the three largest DG values. In the RRKM calculation, we used all the molecular parameters corresponding to the structure with a ˚ have one maximum DG a for each temperature. Since the transition structures of HNO 3 with N–O ) 1.8 A vibrational frequency less than 100 cmy1 , we substituted this mode with the computed reduced moments of inertia corresponding to the free internal rotation. As the DG maxima along the reaction path are located between the calculated structures, the corresponding moments of inertia and vibrational frequencies were obtained by interpolation. 2.2.2. VTST calculation for the reaction HO2 q NO s HOONO The intermediate HOONO formed in the reaction of OH and NO 2 , has three possible rotational isomers due to the rotation along the NO and OO bonds, namely cis–cis Žcc., cis–perpendicular Žcp. and trans–perpendicular Žtp.. Since these rotational isomers are very close in energy, as mentioned by Sumathi and Peyerimhoff w11x, VTST calculation from any one of these rotamers could be considered as a reliable one. Despite our numerous attempts, we were unable to get a reliable PES for the incoming channel, i.e., OH and NO 2 forming HOONO. At the B3LYP level of theory the variational PES obtained at different points along the reaction path was either very scattered or the energy increase monotonically, and cannot be improved by mere energy correction in the frame work of the G2M method. The problem is more multiconfigurational in nature and a more expensive MCSCF calculation along the reaction path might provide a reliable PES. On the other hand, it is known from the experimental work of Molina and coworkers w10x that the reverse channel forming HO 2 and NO is pressure-independent because the reaction occurs via a short-lived intermediate HOONO and our theoretical PES at the G2M level indicates that this channel is endothermic by 7.0 kcalrmol. Thus, the rate constant for the reverse process from HO 2 and NO via the HOONO intermediate is controlled by the initial association reaction and the rate constant for the forward reaction of OH and NO 2 can be effectively obtained by using the principle of microscopic reversibility. Since our work aimed at the correlation between the theoretically predicted and experimental rate constants, the reliability of such approximation can be judged through the agreement between theory and experiment. We performed variational calculations for all three rotational isomers of HOONO for the outgoing channel forming HO 2 and NO. Both the cc and cp rotamers produce multiple imaginary frequencies at some points along the reaction path and have thus not been included in our canonical variational calculation. Instead, we used the potential energy surface for the dissociation of the tp-HOONO isomer. The dissociating NO bond ˚ with the interval of 0.1 A. ˚ Like the reaction path a, all the distance of tp-HOONO was varied from 1.8 to 2.7 A intermediate transition structures were optimized with respect to all other geometric parameters, except the reaction path and the 3N-7 vibrational frequencies projected out of gradient direction were calculated. The B3LYP energy along the reaction path at each point was scaled using the scale factor obtained by comparing the NO bond dissociation energy at the G2M and B3LYP levels of theory. The position of DG a at various temperatures in the range of 300 to 1500 K were then evaluated in the same manner as described in the preceding section using the computed energies, vibrational frequencies and moments of inertia. The RRKM rate constants were then calculated using the molecular parameters corresponding to the maximum DG a at each temperature obtained by the method of interpolation as described above.
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3. Results and discussion 3.1. Potential energy surface Sumathi and Peyerimhoff w11x have recently studied the PES of the OH–NO 2 system in great detail. We focus our study on the part of PES which is relevant to the OH q NO 2 recombination and decomposition processes mentioned above. The optimized geometries of reactants and intermediates for this reaction are shown in Fig. 1; the potential energy surface obtained at the G2M level is drawn in Fig. 2. The relative energies of the reactants and intermediates are compiled in Table 1 and the vibrational frequencies and moments of inertia of all species in Table 2. There are two possible reaction mechanisms for the interaction of OH with NO 2 as shown in Fig. 2. The first channel corresponds to the attachment of oxygen of OH at the N-terminal of NO 2 forming HNO 3 , whose energy at the G2M level of theory is 50.5 kcalrmol lower than the energy of the reactants. The calculated dissociation energy at this level of theory agrees very well between G2 and G2ŽMP2. as shown in Table 1, but is higher by 2.8 kcalrmol than the experimental dissociation energy Ž47.7 kcalrmol. given by the JANAF table w21x. Our G2M-predicted dissociation energy also agrees well with the calculated dissociation energy of 49.3 kcalrmol by Lee at the CCSDŽT.rTZ2P level w22x.
Fig. 1. The optimized geometries of reactants, products and intermediates at the B3LYPr6-311GŽd,p. level of theory.
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Fig. 2. Potential energy profile for the OH q NO 2 reaction based on the G2M calculation.
