Decomposition, Isomerization, and Ring Expansion in 2-Methylindene: Single-pulse Shock Tube and Modeling Study

Article abstract of DOI:10.1021/jp031160a

The thermal reactions of 2-methylindene diluted in argon were studied behind reflected shock waves in a 2 in. i.d. pressurized driver single-pulse shock tube over the temperature range 1050-1300 K and overall densities of ～3 × 10^-5 mol/cm³. A plethora of products resulting from decompositions, isomerizations, and ring expansion were found in the post shock samples. They were naphthalene as the product of five-membered ring expansion, 1- and 3-methylindene due to isomerizations, and CH₄, C₂H₄ C₂H₆, C₂H ₂, benzene, toluene, ethylbenzene, styrene, phenylacetylene, and indene as the result of fragmentation. Very minute yields of some other compounds were also observed. Except for the isomerizations that take place from the reactant as a starting material, the production of all the other products involve free radical reactions. The initiation of the free radical mechanisms in the decomposition of 2-methylindene takes place via ejection of hydrogen atoms from sp³ carbons and dissociation of the methyl group attached to the ring. The H atoms and the methyl radicals initiate a free radical mechanism by abstraction of hydrogen atoms from sp³ carbons and by dissociative recombination of H atom and removal of a methyl group from the ring. In addition to these dissociation reactions there are several breakdown processes that involve cleavage of the five-membered ring to produce both stable and unstable products. The ring expansion process that leads to the production of a high yield of naphthalene takes place only from a methylene indene radical intermediate rather than methylindene itself, whereas isomerizations take place from both the radical intermediates and the molecule. The total decomposition of 2-methylindene in terms of a first-order rate constant is given by: k _total = 10^13.69exp (-59.4 × 10³/RT) s^-1. A reaction scheme containing 34 species and 71 elementary reactions was composed and computer simulation was performed over the temperature range 1050-1300 K at 25 K intervals. The agreement between the experimental results and the model prediction for most of the species is satisfactory.

Full text of DOI:10.1021/jp031160a

3430
J. Phys. Chem. A 2004, 108, 3430-3438
Decomposition, Isomerization, and Ring Expansion in 2-Methylindene: Single-pulse Shock
Tube and Modeling Study
Assa Lifshitz,* Carmen Tamburu, Aya Suslensky, and Faina Dubnikova
Department of Physical Chemistry, The Hebrew UniVersity, Jerusalem 91904, Israel
ReceiVed: October 13, 2003; In Final Form: January 26, 2004
The thermal reactions of 2-methylindene diluted in argon were studied behind reflected shock waves in a 2
in. i.d. pressurized driver single-pulse shock tube over the temperature range 1050-1300 K and overall densities
of ∼3 × 10-5 mol/cm3. A plethora of products resulting from decompositions, isomerizations, and ring
expansion were found in the post shock samples. They were naphthalene as the product of five-membered
ring expansion, 1- and 3-methylindene due to isomerizations, and CH4, C2H4, C2H6, C2H2, benzene, toluene,
ethylbenzene, styrene, phenylacetylene, and indene as the result of fragmentation. Very minute yields of
some other compounds were also observed. Except for the isomerizations that take place from the reactant as
a starting material, the production of all the other products involve free radical reactions. The initiation of the
free radical mechanisms in the decomposition of 2-methylindene takes place via ejection of hydrogen atoms
from sp3 carbons and dissociation of the methyl group attached to the ring. The H atoms and the methyl
radicals initiate a free radical mechanism by abstraction of hydrogen atoms from sp3 carbons and by dissociative
recombination of H atom and removal of a methyl group from the ring. In addition to these dissociation
reactions there are several breakdown processes that involve cleavage of the five-membered ring to produce
both stable and unstable products. The ring expansion process that leads to the production of a high yield of
naphthalene takes place only from a methylene indene radical intermediate rather than methylindene itself,
whereas isomerizations take place from both the radical intermediates and the molecule. The total decomposition
of 2-methylindene in terms of a first-order rate constant is given by: ktotal ) 1013.69exp (-59.4 × 103/RT) s-1.
