Unimolecular reaction mechanisms involving C3H4, C4H4, and C6H6 hydrocarbon species

Twenty-Fourth Symposium (International) on Combustion/The Combustion Institute, 1992/pp. 621-628

UNIMOLECULAR

REACTION

MECHANISMS

INVOLVING

C3H4, C4H4, A N D C6H 6 HYDROCARBON SPECIES CARL F. MELIUS AND JAMES A. MILLER Combustion Research Facility Sandia National Laboratories Livermore, California 94551-0969, USA AND

EARL M. EVLETH Dynamique des Interactions Moleculaires Universit~ de Pierre et Marie Curie 4 place Jussieu 75252 Paris 05, France

The unimolecular rearrangement processes of unsaturated aliphatic hydrocarbons representative of intermediates in rich hydrocarbon flames have been investigated using the quantum chemical BAC-MP4 method. In particular, we have investigated the unimolecular reaction mechanisms involving (1) allene-cyclopropene-propyne rearrangement, (2) vinylacetylene pyrolysis leading to acetylene and diacetylene, and (3) various C6H6 compounds, including 1,5hexadiyne, 1,2,4,5-hexatetraene, and 1,2-hexadien-5-yne leading to 3,4-dimethylenecyclobutene, fulvene, benzene, 2-ethynyl-l,3-butadiene, and other C6H6 species. Rate constants for various reaction steps give good agreement with available experimental measurements. The reaction mechanisms are also consistent with various deuterium isotope labeling experiments. The results indicate that many different types of reaction mechanisms occur, including concerted pathways involving carbene and vinylidene intermediates and insertion reactions of vinylidenes into C - - H bonds and C - - C multiple bonds. New decomposition pathways are presented for vinylacetylene pyrolysis, for conversion of 1,2-hexadien-5-yne to fulvene, and for conversion of fulvene to benzene.

Introduction The mechanisms of aromatic hydrocarbon and soot formation in flames have been of continuing interest to the combustion community. A recent review of shock tube studies of possible hydrocarbon soot precursors has been given by Kern and Xie.1 The pyrolysis of vinylacetylene has been studied because of its possible role in soot formation from fuelbound hydrocarbons.l-4 These studies indicate that the ultimate major decomposition products are acetylene and diacetylene with a nearly constant product ratio of C2Hz/C4H2 of - 5 - 1 0 . While Colket2 proposed a radical chain mechanism for decomposition, Kiefer et al.3 proposed a unimolecular 2,2-elimination of acetylene involving vinylidene, CH2=CH--C=z---CH ~ CH2~C: + HC=:--CH HC==--CH + HC==---CH,

(1)

*This work sponsored in part by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences.

with a similar substituted vinylidene (or methylenecarbene) for C4H2 formation, C H z = C H - - ~ - - - C H ~ HC=z---C--CH~---C: + Hz ~ HC=z---C--~CH + Hz.

(2)

Benson, ~ however, has recently questioned this mechanism on thermodynamics grounds and proposes a 1,4-biradical C H ~ C H - - C H = C H as the intermediate. The rearrangements of C6H6 species6"7 also represent important reaction mechanisms in soot formation. Recently, the propargyl radical, H2CCCH, has received considerable support as a precursor of benzene formation. 8-13A7 Westmoreland et al. 13 found high concentrations of the propargyl radical in rich hydrocarbon flames. Kern and coworkers,8 in a key study on allene and propyne pyrolysis, proposed that the reaction of the propargyl radical with itself was responsible for benzene formation, HzCCCH + H2CCCH ,~ benzene.

621

(3)