In the second channel, the reaction takes place by the attachment of oxygen of OH with one of the oxygen atoms of NO 2 forming an HOONO intermediate which in turn dissociates into HO 2 and NO. The HOONO intermediate can exist in three possible conformers with respect to the rotation along the O–O and N–O bond as reported by Sumathi and Peyerimhoff w11x. Our calculations at the B3LYPr6-311GŽd,p. level also reveal that the energies were very close for these three stable minima. The calculated energy of the trans–perpendicular conformer of HOONO is included in Table 1. The calculated energy of this rotamer is lower than the energy of the reactants by 19.3 kcalrmol at the G2M level of theory, whereas the product HO 2 and NO is endothermic by 7.0 kcalrmol.
Table 1 Relative energies Žkcalrmol. of reactants, products and intermediates for the reaction of OH with NO 2 Reaction
B3LYPr6-311GŽd,p.
CCSDŽT.r6-311GŽd,p.
QCID a
G2MŽRCC, MP2.
G2
OH q NO 2 HO 2 q NO HOONO HNO 3
0.0 7.24 y11.2 y44.5
0.0 4.4 y15.6 y47.4
0.0 3.7 y17.6
0.0 7.0 y19.3 y50.5
0.0 8.1b y20.3 b y50.1
a b
QCISDr6-311q q GŽ2df,2pd.rrMP2Ž6-311 q q GŽd,p. level from Ref. w11x. Taken from Ref. w11x.
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Table 2 Calculated harmonic frequencies Žin cmy1 . and moments of inertia Žin au. for all the reactants, products and intermediate at B3LYPr6311GŽd,p. level
y1 y2 y3 y4 y5 y6 y7 y8 y9 Ia Ib Ic a
OH
NO
NO 2
HO 2
HNO 3
HOONO
Expt.a
3702
1989
1706 1399 767
3610 1427 1162
3734 1787 1358 1324 912 777 655 589 481 138.5 149.7 288.2
3748 1823 1407 1014 808 459 358 293 212 33.1 367.9 395.2
3546 1704 1395 960 794 — — — —
3.2 3.2
35.2 35.2
7.5 138.3 145.8
2.9 53.5 56.4
Taken from Ref. w29x for HOONO measured in Ar and N2 matrices.
3.2. Recombination of OH and NO2 forming HNO3 3.2.1. Effect of pressure The effects of pressure on the recombination reaction of OH and NO 2 are shown in Fig. 3A. The bimolecular recombination rate of OH and NO 2 was calculated at 300–2000 K at varying pressures to compare with the available experimental results. Our calculated high-pressure limit rate constant can be expressed by k `a s 2.4 = 10y1 1 eŽ240r T . cm3r Ž molecule s . At 300 K, k `a s 5.5 = 10y11 cm3rŽmolecule s. which agrees reasonably well with the recent result of Troe and coworkers w23x Ž7.7 = 10y1 1 . and the lower limit set by Tsang and Herron w6x Ž) 4.0 = 10y1 1 . as shown in Fig. 3A. Experimental results with both Ar and N2 as diluent are included in the figure although calculations were made only with Ar as bath gas, using the Lennard–Jones collision parameters assumed by Troe w24x and the average collision energy transfer step-size, - D E ) , reported by Wooldridge et al. w7x. At room temperature, our calculated fall-off curve shows a systematic overestimation in comparison with the available experimental results but can account for the fall-off behavior reasonably well. Such systematic overestimation in the fall of curve can be attributed to several factors: The collision parameters, the energy transfer stepsize and the higher value of N–O bond dissociation energy of HNO 3 at our G2M level of calculation. As a test case, we calculated the fall-off behavior with the experimental dissociation energy and the calculated results show a slightly better agreement with the experimental results. 3.2.2. Effect of temperature The termolecular recombination rate of OH q NO 2 q M forming HNO 3 determined in the temperature range between 300 to 2000 K is shown in Fig. 3B. All the experimental results for this recombination reaction are available for a relatively low temperature range, i.e., - 600 K and at high temperatures, the available experimental results are for the reverse decomposition reaction. Our VRRKM predicted rate constants over the entire temperature range Ž300–2000 K. are aimed at the correlation of the low temperature recombination and high temperature decomposition experimental rate constants. All the RRKM calculations were made using Ar as the bath gas. The high temperature decomposition rate constants were converted to recombination rate constants using the principle of microscopic reversibility. In the RRKM calculations, both the G2M calculated and experimental well depths were used. It is evident from Fig. 3B that at low temperature, our results agree well
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Fig. 3. ŽA. Calculated RRKM rate constants for the OHqNO 2 qAr s HNO 3 qAr reaction as a function of total pressure at 300 K. v, Ref. w23x; (, Ref. w38x; , Ref. w5x; %, Ref. w31x; ^, Ref. w32x; l, Ref. w37x, , this study with Des 50.53; – – –, this study with Des 47.7 kcalrmol. ŽB. Arrhenius plot for the same reaction rate constant comparing the present results with literature data. %, Ref. w30x; B, Ref. w31x; l, Ref. w32x; I, Ref. w5x; , Ref. w34x; (, Ref. w7x; =, Ref. w25x; ^, Ref. w35x; e, Ref. w36x; ', Ref. w26x; , Ref. w37x; \, Ref. w38x; , Ref. w39x, q, Ref. w40x; v Ref. w41x; , this study with Des 50.53; – – –, this study with Des 47.7 kcalrmol.