A reaction scheme containing 34 species and 71 elementary reactions was composed and computer simulation
was performed over the temperature range 1050-1300 K at 25 K intervals. The agreement between the
experimental results and the model prediction for most of the species is satisfactory
Introduction
isomerizations in these molecules were reported. It has been
found also that the methyl group shifts play a very important
role in the ring expansion process as the energy barriers for the
process differ from one isomer to another. Thus, for several
isomers isomerization followed by ring expansion is faster than
a direct ring expansion.
As far as we are aware, the thermal reactions of 2-methyl-
indene have never been studied in the past. In this investigation
we present experimental results and computer modeling of the
thermal reactions of 2-methylindene. The rate parameters of the
isomerizations and of the ring expansion for the kinetic scheme
are based on quantum chemical calculations (at QCISD(T)//
B3LYP level of theory). Similarly, the calculated thermody-
namic properties of the various radical intermediates are based
on the same calculations.
When a five-membered ring with a methyl group attached to
the ring is subjected to high temperatures, in addition to
fragmentation, ring expansion and migration of the methyl group
from its original site also take place. Moreover, the ring
expansion and isomerization products are found to be of very
high yield. Experimental results were obtained, modeling and
quantum chemical calculations of potential energy surfaces have
been performed on molecules such as methylpyrrole,1-3 di-
methylpyrrole,4 methylindole,5 methylcyclopentadiene,6-8 meth-
ylindene (quantum chemical calculations)9 and others. Some of
the studies have been published and some are still in the process
of data reduction.
Upon ring expansion methylpyrrole produces pyridine, di-
methylpyrrole produces two isomers of picoline (methylpyri-
dine), methylindole produces quinoline and isoquinoline, and
methylcyclopentadiene produces benzene and higher aromatics.
All at high yields.
Quantum chemical calculations on all the compounds men-
tioned have shown that the ring expansion process does not take
place from the molecules but rather from the intermediate
radicals that have a methylene group attached to the ring.
Isomerizations, on the other hand, take place from both the
molecules and the radical intermediates. Except for isomeriza-
tions resulting from migrations of the methyl group, no other
Experimental Procedure and Data Reduction
Shock Tube. The thermal reactions of 2-methylindene were
studied behind reflected shock waves in a 2 in. i.d. single pulse
shock tube. The driven section, 4 m long, was divided in the
middle by a 2 in. ball valve. The driver had a variable length
up to a maximum of 2.7 m and could be varied in small steps
in order to tune for the best cooling conditions. A 36-L dump
tank was connected to the driven section near the diaphragm
holder in order to quench transmitted shocks. The driven section
was separated from the driver by Mylar polyester film of various
thicknesses depending upon the desired shock strength. The tube,
* Corresponding author. E-mail: Assa@vms.huji.ac.il
10.1021/jp031160a CCC: $27.50 © 2004 American Chemical Society
Published on Web 03/19/2004

Thermal Reactions of 2-Methylindene in Argon
J. Phys. Chem. A, Vol. 108, No. 16, 2004 3431
the gas handling system, the reaction mixture bulbs and the
transfer tubes were heated and maintained at 170 °C with an
accuracy of (1 °C.
Reflected shock temperatures were determined from the extent
of decomposition of 1,1,1-trifluoroethane which was added in
small quantities to the reaction mixtures to serve as an in-
ternal standard. Its decomposition to CH2dCF2 + HF is a first-
order unimolecular reaction that under the temperature and
pressure of this investigation has a rate constant of kfirst
)
1014.85exp(-74.05 × 103/RT) s-1, where R is expressed in units
of cal/(K mol).9
Reflected shock temperatures were calculated from the
relation
1
At
T ) -(E/R)/ ln - ln(1-ø)
[
{
}
]
where t is the reaction dwell time, approximately 2 ms, A and
E are the Arrhenius parameters of the standard reaction, and ø
is the extent of decomposition defined as
ø ) [CH2dCF2]t/([CH2dCF2]t + [CH3CF3]t)
Density ratios were calculated from the measured incident
shock velocities using the three conservation equations and the
ideal gas equation of state. Cooling rates were approximately 5
× 105 K/s.
Materials and Analysis. Reaction mixtures containing 0.5%
of methyl indene diluted in argon were prepared and stored at
1 atm in 12 L glass bulbs. The concentration of the internal
standard was 0.1%. The bulbs and the gas handling manifold
were pumped down to ∼10-5 Torr. The argon and helium used
were of high purity and were used without further purification.