622

REACTION KINETICS

Alkemade and Homann lz studied reaction (3) and found 1,5-hexadiyne, 1,2,4,5-hexatetraene, and 1,2hexadien-5-yne as primary products and benzene and 1,3-hexadien-5-yne as secondary products. Stein and coworkers n studied the subsequent unimolecular reactions of 1,5-hexadiyne. They observed the formation of 3,4-dimethylenecyclobutene, fulvene, and benzene, consistent with earlier experimental results of Huntsman and Wristers 14 and Kent and Jones. 15 Hopf 16 studied the pyrolysis of 1,2-hexadien-5-yne, observing the branched 2-ethynyl-l,3-butadiene as the only product. Miller and coworkers, 17 using detailed kinetics modeling of hydrocarbon flames, support the finding that the propargyl radical is primarily responsible for aromatic formation (forming phenyl + hydrogen atom in lieu of benzene) for these rich hydrocarbon flames. They proposed that the pathway through 1,2-hexadien-5yne is a major pathway for aromatic formation, consistent with the experimental observations of AIkemade and Homann.12 The differences in product formation observed in Alkemade and Homann's experiments 12 (benzene and 1,3-hexadien-5-yne), in Stein et al.'s experiments 11 (3,4-dimethylenecyclobutene, fulvene, and benzene) and in Hopf's experiments 16 (2-ethynyl-l,3-butadiene) requires further investigation. Furthermore, Stein et al. were not able to determine the relation between the fulvene and benzene reaction pathways. We therefore have applied the quantum chemical BAC-MP4 methodlSto investigate the reaction pathways and rate constants involved in the unimolecular rearrangements of unsaturated hydrocarbons. In particular, we have calculated the thermochemistry of the various tautomers and transition-state structures of C3H4, C4H4, and C6H6 species, including cyclic species and carbene species of potential relevance. Theoretical Approach The Bond-Additivity-Corrected M0ller-Plessett 4th order perturbation method, BAC-MP4, has been used to determine the thermochemical properties of the intermediates and transition state structures. Details of the method have been presented elsewhere. Is While the BAC-MP4 method has been used successfully for stable species, radicals, and transition state structures involving radicals, 19 it has not been extensively tested for unstable sing,let-state structures such as carbenes and unimolecular rearrangements of closed-shell molecules. For limited biradical character, such as carbenes and ozone, an unrestricted Hartree-Fock instability correction has been included that gives reasonable results (AHf(1CHz) = 429.8 kJ-mul-I and AHf(IOa) = 144.5 kJ-mol-l). The calculated AHy of vinylidene (H2C:C:) of 418.4 kJ-mo1-1 (see Table I) is in

agreement with, though slightly higher than, other theoretical methods. 2~ The barrier to isomerization of H 2 C : C : to HCCH of 3.3 kJ-mol -I is in the range calculated by other ab initio methods (08 kJ-mol- 1).2o The ability, of the BAC-MP4 method to treat accurately the concerted decomposition mechanism has been demonstrated for pyrolysis of trioxane (C3H603 ~ 3 CH20) by Aldridge et al. z~ The pyrolysis of ethylene to give acetylene and molecular hydrogen, C2H4 ~ H2CC: + Hz ,~-- HCCH + H2

(4)

yields a calculated high-pressure-limit rate constant of k4 = 10156 exp(-424.5/RT) (Rate constant activation energies in this paper are given in kJ-mol-l. The calculated rate constants presented in this paper correspond to the high pressure limit). The calculated rate constant, k4, is consistent with experimental rate constants (see ref. 23 and references therein), which are in the fall-off or low-pressure region. Compared to our high-pressure-limit rate constant, k4, the experimental rate constants at one atmosphere pressure are a factor of -40-50 lower at ~ K, a factor of - 9 - 1 1 lower at 2000 K, and a factor of -0.9-1.8 lower at 1500 K, in good agreement with the expected fall-off behavior. It is likely that the BAC-MP4 calculated activation energy of reaction (4) may be as much as 10 kJ-mol-Z too high, given the underestimation of the rate constant at 1500 K. We find that the reverse reaction, vinylidene insertion, has an activation energy of 43.3 kJ-mol-1 above the heat of formation of vinylidene. A test of cyclobutene isomerization to 1,3-butadiene, [ ] ~ CH2-~--CHCH~CHz,

(5)

gives a conrotary transition state structure with a rate constant of k5 = 10134 exp(-137.7/RT) which is in reasonable agreement with the experimental value of ks = 10133 exp(-122.2/RT), z4 With these encouraging results, we consider the decomposition reactions involving C3H4, C4H4, and C6H6 species. As we shall see, the comparison of the BAC-MP4 rate constants with the experimental measurements are quite acceptable.

Allene-Cyelopropene-Propyne Isomerization The isomerization process between allene, eyclopropene, and propyne, C H 2 ~ C ~ C H 2 ~-- C H 3 - - ~ H ,

(6a)

~> ~ C H 3 - - ~ H ,

(6b)

~> ~ CH2-~-C=Ctt2,

(6c)

and

U N I M O L E C U L A R REACTION MECHANISMS INVOLVING HYDROCARBONS Energetlcs of H3CCCH ,-' H2CCCH 2

623

CH2~---C~CH2 is in total agreement with the 24.5 kJ-mo1-1 value determined by Bailey and Walsh. 26

480--

Vinylaeetylene Pyrolysis

400-

The BAC-MP4 reaction diagram for pyrolysis of vinylacetylene is given in Fig. 2. The resulting BACMP4 thermochemical properties for the reactants, intermediates, and transition state structures are given in Table I. In addition to reactions (1) and (2) involving reverse vinylidene insertion type reaction pathways from CH2CHCCH, we also have identified a reverse vinylidene insertion pathway from the methylenecyclopropene intermediate,

32o

240 16o

FIG. 1. BAC-MP4 reaction pathway diagram for the molecular isomerization between propyne, cyclopropene, and allene. Shaded curve estimated from ref. 31.

has been studied in detail both experimentallys'zs20 and theoretically.2s-31 Waish26 proposed cyclopropene as an intermediate in the reaction mechanism. York et al. 32 proposed a vinylcarbene as an intermediate in the cyclopropene pyrolysis leading to propyne. The BAC-MP4 reaction diagram for allene-cyclopropene-propyne interconversion is given in Fig. 1. The resulting BAC-MP4 thermochemical properties for the reactants, intermediates, and transition state structures are given in Table I. The BAC-MP4 results for allene-propyne conversion (reaction 63) are consistent, for the most part, with the theoretical calculations of Honjou and coworkers, 30,31 Karni et al. z9 and Kakumoto et al. zs The key points, as indieated in those papers, is that the rate limiting step involves a 1,2-hydrogen shift between allene and vinylearbene, C H 2 ~ C H - - C H : . Our calculated rate eonstant for allene ~ propyne, k6a = 1014'70 exp(-286/RT) is in excellent agreement with the theoretical results of Kakumoto et al e8 (ksa = 1014"23e x p ( - 2 7 9 / R T ) ) and with most of the various experimental rate constants presented in fig. 8 of that paper. 2s As indicated elsewhere, 3~ the barrier for the 1,3-hydrogen shift between allene and propyne is much higher in energy (see Fig. 1). We find that the 1,2-hydrogen shift between propyne and vinylcarbene is also higher than the 1,3-hydrogen shift between vinylcarbene and methylvinylidene, C H a - - C H ~ C : . Our results are consistent with the experimental results z6,z'32 for cyclopropene being converted to propyne faster than to allene. Our rate constant for the cyclopropene going to propyne, k6b = 1014~ e x p ( - 1 7 0 . 4 / R T ) is in excellent agreement with the high-pressure rate constant of k6b = 1013~5 exp(-156.8 kJ-mol-1/RT) by Bailey and Walshz6 Our calculated activation energy difference of 25.2 kJ-mol-1 for ~> ~ CH3--Cxx::------CHand ~> --o

C H 2 ~ C H - - C ~ C H ~-- ~>~ ~ CH2~---C: + HC=:--CH ~ HCx=---CH+ H ~ H ,

(7)

and a concerted 6-centered reaction mechanism involving the butatriene intermediate, CH2~---CH--C::::---CH~ C H 2 ~ C ~ C ~ C H z HCx:x----C--~--CH + H2.

(8)

None of these reaction pathways involve biradical character. Reaction (7), corresponding to insertion into a multiple bond, is slightly more favorable than insertion into the C - - H bond (reaction 1), consistent with experimental evidence for insertion reactions by carbenes. 33 The concerted reaction (8) to form H2 is significantly lower in energy than the 1,1-elimination mechanism (reaction 2). The resulting rate constant of k7 = 1015~ e x p ( - 3 6 2 / R T ) is in good agreement with the experimental results of Kiefer et al. 3 of kl ,,r 7 =

10 5.11 e x p ( - 3 4 5 / R T ) .