with the existing experimental results. However, at high temperatures, the calculated and experimental rate constants show some deviation, especially near the fall-off region of the theoretical curve Žat ca. 800 K.. Fig. 3B indicates that for this reaction, which is mainly controlled by collisional deactivation, the calculated rate constants are noticeably dependent on the N–O bond dissociation energy and hence, the calculations based on experimental dissociation energy show a systematic lowering of theoretical rate constants. Both of the calculated curves show a deviation from the experimental results of Harrison et al. w25x near the fall-off region but agree reasonably well with the high temperature observed rate constants of Wooldridge et al. w7x and Glanzer ¨ et al. w26x. Such a deviation of the theoretical results near the fall-off region may be due to the limitation of the canonical variational approach, and it might be possible to improve it by means of a more elaborate theoretical model which includes the conservation of angular momentum w27x. The calculated rate constants for the termolecular recombination reaction and the reverse decomposition reaction in the temperature range 300–2000 K are summarized in Table 3.
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Table 3 Calculated rate constants for the OH and NO 2 recombination-decomposition reaction at various temperatures TrK k wOH q NO 2 q Ar s HNO 3 q Arx k wHNO 3 q Ar s OH q NO 2 q Arx k wOH q NO 2 s HO 2 q NOx k wHO 2 q NO s OH q NO 2 x 300 400 500 600 700 900 1000 1200 1400 1500 2000
1.14 = 10 18 3.35 = 10 17 1.57 = 10 17 8.11 = 10 16 4.71 = 10 16 1.89 = 10 16 1.27 = 10 16 5.83 = 10 15 2.82 = 10 15 2.00 = 10 15 4.10 = 10 14
7.06 = 10y17 5.30 = 10y8 1.09 = 10y2 3.16 = 10 1 8.52 = 10 3 1.14 = 10 7 1.28 = 10 8 3.79 = 10 9 3.74 = 10 10 7.69 = 10 10 8.09 = 10 11
7.43 = 10y16 1.02 = 10y14 4.83 = 10y14 1.16 = 10y13 2.18 = 10y13 4.62 = 10y13 7.68 = 10y13 1.30 = 10y12 2.36 = 10y12 2.66 = 10y12
1.05 = 10y11 8.27 = 10y12 7.11 = 10y12 5.54 = 10y12 4.69 = 10y12 3.48 = 10y12 4.02 = 10y12 3.96 = 10y12 4.87 = 10y12 4.71 = 10y12
Fig. 4. ŽA. Calculated high-temperature Ž700–2000 K. decomposition rate constants for the reaction HNO 3 qAr sOHqNO 2 qAr and comparison with available shock tube data. %, Ref. w7x; ^, Ref. w25x; e, Ref. w35x; , Ref. w36x; Q, Ref. w26x; , this study with Des 50.53; – – –, this study with Des 47.7 kcalrmol. ŽB. Arrhenius plot for the same decomposition reaction in the entire temperature range w300–2000 Kx. Low-temperature experimental results are obtained by converting the corresponding recombination rate constants carry the same symbol as in Fig. 3B. High-temperature shock tube results are the same as in A. Calculated rate constants were obtained by converting the recombination rate constant using equilibrium constant. , Des 50.53; – – –, Des 47.7 kcalrmol.
