L. V. Moskaleva and M. C. Lin Department of Chemistry Emory University, Atlanta, GA 30322, USA

Transcription

1 The Spin-onserved Reaction H + 2 H + : A Major Pathway to Prompt O Studied by Quantum/Statistical Theory alculations and Kinetic Modeling of Rate onstant L. V. Moskaleva and M.. Lin Department of hemistry Emory University, Atlanta, GA 30322, USA ABSTRAT A new spin-conserved path for the H( 2 Π) + 2 reaction at temperatures relevant to prompt O formation has been theoretically investigated by means of ab initio MO calculations at the G2M level of theory. The result of the calculation reveals that the H( 2 Π) + 2 reaction takes place primarily via the ground electronic doublet potential energy surface producing H +, instead of the commonly assumed, spin-forbidden H + ( 4 S) products. The overall rate constant for production has been computed by a multichannel canonical variational RRKM calculation for the temperature range K at atm pressure: k 3 = T 1.48 exp (-11760/T) cm 3 /(mol s). The theoretically predicted rate constant was found to be in good agreement with high-temperature shock-tube data kinetically modeled with the new mechanism that includes reactions. In addition, k 3 was also found to be consistent with the apparent rate constants previously modeled for prompt O formation in several flame studies. ITRODUTIO For nearly three decades since Fenimore [1] first suggested that the H( 2 Π ) + 2 H + ( 4 S) reaction might be a potential "prompt" O precursor process, there have been numerous experimental [2-14] and theoretical [15-21] studies on the reaction. The kinetics of the H + 2 reaction reported prior to 1983 were first interpreted in terms of the following global mechanism involving an internally excited H adduct: a H( 2 Π) + 2 H c H + ( 4 S) (1) b d H (2) +M by Berman and Lin[5], who measured the pressure- and temperature-dependent bimolecular rate constant (k 2 ) by laser-induced fluorescence, monitoring the decay of H. Their low-temperature ( K) P-dependent data, which have been corroborated in subsequent independent studies [10-13], were correlated with high-temperature O formation results by Blauwens et al. [2] with the Rice-Ramsperger-Kassel-Marcus (RRKM) theory. More recently, there have been two independent shock-tube studies which provide the much needed, reliable high-temperature kinetic data [8, 9]. Theoretically, the production of atoms by reaction (1) has been investigated by Manna and Yarkony [15,16] on the quantum-mechanical properties of the doublet-quartet surface crossing and by Walch [17], and Seideman and Walch [18] on the potential energy surface (PES) involved. Recently, Miller and Walch [19] calculated k 1 with the RRKM theory above 1000 K, ignoring the

2 possible effect of the doublet-quartet crossing; they concluded that the high-temperature shock-tube data [8, 9] could be satisfactorily accounted for theoretically. On the other hand, the result of a more comprehensive calculation by ui et al. [21], based on their more detailed PES [20] with the inclusion of the surface-crossing effect, indicated that the predicted rate constant is at least two orders of magnitude smaller than the shock-tube result. In this work, we study the mechanism of the H + 2 reaction, centering on the reaction path over the ground electronic doublet PES. The result of this high-level ab initio molecular orbital calculation, aided by a multichannel RRKM analysis and kinetic modeling for H decay and production reveals unambiguously that the prompt O observed in hydrocarbon flames actually arises primarily from the spin-allowed reaction, H( 2 Π) + 2 H + ( 3 Σ g - ). (3) The reaction occurs via two -(H)- ring intermediates and the H radical, whose decomposition reaction gives rise to. The prompt O can be formed by the facile, exothermic oxidation of by O, OH and O 2 present in the flame. OMPUTATIOAL METHODS The geometries of the transition states and local minima were optimized at the B3LYP level (Becke's three parameter density functional [22] with the nonlocal correlation functional of Lee, Yang, and Parr [23]) with the standard 6-311G(d,p) basis set. The vibrational frequencies used for characterization of stationary points, ZPE corrections and RRKM calculations, were computed at the same level of theory. Based on optimized geometries, single point calculations were then performed according to the G2M(R2) [24] procedure, a modified version of the G2 method of Pople and coworkers [25], which involved a series of calculations at MP2, MP4 and RSD(T) levels of theory with large to moderate basis sets. The scheme calculates the base energy E bas at the MP4/6-311G(d, p) level of theory and improves it with several corrections to approximate the RSD(T)/6-311+G(3df,2p) energy: E[G2M(R)] = E bas + E(+) + E(2df) + E(R) + + E(HL, R) + ZPE, where E bas = PMP4/6-311G(d, p), PMP4 stands for spin-projected PUMP4 energies for open shells and restricted RMP4 energies for closed shells, E(+) = E[PMP4/6-311+G(d,p)] E bas, E(2df) = E[PMP4/6-311G(2df,p)] E bas, E(R) = E[RSD(T)/6-311G(d,p)] E bas, = E[MP2/6-311G(3df,2p)] E[MP2/6-311G(2df,p)] E[MP2/6-311+G(d,p)] + E[MP2/6-311G(d,p)], E(HL, R) = n β n α with HL standing for the empirical higher level correction, and n α, n β are the numbers of α and β valence electrons, respectively. All MO calculations were performed with the Gaussian 94[26] and MOLPRO96[27] program packages. A. Ab Initio MO alculations RESULTS AD DISUSSIO 2