The theoretically determined ratio of C2Hz/C4Hz of - 4 0 - 5 0 : 1 (ks = 101395 exp(-370/RT)) is in qualitative agreement with the experimental ratios of 5:1 by Kiefer et al., 3 7-10:1 by Colket, 2 and 10:1 by Hidaka et al. 4 A decrease in the BAC-MP4 activation energy of 15-25 kJ-mol- 1 for reaction (8), which is quite acceptable considering the large error estimate resulting from biradical character, would put the theoretical ratio in much better agreement with the experimental results. The agreement is significantly better than if one were to use reaction (2) instead of reaction (8). Reaction (2) has a 59 kJmo1-1 higher enthalpy of activation than reaction (8). Our theoretical results are consistent with the conclusion of Kiefer et al. 3 that the pyrolysis process forming acetylene involves the vinylidene intermediate, rather than a radical chain process. These results and this conclusion are clearly appropriate for pressures sufficiently low that collisional excitation to higher energy channels is unlikely but high enough that the "'high pressure limit" is reached

624

REACTION KINETICS

TABLE I BAC-MP4 heats of formation at 298 K (• estimates). A double arrow between two species indicates a transition state structure. A colon after a C or CH group indicates a carbene. Energies in kJ-mol -~ Molecular species

AH~os

HCCH HzCC: HCCH ~ H2C~C: CH2CH2 ~ H2CC: + H2 H2CCCH H3CCCH H2CCCH~ Cyclopropene CHaCHC: CH2CHCH CH3CCH ~ C H 3 C H ~ C : CH3CH~---C: ~ Cyclopropene or C H ~ C H C H : H2C~C~---CH~ ~ HzC~---CHCH: CHzCHCCH

H.2CCCCH2 M ethylenecyclopropene CHz=CHCH~C: CH2CCHCH: CH2CHCHC: ~ CH2CCHCH H~C=C: + HCCH Methylenecyclopropene CH2CCHCH ~-~ CHeCCCH2 H2CCCCH2 ~ H C C C C H + H2 H2CC: + HCCH CH~CHCCH anti HCCCHC: + H~ HCCCHCH~ trans Benzene Fulvene CH~CHCHCHCCH 1,2-Dimethylene-3-cyclobutene

226.8 418.4 421.9 461.8 347.4 191.5 199.5 284.5 398.4 451.5 375.7

• • • • +• • • • • •

4.2 6.2 8.5 9.6 24.3 10.9 14.4 11.4 5.8 14.1 5.7

451.1 478.1 289.3 316.0 401.1 490.9 588.9 578.1

+• + + • • •

18.1 6.9 13.7 25.4 23.3 10.8 15.1 12.0

641~3 • 27.2 642.3 • 15.3 644.0 • 34.9

• • -+ • +-

7.3 10.3 9.6 19.2 15.7

for k7 and ks. The BAC-MP4 bond dissociation energy, BDE, for CH2CHCCH ~ CH2CCCH + H

(9)

is 395 kJ-mol.-1 The pre-exponential factor for C - - H bond seissioning (which is reduced somewhat relative to normal C - - H bond scissioning, due to the resonant structure of the resulting radical) should be larger than that for the reverse vinylidene insertion. Thus, thchain reaction pyrolysis mechanism, such as proposed by Colket, 2 involving reaction (9), may be a reasonable mechanism for high pressures. C6H

CH2CHCCCHCH2 CH2C(CCH)CHCHz Bicyclo [3.1.0]Hexa-l,3-diene 1,2,4-Cyclohexatriene CH2CCHCHCCH2 HCCCH2CHzCCH HCCCH2CHCCH2 I

CH2C:CHCHCHCH

6 Isomerizations

The BAC-MP4 reaction diagram for rearrangements of C6H6 species leading to benzene forma-

I

I

339.8 344.6 375.5 379.5 403.8 432.3 436.5

--+ • • • •

24.0 17.5 20.2 24.3 28.3 16.8 22.2

477.0 • 13.0 I

477.8 • 20.8

CH~C(~CHz)CHCHC:

CH~CHCHCHCCH --~ 460.1 • 49.1

1,2,4-Cyclohexatriene

CH2CCHCHCCH2 Dimethylenecyclobutene CH~CHCHCHCHC: ~ Benzene Bieyclo [3.1.0]Hexa- 1,3-diene I