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3.3. Decomposition of HNO3 The theoretically predicted second order decomposition rates of HNO 3 in the temperature range 700 to 2000 K are shown in Fig. 4A and the correlation of those measured for both directions covering the entire temperature range is shown in Fig. 4B. The calculated recombination rate constants were converted to these decomposition rates using equilibrium constants obtained from the JANAF thermochemical table w21x. It is evident from the figure that the calculated rate constants are in reasonably good agreement with the available high temperature shock tube data for the decomposition reaction. 3.4. Rate constants for the reaction OH q NO2 s HO2 q NO The calculated rate constants for the forward and reverse reactions for this channel are shown in Fig. 5A and B, respectively. Both reactions go through the formation of a short-lived intermediate HOONO as shown in Fig. 2. The rate constants for both directions were measured extensively by Howard w8,9x by means of the laser magnetic resonance technique. Recently, Molina and coworkers reported the rate constants for the reverse reaction forming OH and NO 2 from HO 2 and NO using the turbulent flow technique w10x. Their study indicates that this reaction path is pressure-independent and their rate constant is in agreement with the earlier
Fig. 5. ŽA. Arrhenius plot for OHqNO2 s HO 2 qNO rate constant comparing the present results with literature data. \, Ref. w8,9x; I, Ref. w37x; l, Ref. w42x; , Ref. w43x; (, Ref. w44x; =, Ref. w10x; , this study. ŽB. Arrhenius plot for the reverse reaction HO 2 qNOsOHqNO 2 . ^, Ref. w8,9x; %, Ref. w37x; (, Ref. w44x; l, Ref. w42x; , Ref. w43x; =, Ref. w10x; , this study.
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determination by Howard w8,9x. The negative temperature-dependency of their result suggests that the reaction proceeds via the formation of an HOONO intermediate. In our RRKM calculation for this channel, the decomposition of the HOONO intermediate to HO 2 and NO as described in the preceding section, was made by using the calculated G2M dissociation energy of 26.3 kcalrmol in the temperature range 300 to 1500 K. The calculated rate constants are summarized in Table 3, corresponding to the high pressure limit show reasonably good agreement with the experimental results. Since the VTST calculation fails to locate any DG maximum below 300 K, our theoretical result is limited to this temperature and cannot account for the lower-temperature observed rates for this reaction. An extrapolation of the theoretical result to low temperature indicates an overestimation in theoretical rate constants in the low-temperature range, although the agreement with the observed rate constants is good at high temperatures. The rate constants for the forward reaction were obtained by converting the calculated rate constants for the reverse reaction of HO 2 and NO using the equilibrium constant. The equilibrium constant is calculated using the thermochemical data available in the literature for all the species. Controversy exists between the reported heats of formation of HO 2 in the literature w8,21,28,33x. The JANAF-value w21x is very low and the calculated equilibrium constants based on the JANAF data agree poorly with the experimental results. To circumvent this problem, we used the heat of formation of 2.5 kcalrmol for HO 2 at 298 K following the recommendation of Howard in the equilibrium constant calculation. Howard’s value has been shown to be in good agreement with the high level ab initio MO result of Bauschlicher w28x. Our predicted heat of formation of HO 2 at the G2M level is 3.3 kcalrmol at 0 K agrees very well with the calculated value of Bauschlicher Ž3.5 kcalrmol at 0 K and 2.8 kcalrmol at 298 K. and also suggests a higher value of heat of formation for HO 2 . All the experimental results for the reverse reaction were then converted to the forward reaction rate for comparison using the calculated equilibrium constants. Fig. 5A shows that our calculated rate constants agree well with the available experimental results, which in turn establishes Howard’s recommendation of the heat of formation for HO 2 . 4. Conclusions In this work, we calculated the rate constants for both channels of the OH q NO 2 reaction using ab initio MO and VRRKM theories. A correlation between the available low and high temperature experimental results for the recombinationrstabilization reaction of OH and NO 2 producing HNO 3 was successfully made using the theoretical rate constants for the temperature range 300 to 2000 K. We believe that such a correlation of the experimental results based on the theoretically predicted rate constants for this channel is reliable throughout that temperature range. The theoretically predicted rate constants for the other channel producing HO 2 q NO via the HOONO intermediate and its reverse process also show reasonably good agreement with the available experimental results. The correlation between the predicted rate constants for the forward and reverse channels for this reaction indicates the poor value of the heat of formation of HO 2 given in JANAF tables and supports the recommendation of Howard and Bauschlicher for the same. Acknowledgements The authors gratefully acknowledge the support of this work by the Caltech MURI project under ONR grant No. N00014-95-1338, Dr. R.S. Miller, program manager. We thank the Cherry L. Emerson Center for Scientific Computation for the use of computing facilities and various programs. References w1x P.J. Crutzen, J.R. Quart, Meteorol. Soc. 96 Ž1970. 320. w2x C.J. Howard, K.M. Evenson, Geophys. Res. Lett. 4 Ž1977. 437.
D. Chakraborty et al.r Chemical Physics 231 (1998) 39–49 w3x w4x w5x w6x w7x w8x w9x w10x w11x w12x w13x w14x w15x w16x w17x
w18x w19x w20x w21x w22x w23x w24x w25x w26x w27x w28x w29x w30x w31x w32x w33x w34x w35x w36x w37x w38x w39x w40x w41x w42x w43x w44x
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