3 The reaction occurring by the quartet state producing H + ( 4 S) has been studied extensively as alluded to in the introduction. The most recent result reported by ui et al.[20] for this reaction channel, which involves an intersystem-crossing between the doublet and quartet surfaces, computed at the G2M level of theory is presented in Fig. 1 by the dashed curve. The reaction taking place via the ground electronic doublet surface, given by the solid curve, proceeds from the cyclic intermediate IT1 via a concerted transition state TS3 directly to H radical as confirmed by an IR analysis [28]. * This transition state is 11.7 kcal/mol above H + 2 at our best G2M(R) level, which is about as high as the entrance transition state, TS1. We were also able to find a stepwise pathway from IT1 to IT3 involving another cyclic H isomer with the hydrogen atom attached to one of the -atoms. This pathway obtained at the MP2/6-311G(d,p) level of theory, was not considered important because of the very high activation barrier ca. 46 kcal/mol relative to H + 2 for the H-shift. The doublet product channel, + H, is 18.1 kcal/mol more endothermic than the quartet H +, however, the apparent barrier for the H dissociation would be much lower at high temperatures because of the entropic contribution which reduces the values of G as the temperature increases. The theoretical value for the heat of formation at 0 K obtained based on reaction (3), kcal/mol, is in good agreement with the recently reported experimental value by eumark and co-workers [29], ± 0.7 kcal/mol (0 K) and by lifford et al. [30], ± 3.2 kcal/mol (0 K). The latter authors also reported the H- bond dissociation energy to be 81.7 ± 1.0 kcal/mol (0 K) that compares well with our theoretical result, 84.0 kcal/mol. There exists a separate doublet surface involving the formation of the H (diazomethyl) radical, which can cyclize to produce the ring intermediate, IT2, after overcoming a large isomerization barrier of 58.7 kcal/mol [20] at the G2M(R) level, which translates into 30.9 kcal/mol above H + 2. onsequently, this part of the ground state PES must be irrelevant to the formation of H + even at high combustion temperatures, while it is mainly responsible for the H formation at low temperatures as was predicted by Bergman and Lin [5] in the first RRKM analysis of the H + 2 reaction. B. Kinetics and Mechanism for the H + 2 Reaction H + 2 H The H + 2 reaction below 1000 K occurs exclusively by the association/stabilization process on account of the large energy barriers required for the production of H + and H +. The association reaction producing the H radical in the ground electronic doublet state takes place barrierlessly with apparent negative activation energy which vary with pressure and temperature [5,10-12]. There have been numerous studies on the P,T-dependent association process since the first detailed kinetic and mechanistic study by Berman and Lin in 1983 [5]. This low-temperature process is not directly relevant to high-temperature prompt O formation as aforementioned. Accordingly, we will not attempt to correlate all existing low-temperature kinetic data in this limited space. H + 2 H + * Initially, we found another minimum for the H structure, that was ca. 10 kcal/mol less stable at both B3LYP/6-311G(d,p) and MP2/6-311G(d,p) levels. After a more careful check, we tend to think that our earlier minimum was an artifact, since it could only be obtained with the GAUSSIA98 code and was not reproducible with the G94 version or with different optimization methods. 3

