The reactions of imidogen with nitric oxide and molecular oxygen

THE

REACTIONS

OF IMIDOGEN MOLECULAR

WITH NITRIC OXYGEN

OXIDE

AND

JAMES A. MILLER AND CARL F. MELIUS Combustion Research Facility Sandia National Laboratories Livermore, CA 94551-0969 USA

Using potential energy surface information from BAC-MP4 calculations and statistical-dynamical methods, we have calculated the branching fraction for the NH + NO reaction, NH + NO---> N2 + OH

(1)

NzO + H.

(2)

We find that reaction (2) dominates over the entire temperature range considered, 300 K < T < 3500 K, with f = k~/(kj + k2) varying from about 0.19 at room temperature to about 0.30 at 3500 K. In addition, we have calculated rate coefficients for the two-channel process, NH+02~HNO+O

(3)

---, NO + OH.

(4)

In this case we find that reaction (4) dominates at low temperature, reaction (3) at high temperature. Between 300 K and 3300 K these rate coefficients can be expressed as (cm:~/ mole-sec) k3 = 4.61 • l0 s T z~ exp (-6500/RT) and k4 = 1.28 x 10~ T 15 exp (-IO0/RT). All these results are in good agreement with available experimental data.

Introduction Reactions of imidogen (NH) play a role in many aspects of nitrogen chemistry in combustion./1) Perhaps most importantly, the reaction of NH with nitric oxide is believed to be one of the two principal sources of nitrous oxide (N20) in gas-phase combustion, the other being the reaction of NCO with NO ~l/ Nitrous oxide is known to contribute to the depletion of stratospheric ozone, and fossil fuel combustion may be be a significant source of N20 in the atmosphere. Clearly the development of chemical kinetic models to predict N20 formation and destruction in combustion is highly desirable. In the present investigation we treat theoretically two different reactions involving imidogen: the reaction of NH with NO, NH + NO----> N2 + OH N20 + H,

(1) (2)

These reactions play significant roles ill determining the levels of N20 and NO produced in the lowtemperature oxidation of ammonia and in the abatement of NO by ammonia addition, competing with each other for the NH under many conditions. 2 For the NH + NO reaction there is now a considerable amount of experimental data on the total rate coefficient, 3-7 kt + k2, but veu' little quantitative information exists on the branching fraction, a parameter that is critical in predicting N20 levels in combustion systems. For the NH + 02 reaction there is direct experimental information at temperatures below 600 Ks-ll and above 2200 K, 7 but there are no data in between. Additionally, recent indirect data on NH + 02 from flame experiments 12'13 conflict badly with the direct determinations. In the present paper we predict the branching fraction, f = kl/(kl + k2), for the NH + NO reaction and both the total rate coefficient and product distribution for the NH + 02 reaction over a wide range of temperatures. In both cases we discuss our results in terms of the experimental data available.

and the reaction of NH with molecular oxygen, Theory

NH + 0-2---->HNO + O

(3)

---> NO + OH.

(4) 719

As in our previous investigations of this type, 14-17 we utilize the BAC-MP418 method to determine the

720

REACTION KINETICS

necessary properties of the potential energy surfaces (PES). In this method geometries of saddle points and relative minima on a PES and the vibrational frequencies at these points are calculated at the Hartree-Fock level. Using these geometries the potential energies at these points are refined first by an MP4 calculation (M611er-Plesset fourthorder perturbation theory) and then by a series of semi-empirical corrections. The resulting PES properties are generally quite accurate. A summary of the PES properties used in the present calculations is given in Table I. The dynamics on the resulting potential energy surfaces are calculated statistically. This requires two fundamental assumptions, the transition-state approximation and the strong-coupling, or RRKM, approximation. In addition, we assume that the reaction coordinate is separable from the rest of the Hamiltonian and that the rest of the Hamiltonian is separable into harmonic-oscillator and rigid-rotor parts. Non-classical reaction coordinate motion (tunneling) is computed one-dimensionally with the assumption of Eckart barriers, the properties of which come from the BAC-MP4 calculations. However, tunneling effects are negligible in the reactions considered here. All state counting is done exactly. In this paper we use the terms "loose" and "tight"

to characterize transition states. A loose transition state is one with one or more low vibrational frequencies; loose transition states generally have at least one relatively large interatomic distance. Tight transition states have high vibrational frequencies and relatively small interatomic distances. Loose transition states lead to large rate coefficients, tight transition states lead to small ones.