Gas chromatographic analyses of the post shock mixtures
provided the product distribution and the temperature (calculated
from the ratio [CH2dCF2]t/[CH3CF3]0). Flame ionization detec-
tor (FID) and a temperature-programmed 2-m Porapak N column
were used.
Figure 1. Gas chromatograms of a post-shock mixture of 0.5%
2-methylindene in argon heated to 1258 K, taken on FID.
i in the shocked sample, S(pri) is its sensitivity relative to
reactant, and n(pri) is the number of its carbon atoms. F5/F1 is
the compression ratio behind the reflected shock wave, and T1
is the temperature of the reaction mixture prior to shock heating,
i.e., the temperature of the shock tube, 170 °C in the present
studies.
The areas under the GC peaks were evaluated using Chro-
matograph Station for Windows software (CWS ver. 1.7) from
DataApex Ltd.
Results
Phenyl acetylene and styrene, both products of 2-methylin-
dene decomposition could not be separated on the columns used,
so their concentrations were determined with the SIM mode of
the GC-MS. The two isomerization products 1-methyl indene
and 3-methyl indene could not be separated and could not be
determined separately in the GC-MS because of very similar
mass spectra. They are presented as one entity.
Evaluation of the Product Concentrations. To avoid errors
resulting from irreproducibility of the detector responses,
concentrations of reaction products C5(pr)i were calculated
relative to the concentration of the reactant. Evaluation of the
concentrations from the integrated GC peak areas was done
using the following relations:
To determine the distribution of reaction products, some 35
tests were run with mixtures containing 0.5% 2-methylindene
and 0.1% 1,1,1-trifluoroethane in argon, covering the temper-
ature range 1050-1300 K. Extents of reaction starting from a
few hundredths of one percent were determined. A typical
chromatogram of a post shock mixture of 2-methylindene in
argon, heated to 1258 K, divided into two parts, is shown in
Figure 1. The two peaks CH3CF3 and CH2dCF2 in the upper
part are those of the chemical thermometer, the ratio of which
is used to calculate the temperature behind the reflected shock.
The product distribution is shown graphically in Figure 2.
Products of minute quantities were not included. Points for
toluene are available only from 1170 K and higher because of
unexplained very high scatter. The product distribution is later
being used as a basis for comparison between the model
prediction and the experimental results.
C5(pr)i ) A(pri)t/S(pri) × {C5(reactant)0/A(reactant)0}
C5(reactant)0 ) {p1 × %(reactant) × (F5/F1)/100RT1}
Figure 3 shows the rate constant for the overall decomposition
of 2-methylindene, calculated as a first-order rate constant from
the relation
1
n
A(reactant)0 ) A(reactant)t + Σ[n(pri) × A(pri)/S(pri)]
where C5(reactant)0 is the concentration of the reactant behind
the reflected shock prior to decomposition, A(reactant)0 is its
calculated GC peak area prior to decomposition, and n is the
number of its carbon atoms. A(pri)t is the peak area of a product
ktotal ) -ln{[2-methylindene]t/[2-methylindene]0}/t
The value obtained at the low-temperature end is ktotal ) 1013.69
exp(-59.4 × 103/RT) s-1, where R is expressed in units of cal/

3432 J. Phys. Chem. A, Vol. 108, No. 16, 2004
Lifshitz et al.
Figure 3. Arrhenius plot of a first-order rate constant for the overall
decomposition of 2-methylindene. The rate constant is calculated
from the relation ktotal ) -ln{[2-methylindene]t/[2-methylindene]0}/t.
The value obtained for the low-temperature end is ktotal ) 1013.69
exp(-59.4 × 103/RT) s-1
.
Figure 2. Distribution of reaction products as a function of temperature.
(K mol). Figure 4 shows Arrhenius plots of the first-order
production rate of several products, calculated from the relation
[product]
kproduct
)
× ktotal
[2-methylindene]0 - [2-methylindene]t
Note that the calculated values correspond to production rates
and not to the depletion rate of the reactant due to the production
of a given product. Values of E obtained from the slopes of the
lines and their corresponding preexponential factors are sum-
marized in Table 1. The lines are calculated for the lower
temperature range of the reaction before further decomposition
of the products begins to take place. Since the production of
almost all the stable products is associated in one way or another
with free radical reactions and are the result of consecutive series
of reactions, their parameters do not represent true first-order
rate constants. They do provide, however, a convenient way to
summarize general rates. Note that the ethane production rate
has a high temperature dependence. The reason for this is the
relatively high dependence of methyl radical formation as was
obtained by the model calculations. Since the only channel for
ethane formation is practically methyl radical recombination,
its temperature dependence can be as high as twice that of the
methyl radical formation.
Figure 4. Arrhenius plots for the formation of several reaction products
calculated from the relation kproduct ) ([product]t)/([reactant]0
-
[reactant]t) × ktotal

Thermal Reactions of 2-Methylindene in Argon
J. Phys. Chem. A, Vol. 108, No. 16, 2004 3433
TABLE 1: First Order Arrhenius Parameters for
Production Rates of the Various Reaction Products
TABLE 2: Glossary and Calculated Thermodynamic
Properties of Various Species
product
log (A, s-1
)
E (kcal/mol) temp range (K)
2-methylindene
(total decomposition)
1- and 3-methylindene
CH4
C2H4
C2H6
C2H2
C6H6
C6H5-CH3
C6H5-CH2CH3
C6H5-CHdCH2
C6H5-CtCH
indene
13.69
59.4
1050-1160
12.65
14.63
14.12
19.53
12.74
10.18
9.96
16.29
8.45
27.31
18.13
18.4
54.5
68.9
72.4
98.1
67.1
54.1
52.9
85.1
42.7
151.8
88.1
90.9
1050-1150
1050-1250
1050-1300
1050-1235
1050-1300
1050-1300
1050-1300
1050-1205
1050-1300
1060-1250
1050-1190
1040-1220
naphthalene
Figure 5. Total decomposition of 2-methylindene. The filled circles
are the experimental values and the solid line represents the model
prediction. The model calculations were carried out at 25 K intervals
and the results are shown as + on the solid line.
Reaction Mechanism. Among the reaction products we find
both aromatic and aliphatic hydrocarbons. The main source for
the aliphatic components is the methyl group on the cyclopen-
tadiene ring. It can be removed from the ring either by
dissociation or by dissociative recombination with hydrogen
atoms, where the latter are obtained by the dissociation of the
3
C(sp )-H bonds in the molecule. Three such bonds exist in the
methyl group and one in the ring.
The methyl radicals and hydrogen atoms, via a free radical
mechanism, produce hydrocarbons, particularly methane, ethane,
ethylene, and others in a mechanism that is quite well known
and will not be discussed here.
Important reaction channels, without which many of the
product yields could not be accounted for, are unimolecular
decompositions of the five-membered ring in methylindene.
These channels are the unimolecular decompositions to benzyl
+ propargyl radicals and to styrene + acetylene. They were
included in the kinetic scheme. Similar decompositions of the
radical intermediates had almost no effect on the distribution
of reaction products because of their low concentrations and
were thus removed from the kinetic scheme after examining
their effect by the sensitivity analysis.
undergo three main processes. They can isomerize, where the
methyl or methylene groups change their position relative to
their original site; they can undergo unimolecular decomposi-
tions similar to those that take place in the stable molecules
(already mentioned before); and those radical intermediates
having a methylene group can undergo ring expansion to
produce hydronaphthalene radical and then naphthalene. It has
been shown by quantum chemical calculations that ring expan-
sion of radical intermediates where the methylene group is
The ejection of the methyl group from methylindene and
abstraction of hydrogen atoms by either hydrogen or methyl
produces a large number of radical intermediates that can

3434 J. Phys. Chem. A, Vol. 108, No. 16, 2004
Lifshitz et al.
TABLE 3: Reaction Scheme for the Decomposition, Isomerization, and Ring Expansion of 2-Methylindene
A
E
kf
kr
∆Sr
∆Hr
No.
reaction
(mol, s-1, cm-3
)
(kcal/mol)
(1150 K)
(1150 K)
(1150 K) (1150 K)
ref
1
2
3
4
5
6
7
8
9
2-mindene f mindene(R1)• + H•
1.0 × 1015
7.0 × 1014
4.0 × 1016
1.0 × 1014
1.0 × 1014
8.0 × 1013
1.0 × 1013
1.0 × 1013
2.86 × 1013
7.21 × 1013
3.0 × 1015
1.0 × 1015
1.0 × 1016
1.0 × 1014
1.0 × 1014
8.0 × 1013
1.0 × 1013
1.0 × 1013
1.0 × 1015
1.0 × 1015
4.0 × 1016
1.0 × 1014
1.0 × 1014
8.0 × 1013
1.0 × 1013
1.0 × 1013
3.0 × 1013
3.0 × 1013
1.50 × 1013
1.28 × 1013
2.46 × 1013
1.98 × 1013
1.0 × 1013
6.0 × 1013
6.0 × 1013
6.0 × 1013
1.0 × 1014
3.0 × 1014
2.0 × 1014
4.0 × 1014
5.0 × 1015
5.0 × 1015
5.0 × 1015
2.0 × 1014
2.0 × 1014
2.0 × 1014
2.0 × 1014
2.0 × 1014
2.0 × 1014
2.0 × 1014
2.0 × 1016
5.78 × 1013
1.60 × 1015
2.0 × 1016
5.78 × 1013
6.0 × 1015
1.15 × 109
1.58 × 1011
74
78
93
12
12
10
12
12
58.5
38.6
86
70
65
13
12
10
12
12
74
76
93
12
12
10
12
8.66
1.05
3.39 × 1013
5.44 × 1013
5.97 × 1012
1.17 × 105
1.55 × 106
5.29 × 106
2.18 × 105
2.88 × 106
1.06 × 103
7.59 × 105
4.79 × 1013
2.59 × 1013
1.04 × 1013
6.82 × 106
1.56 × 104
1.09 × 106
1.96 × 107
2.90 × 104
9.16 × 1013
8.39 × 1013
5.65 × 1012
3.18 × 105
6.98 × 105
4.79 × 106
5.90 × 105
1.30 × 106
32.5
32.5
46.6
5.04
5.04
8.31
-1.70
-1.70
-0.810
0.510
36.0
33.3
40.4
8.55
5.85
9.12
1.81
77.4 est
2-mindene f mindene(R2)• + H• (Rev)
83.3 est
100.3 est
-29.2. est
-23.3 est
-18.2 est
-30.3 est
-24.4 est
2-mindene f mindene(R3)• + CH3
8.50 × 10-2
5.24 × 1011
5.24 × 1011
1.01 × 1012
5.24 × 1010
5.24 × 1010
•
2-mindene + H• f mindene(R1)• + H2
2-mindene + H• f mindene(R2)• + H2
2-mindene + H• f indene + CH3
•
2-mindene + CH3• f mindene(R1)• + CH4
2-mindene + CH3• f mindene(R2)• + CH4
2-mindene f 1-mindene
219
2.68
-2.80
9
9
10 1-mindene f 3-mindene
3.33 × 106
11 1-mindene f mindene(R4)• + H•
12 1-mindene f mindene(R5)• + H•
13 1-mindene f mindene(R6)• + CH3
0.136
91.8 est
73.8 est
69.6 est
49.9
4.45 × 103
3.39 × 1011
5.24 × 1011
1.01 × 1012
5.24 × 1010
5.24 × 1010
8.66
•
14 1-mindene + H• f mindene(R4)• + H2
15 1-mindene + H• f mindene(R5)• + H2
-14.9 est
-32.9 est
-20.9 est
-15.9 est
16 1-mindene + H• f indene + CH3
•
17 1-mindene + CH3• f mindene(R4)• + CH4
18 1-mindene + CH3• f mindene(R5)• + CH4
19 3-mindene f mindene(R7)• + H•
-0.889 -33.9 est
32.8
32.8
46.9
80.1 est
81.9 est
20 3-mindene f mindene(R8)• + H• (Rev)
3.61
21 3-mindene f mindene(R9)• + CH3
8.50 × 102
5.24 × 1011
5.24 × 1011
1.01 × 1012
5.24 × 1010
5.24 × 1010
1.32 × 103
9.25 × 107
7.17 × 107
1.30 × 103
6.75 × 1010
2.64 × 1010
1.15 × 108
6.0 × 1013
6.0 × 1013
6.0 × 1013
2.69 × 1013
5.44 × 105
9.76 × 104
3.02 × 105
0.844
100.5 est
-26.6 est
-24.8 est
-18.1 est
-27.6 est
-25.8 est
•
22 3-mindene + H• f mindene(R7)• + H2
23 3-mindene + H• f mindene(R8)• + H2
5.34
5.34
8.61
-1.40
-1.40
0
-2.70
-2.70
0.806
1.89
4
24 3-mindene + H• f indene + CH3
•
25 3-mindene + CH3• f mindene(R7)• + CH4
26 3-mindene + CH3• f mindene(R8)• + CH4
27 mindene(R2)• f mindene(R5)•
12
54.5
29
64.5
-6.90
-18
9
est
28 mindene(R4)• f mindene(R5)• (Rev)
29 mindene(R4)• f mindene(R7)• (Rev)
30 mindene(R1)• f intermediate(R)•
31 intermediate(R)• f mindene(R4)• (Rev)
32 intermediate(R)• f HNaphthalene(R)•
33 HNaphthalene(R)• f naphthalene + H•
34 mindene(R3)• + H• f indene
1.37 × 105
4.90 × 105
5.82 × 105
6.62 × 1010
5.67 × 106
8.75 × 1012
28
-14.5 est
52.6
13.5
15.1
26
0
0
0
3
46
49
48
83
83
83
75
75
75
103.6
97.7
85.5
99.3
73.1
8
86.9
96
8
106
51.7
58.4
88.8
35
0
3
0
12.3
0
13.5
32
37.2
5.17
8.29
0
14.9
2.13
-14.7
9
9
9
20.2
22.7 est
-118.5 est
-90.5 est
-118.6 est
-36.8 13
44.5 13
40.7 13
47.0 13
90.7 est
88.1 est
90.9 est
46.9 est
44.2 est
47.0 est
83.4 est
77.5 est
68.1 est
79.1 est
78.2 14(mod)
-15.3 est
93.9 11
102.5 est
-11.1 15
113.6 16
22.8 17
38.5 14
39.4 est
32.2 est
4.49 × 10-6 -38.3
2.77 × 10-2 -31.3
4.30 × 10-6 -38.3
5.17 × 107 -28.6
35 mindene(R6)• + H• f indene
36 mindene(R9)• + H• f indene
37 indene + H• f indanyl(R)•
38 indanyl(R)• f benzyl• + C2H2
2.92 × 108
3.87 × 107
2.13 × 109
9.0 × 109
48.9
46.3
46.0
55.8
56.6
56.1
48.4
49.2
48.7
50.1
50.1
70.8
50.1
41.5
39 indanyl(R)• f C3H3• + benzene
40 indanyl(R)• f phenylacetylene + CH3
•
•
41 2-mindene f benzyl• + C3H3
•
42 1-mindene f benzyl• + C3H3
0.844
0.844
1.12
1.12
1.85 × 109
8.15 × 109
2.26 × 103
43 3-mindene f benzyl• + C3H3
•
44 2-mindene f styrene + C2H2
45 1-mindene f styrene + C2H2
465
46 3-mindene f styrene + C2H2
1.12
2.05 × 103
3.08 × 104
3.08 × 104
3.07
47 mindene(R1)• f styrene(R)• + C2H2
48 mindene(R2)• f styrene(R)• + C2H2
49 mindene(R6)• f styrene(R)• + C2H2
50 mindene(R8)• f styrene(R)• + C2H2
51 ethylbenzene f benzyl• + CH3• (Rev)
4.11 × 10-6
5.43 × 10-5
1.13 × 10-2
2.70 × 10-5
3.08 × 104
1.50 × 1013
6.64 × 107
1.40 × 1014
1.84 × 1013
1.84 × 109
6.59 × 1013
257
52 ethylbenzene + H• f benzene + C2H5
1.74 × 1012
4.99 × 10-2
1.14 × 10-2
1.74 × 1012
4.31 × 10-5
0.172
6.89
33.8
42.3
•
53 toluene f benzyl• + H• (Rev)
54 toluene f phenyl• + CH3• (Rev)
•
55 toluene + H• f benzene + CH3
3.96
56 benzene f phenyl• + H• (Rev)
57 ethylbenzene f benzene + C2H4
58 styrene f benzene + C2H2
59 styrene f phenylacetylene + H2
60 styrene(R)• f phenylacetylene + H•
61 styrene(R)• + H• f styrene
62 C3H3• + C3H3• f phenyl• + H•
63 C3H3• + C3H3• f benzene
64 CH4 + H• f CH3• + H2
38.4
31.6
29.4
28.8
22.1
44.4
1.24
9.10 × 105
3.45 × 103
3.94 × 1012
7.95 × 1012T0.44
1.0 × 1013
2.36 × 10-3
2.23 × 106
2.0 × 1014
5.38 × 1011
3.0 × 1012
6.62 × 1011
1.11 × 1013
8.19 × 1010
8.30 × 109
1.80 × 106
2.98 × 1012
2.55 × 1010
5.75 × 1011
2.0 × 1014
1.38 × 10-5 -34.1
1.59 × 1010 -22.1
5.81 × 10-8 -60.4
-113.9 est
-33.4 18
-147.1 19
1.07 11
-90.7 20
11.5 21
-57.0 22
38.2 23
-4.39 23
-5.47 23
-69.5 23
2.0 × 1012
3.0 × 1012
1.44 × 1014
1.01 × 1015T -0.64
3.01 × 1013
1.0 × 1016
3.56 × 1010
6.74
-40.4
65 CH3• + CH3• f C2H6
0.462
66 CH3• + CH3• f C2H5• + H•
67 CH3• + CH3• f C2H4 + H2
68 C2H5• f C2H4 + H•
1.42 × 1014 -4.80
5.59
-7.55
24.7
8.18
1.44
-9.49
4.80 × 109T1.19
1.22 × 1013
7.12 × 109
1.13 × 109
4.15
69 C2H6 + H• f C2H5• + H2
70 C2H6 + CH3• f C2H5• + CH4
71 C2H5• + CH3• f CH4 + C2H4
554.T3.50
0.548 T4.0
1.95 × 1013T-0.50

Thermal Reactions of 2-Methylindene in Argon
J. Phys. Chem. A, Vol. 108, No. 16, 2004 3435
Figure 6. Experimental yields of twelve reaction products plotted against the temperature. The filled circles are the experimental yields and the
solid line is the best fit to the calculated yields carried out at 25 K intervals and are shown as + on the solid line.
bound to an sp2 carbon is rather slow and the migration of the
methylene group to an sp3 carbon followed by ring expansion
is faster. The kinetic scheme thus contains ring expansion only
from mindene(R4)• and not from both mindene(R1)• and
mindene(R7)•. Note that the ring expansion from mindene(R4)•
goes via a stable intermediate having a three-membered ring
fused to the cyclopentadiene ring (see glossary in Table 2).
Thermochemistry of the Radical Intermediates. Table 2
provides a glossary and calculated thermodynamic properties
of the radical intermediates that are formed by the loss of a
hydrogen atom or a methyl group from stable methylindene
isomers and some additional species. The values were obtained
by quantum chemical calculations at the QCISD(T)//B3LYP
level of theory, with Dunning correlation consistent polarized
valence double ú (cc-pVDZ) basis set. The values of the heats
of formation of the radical intermediates are based on the heat
of formation of 2-methylindene taken as 41.7 kcal/mol at 298
K. Any uncertainty in this value is carried over to the other
species in the table. Note that the radical mindene(R3)• obtained
by removal of a methyl group from an sp2 carbon is considerably
less stable than all the other radicals.
Computer Modeling. Reaction Scheme. To model the
observed product distribution we have constructed a reaction
scheme that is shown in Table 3. The scheme contains 34 species
and 71 elementary reactions. The symbol (Rev) at the end of a
listed step in the scheme indicates that after a reaction time of
2 ms (or earlier), the reaction proceeds in the reverse direction.
The rate constants listed in the table are given as k ) A
exp(-E/RT) or k ) A′ ×T n exp(-E/RT), when the rate constants
taken from the database fit a wide temperature range. Units are

3436 J. Phys. Chem. A, Vol. 108, No. 16, 2004
Lifshitz et al.
TABLE 4: Sensitivity Analysis: Percent Change in the Yield of a Component i Due to an Increase in the Rate Constant of
Reaction j by a Factor of 3, at 1100/1250 K
No.
reaction
1-mindene
3-mindene
indene
naphthalene
41/18
ethylbenzene
styrene
1
4
5
6
7
8
9
12
13
19
27
30
35
38
41
43
44
51
53
65
2-mindene f mindene(R1)• + H•
- / -30
- / -30
50/19
-21/-
-22/-
39/-
- / -15
2-mindene + H• f mindene(R1)• + H2
2-mindene + H• f mindene(R2)• + H2
2-mindene + H• f indene + CH3
•
2-mindene + CH3• f mindene(R1)• + CH4
2-mindene + CH3• f mindene(R2)• + CH4
2-mindene f 1-mindene
- / -20
- / -19
139/-
- / -20
- / -19
140/-
16/16
13/16
60/-
-/16
13/-
-/13
42/-
63/-
-17 / -14
-17 / -14
16/-
50/-
-/18
11/-
-/15
26/-
38/-
18/12
1-mindene f mindene(R5)• + H•
- / -29
- / -29
- / -12
1-mindene f mindene(R6)• + CH3
•
3-mindene f mindene(R7)• + H•
mindene(R2)• f mindene(R5)•
mindene(R1)• f intermediate(R)•
mindene(R6)• + H• f indene
indanyl(R)(R)• f benzyl• + C2H2
- / -24
- / -24
- / -10
-/-10
-/-11
-/19
-/29
187/109
-/42
2-mindene f benzyl• + C3H3•
•
3-mindene f benzyl• + C3H3
2-mindene f styrene + C2H2
ethylbenzene f benzyl• + CH3• (Rev)
Toluene f benzyl• + H• (Rev)
CH3• + CH3• f C2H6
188/135
39/-
-24 / -47
- / -17
0
-3
- / -16
No.
reactions
phenylacetylene
toluene
benzene
C2H6
C2H4
43/34
-15/-
C2H2
CH4
1
4
5
6
7
8
9
2-mindene f mindene(R1)• + H•
138/75
-39/-
-40/-
30/23
-17/-
-18/-
-37/-
23/-
18/-
-15/-28 0/-18
-/25
20/-
2-mindene + H• f mindene(R1)• + H2
2-mindene + H• f mindene(R2)• + H2
2-mindene + H• f indene + CH3
20/-
•
2-mindene + CH3• f mindene(R1)• + CH4
2-mindene + CH3• f mindene(R2)• + CH4
2-mindene f 1-mindene
14/17
-/13
65/-23
19/68
11/-
14/53
11/10
-/-13
60/-
93/-
-14/-47
-50/-16 -50 / -14
-51/-16 -52 / -15
34/40
33/41
157/11
198/-
-/30
44/-
-/24
- / -14 61/-
12
13
19
25
26
27
30
35
38
39
40
41
43
44
46
51
53
62
63
65
66
69
70
1-mindene f mindene(R5)• + H•
•
1-mindene f mindene(R6)• + CH3
35/-
19/-
3-mindene f mindene(R7)• + H•
3-mindene + CH3• f mindene(R7)• + CH4
3-mindene + CH3• f mindene(R8)• + CH4
mindene(R2)• f mindene(R5)•
-/20
- / -13
23/-
-/15
20/-
28/-
-18/-41
-/16
mindene(R1)• f intermediate(R)•
mindene(R6)• + H• f indene
14/-
34/-
-11/-28
indanyl(R)• f benzyl• + C2H2
-/25
indanyl(R)• f C3H3• + benzene
-/19
•
indanyl(R)• f phenylacetylene + CH3
194/180
2-mindene f benzyl• + C3H3•
197/128
-/35
529/135
13/42
•
3-mindene f benzyl• + C3H3
2-mindene f styrene + C2H2
3-mindene f styrene + C2H2
ethylbenzene f benzyl• + CH3• (Rev)
toluene f benzyl• + H• (Rev)
C3H3• + C3H3• f phenyl• + H•
C3H3• + C3H3• f benzene
187/116
-/39
-46/-
123/63
-/16
-/-16
129/17
CH3• + CH3• f C2H6
- / -32
102/32
26 / -12
89/17
76/94
-17/-32
CH3• + CH3• f C2H5• + H•
C2H6 + H• f C2H5• + H2
C2H6 + CH3• f C2H5• + CH4
20/50
cm3, mol-1, s-1, and kcal/mol. The Arrhenius parameters for
the reactions in the scheme are either estimated or taken from
various literature sources. These sources are specific articles
relevant to the present system and databases, mainly the NIST-
Kinetic Standard Reference Data Base #17. The parameters for
the reactions that were taken from the NIST-Kinetics Data Base
are, in many cases, best fits to a large number of entries. The
rate parameters for the ring expansion of mindene(R4)• and of
the methyl/methylene group shifts are based on the quantum
chemical calculations. The thermodynamic properties of the
species in the scheme were also taken from specific articles
and various literature sources. