7361
J. Phys. Chem. 1992,96,7361-7367
Radiative Recombination in the Electronic Ground State John R. Barkert Department of Atmospheric, Oceanic, and Space Sciences, Department of Chemistry, and Space Physics Research Luboratory, The University of Michigan, Ann Arbor, Michigan 48109- 2143 (Received: March 31, 1992; In Final Form: May 27, 1992)
Detailed master equation calculations were carried out on radical recombination reactions that produce ethane, propane, n-butane, benzene, and toluene. When infrared emission from the excited species is included, the recombination reactions occur at low and moderate temperatures with near unit efficiency, even in the complete absence of stabilizing collisions. Unimolecular reaction rate calculations that neglect this effect may be seriously in error. It is also shown that the vibrationally excited recombination product is stabilized subsequently in a stepwise fashion (mostly due to emission from the C-H stretch modes) and the population distribution wolves in a characteristic fashion. Because these reactions can occur efficiently without cdlisional stabilization, they may be useful in molecular beams for Preparing highly excited species. In the interstellar medium, the infrared emission from the excited species may contribute to the molecular infrared emission observed in many astronomical objects. A simple model produces results in good agreement with the master equation calculations.
I. Introduction Radiative association involving ions and electronically excited neutrals is well-known experimentally and theoretically.’s2 If the adduct formed by the assoCiation reaction is in an excited electronic state, it may be efficiently stabilized against redissociation by emission of visible or ultraviolet light, as long as the radiative transition is allowed by the dipole selection rules and favorable Franck-Condon factor^.^ Ground electronic state ionic reactions are usually studied under conditions of low densities, where the collision frequency is not suffcient to stabilize the excited adduct formed in the initial association reaction but when infrared emission can do so! Radical-radical recombination reactions, on the other hand, are usually investigated at relatively high pressures, where collisions dominate. Even in experimental methods based on the very low pressure pyrolysis (VLPP) techn i q ~ ethe , ~ frequencies of collisions with the walls are >lo4 s-l, which is much greater than the 10-100.~-~ infrared emission rates typical of most chemical species at moderate excitation energies. The purpose of this paper is to computationally investigate the effects of infrared emission on the rates of radical-radical recombination reactions in low-pressure environments, such as in the interstellar medium (ISM) and in molecular beams. Most chemical schemes designed for the ISM place heavy reliance on ion-molecule reactions? because of their large cross sections and the known properties of radiative a~sociation,~.” but reactions involving neutral species also may be important under some circumstances. For example, Smiths has carried out calculations on radiative association of relatively small neutral free radicals at temperatures characteristic of the ISM and found that the rate coefficients were significant. Also, it has been hypothesi~ed~.’~ that the so-called “unidentified infrared emission bands” (UIR bands), observed in emissions from interstellar dust clouds and other astronomical objects, are emitted by highly vibrationally excited polycyclic aromatic hydrocarbon derivatives (PAHs). Absorption of ultraviolet or visible light followed by radiationless transitions to high vibrational levels of the electronic ground state is a likely excitation mechanism, but recombination of free radicals with hydrogen atoms to produce an excited adduct is also possible.1° The present work shows that the latter process often has essentially unit efficiency at temperatures common in the ISM and in molecular beams. In the present work, several representative reactions involving moderately large species are considered: H + C6H5 C6H6 (R1) CH3 + C ~ H S C ~ H S C H ~ (R2) CH3 + CH3 -w C2H6 (R3) CH3 C2HS C3Hs (R4)
-
2CzH5 n-C4Hlo (R5) Reaction R1 is representative of recombinations of H atoms with aromatic radicals, such as might be found in interstellar clouds that contain PAHs. Similarly, reaction R2 is representative of reactions between alkyl and aromatic radicals. Reactions R3-R5 are important in combustion and pyrolysis systems. Moreover, they are representative of reactions that may be important in interstellar clouds and in the atmospheres of planets and moons.11 As is shown below, infrared radiative stabilization in the electronic ground state significantly enhances the efficiencies of these reactions at low preapure. Furthermore, larger alkanes and aromatia will be produced even more efficiently. In the next section, the theory is briefly reviewed, and the master equation formulation and solution are described. In section 111, the computational results are presented along with a simple model; conclusions are reached in section IV.
II. Theory The standard theory of recombination reaction^'^-*^ is based on the Lindemann-Christiansen mechanism: A + B C(E) (1) C(E) A + B (-1) C(E) M C(E’) M (2) where A and B are the reactants and C(E) is the association complex, which is formed initially with excitation energy E. If the average amount of energy transferred in a collision is sufficiently large, the redissociation of complex C(E) is effectively stopped, because the rate constant k-l(E)of reaction -1 is a strong function of energy. In the absence of collisions, this mechanism predicts that C(E) will always redissociate. Stabilization of the complex by photon emission is introduced by extending the Lindemann scheme: C(E) C(E-hv) + hv (3) Here hv designates a photon (and its energy) emitted spontaneously by the highly excited complex. The radiative recombination process and subsequent stabilization are shown schematically in Figure 1. Reactions 1-3 are combined by applying the pseudo-steady-state assumption to complex C(E) to obtain the following expressions:
+
--
+
+
-
+
+
t Internet:
+
koo(E) =
k l A3
(k-i
usergblg~um.cc.umich.cdu.