I

I

495.5 • 28.0 519.2 • 38.0 523.6 - 18.4

CH2C:CHCHCHCH I

CH2C(:CH2)CHCHC: ~Fulvene HCCCH2CDCCH2 ~.~ DCCCH2CHCCH2 CH~CCHCHCCH2 ~.~ I

655.0 • 41.5 702.6 71.1 218.5 334.5 334.4

AH~s

Molecular species

I

CH~C(~CH~)CHCHC: HCCCHzCHzCCH CH2CCHCHCCHz CH2CHC(~CH2)CHC: CHzCCHCH2CCH CH2CHC(~CH2)CHC: ~Fulvene

527.4 • 10.1 536.1 --- 52.0 536.2 • 47.4 547.3 --- 52.9 570.3 • 74.8 588.1 -+ 24.3

tion arising from 1,5-hexadiyne and 1,2,4,5-hexatetraene is given in Fig. 3. The corresponding reaction diagram arising from 1,2-hexadien-5-yne is given in Fig. 4. The resulting thermochemical properties for the reactants, intermediates, and transition state structures are given in Table I. Additional reaction pathways have been identified with respect to those in Ref. 17. The possible types of reaction mechanisms encountered are quite varied, due to the many degrees of freedom that exist as the hydrocarbon species become larger. Also, due to the high initial heat of formation of the starting compounds relative to benzene and fulvene, carbene intermediates are more accessible. The most significance observation, however, is the availability of concerted reaction mechanisms involving ringed transition state structures which provide low-acti-

UNIMOLECULAR REACTION MECHANISMS INVOLVING HYDROCARBONS VinylacetyleneDecomposition

1

625

CH2=C=CHCH2CH=C: 1 - ~ CH \ - - C'\z=C D~-v.:.~-~.,,o.=c= ....... HCCH2C~'CH CH2=CHCH=CHC"H=+CH: Molecular Rearrangements of CH2CCHCH2CCH .,

~

.:coo...

56O

c..,

~

;

1

=,oj o.:..c__c.

/ /

FIG. 2. BAC-MP4 reaction pathway diagram for the pyrolysis of vinylacetylene. Shaded curve estimated from Fig. l. vation-energy pathways. In particular, isotopically labeled 1,5-hexadiyne and 1,2,4,5-hexatetraene can undergo concerted isomerization involving only C - - C bond breaking and forming, 6'7 (i.e., no hydrogen shifts), CDCCH2CH2CCD ~ CH2CCDCDCCHz

(10)

and similarly for the analogous self isomerization for 1,2-hexadien-5-yne, CDCCH2CHCCH2 ~ CHCCH2CDCCH.2.

(11)

The calculated rate constant for reaction (11), kll = 101167 exp(-103/RT), compares with the experimental rate constant of kH = 101~ exp(-129/ RT) determined by Hopf. 16 For reaction (10), the 720-

2

CH2CCH "~

Molecular Rearrangements of

--

CHCCH2CH2CCH 9

i 4OO-HC~_C . CH2CHH2C=_C fC~-CC

3~24O-

~ o~oj_ ~

-J

[~U

FIG. 4. BAC-MP4 reaction pathway diagram for the molecular rearrangement of C~H6 species involving 1,2-hexadien-5-yne. Shaded curve estimated from triplet surface. Additional reaction pathways involving fulvene and benzene are shown in Fig. 3. 1,2,4,5-hexatetraene undergoes further conrotary cyclization6 to dimethylenecyclobutene,

CH2CCHCHCCH2 ~'~"

The calculated rate constant for reaction (10), klo = 1012z8 e x p ( - l l 8 / R T ) , compares with the experimental rate constant of kl0 = 101173 exp(-150/ RT) determined by Stein et al. 11 and klo = 101147 exp(-144/RT) determined by Huntsman and Wristers. 14 These results suggest that the BAC-MP4 transition state enthalpy may be too low by - 2 5 kJ-mol. -1 The calculated concerted transition state structures for reactions (10) and (11) are in agreement with the isotope labeling studies for reaction (10) of Jones and Bergman 34 and for reaction (11) of Hopf. 16 The 1,2,4,5-hexatetraene can undergo another concerted reaction involving only C - - C bond breaking and forming, leading to the methylenepentene carbene intermediate (see Fig. 3) which undergoes a 1,2-hydrogen shift to form fulvene, i

I

CHeCCHCHCCH2 ~,~CH2C(~CH2)CHCHC: ~- fulvene

FIG. 3. BAC-MP4 reaction pathway diagram for the molecular rearrangement of C~H6 species involving 1,5-hexadiyne and 1,2,4,5-hexatetraene. Additional reaction pathways involving fulvene and benzene are shown in Fig. 4.