The NH + NO Reaction This reaction has been discussed qualitatively from a theoretical perspective at least twice previously, ls-m Our objective here is to predict quantitatively the product distribution as a function of temperature. A reaction coordinate diagram, based on BACMP4 calculations, is shown in Fig. 1. There are two possible product channels, NH+ NO~N2+ and

OH

(i)

NH + NO --) NzO + H.

(2)

If we assume that the NNOH complex shown in Fig. 1 always decomposes to Nz + OH (a safe assumption since this dissociation has no potential en-

TABLE I Molecular parameters of reactants and transition state structures used in calculating rate constants for the reactions NH + NO ~ products and NH + Oz --* products. AH~ (Kcal-mol-l)

Moments of Inertia (amu-a,,2)

3NH

87.0

2NO

21.6

302

0.0

0.000 3.519 3.519 0.000 33.866 33.866 0.000 38.943 38.943 9.686 147.907 157.593 30.220 103.004 133.224 50.079 78.794 122.607 29.957 149.932 178.375

Molecular Species

HNNO ---> H + NNO

80.4

HNNO ---) NNOH

86.2

HNOO --~ Cyclic-NHOO-

88.8

3HNOO---) HNO + 30

97.3

Frequencies (cm -l) 3150.2

1983.2

1784.2

-1286.9 590.1 1173.6 -2427.0 806.7 1279.9 -674.7 904.4 1418.9 -886.6 463.0 1403.7

375.0 759.4 1829.2 481.3 957.5 1768.5 880.8 1115.8 3278.1 311.5 1020.3 3246.9

REACTIONS OF NH WITH NO AND O2

120-

~

Reaction of NH + N O

#1

~

TABLE II Branching fraction f for the NH + NO reaction,

+O

N2H

f = k~/(k~ + k2)

4~

ReactN~i l inatl"iiii'ram~

N2+O H

o

721

T (K)

f (dimensionless)

300 500 750 1000 1500 2000 2500 3000 3500

0.194 0.210 o. 226 0.239 0.258 o. 272 0.283 0.291 0.298

FIG. 1. Reaction coordinate diagram for the NH + NO reaction. ergy barrier), we can write the thermal rate coefficients as follows:

k~(T)

-

g(T) (21 + 1) hQn(T) ] 9fo

F1F2 [ ] ~, exp 7- E dE ~ ~+ F3) (F~ + F~ LkBTJ

(El)

and k~(T) =

g(T) E (21 + 1)

hOn(f') 1 9fo ~

F#F "

(Fr + F~

+

r exp ---E

F3)

LkBTJ

dE

(E2)

In these expressions ks is Boltzmann's constant, h is Planck's constant, J is the total angular momentum quantum number, T is the temperature, and Qn(T) is the vibrational-rotational-translational partition function of the reactants (not including electronic or center-of-mass translational contributions). The factor g(T) is the ratio of the electronic partition function for the potential on which the reaction occurs to the electronic partition function for the reactants,

g(T) = 2/[3" 2{1 + exp (-174/T)}].

(E3)

The temperature dependence in the denominator of (E3) is due to the spin-orbit interaction in NO (2//); the other factors are spin degeneracies. The functions F~ (E, J)/h, i = 1. . . . 3, represent microcanonical/fixed J probability fluxes per unit energy through the transition-state dividing surfaces (TSDS's) of Fig. 1 indicated by the subscripts; they are the same in both directions because of micro-

scopic reversibility. In the absence of tunneling, F~ (E, J) becomes W7 (E, J), the sum of states with angular momentum quantum number equal to J and energy less than or equal to E. In the present investigation we are not interested in kl and k2 individually, but only in the branching fraction, which we define as

f = kl/(kx + k2).

(E4)

Because TSDS-2 and TSDS-3 lie well below TSDS1 on the potential energy surface, f is substantially independent of the properties of TSDS-1, which really determines only the total rate coefficient. For this reason, and because an accurate calculation of F[' (E, J) would require use of variational transition-state theory (there is no intrinsic potential energy barrier), which in turn requires considerably more PES information than we have at our disposal, we have simply constructed a single transition state for TSDS-1 that gives reasonable values for the total rate coefficient and have confirmed that f is independent of its properties. Table II gives our predictions for f as a function of temperature. The same results are plotted in Fig. 2. The branching fraction increases from a value of f ~- 0.19 at room temperature to a value of f 0.30 at T = 3500 K. The increase in f with temperature is because of the larger potential energy barrier for forming N2 + OH from the HNNO complex, TSDS-2, than for forming N20 + H, TSDS-3. As temperature increases the difference in potential becomes less a factor and f approaches a value determined simply by entropic factors as T goes to infinity. The branching fraction can be accurately represented by the function f = 7.36 • 10-z T ~ in the temperature range covered here. Tunneling has no effect whatsoever on the present predictions for kl, k-z, or f. The internal energy of the HNNO complexes formed from NH + NO causes them to lie at least 22 kcal/mole above the

722

REACTION KINETICS

exaCtcalculations ~

.........

o"N

represented satisfactorily L2'7 by the expression kr = 2.94 x 10 ]4 T - ~ cm3/mole-sec from room temperature to above 3000 K. Combining this with the expression for f given above, we obtain the following expressions for kl and k2: kl = 2.16 • 1013 T -~

~o-

cma/mole-sec

and k2 = (2.94 • 1014 T - ~ - 2.16 • 1013T -~ 9cma/mole_sec lo~o

1~ 2obo 2r,bo Temperature (K)

3o'oo 3 ~

FIG. 2. Branching fraction, f = kl/(kl + k~), for the NH + NO reaction.

barrier to H-atom transfer and 28 above that for H ejection. So, even though the imaginary frequency for the hydrogen transfer exceeds 2000 cm -1, the energies involved are so high above the barrier that tunneling through the barrier is inconsequential. This contrasts with similar calculations for the reaction H + N20 ---> N2 + OH, 2~ where the same HNNO complex and the same barrier are involved, but the energies involved are much lower and tunneling is of paramount importance. The only direct experimental determination o f f of which we are aware is that of Mertens, et al.,7 who give a value o f f = 0.19 --- 0.1 for 2940 K < T < 3040 K. This agrees well with our value of f = 0.291 at 3000 K. Harrison, et al, 6 in their discussion of the present reaction state that "reaction (1) is probably the major ch~mnel, and may be the only channel, for the reaction of NH with NO," even though their attempts to detect OH as a product were unsuccessful. This appears to be an attempt to justify the speculation that the OH produced in experiments on NH2 + NO 1 comes from a secondary reaction of NH with NO. Based on electronic structure calculations similar to those used here, Harrison and Maclagan 19 conclude that the primary products of the NH + NO reaction are N2 + OH "owing to the stability of the HNNO complex." The stability of the HNNO complex does not really play any role in determining the products of the reaction in cases such as this one in which the complex lifetime is much shorter than the time between collisions. Only the transition-state properties determine the branching fraction (see Eqs. (El) and (E2)). Indeed, the calculations of Harrison and Maclagan show that formation of N20 + H from the HNNO complex is favored over formation of N2 + OH by about 10 kcal/mole. The total rate coefficient, kT = kl + k2, may be

We recommend the use of these expressions in modeling. Note that Chemkin-IIzz accepts such sums and differences of rate expressions as input. Up to this point we have not mentioned the third product channel shown in Fig. 1, NH + N O ~

NNH + O.

(U)

These products are the only ones that can be formed on the excited-state 2A" surface. They are also available on the ground-state surface, but on the ground-state surface this channel cannot compete with the N20 + H and N2 + OH channels, which are much more readily accessible energetically. We can make a crude estimate of kt, on the ZA" surface by considering the reverse reaction. If we estimate 3 k-u ~ 5 • 10 13 cm/mole-sec independent of temperature (a value typical of such radical-radical reactions) and calculate k~, from the equilibrium constant, we find that ku is not negligible at high temperature. For example, at T = 3000 K we calculate ku = 4.6 • 1012 cm3/mole-sec whereas k~ = 1.12 • 1013 cm3/mole-sec (calculated from the expression given above). This has the effect of decreasing the overall branching fraction to OH, leading to better agreement between our predictions for the branching fraction and Mertens' experiment. This third channel also can explain the slight increase in the overall rate coefficient with temperature that Mertens observes. Reaction (U) is negligible compared to reactions (1) and (2) below about 2000 K, however.

The NH + Og Reaction Figure 3 shows the potential energy diagram on which our rate Coefficient calculations are based. Reaction can take place either on a singlet surface or a triplet surface. Reaction on the singlet surface leads either to NO + OH or NO2 + H. As shown on the diagram the NO + OH products are strongly favored energetically, and we shall assume that they are the only products (in agreement with experiment), 11 although our rate coefficient can equally

REACTIONS OF NH WITH NO AND O2 well be taken as that for the sum of the two channels. The rate-limiting step in reaction (4) is the formation of the three-membered ring from the initial HNOO adduct, The transition state for this process, TSDS-1, lies slightly higher than the reactants and is extremely tight. Thus we can write the rate coefficient for this reaction as

k4 =

gl(T)

E

hQR(T) ]

Reaction of NH + 0 2 120"

100"

80"

0 E

SO"

(2,] -{- 1)

9fo~F'~ (E,J) exp(~sT)dE,

(E5)

where F~ (E, J)/h is the probability flux per unit energy through TSDS-1 of Fig. 3. The function gl(T) is the electronic degeneracy factor for reaction on the singlet surface, g](T) = 1/9. One must be careful to include a symmetry number of 2 for molecular oxygen in Qn(T), the reactant partition function. Actually, the BAC-MP4 results are not definitive in themselves about the barrier height at TSDS-1; TSDS-1 could be lower in energy than the reactants. However, if this were the case the rate-limiting step would be adduct formation, TSDS-3. In exploring this possibility we found that it was not possible to predict both the absolute value and temperature dependence of k4 at low temperature if the rate-limiting step were adduct formation. This part of the potential is too loose. Even if we arbitrarily construct a transition state that has moments of inertia and vibrational frequencies that are identical to those of the HNOO adduct and use a barrier height that reproduces the room-temperature rate coefficient, the rate coefficient rises much too rapidly with temperature. On the triplet surface the products are HNO + O, and the rate-limiting step is breaking the O-O bond in the HNOO adduct. Thus we can write for k3 the expression, k3 =

723

g:(r) ~] (2/+ 1) hQR(T) j (E6)

where Fr (E, J)/h is the probability flux per unit energy through TSDS-2 of Fig. 3. The function g2(T) is the electronic degeneracy factor for reaction on the triplet surface, g2(T) = 1/3. Our results for ka(T) and k4(T) are given in Table III and compared with experiment in Fig. 4. Up to a temperature of approximately 1800 K reaction on the singlet surface, leading to NO to OH, is dominant. Above T = 1800 K, however, the HNO

O" ~

FIG. 3. Reaction coordinate diagram for the NH + 02 reaction. + O products are dominant. This occurs because TSDS-2 is much looser than TSDS-1, so even though the potential barrier at TSDS-2 is much higher, k3 > k4 at sufficiently high temperature. As can be seen in Fig. 4, our calculations for k4 replicate the experimental results of Hack, et al. 11 at low temperature very accurately. However, our predictions for kr = k3 + k4 at high temperature lie just below the lower error limit of the direct measurements of Mertens, et al. 7 Considerably better agreement with Mertens' experiments is achieved by reducing the barrier height from 10.3 kcal/mole to 8.3 kcal/mole above reactants at TSDS2, an adjustment that is within our normal confidence limits for BAC-MP4 barrier heights. The resuits of this calculation are also shown in Fig. 4. Our predictions lie well below the indirect results from flame experiments of Bian, et al. 12'13 in either case. It is interesting to compare the rate coefficient at low temperature for reaction (4) with the analogous rate coefficient for the isoelectronic 3CH2 + Oz reaction, which involves a similar series of rearrangements. The latter rate coefficient is approximately 2 • 1012 cm3/mole-sec at room temperature, compared with k4 ~ 6 • 109 cm3/mo]e-sec. The 3CH2 + Oz reaction is much faster because of the stronger bond formed in the initial CH2 - 02 adduct. This results in the transition state for the ring closure step in the 3CH2 + 02 reaction lying well below the reactants on the potential energy surface, and thus not limiting the rate coefficient.21 In the 3CH2 + 02 reaction the rate coefficient is determined by the rate of adduct formation; for the NH + 02 reaction the rate coefficient is determined by the ring closure step, which involves a much tighter transition state, and thus there is a much smaller rate coefficient. If we use the adjusted barrier height at TSDS-

724

REACTION KINETICS TABLE III Rate coefficients for the NH + O2 reaction (cm3/mole-sec.)

T(K)

k3

k3

(Eo = 10.3 kcal/mole)

(Eo = 8.3 kcal/mole)

300 400 500 600 750 1000 1500 2000 2500 3300

I0'='-

2.22 1.61 2.24 1.36 8.79 6.39 5.81 2.07 4.90 1.27

: .......:

8ian et eL

• • • • • • x • • •

104 10~ 107 108 l0 s 109 101~ I0 n I0 n 10 ]2

6.34 2.00 1.68 7.26 3.36 1.75 1.14 3.42 7.32 1.73

10"

\

--<..

10~

o

•

• • •

10~ 107 108 10s 109 101~ 101' I0 n 10 n 1012

6.31 1.08 1.51 1.94 2.61 3.84 6.89 1.08 1.55 2.48

x • • • • • •

• • •

109 10 ~~ 101~ 1019 1019 101~ 101~ 10" 10 I1 1011

dynamical methods. For the NH + NO reaction we find that the dominant products are NzO + H over the entire temperature range considered, 300 K < T < 3500 K. The function f = 7.36 • 10 -.9 T~ where f = k]/(kl + kz) and kl and k2 are the rate coefficients for the reactions,

m

!~\i

x • • • • •

k4

.........

10"

E

NH+NO~N2+OH 10'o

10'

---> NzO + H,

i

i

i

5

10

15

i

i

i

i

t

20

25

30

36

4.0

1000Oft(K) FIG. 4. Comparison of theoretical predictions with experiment for the NH + 02 reaction. The rate coefficient kr (adj.) is the total rate coefficient, kr = k3 + k4, for the case in which the barrier height at TSDS-2 is reduced from 10.3 kcal/mole to 8.3 kcal/mole.

2, the following rate expressions represent our predictions accurately from T = 300 K to T = 3300 K: k3 = 4.61 • 10.5 T 2"~exp(-6500/RT)

k4 = 1.28 • 106 T 1"5 exp(- lOO/RT) We recommend the use of these expressions in modeling.

Summary We have treated the reactions of imidogen with nitric oxide and molecular oxygen theoretically using BAC-MP4 potential parameters and statistical

(1) (2)

represents the theoretical branching fraction quite accurately. We recommend the following rate expressions for modeling (cm3/mole-sec.): kl = 2.16 • 1013 T -~

kz = (2.94 x 1014 T - ~

- 2.16 • 1013 T 0.23)

Our prediction for f is in excellent agreement with the experimental result of Mertens, et al, (7/ For the reaction of NH with 02, NH + 02---> H N O + O

(3)

---, NO + OH,

(4)

we find that at low temperature reaction primarily occurs on the singlet surface, leading to NO + OH. For modeling we recommend use of the expression (cm3/mole-sec) k4--- 1.28 • 106 T t5 exp(-lOO/RT). At temperatures above roughly 1500 K reaction on the triplet surface begins to dominate, leading to H N O + O. We recommend the expression (cm3/ mole-sec), k3 = 4.61 • 105 T 2 o exp(-6500/RT).

REACTIONS OF NH WITH NO AND Oz All these results are in good agreement with experinaent.

Acknowledgements We would like to thank Fran Rupley for her help in preparing the figures for this paper. We would also like to thank John Mertens for discussing his experiments with us. John was the first to realize the possible influence of the NNH + O channel in the NH + NO reaction an high temperature. Work sponsored by the United States Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences.

REFERENCES 1. MILLER, J. A..aNt) BOWMAN, C. T.: Prog. Energy Combust, Set. 15, 287 (1989). 2. GLAaBORG, P., DAM-JOHANSEN, K., KEE. R. J. AND MILLER, J. A.: Modeling the Thermal DeNOx Process in Flow Reactors: Nitrous Oxide Formation and Surface Effects, submitted to International Journal of Chemical Kinetics. 3. GORDON, S., MULAC, W. ANt) NANGIA, P.: J. Phys. Chem. 75, 2087 (1971). 4. HANSEN, I., HOINGHAUS, K., ZETSCH, C. AND STUrtL, F.: Chem Phys. Lett. 42, 370 (1976). 5. Cox, J. w . , NELSON, H. H. AND McDoNALD, J. R.: Chem. Phys. 96, 175 (1985). 6. HARRISON, J. A., WHYTE, A. R. AND PHILLIPS, L. F.: Chem. Phys. Lett. 129, 346 (1986). 7. MERTENS, J. D., CHANG, A. Y., HANSON, R. K. AND BOWMAN, C. T.: Int. J. Chem. Kinetics 23, 173 (1991). 8. MEABtJRN, G. W. AND GORDON, S.: J. Phys. Chem. 72, 1592 (1968). 9. ZETSCH, C. AND HANSEN, I.: Ber. Bmlsenges. Phys. Chem. 82, 830 (1978).

725

10. PAGSBERG, P. B., ERIKSEN, J. AND CHBISTENSEN, H. C.: J. Phys. Chem. 83, 582 (1979). 11. HACK, W., KURZKE, H. AND WAGNER, H. GG.: J. Chem. Soc. Faraday Trans. 2 81, 949 (1985). 12. BIAN, J., VANDOOREN, J. AND VAN TIGGELEN, P. J.: Twenty-First Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, p. 953, 1988. 13. BIAN, J., VANDOOREN,J. AND VAN TIGGELEN, P. J.: Twenty-Third Symposimn (International) on Combustion, The Combustion Institute, Pittsburgh, p. 379, 1991. 14. MILLER, J. A., PARt~tSH, C. AND BROWN, N. J.: J. Phys. Chem. 90, 3339 (1986). 15. MILLER, J. A. AND MELIUS, C. F.: Twenty-First Symposimn (International) on Combustion, The Combustion Institute, Pittsburgh, p. 919, 1988. 16. MILLER, J. A. AND MELIUS, C. F.: Twenty-Second Symposium (International) on Combustion, The Combustion Institute, Pittsburgh, p. 1031, 1989. 17. MILLER, J. A. AND MELIUS, C. F.: A Theoretical Analysis of the Reaction Between Hydrogen Atoms and Isocyauic Acid, Int. J. Chem. Kinetics 24,421 (1992). 18. MELIUS, C. F. AND BINKLE'I, J. S,: Twentieth Symposium (International) on Combustion, The Combustion Institute, Pittshurgh, p. 575, 1985. 19. HARRISON, J. A. AND ,~,IAI:LAGAN, R. G. A. R.: J. Chem. Soc. Faraday Trans. 86, 3519 (1990). 20. MARSIIALL, P., FONTIJN, A. AND XIELIUS, C. F.: J. Chem. Phys. 86, 5540 (1987). 21. MILLER. J. A., SMOOKE, _XI. D., GRr:EN. R. M. AND KEE, R. J.: Combust. Sci. Tech. 34. 149 (1983). 22. KEE, R. J., RUPLEY, F. M. ~ND Nllt.t.r:r~, J. A.: Chelnkiu-II: A Fortran Chemical Kinetics Package for the Analysis of Gas-Phase Chemical Kinetics, Sandia National Laboratories Report SAND89-8009 (1989).

COMMENTS Gunnar Nyman, The University of GOteborg, Sweden. You make the rigid rotor harmonic oscillator approximation. Have you made any estimates of the validity of this assumption under tile conditions you have? For the NH + NO reaction, the reduced mass is substantially different between the product channels. Thus, conservation of angular momentum may restrict the available phase space quite differently for the different product channels. Have you considered this?

Author's Reply. No, we have not made any systematic study of the effect of the rigid-rotor/har-

monte-oscillator approxilnation on our results. However, we believe that this is not a very serions concern for the reactions we consider. Possible errors in relative barrier heights potentially are a much more serious problem. Angular momentum is strictly conserved in our calculations. The effect you describe is taken into account to no approximation.

Joseph W Bozzelli, New Jersey Institute of Technology, USA. In the reaction of :~NH + 02 you re-

726

REACTION KINETICS

Joseph W Bozzelli, New Jersey Institute of Technology, USA. In the reaction of NH + 0 2 is it pos-

fer several times to the energy difference between the channels as the controlling parameter even for conditions of very high temperature. I find this somewhat misleading as the channel with the loose transition state (TST) will often dominate over one with a tight TST state but lower Eo, at high temperatures. While the calculations correctly incorporate this; it is the concept of tight or loose TST control at high temperature (high energy in the adduct) over that of energy control that I wish to emphasize. Examples here would be: i. Reaction of the HNO2* isomer to H + NO.2 has a higher barrier, but also a loose TST (equivalent of 100 to 1000 times higher Arrhenius A factor) compared to the tight TST for isomerization to HONO. ii. Isomerization of the 1HNOO adduct to HNO2 via the cyclic HNO2 complex has a tight TST, while dissociation to HNO + O requires a much higher energy, but also has a loose TST.

Author's Reply. Our calculations indicate that the ring closure step is favored over the 1,3 hydrogen shift you describe. More importantly, based on our electronic structure calculations we believe that dissociation of NOOH to NO + OH has a very high potential energy barrier, thus prohibiting this path from being competitive with the ones described in the paper. Regardless of any 1,3 hydrogen shift, however, I do not believe H + NO2 is ever a dominant path at temperatures of interest here.

I would expect the H + NO2 channel from HN02* to be important relative to HONO formation over the temperature range of your calculations and the HNO + O channel to become important at temperatures above 2000 K.

P. Van Tiggelen, Universite Catholique de Louvain, Belgium. The NH + 02 rate coefficients you

Author's Reply. We must not have communicated very well during my presentation. I cannot disagree qualitatively with what you say. I intended to make the point about the energy difference being the dominant effect primarily for the NH + NO reaction. In this case the Nz + OH channel is deficient both "energetically" and "'entropically." Naively, one might expect that at high temperatures the N20 + H channel, being favored entropically, would become even more dominant. However, this is not the case. The branching fraction to the Nz + OH channel actually increases with temperature because the energy difference becomes less important at higher temperatures. With respect to the NH + 02 reaction, the points you raise are discussed somewhat in the paper. The only point with which 1 would argue is that the NO2 + H channel could be significant in the temperature range of interest. NO + OH is favored over NO2 + H on the singlet surface by about 25 keal/mole. That is far too great an energy deficit to make up "entropically" over this temperature range. However, our value of k4 would be valid regardless of the distribution of products on the singlet surface.

sible that ~HNOO isomerization via the NOOH intermediate could have a slightly lower barrier than your calculations show, and thus be an important path for OH + NO production. This would then allow the ~HNO2 isomer to form predominantly H + NO~ resulting from the loose TST for this H + NO2 dissociation versus a tight TST for isomerization to HONO.

calculated are not in agreement with the flame data and, indeed, it seems difficult to reconcile them. However, we need a rate coefficient ten times higher to take into account the amount of NO produced in all NH3 flames we have studied in the past (1,2,3). Would it be possible that vibrationnally excited species could modify the conclusions of your computation?

REFERENCES 1. BIAN, J., VANDOOREN, J. AND VAN TIGGELEN, P. J.: Twenty-First Symposium Combustion 1988 p 953. 2. BIAN, J., VANDOOREN, J. AND VAN TIGGELEN, P. J.: Twenty-Third Symposium Combustion 1990 p 379. 3. VANOOOaEN, J.: Combust. Sci Tech. in press.

Author's Reply. I do not think vibrationally excited species are involved. I believe a different mechanistic interpretation of your flame profiles would lead to different conclusions about NH + 02. I know that the results of your reference (1) are compatible with a mechanism in which NH + 02 plays a relatively minor role in NO formation.