0022-3654/92/2096-7361$03.00/0
0 1992 American Chemical Society
+ -43)
7362 The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 A
I
+ B -* C(E) + C(E') + hvj,
I
.A. /
Barker can be neglected, except, perhaps, in the case of reaction R3.I4 Smiths found that tunneling increased the recombination rate constants at very low temperatures (- 10 K)by only about a factor of 2. The energy-dependent emission rate coefficient is given
I
-
Figwe 1. Schematic of the infrared radiative recombination process, where the excited species C(E) formed in distributionATJ?) is stabilized by emission of a single infrared photon, followed by subsequent deactivation by means of emission of successive photons. RABis the reaction coordinate, E is the internal energy, and Eo is the threshold energy for reaction.
where k l , k+ and k2are the rate constants for the corresponding reactions and A3 is the energy-dependent rate coefficient for spontaneous emission by the complex. Equations 4a-4d give the general bimolecular recombination rate amstant, its low-pressure l i t , its mepressure limit (complete absence of colliisions), and its high-pressure limit, respectively. If spontaneous emission is neglected, the equations are the same as in conventional unimolecular rate theory. For unimolecular reactions, the pressure falloff is conveniently expressed by the ratio k/k,, which applies to both the dissociation and the recombination reactions. In the present work, this ratio is also convenient for expressing the efficiency of radiative recombination, because the ratio does not require knowledge of the temperature dependence of the high-pressure limiting rate constant, which is controversial at intermediate temperatures and unknown at low temperature^.'^ Equations 4c and 4d must be averaged over the energy distribution of the nascent species to obtain the efficiency of radiative stabilization in the complete absence of stabilizing collisions:
where AT,E) is the normalized energy distribution of nascent species formed at temperature T, and the energy dependences of k-,(E)and A3(E)are noted explicitly. For association reactions, the distribution AT,E) is the chemical activation distribution function,'2-'s which is given by AT31 =
k-@)
s,,k-l(E)
P,(E)exp(-E/W
(6) &(E) exp(-E/W d E
where Eo is the threshold energy for reaction, p,(E) is the density of states for s degrees of freedom in complex C, and the denominator is proportional to the high-pressure rate constant for the dissociation. Rate constant k-,(E)is given by RRKM theory or some other statistical model. To obtain the absolute rate constant for the radiative assoCiation reaction at any temperature, the k:/k, ratio from eq 5 is multiplied by the high-pressure limiting rate constant. For moderately large species angular momentum effects and quantum mechanical tunneling can be safely neglected to a first approximation,14but these processes must be considered explicitly for smaller species, especially at low temperatures.68 As is pointed out in treatises on unimolecular reactions, the effect of angular momentum conservation is to increase the average reaction rate coefficient at low p r e s s ~ r e s . l ~The - ~ ~ effects of angular momentum conservation are small for most of the systems considered here and
where A,'*o,is the Einstein coefficient for the u = 0 u = 1 vibrational transition of the ith oscillator and pPl(E - uihvi) is the density of states for the s - 1 degrees of freedom that remain after omitting the emitting mode and the energy it contains. A discussion of the derivation and experimental tests of eq 7 can be found elsewhere.Is It is worth noting that several experimental tests have verified the accuracy of eq 7.'* It is noteworthy that the observed infrared emission near 3.3 Fm from benzene excited to -4OOOO cm-l shows anharmonically shifted hu = -1 transition featura with intensities in excellent agreement with those predicted by eq 7.19 Equation 5 is based on the assumption that emission of a photon of any size is sufficient to stop reaction -1 and stabilize the complex. In many systems this approximation may be acceptable, but excited molecules emit infrared photons at many wavelengths and if the temperature is high enough, reaction -1 is not negligible after only a single low-energy photon has been emitted. When multiple reaction paths with differing threshold energies must be included, eq 5 can be generalized, but it cannot account properly for the reactions of the chemically activated species. For these reasons, a master equation formulation is preferred to the a p proximate eq 5. Furthermore, a master equation treatment allows investigation of the deactivation of the excited molecule at energies lower than the lowest reaction threshold. The infrared emission spectrum produced concurrently with the deactivation process is of interest, because it may be related to the UIR bands.I9 For high vibrational energies, the state densities are very large and the highly excited species may be found at virtually any energy. Assuming a continuum of energies, the master equation consists of the infinite set of coupled differential equations describing the rates of change of the population at every energy. For species N at energy E and time t, the rate of change of concentration can be written
where Pc(EB?is the probability of the collisional transition from energy E'to energy E, k, is the bimolecular collision rate constant, [MI is the concentration of colliders, and the other terms have been defied above. The fvst term describes production of N(E) by collisional transitions, the second term accounts for production of N(E) by the radiative deactivation of more highly excited species, the third and fourth terms refer to collisional and radiative deactivation of N(E), and the last term accounts for chemical reactions. A common strategy for solving the master equation is to use yenergy graining", in which the energy scale is divided into increments (grains) and the infinite set of coupled differential equations is thence reduced to a set of finite difference equations, which is solved numerically by one of several standard t e c h n i q ~ . ' ~ An alternative approach is to use stochastic techniques to solve the continuum master equation.20,2' The accuracy of the finite difference approach depends on the grain size, while the precision of the stochastic approach depends on the number of stochastic trials. Most features of the master equation formulation used in the present work have been described previously:' but the computer code has been enhanced in several ways for the present application.
Radiative Recombination in the Electronic Ground State
The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 7363
Briefly, the master equation is solved by the Gillespie exact s t e chastic method,2owhich is exact in the l i t of an infinite number of stochastic trials. State counting m e t h o d ~ ~(grain ~ , ~ ’ size of 25 cm-I) are used to obtain sums and densities of states, which are used to calculate RRKM specific rate constants (for up to three simultaneous reaction channels), the infrared emission rates according to eq 7, and the chemical activation energy distribution functions according to eq 6. When collisions are considered, detailed balance and microscopic reversibility are obeyed and the collision stepsize distribution function can be selected from among several idealized models. There is no explicit energy graining in the master equation formulation used here, because all energydependent molecular properties are obtained by interpolation. The results of the calculations are “binned” in various ways for convenience, but the binning does not affect the accuracy of the master equation solution. The stochastic method used here is not the most computationally efficient technique for the present problem, but the code is well-tested and required relatively little revision for the present application. It would be desirable and in principle straightforward to incorporate infrared emission deactivation into more conventional numerical codes, which also include provision for angular momentum conservation. The RRKM rate constants for the dissociation reactions were calculated based on molecular models consisting of collections of harmonic oscillators and free rotors, as appropriate, and the models used in the present work are described in the Appendix. In principle, models consisting of nonseparable degrees of freedom could also be used,at some sacrifice of convenience.21 According to RRKM unimolecular rate t h e ~ r y , I the ~ - ~specific ~ rate constant is given by
Infrared Emission from Benzene 20
Normal Modes
5
15
5
10
5
0
10000
0
20000
30000
40000
50000
Vibrational Energy (cm-1) Figure 2. Energy-dependent infrared emission rate cocfficients for exbenzene. 65000 Chemical Activation Distribution 60000
40000 (9) 35000
where P ( E ) is the sum of states of the transition state and I and I’ are the moments of inertia of the molecule and the transition state, respectively. The reaction path degeneracy (g,) can be considered separately or it can be incorporated into the sums and densities of states.14 For many purposes, the full RRKM rate expression is not needed and the inverse Laplace transform app r o ~ i m a t i o nis~ sufficient: ~
where A, and E, are the Arrhenius parameters for the thermal unimolecular rate constant for dissociation at the high pressure limit. Equation 10 would be exact if the high-pressure rate constant obeyed the Arrhenius expression for all temperatures. Because the Arrhenius equation is only approximately obeyed, eq 10 is only approximate, but it has the advantage that specification of a transition state is not required.
III. R d Q .nd Discussion Reactions Rl-RS are considered in the present work. Reaction R1 was considered in more detail than the others, because of its immediate relevance to recent work in this laboratory related to PAHs10-19s26 and to energy transfer involving ar~matics.~’ For reactions R1 and R3, spontaneous emission Einstein coefficients were calculated from infrared transition intensities taken from the literature.28 For the other species, the infrared transition intensities were estimated using Wexler’s tab~lations.2~ In all cases, emission from the C-H stretch modes dominates at energies near the reaction thresholds, largely because the spontaneous emission Einstein coefficients depend on the square of the vibrational frequency. Although some lower frequency modes have significant intensities, their emission rates are lower than those of the C-H stretch modes, because of the 2 factor. At lower energies, the density of states ratios in eq 7 become smaller for the high-frequency modes and the low-frequency modes then dominate the emission, as shown in Figure 2. The vibrational assignments, Einstein coefficients, and unimolecular reaction parameters are given in the Appendix.
i
0
O.ooo4
0.0008
0.0012
0.0016
0.002
f(T,E) (units: llcm-1)
Figure 3. Nascent population distributions as a function of temperature for reaction 1.
Reaction R1 is characterized by a strong C-H bond and moderate emission rates,mostly from the C-H stretch modes. The nascent excited molecule is formed with an energy somewhat in excess of the reaction threshold, as is shown for several temperatures in Figure 3. The rate constant for dissociation increases nearly exponentially with energy above the reaction threshold, while the infrared emission rate increases approximately linearly with total energy. Thus, if the energy is high enough, the excited molecule will r e d i i a t e with a lifetime shorter than the infrared emission lifetime. Otherwise, emission will stabilize the molecule, which subsequently is thermalized by infrared emission. At high temperatures, redissociation dominates, because most nascent molecules are formed with relatively high energies, but at moderate and low temperatures, many nascent molecules are formed with energies just above the reaction threshold and infrared deactivation is faster than dissociation. At sufficiently high temperatures, the nascent distribution is highly excited and emission of a single photon is not sufficient to stabilize the molecule. Under these conditions, the extended Lindemann mechanism is no longer an adequate description and a master equation must be used. The surprising importance of infrared radiative stabilization in reaction R1 is shown in Figure 4, where it is clear that koo/k, 1 0.5 for temperatures less than -500 K. This important result shows that there is little pressure falloff for reaction Rl at low and moderate temperatures. Computational tests on reaction R1 showed that k:/k- is not very sensitive to the choice of reaction threshold energies. For higher threshold energies, the densities of states arc greater, leading to lower rate constants for dissociation, but within the 1oooCm-I range of uncertainties of the C-H bond strengths?O there is little change in the radiative recombination efficiency. Substitution of the approximate inverse Laplace transform expression for the specific rate constant reduced the calculated k:/k- by only -3096
-
7364 The Journal of Physical Chemistry, Vol. 96, No. 18, 1992
Barker because toluene emits somewhat more strongly than benzene and because it has more degrees of freedom (including a free rotor) and thus a slower rate constant for dissociation, even though the C-C bond strength is less than that of the C-H bond. Toluene also has a second pathway available for decomposition:
ir Radiative Recombination I
0.8
C7Hs 0.6
ko, I k,
C7H7 + H
(R6)
This reaction is more endothermic than reaction -R2, but the threshold energies are not greatly different and the upper pathway is accessible to a high-energy fraction of the nascent toluene produced by reaction R2. At 1100 K,for example, 17% of the toluene redissociation proceeds according to reaction R6, rather than reaction -R2. An important conclusion to be drawn from the results obtained for benzene and toluene is that recombination reactions to produce larger spacia with the same bond energies will p r d even more efficiently, because the rates of the dissociation reactions are slower and the infrared emission rates are faster for larger species. At 10-100 K,temperatures common in interstellar clouds, benzene and toluene are formed with virtually unit efficiency. This means that recombination reactions of H atoms with large PAH free radicals will proceed with effectively unit efficiency at relatively high temperatures. Moreover, such reactions should proceed efficiently in molecular beams and free jets, potentially opening a new avenue to producing highly excited species in laboratory studies. Reactions R3-R5 proceed with efficiencies that depend on the size of the nascent molecule. This result is, as mentioned above, a direct consequence of the competition between infrared emission stabilizationand the dissociation reaction. The C-C bond energies for all three species are similar and hence the reaction threshold energies are practically the same. Moreover the infrared emission rates for each species are also similar. The major variable is the molecular size,which reduces the unimolecular rate constants due to the density of states factor in the denominators of eqs 9 and 10. As in the dissociation of excited toluene, n-butane can dissociate by more than one p a t h ~ a y , ~including ' . ~ ~ reactions -R5 and R7:
-
0.4
0.2 n "
+
o
200
400
aoo
600
io00
1200
Temperature
Figure 4. Efficiency of infrared radiative recombination as a function of temperature.
40000
30000 r
5
v
2.
F 20000 a c w
-
10000
n-C4Hlo CH3 + n-C3H7
0.0
0.2
0.4
0.6
08
10
Time (s) Figure 5. Evolution of the population distribution for excited benzene formed in reaction R1 at 200 K. Note the 'stepwise" character of the process at early times. Energy expressed in cm-*,population expressed in parts per IO'; contours at 1000,2000,3000,4000, 5000, 6000,8000, 1oo00,and 15000 parts per lo'.
(at 600 K). Therefore, the calculated result appears to be robust. Because most infrared emission from excited benzene initially formed in reaction R1 occurs with frequency near 3050 cm-I, the excited benzene is deactivated in an almost stepwise fashion at the beginning of the decay, as shown in Figure 5. The population distribution initially localized near 4OOOO cm-l is gradually depleted, while that near 37000 cm-' grows and then decays. The same successive behavior is apparent near 34 OOO and near 3 1 OOO cm-l. The steps are obscured at later timea because the population distribution spreads due to contributions from infrared emissions at frequencies other than 3050 cm-I, as indicated in Figure 2. Eventually, the population distribution collapses into the narrow 200 K Boltzmann distribution, when thermalization is complete. At higher temperatures, the nascent population distribution is broader, which tends to obscure the stepwise nature of the deactivation, but the emission spectrum of excited benzene shows the greatest energy flux near 3050 cm-I, with only minor contributions at other vibrational frequencies. The other reactions investigated (see Figure 4) show the same qualitative behavior as reaction R1. The formation of toluene in reaction R2 occurs with greater efficiency than reaction R1,
(R7)
Because this reaction pathway has the same assumed Arrhenius parameters3I as reaction -R5, the redissociation produces one methyl and one n-propyl radical for each pair of ethyl radicals produced. Several conclusions can be drawn from the efficiencies of reactions R3-R5. First, even ethane can be produced relatively efficiently at temperatures common in the ISM and in molecular beams. The present calculation utilized a model (see Appendix) that included vibrations and a free intemal rotor, along with one active external rotation, but it was not carefully optimized and angular momentum constraint^'^ were not included. Thus, the results are only semiquantitative,but they show efficiencies greater than 10% for radiative recombination at temperatures as high as 50 K (a more accurate model will show the same qualitative behavior, but the results obtained by Smiths indicate the more accurate model may predict a lower efficiency). Second, alkyl radical recombination reactions to produce propane, butane, and larger alkanes should exhibit little pressure falloff when investigated at room temperature. In a recent study, Benson et al.33investigated the disproportionation and recombination of ethyl radicals (reaction R5) in a low-pressure reactor and observed anomalously low yields of n-butane. One potential concern was that pressure falloff may have reduced the yields. The present results using a statistical model show that this is not an important concern, because k,,O/k, = 0.7 at 300 K,even with no collisions, and under the actual experimental conditions collisions are rapid and the calculated k,,/k, 1.0 (for a statistical model). Thus, the explanation for the anomalously low n-butane yields must be found elsewhere. Benson et al. interpreted their results as evidence for nonstatistical behavior in reaction R5. This interpretation is controversial, because the conventional view of such reaction^^^-'^ is that they
-
The Journal of Physical Chemistry, Vol. 96, No. 18, 1992 7365
Radiative Recombination in the Electronic Ground State
:, Infrared Radiative Recombination H + C,H,
\
,1
-
24'
I
'8t '
10'-
H + C,H, (+ M) + C,H, (+ M)
I 1
2° I
i
I
,
700 K
J
TI'
Infrared Emission Neglected ,,,,,,
'0;Ol
,,
10'
,
,,,,,,,
,
,
,
~
, , , , , , , ,
,
,
,
1
100
102
Argon Pressure (torr) Figure 6. Pressure falloff (argon collider, 700 K) for reaction R1. The effect of infrared emission deactivation is shown (the random fluctuations and 20 error bars reflect statistical uncertainties in the stochastic results).
can be described accurately by statistical models. The rates of radiative stabilization are so slow that its effects are not observable, except at low pressures. For example, if the radiative rate is 10 s-l, the pressure must be lo4 Torr for radiative stabilization to dominate. This pressure is some 3-6 powers of ten lower than the usual pressures employed in experiments on recombination of neutrals. For, the larger species, moreover, radiative stabilization is more efficient, but pressure falloff is reduced. This combination of factors conspires in typical experiments to conceal the effects of the radiative stabilization for neutral species, although it is well-known in ion-molecule association reaction^.^.^^^ For comparison, calculated pressure falloff curves for reaction R1 are presented in Figure 6 for cases with and without infrared emission stabilization. At low pressures, the two cases diverge greatly. To make simple estimates of the efficiency of radiative recombination, the Whitten-Rabinovitch approximatiod4for sums and densities of states can be used with eqs 5 and 6. For simplicity and because the infrared emission rate is only a weak function of temperature, the emission rate coefficient may be assumed to be constant and equal to its value near the reaction threshold. Results from this approximate method with two assumed infrared emission rates are shown in Figure 7 for reaction R1. For best accuracy, this approximate method requires the validity of the Whitten-Rabinovitch approximation, the assumption that deactivation is complete when one photon of any energy is emitted, and that a single reaction channel is dominant. The second assumption breaks down at high energies, where emission of several photons is needed to deactivate the molecule and the simple method overestimates the efficiency of infrared emission deactivation. This effect is particularly evident for the total infrared emission rate, and a slightly better approximation is to use just the emission rate corresponding to the C-H stretch modes, since they have higher frequencies and therefore deactivate the molecule more effectively when only a single photon is emitted. The master equation treatment includes all of these effects in the proper manner. Better approximations can be formulated for the simple model, but they hardly seem justified. Dunbar has obtained an even simpler empirical expression which may be useful for order-of-magnitude estimate^.^
-
-
IV. Conclusions The most important conclusion reached in the present work is that infrared emission from the nascent species is very efficient in deactivating and stabilizing the adduct in recombination reactions at low and moderate temperatures. At room temperature and below, this process can be neglected only in the recombination of methyl radicals, among the reactions considered here. Because the radiative stabilization is so efficient, stabilization by collisions is not necessary and pressure falloff becomes negligible. Thus, unimolecular reaction rate calculations that neglect radiative
0.4
0
1
,/All
',
"
300
"
~ 450
'
"
600
"
"
" 750
+ C,H,*
-1
Simple Modal Modes ,C-ti Stretch, Only
~
'
900
"
~
1050
1200
Temperature Figure 7. Comparison of the simple model (which uses the WhittcnRabinovitch approximation) with master equation calculations for reaction R1. Two different assumptions about infrared emission rate are compared.
stabilization may be seriously in error at low and moderate temperatures. These conclusions will have relatively little effect on laboratory investigations that use conventional and VLPP experiments, because pressures are sufficiently high so that collisional stabilization always dominates. In low-pressure environments, however, radiative stabilization is dominant and rapid enough so that there is very little pressure falloff. This means that recombination reactions of the type considered here will occur efficiently in molecular beams, creating possibilities for new laboratory techniques of preparing highly excited molecules. These reactions also will occur efficiently in the interstellar medium, where recombination reactions of neutral species may make greater contributions than are currently recognized. Acknowledgment. This work was funded in part by the Department of Energy, Office of Basic Energy Sciences. Thanks go to J. D. Brenner for a careful reading of the manuscript and for interesting discussions and to R. C. Dunbar for discussions and for copies of papers prior to publication. APpedX The parameters used in the master equation calculations are given in this Appendix. In all cam, exact state countsz2were used to obtain vibrational sums and densities of states. When free rotations were involved, Troe's modifi~ation~~ of the Stein-Rabinovitch22exact count method was used. For reactions 1 and 3, transition states were defined and the full RRKM theory was used, while for the other reactions the inverse Laplace k(E) was employed. The Einstein coefficients for spontaneous emission were estimated by using Wexler's tablesz9of infrared transition strengths, except in the cases of excited benzene and ethane, where literature values were used. Reaction R1: H C f i C&. The vibrational assignment for benzene was taken from Goodman et al.?5 which is similar to that given by Shiman~uchi.~~ The transition state was assigned by designating a C-H stretch as the reaction coordinate and then adjusting the other frequencies according to Benson's rules?' The lower frequency modes were adjusted downward still further in order to approximately reproduce the high-pressure limiting d e composition rate constants reported by Kiefer et al.38and by Hsu et al.,39which are in good agreement with each other and are in fair agreement with those reported by Rao and Skinner.40 The product of the reaction path degeneracy and the moments of inertia was taken from Rao and Skinner and is assumed to be given by g,.I*/Z = 6.6. The critical energy was assumed to be Eo = 39 175 cm-I. The resulting model gives k, = 2.3 X 10'' exp(-59764/7') s-l for 1700 K 5 T I2200 K. Benzene Vibrational Frequencies (multiplicities in parentheses): 3073.94, 3064.37 (2), 3057, 3056.70 (2), 1600.98 (2), 1483.99
+
-
7366 The Journal of Physical Chemistry, Vol. 96, No. 18. 1992
(2), 1350, 1309.40, 1177.78 (2), 1149.70, 1038.27 (2), 1010, 993.07, 990, 967 (2), 847.10 (2), 707, 673.97, 608.13 (2), 398 (2). Transition State Vibrational Frequencies: 3074, 3064, 3057 (3). laoO(2), 1484 (2), 1350, 1309, 1178, 1150,1038, 1010,993, 990, 967, 847, 670, 608 (2), 500, 487, 380 (2), 350, 200 (2). Collision parameter^:^^ Benzene deactivation by argon collider gas; k, = 4.07 X 10-I0cm3S-I; (AE)d,,/cm-l = 17.8 + 5.82 X lW3E- 9.91 X lo4@, where E is the microcanonicalvibrational energy (in cm-I). The Einstein coefficients (multiplied by the degeneracy) for spontaneous emissionZB are given in the following (mode degeneracies in parentheses):
-
High-pressure Arrhenius parameters: C3H8 CZH5 + CH3
-
A , = 5 x 1015 s-1;
C3H8
E, = 29258 cm-' (ref 31)
i-C3H7+ H
A, = 2 x 1017 s-1;
C3Hs
-+
E, = 34771 cm-l (estimated)
n-C3H7 + H
A, = 8 X lOI7 5-I;
E, = 35751 cm-' (estimated)
The Einstein coefficients for spontaneous emissionZ9are given in the following (total strength for each band):
frequency (cm-l)
A'*O (s-l)
frwuencv (cm-l)
Also (s-I)
3064.4 (2) 1484.0(2) 1038.3 (2) 674.0 (1)
72.46 3.69 1.21 5.097
2962 1462 1378 748
286.1 7.3 2.2 0.16
+
-
Reactioa R2: CH3 C a s C W 3 . Toluene vibrational frequencies: 3067,3056 (2), 3039 (2), 2933 (2), 2921,1611,1585, 1500,1463,1453,1436,1384,1330,1278,1212,1178,1155,1083,
1043,1030,1004,980 (2), 964,894,843,786,730,695,623,521, 462, 405, 341, 205. Free rotor reduced moment of inertia: I f , = 3.139 amu AZ (1-fold barrier). High-pressure Arrhenius parameters: C6H5CH3 C6H5 CH3
-
+
A, = 8.9 X 10l2 s-l;
C6HsCH3
Barker
+
E, = 25 392 cm-' (ref 42)
C~HJCH +~H
A, = 1.8 X 10l6 s-I;
E, = 32 100 cm-' (ref 43)
The Einstein coefficients for spontaneous emissionZ9are given in the following (total strength for each band): frequency (cm-I) A'-o (d) 3056 2900 1370 760 700
-
68.6 58.2 0.56 5.7 1.3
Reaction R 3 CH3 + CH3 C2&. Ethane vibrational freq ~ e n c i e s :2985 ~ ~ (2), 2969 (2), 2954,2896, 1469 (2), 1468 (2), 1388, 1379, 1190 (2), 995, 822 (2). Free rotor reduced moment of inertia:I4 Zfr = 1.6 amu A2(3-fold barrier). Transition-state frequencies: 2985 (2), 2969 (2), 2954,2896, 1469 (2), 1468 (2), 1388, 1379, 220 (2), 135 (2). Free rotor reduced moment of inertia:14 Zfr = 1.78 amu A2 (3-fold barrier). Active external moment of inertia:I4 I = 7.13 amu A2. Threshold energy:14 Eo = 30640 cm-I. gJ*/Z = 6.2 High-pressure rate constant calculated with the model: k, = 1.9 X lo1' exp(-46825/T) s-l for 1000 K 5 T 5 2200 K The Einstein coefficients for spontaneous emission29are given in the following (total strength for each band): freauencv (cm-l)
2968 1460 1380 747
A'qo (s-I)
-
372.8 8.52 2.69 0.164
Reaction R4: CHa + CzHd CJ-18. Propane:36 2977,2973, 2968 (2), 2967,2962,2887 (2), 1476, 1472, 1464, 1462, 1451, 1392, 1378, 1338, 1278, 1192, 1158, 1054,940,922, 869,748, 369, 268, 216.
-
Reaction RS: ZC2H5 a-CJIIw Butane (gauche):36 2968 (4), 2920 (2), 2870 (2), 2860 (2). 1460 (4), 1450 (2), 1380 (2), 1370,1350,1281,1233,1168,1133,1077,980 (2), 955,827,788, 747, 469, 320, 201, 197, 101. High-pressure Arrhenius parameter^:^^ C4H10
-
2C2HS
A, = 2 x 10'6
C4HI0
5-1;
E, = 28422 cm-I
n-C3H7+ CH3
A, = 2 x 10'6 s-1;
E, = 28422 cm-l
The Einstein coefficients for spontaneous emission29are given in the following (total strength for each band): frequency (cm-I)
A1v0(s-I)
2968 1460 1380 747
372.8 8.5 2.7 0.16
Resbtry No. Ethane, 74-84-0;propane, 74-98-6;n-butane, 106-97-8; benzene, 71-43-2; toluene, 108-88-3.
References and Notes (1) Smith, I. W. M. Kinetics und Dynumics of Elementury Gar Reactions; Butterworth: Boston, 1980;p 224. (2)Duley, W. W.; Williams, D. A. Interstellar Chemistry; Academic Press: London, 1984. (3) Herbst, E.;Bates, D. R. Astrophys. J. 1988,329,410and references therein. (4)Dunbar, R.C.Int. J . Mars Spectrom. Ion Proc. 1983,54,109; Chem. J. Am. Chem. SOC.1988,110,3080;J. Am. Chem. Phys. Leii. 1988,151,128; SOC.1989,I 11,5572,6497;J . Chem. Phys. 1909,90,7369;J . Chem. Phys. 1989,91,6080;J . Phys. Chem. 1989,93,7785;Int. J . Muss Specirom. Ion Prm. 1990,100, 423 and references therein. (5) Spokes,G. N.; Golden, D. M.; Benson, S.W. Angew. Chem., I n i . Ed. Engl. 1973, 12,534. (6)Herbst, E.; Dunbar, R. C. Mon. Nor. R. Asiron. SOC.1991,253,341. (7) Bates, D. R.;Herbst, E. In Rate Cwf/icienis in Asircchemistry; Millar, T. J., Williams, D. A., Eds.; Kluwer: Dordrecht, 1988;p 17 and references therein. (8) Smith, I. W. M. Chem. Phys. 1989,131,391. (9) Leger, A.; Puget, J. L. Asrron. Asrrophys. 1984,137,L5. Puget, L. J.; Leger, A. Ann. Rev. Astron. Asirophys. 1989,27, 161 and references therein. (10)Allamandola, L. J.; Tielens, A. G. G. M.;Barker, J. R. Asirophys. J . (Lett.) 1985,290,L25. Barker, J. R.; Allamandola, L. J.; Tielens, A. G. G. M. Astrophys. J. (Lett.) 1987,315,L61;Astrophys. J. Suppl. Ser. 1989, 71, 733 and references therein. (1 1) Atreya, S. K.; Sandel, 8. R.; Romani, P. N. In Uranus; Bergstralh, J. T., Miner, E. D., Matthews, M. S.,Eds.; University of Arizona Press: Tucson, 1991;p 110. (12) Robinson, P. J.; Holbrook, K. A. Unimolecular Reactions; WileyInterscience: London, 1972. (13) Forst, W. Theory of UnimoleculurReuctions; Academic Press: New York, 1973. (14) Gilbert, R. G.; Smith, S . C. Theory of Unimoleculur und Recombinution Reactions; Blackwell: Oxford, 1990. (15) Rabinovitch, B. S.;Diesen, R. W. J. Chem. Phys. 1959,30, 735. (16) Herzberg, G. Infrared and Ramon Spectru; Van Nostrand Princeton, 1945.
7367
J. Phys. Chem. 1992, 96, 7367-7375 (17) Durana, J. F.; McDonald, J. D. J. Chem. Phys. 1977, 64, 2518. (18) Shi, J.; Bernfeld, D.; Barker, J. R. J. Chem. Phys. 1988, 88, 6211. in press. (19) Brenner, J. D.; Barker, J. R. Astrophys. J . (Le??.), (20) Gillespie, D.T. J . Comput. Phys. 1976,22,403; J. Phys. 1977,81, 2340, J. Comput. Phys. 1978, 28, 395. (21) Barker, J. R. Chem. Phys. 1983, 77,201. Shi, J.; Barker, J. R. In?. J. Chem. Kinet. 1990, 22, 187. (22) Stein, S. E.; Rabinovitch, B. S . J . Chem. Phys. 1973, 58, 2438. (23) Astholz, D. C.; Troe, J.; Wieters, W. J. Chem. Phys. 1979, 70,5107. (24) Barker, J. R. J . Phys. Chem. 1987,91,3849. Toselli, B. M.; Barker, J. R. Chem. Phys. Lert. 1989,159,499. Toselli, B. M.; Barker, J. R. J. Phys. Chem. 1989, 93,6578. (25) Forst, W. J . Phys. Chem. 1972, 76, 342. (26) Cherchneff, I.; Barker, J. R. Asrrophys. J . (Lert.) 1989, 341, L21. Cherchneff, I.; Barker, J. R.; Tielens, A. G. G.M.Astrophys. J . 1991, 377, 541; Astrophys. J., in press. (27) Yerram, M. L.; Brenner, J. D.; King, K. D.; Barker, J. R. J . Phys. Chem. 1990,94,6341. Toselli, B. M.; Barker, J. R. Chem. Phys. Lett. 1990, 174, 304. Toselli, B. M.; Brenner, J. D.; Yerram, M. L.; Chin, W. E.; King, K. D.; Barker, J. R. J . Phys. Chem. 1991.95, 176. Toselli, B. M.; Barker, J. R. J. Chem. Phys. 1991, 95, 8108. (28) Bishop, D. M.; Cheung, L. M. J . Phys. Chem. Ref Data 1982, 11, 120. (29) Wexler, A. S . Appl. Specrrosc. Rev. 1967, 1, 29.
(30) McMillen, D. F.; Golden, D. M. Annu. Rev. Phys. Chcm. 1982,33, 493. (31) Warnatz, J. In Combustion Chemistry; Gardiner, W. C., Jr., Ed.; Springer-Verlag: Berlin, 1984; p 197. (32) Tsan& W.; Hampson, R. F. J. Phys. Chem.Ref Data 1986,15,1087. (33) Benson, S.W.;Dobis, 0.;Gonzalez, A. C. J. Phys. Chem. 1991,95, 8423. (34) Whitten, G. Z.; Rabinovitch, B. S . J . Chem. Phys. 1964, 41, 1883. (35) Goodman, L.; Ozkabak, A. G.; Thakur, S . N. J. Phys. Chem. 1991, 95. 9044. - (36) Shimanouchi, T. Natl. Stand. Ref Data Ser., Natl. Bur. Stand. (US.)1972, No. 39. (37) Benson, S . W. Thennochemical Kinetics,2nd ed.;Wiley: New York, 1976. (38) Kiefer, J. H.; Mika,L.J.; Patel, M. R.; Wei, H . 4 . J. Phys. Chcm. 1985, 89, 2013. (39) Hsu, D. S.Y.; Lin, C. Y.; Lin, M. C. Symp. (Int.) Combusr. [Proc.] 1985, 20, 623. (40)Rao, V. S.;Skinner, G. B. J . Phys. Chem. 1988.92, 2442. (41) Toselli, B. M.; Barker, J. R. J. Phys. Chem., in press. (42) P a ” u k k a l a , K.M.; Kern, R. D.; Patcl, M. R.; Wei, H. C.; Kiefer, J. K. J . Phys. Chem. 1987, 91, 2148. (43) Brand, U.; Hippla, H.; Lindemann, L.; Troe, J. J. Phys. Chcm. 1990, 94, 6305.
-.
Thermal Decomposition of 5-Methylisoxazoie. Experimental and Modeling Study Assa Lifshitz* and Dror Wohlfeilert Department of Physical Chemistry, The Hebrew University, Jerusalem 91904, Israel (Received: February 18, 1992; In Final Form: May 14, 1992)
The thermal decomposition of 5-methylisoxazole was studied behind reflected shocks in a pressurized driver single-pulse shock tube over the temperature range 85Ck1075 K and overall densities of -2.5 X lV5 mol/cm3. Propionitrile and carbon monoxide are the major decomposition products, followed by ethane, methane, acetonitrile, and hydrogen cyanide. There is no effect of large quantities of toluene ([toluene]/[5-methylisoxazole] 10) on the concentrationsof propionitrile and acetonitrile,indicating that no radical chains are involved in their production. It is suggested that the formation of C2HSCN and CO in 5-methylisoxazole involves an N-O bond cleavage in the 1,2-position, a methyl group shift from position 5 to 4, and a rupture of the C(4)-C(S) bond with the removal of carbon monoxide from the ring: 5,m-isox CzH5CN+ CO (1). In contradiction to findings in isoxazole, this process requires a very large N-O bond stretch which results in a very loose transition state corresponding to a biradical mechanism. The rate constant for this reaction is kl = exp(-7O X l @ / R T )s-* where R is expressed in units of cal/(K mol). The presence of ethane and methane in the postshock mixtures indicates the presence of methyl radicals in the hot phase. It is suggested that the formation of methyl radicals involves the same N-O bond cleavage as in reaction 1 but without the methyl group shift: 5,m-isox CH2CN’ CH3CO’ (2) followed by CH3CO’ CH; + CO (3). This is an endothermic reaction which proceeds at a lower rate that reaction 1 but at a much higher rate than a direct methyl group ejection from the ring.
-
+
-
-
Introduction We have recently published a detailed investigation on the decomposition of i s o m l e behind reflected shocks in a singlepulse shock tube.’ On the basis of the experimental findings (including tests in the presence of free radical scavengers) and on thermochemical considerations, we suggested a reaction mechanism, constructed a kinec scheme, and performed computer simulation with good agreement between the computed and experimental results. Isoxazole is isoelectronic to furan. Although it is kinetically much less stable than the latter, its thermal reactions, that take place at much lower temperatures, are very similar to those occurring in furan.2 Products with a a H group in furan are replaced by O N group in i s o m l e . Thus, C H 3 C H which is the main product in the decomposition of furan is replaced by CH3C=N which is the main product in isoxazole. This is true also for other products. 5-Methylisoxamle is another member of the isoxazole family. It is isoelectronic with 5-methylfuran. In view of the identical ‘In partial fulfillment of the requirements for a Ph.D. Thesis to be submitted to the Senate of the Hebrew University by D.W.
0022-3654/92/2096-7367$03.00/0
+
ring structures it is expected that these two molecules will show similar reaction patterns in their decompositions, as isoxazole and furan do. Owing to the weak N-O bond in the ring, a low kinetic stability, and thus decomposition at relatively low temperatures, is expected. It is believed also that the stretching of this bond will be the first step in the decomposition. It would be of great interest therefore to compare the thermal reactions and the kinetic stability 5-methylisoxazole to those of 5-methylfuran on one hand and to isoxazole on the other hand and to observe similarities and differences. As far as we are aware, the decomposition of 5-methyIisoxazde has never been studied in the past. It is expected that the results obtained in this investigation will help to establish a decompoeition mechanism and to construct a kinetic scheme for computer simulation.
Experimental Section A p p u a h The decomposition of 5 - m e t h y h m l e was studied behind reflected shock waves in a single-pulse shock tube using the same technique which was used in the study of isoxazole decomposition. It will be described here only very briefly. The tube is made of 52-mm4.d. stainless steel tubing with 4-m driven 0 1992 American Chemical Society