(12)

(13)

The calculated transition state structures are consistent with the isotope labeling experiments of Henry and Bergman, ~ in which CDCCH2CH2CCD formed 1,2-dideuterated fulvene. We find that fulvene can undergo a concerted ring-closing reaction to form a bicyclo intermediate that can undergo another concerted ring opening to form the cyclo-

626

REACTION KINETICS

hexadiene carbene intermediate, which then undergoes a 1,2-hydrogen shift to form benzene,

CHzC(CCH)CHCH2 ~ CHzC(CHC:)CHCHa

fulvene ~ bicyclo [3.1.0]hexa-l,3-diene~ I

fulvene.

I

CHzC:CHCHCHCH ~ benzene.

diene can convert to fulvene through a substituted vinylidene insertion,

The calculated rate constant for reaction (14), kla = 1013s8 exp(-309/RT), is consistent with the experimental results of Gaynor et al., ~ but out activation energy is higher by - 3 0 kJ-mol-1. The resulting reaction mechanism, shown in fig. 3, results in CDCCH2CH2CCD forming ortho-dideuterated benzene, again in agreement with the isotope labeling experiments of Henry and Bergman. ~176 The calculated rate constant for dimethylenecyclobutene forming fulvene and subsequently benzene, which occurs by way of 1,2,4,5-hexatetraene,

Similarly, fulvene can undergo a reverse insertion reaction to form 1,3-hexadien-5-yne, Fulvene ~ CH2CHCHCHCHC: CHzCHCHCHCCH.

~.~-- CH2CCHCHCCHz

(15)

of k15 = 10la'm e x p ( - 2 0 6 / R T ) is in excellent agreement with the observed rate constant of k15 = 10tz9 exp(-209/RT) of Stein et al. H We find that the benzene is formed sequentially from fulvene rather than in parallel with fulvene, as suggested by Stein et al. The enthalpy of the transition state for fulvene going to benzene is slightly lower by several kJ-mol -I and the pre-exponential factor is smaller by one order of magnitude than the same parameters for the transition state for ~]'going to fulvene. Thus, the relative proportion of fulvene to benzene formed in the pyrolysis of 1,5-hexadiyne and 1,2,4,5-hexatetraene will be strongly pressure and temperature dependent. H'tS'a~ The reaction pathways for 1,2-hexadien-5-yne (Fig. 4) have some similarities with the pyrolysis of 1,5hexadiyne and 1,2,4,5-hexatetraene. Reaction (11) is the analog of reaction (10), as discussed above. The analogous concerted pathway of reaction (13) is the formation of 2-ethynyl-l,3-butadiene through a vinylidene intermediate, CHCCH2CHCCH2 ~ CHzC(CttC:)CHCHz CH2C(CCH)CHCH2.

(16)

The reaction mechanism is consistent with the isotope labeling experiments carried out by Hopf. 16 As observed in the propyne-allene isomerization, substituted vinylidene ( R - - C H i C : ) intermediates are -200 kJ-mo1-1 above the substituted ethyne (R--C~CH), making the vinylidene insertion reactions possible. We find that 2-ethynyl-l,3-buta-

(18)

We find that the resulting 1,3-hexadien-5-yne can convert to benzene through the CH2CHCHCHCHC: vinylidene intermediate Ctt~CHCHCHCCH ~ CH2CHCHCHCHC: (~,

~-- fulvene & benzene,

(17)

(14)

(19)

consistent with the experimental results of Hopf and Musso. 37 An alternative, lower-energy concerted pathway converting fulvene to benzene has been discussed above (reaction 14). The ethynl group of 1,2-hexadien-5-yne can form a substituted vinylidene, which is lower in energy than two propargyl radicals. This can undergo a vinylidene insertion reaction to form 1,2,4-hexatriene, which can undergo a concerted reaction to form 1,3-hexadien-5-yne, CH2CCHCHzCCH ~ CH2CCHCH2CHC: ~--G~-- CH2CHCHCHCCH.

(20)

We have not considered initial carbene intermediates, such as CH2CCHCHCHC(:)H, since the energy to form carbenes is -250 kJ-mo1-1 with an additional - 2 0 kJ-mo1-1 for 1,2-hydrogen shift barriers. At sufficiently high temperatures, these carbenes could become important, as was the case for propyne-allene isomerization.

Conclusions The comparison of the BAC-MP4 theoretical resuits with the various experimental data is quite encouraging, indicating that the BAC-MP4 method ~tn reasonably treat the unimolecular reaction mechanisms involved in unsaturated hydrocarbon pyrolysis. The investigations of the reaction pathways for unimolecular rearrangements in C3H4, C4H4, and C6H6 species have identified a variety of reaction mechanisms. For the larger hydrocarbon species, concerted processes involving only C - - C bond forming and breaking can occur. For highly unsaturated, unstable species, this can lead to carbene

UNIMOLECULAR REACTION MECHANISMS INVOLVING HYDROCARBONS intermediates (resulting from five-membered transition-state ring structures), which can undergo 1,2 hydrogen shifts to more stable isomers. For ethynyl compounds, the formation of substituted vinylidenes provides an opportunity for insertion reactions, both into multiple bonds and sigma bonds. The activation energy for the vinylidene intermediate pathway,

12. 13.

14. R - - ~ - - C H ,~ R - - C H = C :

~,~ insertion

(21) 15.

is --200-250 kJ-mol -I depending on strain energy for insertion. Higher in energy are the carbene intermediates, which can play important roles in hydrogen shift mechanisms. Our results have de-emphasized biradical intermediates, since alternative, lower energy pathways tend to exist for the unsaturated hydrocarbons. The resulting thermochemical data for the various intermediates and transition state structures presented in this paper should provide prototypes for possible reactions occurring in other hydrocarbon pyrolysis systems leading to soot formation. The individual reaction steps identified in this paper need to be tested against experimental kinetics measurements in order to establish the degree of accuracy of the BAC-MP4 method for predicting these energies of activation. In particular, experimental studies of methylenecyclopropene, butatriene, and 2ethynyl-l,3-butadiene would be very informative in further increasing our knowledge of reaction mechanisms leading to soot formation.

1. 2.

3. 4. 5. 6. 7. 8. 9. 10.

11.

627

AND FAHR, A.: Twenty-Third Symposium (International) on Combustion, p. 85, The Combustion Institute, 1991. ALKEMADE, U. AND HOMANN, K. H.: Zeit. f. Phys. Chem. N. F. 161, 19 (1989). WESTMORELAND,P. R., DEAN, A. M., HOWARD, J. B. AND LONCWELL, J. P.: J. Phys. Chem. 93, 8171 (1989). HUNTSMAN,W. D. AND WmSTERS, H. ].: ]. Am. Chem. Soc. 85, 3308 (1963); 89, 342 (1967). KENT, ]. E. AND JONES, A. J.: Aust. ]. Chem.

23, 1059 (197o).

16. HOVF, H.: Chem. Ber. 104, 1499 (1971). 17. MILLER, J. A., KEE, R. J. AND WESTRROOK, C. W.: Ann. Rev. Phys. Chem. 41, 345 (1990); J. A. Miller and C. F. Melius: Combust. Flame 91, 21 (1992). 18. MELIUS, C. F.: in Chemistry and Physies of Energetic Materials; (S. Bulusu Ed.), NATO ASI 309, p. 21, 1990; P. Ho AND C. F. MELIUS: J. Phys. Chem. 94, 5120 (1990). 19. MILLER, J. A. AND MELIUS, C. F.: Twenty-Second Symposium (International) on Combustion, p. 1031 (The Combustion Institute, 1989). 20. CARRINGTON,T., HUBBARD, L. M., SCHAEFER, H. F. AND MILLER, W.: J. Chem. Phys. 80, 4347 (1984). 21. BINKLEY, J. S.: j. Am. Chem. Soc. 106, 603 (1984). 22. ALDRIDGE, H. K., LIU, X., LIN, M. C. AND MELIUS, C. F.: J. Chem. Kinetics 23, 947 (1991). 23. KIEFER, J. H., SIDHU, S. S., KUMARAN, S. S. AND IRDAM, E. A.: Chem. Phys. Lett 159, 32 (1989). 24. BENSON, S. W. AND O'NEAL, H. E.: Kinetic Data REFERENCES on Gas Phase Unimolecular Reactions, NSRDSNBS 21, 1970. KERN, R. D. AND XIE, K.: Prog. Energy Comb. 25. LIFSHITZ, A., FRENKLACK, M. AND BURCAT, A.: Sei. 17, 191 (1991). J. Phys. Chem. 79, 1148 (1975); J. Phys. Chem. COLKET, M. B.: Twenty-First Symposium (In80, 2437 (1976). ternational) on Combustion, p. 851, The Com26. WALSH, R.: J. Chem. Soc., Faraday Trans. 1, bustion Institute, 1986. 2137 (1976); BAILEY, I. M,, WALSH, R. J. Chem. KIEFER, J. H., MITCHELL, K. I., KERN, R. D. Soc., Farad. Trans. 74, 1146 (1978); HOPF, H. AND YONG, J. N.: J. Phys. Chem. 92, 677 (1988). PmEBE, H. AND WALSH, R. J. Amer. Chem. Soc. HIDAKa, Y., TANAKA,K. AND SUGA, M.: Chem. 102, 1210 (1980). Phys. Lett. 130, 195 (1986). BENSON, S. W.: Int. J. Chem. Kin. 21, 233 27. HIDAKA,Y., CHIMORI, T. AND SUGA, M.: Chem. Phys. Lett. 119, 435 (1985); HIDAKh, Y., NAK(1989). AMURA,T., MIYAUCHI,A., SHIRAISHI,T. AND KAGAJEWSKI, J.: Hydrocarbon Thermal IsomeriWANO, H.: Int. J. Chem. Kin. 21, 643 (1989). zation, Academic Press, New York, 1981. 28. KnKUMOTO,T., USmROGOUCHI,T~, Sxrro, K. AND BROWN, R. F. C.: Pyrolytic Methods in Organic IMAMURA, A.: ]. Phys. Chem. 91, 183 (1987). Chemistry, Academic Press, 1980. 29. KARNI, M., OREF, S., BARZILAI-GILBOA, S. AND Wu, C. H. AND KERN, R. D.: J. Phys. Chem. LIFSHITZ, A.: J. Phys. Chem. 92, 6924 (1988). 91, 6291 (1987). KERN, R. D., SINGH, H. J. AND WU, C. H.: Int. 30. HoNJOU, N., PACANSKY, J. AND YOSHIMINE, M.: J. Am. Chem. Soc. 107, 5332 (1985); J. Amer. J. Chem. Kin. 20, 731 (1988). Chem. Soc. 106, 5361 (1984). KERN, R. D., Wu, C. H., YONG, J. N., PAMI31. YOSHIMINE, M., PACANSKY, J. AND HONJOU, N.: DIMUKKhLA, K. M. AND SINGH, H. J.: J. Energy J. Am. Chem. Soe. 111, 4198 (1989). & Fuels 2, 454 (1988). 32. YORK, E. J., DITI'MAR,W., STEVENSON,J. R. AND STEIN, S. E., WALKER, J. R., SURYAN, M. M.

628

REACTION KINETICS

BERGMAN, R. G.: J. Am. Chem. Soc. 95, 5680 (1973). 33. STnNC, P. J.: Chem. Rev. 78, 383 (1978). 34. JONES, R. R. AND BEnGMnN, R. G.: J. Am. Chem. Soc. 94, 660 (1972). 35. HENRY, T. J. riND BERCMAN, R. G.: J. Am.

Chem. Soe. 94, 5103 (1972). 36. GaYNOR, B. J., GILBERT, R. G., KING, K. D. aND HaRMAN, P. J.: Aust. J. Chem. 34, 449 (1981). 37. HOeF, H. riND MUSSO, H.: Angew. Chem. 81, 704 (1969).

COMMENTS John H. Kiefer, University of lllinois at Chicago, USA. Your pathways through cyclic carbenes are elegant and, I suspect, original. Is there any consideration of such paths in the literature?

Author's Reply. We believe that our paper is the first to identify the existence of the concerted fivemembered carbene ring reaction mechanisms as likely reaction pathways. Most of the proposed reaction pathways in the literature, including both fiveand six-membered rings, tend to invoke biradical intermediates (see for instance, the reviews by Brown I and Gajewski2). Brown, in his review, does mention that as an alternative mechanism, the con-

version of fulvene to benzene through the cyclohexadiene carbene intermediate could go through a bicyclic intermediate (reaction 14 of our paper), but states that there was no evidence to support such a mechanism, either stepwise or concerted. Our theoretical calculations now confirm that the concerted pathway for this reaction exists. REFERENCES 1. BROWN, R. F. C. : Pyrolytic Methods in Organic Chemistry, Academic Press, 1980. 2. GAJEWSKI, J.: Hydrocarbon Thermal Isomerization, Academic Press, New York, 1981.