4 The H + 2 reaction at high temperatures of interest to prompt O formation (T>1500 K) occurs predominantly by the ground electronic doublet surface producing H + with an overall endothermicity of 21.5 kcal/mol. Although energetically the formation of this product pair is more endothermic than the formation of H + by 18.1 kcal/mol, the last TS leading to the formation of the latter products is 0.8 kcal/mol higher than H + at the G2M level of theory. In addition, the larger entropy change associated with formation contributes to much smaller Gibbs free energy of activation for the reaction as alluded to above. This qualitative description of the thermodynamic preference for H + production, ignoring the dynamic constraint due to the surface-crossing process which will further limit the formation of the spin-forbidden H + products, can be quantitatively substantiated by the predicted large rate constant for the former spin-allowed process. The rate constant for production was calculated with the multichannel RRKM program previously employed for the H 2 + O reaction [31] using the following simplified scheme: a H + 2 IT2 b IT3 c H + -a -b d +M e +M IT2 IT3 where IT2 is the cyclic-(h)- ( 2 A 2 ) radical and IT3 is the H ( 2 A") radical; " " denotes internal excitation and M represents the third-body, Ar, assumed in our calculation. In the above scheme, IT1 (cyclic-(h)-, 2 A'), which has a shallow well and is located much below TS1 as shown in Fig. 1, is omitted in our calculation for simplicity. This simplification is not expected to have any significant effect on the predicted rate constant for production. As the dissociation of H occurs barrierlessly, we employed the canonical variational transition state theory (VTST) approach, as has been previously used for HOO 2 [32] and HO 2 [33] dissociation reactions, based on the maximum Gibbs free energy criterion [34]. To calculate the Gibbs free energies along the dissociation path, we evaluated the potential energies at various H separations covering from to Å with full geometry optimization and frequency calculation at the B3LYP/6-311G(d,p) level of theory. The computed energies were then scaled with the more accurate G2M dissociation energy for H H + to give: V(r) = D e [1-exp (-β(r-r 0 )] 2 with D e = kcal/mol, r 0 = Å and β = The results of RRKM calcualtions predicted the following rate constants for the formation of, IT2 and IT3 at 1 atm for the 1500 K K temperature range: k c = k 3 = T 1.48 exp(-11760/t) cm 3 /mol s k d = T exp(-7704/t) cm 3 /mol s k e = T exp(-7144/t) cm 3 /mol s 4

5 The rate constant for production, k 3, is presented in Fig. 2 for comparison with experimental data. In the RRKM calculation, effective collision frequencies were evaluated with Troe's weak-collision approximation [35] assuming the following Lennard-Jones parameters: ε(ar) = 116 K and σ(ar) = 3.47 Å; ε(h) ε(ho) = 258 K and σ(h) σ(ho) = 4.42 Å [36]. Under the P,T-conditions employed for the modeling of shock-tube data to be described below, K, atm, collisional stabilization processes are relatively unimportant. Accordingly, in our kinetic modeling of the high-temperature data of Dean et al. [9] and Lindackers and coworkers [8] most reactions involving the radical intermediates can be neglected. Kinetic Modeling of Shock-Tube Data The most direct kinetic data for the H + 2 reaction have been acquired by shock heating between 2000 and 4000 K by Dean et al [9] with laser resonance absorption for H detection and by Lindackers and coworkers [8] with atomic resonance absorption for monitoring -atom production. Because of the chemical complexity in generating the H radical by the thermal decomposition of either H 4 or 2 H 6, extensive computer modeling is required for extraction of the rate constant. On account of the significant difference in the initial products of the H + 2 reaction, H + vs. H + as previously assumed in all H + 2 kinetic analyses, we have carried out a series of kinetic modeling to obtain the rate constant of production for comparison with our theoretically predicted values. In order to simulate -atom production, the kinetics and mechanisms for reactions with the key radicals present in the milieu of shock heated H 4 [9] and 2 H 6 [8] have to be reliably elucidated and their rate constants calculated. As very limited kinetic data on reactions exists in the literature [37], we have embarked an extensive study on the kinetics and mechanisms for reactions with H, H,, H 2 and H 3 by ab initio MO calculations at the G2M(R) level of theory in conjunction with canonical variational RRKM calculations to generate their rate constants for the temperature range K. The predicted rate constants for these reactions are summarized in Table I. Modeling of H Kinetic Data: For modeling of the H kinetic data reported by Dean et al. [9], we used their mechanism to regenerate H concentration profiles with the individual rate constants provided in their paper. The H profiles given by the authors can be quantitatively reproduced as illustrated in Figure 3. These and all other regenerated H profiles were then modeled with our more comprehensive mechanism which combines all reactions listed in Table 1 with their mechanism, replacing H + 2 H + with H + 2 H + using our computed rate constant for the reaction. Figure 3 shows that the reported or regenerated H concentration profiles can be quantitatively modeled with very minor adjustment in k 3. The modeled values of k 3 are presented in Fig 2 by open circles. Modeling of the -production data: Lindackers et al. [8] measured -atom production at temperatures between 2300 and 3150 K using 2 H 6 as the H precursor. Unfortunately, they presented only one -atom profile and provided a partial mechanism, which cannot reproduce the -profile quantitatively. In order to circumvent the shortcoming, we employed the original mechanism of Dean et al. [9] mentioned above to regenerate -atom profiles using the rate 5

6 constant for H + 2 H + reported by Lindackers et al. The predicted -concentration profile for 2410 K and 1.77 atm with 20 ppm 2 H 6 and 40,000 ppm 2 is illustrated in Fig. 4A. The agreement between the regenerated (given by the solid curve) and observed -profiles is satisfactory. In view of the possibility in approximately regenerating the -profile, we proceeded to reproduce three more concentration profiles covering the temperature range employed, K. These profiles, including the one for 2410 K, were kinetically modeled with our mechanism to obtain the rate constants for production as shown in Fig. 4B. The agreement between the modeled -profiles and the regenerated ones, unlike the H case, is marginally acceptable. The apparent large deviation between the two profiles at shorter reaction times has been accentuated by our inability in duplicating the observed -profile with the mechanism of Dean et al. as is evident in Fig. 4A. The modeled values of k 3, given by filled triangles, are compared with our theoretical result in Fig. 2. The drawback in modeling -concentrations for k 3 will become evident according to the result of sensitivity analyses presented below. Sensitivity analyses: The effectiveness in modeling H and -atom concentration profiles for the rate constant of the H + 2 reaction has been examined by sensitivity analysis using the SEKI program [38]. Figure 5A presents the result for H studied at 3065 K, about the mid-point of the temperature range employed by Dean et al. [9], with 30 ppm H 4 and 5% 2 at 0.88 atm. The result of this analysis indicates that the decay of H is affected most strongly by reaction (3) producing. Parenthetically, the result also shows that H is generated most effectively by H 3 decomposition, which directly gives H + H 2 as we had predicted previously [39]. The sensitivity coefficients for atoms are presented in Fig. 5B for 2410 K at 1.77 atm pressure with 20 ppm 2 H 6 and 4% 2. Under this condition, the most influential reactions for - production are the two key H generation processes, H 3 + M H + H 2 + M and H 3 + M H 2 + H + M. Accordingly, it is more difficult to extract k 3 by modeling -profiles. A similar calculation for the condition employed by Dean et al.[9] cited above for the analysis of the H profile at 3065 K, we found that the most important process responsible for -atom production is + 2 +, as was also noted by these investigators, who suggested that -kinetics is less effective for the determination of the H + 2 rate constant.. omparison of the Predicted and Kinetically Modeled k 3 The calculated rate constant for production from H + 2 is presented in Fig. 2 for comparison with the kinetically modeled values using the high-temperature shock-tube data of Dean et al. [9] and Lindackers and coworkers [8] as described above. Also included in the figure are the results of Becker et al. measured by kinetic spectroscopy monitoring the decay of H by laser-induced fluorescence [10] and kinetically modeled values purportedly for k 1 in flame studies [3,7,14]. Significantly, the theoretically predicted rate constant for k 3 agrees closely with the modeled values using shock-tube data, particularly those of Dean et al., and with the results of flame modeling [3,7,14] for k 1. The agreement with that of Becker et al. [10] is, however, rather poor. It is believed that the reaction is too slow to be measured by kinetic spectroscopy at the temperatures employed. The fact that our value of k 3 should agree reasonably with those modeled for k 1 in flame studies is understandable. Under flame conditions, the rates of oxidation of by O, OH, and O 2 are expected to be very fast, the rate constants modeled from these studies should reflect the rate-controlling H + 2 reaction rather than the transformation of or H into O by oxidation. 6

7 OLUSIO We have theoretically investigated the kinetics and mechanism for the H + 2 reaction by ab initio molecular orbital and multichannel RRKM calculations. The result of this study reveals that the major pathway of the H + 2 reaction at temperatures of relevance to prompt O formation occurs by the spin-conserved ground electronic doublet surface producing H +, instead of the spin-forbidden H + products first suggested by Fenimore in 1971 [1]. The theoretically predicted rate constant for H + 2 H + (k 3 ) can quantitatively account for the concentration profiles of H radicals and also reasonably predict -atom profiles measured in high-temperature shock-tube experiments employing a detailed mechanism. The mechanism was constructed with that used by Dean et al. [9] for the H 4 2 system and our theoretically predicted reactions with associated rate constants. In addition, k 3 was found to be in reasonable agreement with kinetically modeled rate constants assumed for H + 2 H + in more recent flame studies. The reason for the agreement has been discussed. AKOWLEDGMET The authors are grateful for the support of this work by the Basic Energy Sciences, Department of Energy, under contract no. DE-FG02-97-ER The assistance of Dr. W. S. Xia for part of the MO calculation on the H 2 + reaction and of Dr. J. Park for sensitivity analysis is greatly appreciated. ML also wants to thank The altech Multidisciplinary University Research Institute under Office of aval Research Grant no , Dr. J. Goldwasser, program manager. References: 1. Fenimore,. P. Proc. ombust. Inst. 13: (1971). 2. Blauwens, J., Smets, B. and Peeters, J. ombust. Inst. 16: (1977). 3. Matsui, Y. and omaguchi, T. ombust. Flame, 32: (1978). 4. Butler, J. E., Goss L. P., Lin, M.. and Hudgens, J. W. hem. Phys. Lett. 63:104-7 (1979). 5. Berman, M. R., Lin, M.. J. Phys. hem. 87: (1983). 6. Duncanson, J. A., Jr., Guillory, W. A. J. hem. Phys. 78: (1983). 7. Matsui, Y. and Yuuki, A. Jpn. J. Appl. Phys. 24: (1985). 8. Lindackers, D., Burmeister, M., Roth, P. ombust. Inst. 23: (1991). 9. Dean, A. J., Hanson, R. K. and Bowman,. T. ombust. Inst. 23: (1991). 10. Becker, K. H., Engelhardt, B., Geiger, H., Kurtenbach, R., Schrey, G. and Weisen, P. hem. Phys. Lett. 195: (1992). 11. Medhurst, L. J., Garland,. L. and elson, H. H. J. Phys. hem., 97:12275 (1993). 12. Brownsword, R. A., Gatenby, S. D., Herbert, L. B., Smith, I. W. M., Stewartt, D. W. A., Symonds, A.. J. hem. Soc. Faraday Trans. 92: (1996). 13. Morley,. ombust. Flame, 27: (1976). 14. Miller, J. A., Bowman,. T. Prog. Energy ombust. Sci.:15, (1989). 15. Manna, M. R. and Yarkony D. R. J. hem. Phys. 95: (1991). 16. Manna, M. R. and Yarkony D. R. hem. Phys. Lett. 188: (1991). 17. Walch, S. P. hem. Phys. Lett. 208: (1993). 18. Seideman, T. and Walch, S. P. J. hem. Phys. 101: (1994). 19. Miller, J. A., Walch, S. P. Int. J. hem. Kinet. 29: (1996). 20. ui, Q., Morokuma, K. Theor. hem. Acc. 102: (1999). 7

8 21. ui, Q., Morokuma, K., Bowman, J. M., and Klippenstein, S. J. hem. Phys. 110: (1999). 22. Becke, A. D. J. hem. Phys. 98: (1993). 23. Lee,., Yang, W. and Parr, R. G. Phys. Rev. B, 37: (1998). 24. Mebel, A. M., Morokuma, K. and Lin, M.. J. hem. Phys. 103: (1995). 25. urtiss, L. A., Raghavachari, K., Trucks, G. W., and Pople, J. A. J. hem. Phys. 94: (1991); Pople, J. A., Head-Gordon, M., Fox, D. J., Raghavachari, K., and urtiss, L. A. J. hem. Phys. 90: (1989); (c) urtiss, L. A., Jones,., Trucks, G. W., Raghavachari, K., and Pople, J. A. J. hem. Phys. 93: (1990). 26. Frisch, M. J., Trucks, G. W., Schlegel, H. B., Gill, P. M. W., Johnson, B. G., Robb, M. A., heeseman, J. R., Keith, T., Petersson, G. A., Montgomery, J. A., Raghavachari, K., Al- Laham, M. A., Zakrzewski, V. A., Ortiz, J. V., Foresman, J. B., ioslowski, J., Stefanov, B. B., anayakkara, A., hallacombe, M., Peng,. Y., Ayala, P. Y., hen, W., Wong, M. W., Andres, J. L., Replogle, E. S., Gomperts, R., Martin, R. L., Fox, D. J., Binkley, J. S., Defrees, D. J., Baker, J., Stewart, J. P., Head-Gordon, M., Gonzalez and., Pople, J. A. GAUSSIA 94, REVISIO A.1; Gaussian, Inc., Pittsburgh PA, MOLPRO is a package of ab initio programs written by Werner, H.-J. and Knowles, P. J., with contributions from Almlöf, J., Amos, R. D., Berning, A., ooper, D. L., Deegan, M. J. O., Dobbyn, A. J., Eckert, F., Elbert, S. T., Hampel,., Lindh, R., Lloyd, A. W., Meyer, W., icklass, A., Peterson, K., Pitzer, R., Stone, A. J., Taylor, P. R., Mura, M. E., Pulay, P., Schütz, M., Stoll H. and Thorsteinsson, T. 28. Gonzalez,. Sosa,., and Schlegel, H. B. J. Phys. hem. 93: (1989). 29. Bise, R. T., hoi, H., and eumark, M. J. hem. Phys. 111: 4923 (1999). 30. lifford, E. P., Wenthold, P. G., Lineberger, W.., Petersson, G., and Ellison, G. B. J. Phys. hem. 101: 4338 (1997). 31. Diau, E. W., Wagner, M. A. G. and Lin, M.. J. Phys. hem. 98: (1994). 32. hakraborty, D., Park, J., and Lin, M.. hem. Phys. 231:39-49 (1998). 33. hakraborty, D., Hsu.-., and Lin, M.. J.hem. Phys. 109: (1998). 34. Garrett, B.. and Truhlar, D. G. J. hem.phys. 70: (1979); 35. Troe, J. J.hem. Phys. 66: (1977). 36. Marchand,., Rayes, J.., Smith, S.. J. Phys. hem. A:162: (1998) 37. He, Y., Wu,. H., Lin, M.. and Melius,. F. Proc. 19th Int. Symp. Shock Waves, 1995, pp Luts, A. E., Lee, R. K., Miller, J. A. SEKI: A FORTRA Program for Predicting Homogeneous Gas-Phase hemical Kinetics with Sensitivity Analysis; Sandia ational Laboratories, Livermore, A. Report o. SADIA , Zabarnick, S., Fleming, J. W., and Lin, M.. J. hem. Phys. 85: (1986). 8

9 Table 1: Rate coefficients for the reactions used for modeling of the H and concentration profiles a for K and 1 atm Reaction A n E a Remarks H + 2 H b H + 2 H b H + M H + + M b + M + + M c H + H b H 2 + H d H 2 + H d H 2 + H 2 (triplet) d H 2 + H 2 (singlet) d H 2 + H d H 2 + H+H d H+ H c H+ H(quartet) c H+ H c + () c c H 3 + H c H 3 + H 2 H c e e a The rate coefficients were computed by ab initio MO/RRKM calculations and fitted to the n Ea / RT expression k = AT e given in units of cm 3, mol and s. b This work. c L. V. Moskaleva and M.. Lin, to be published. d L. V. Moskaleva, W. S. Xia and M.. Lin, to be published. e Ref

10 E rel (kcal/mol) H( 2 A 1 ) H( 2 Π) TS TS2-4.7 TS ( 3 Σ - g )+H 21.5 H( 1 Σ + )+( 4 S) IT1( 2 A ' ) H( 2 A '' ) IT2( 2 A 2 ) IT3 ( 2 A " ) Figure 1. Potential energy diagram for reaction (3) combining the result of ui and Morokuma [20] for the quartet state given by the dotted curve where indicates curve crossing with the present work for the doublet state given by the solid curve. TS1, TS2, and H were recalculated in the present work and are in agreement with ref. [20]. The relative energies are calculated at the G2M(R) level including B3LYP/6-311g(d,p) ZPE correction.

11 28 ln k3/ cm 3 mol -1 s /T Figure 2. Summary of theoretical and experimental data modeled for k 3 and those determined purportedly for k 1. Solid line: RRKM result evaluated for H decay at 0.88 atm based on our computed PES. Open circles: k 3 modeled by H decay based on the data from ref. 9; filled triangles: k 3 determined by -production based on the data from ref. 8; dashed line: k 1, ref. 8; filled squares: k 1 determined by H decay, ref. 10. Other data were obtained by modeling complex chemistry in flames for k 1 : filled circle: ref. 14; dotted line: ref. 7; dash-dotted line: ref.3.

12 H mole fraction (ppm) t, µs Figure 3. Modeled H-concentration profiles (dashed line) in comparison with regenerated experimental profiles (solid line) observed in shock-tube study of Hanson et al. [9]. 1: 2500 K; 2: 3167 K; 3: 3820 K

13 mole fraction (ppm) A t, µs mole fraction (ppm) 8 6 B t, µs Figure 4. A. omparison of the experimental []-profile (circles) at 2410 K and 1.77 atm obtained by Lindackers et al. from shock-tube experiment [8] with that generated by Hanson s mechanism (solid curve) for k 1 = cm 3 /(mol s) as described in the text and with our fit (dashed curve) for the same conditions. B. Modeled -concentration profiles (dashed line) in comparison with regenerated experimental profiles (solid line) observed in shock-tube study of Lindackers et al. [8]. 1: 2342 K; 2: 3150 K; 3: 2807 K.

14 ormalized mole sensitivity (5) (2) (4) (1) H + 2 = + H (2) H 4 + M = H 3 + H + M (3) H 3 + M = H 2 + H + M (4) H 3 + M = H + H2 + M (5) H 2 + M = H + H + M (6) H 2 + M = + H 2 + M (7) H + M = + H + M (8) H + H = + H 2 (7) (6) (3) (A) (8) (1) Time (s) ormalized mole sensitivity (1) + 2 = + (2) H + 2 = + H (3) H + = H + (4) H 3 + = H + 2H (5) H 3 + M = H 2 + H + M (6) H 3 + M = H + H 2 + M (7) H 2 + M = + H 2 + M (8) H 3 + H = 2 H 3 + H (9) H + = 2 + H (5) (4) (6) (1) (3) (7) (8) (9) (2) (B) Time (s) Figure 5. Sensitivity of H-depletion (A) and -production (B) to various reactions considered in our modeling (only those reactions with non-negligible contributions are shown).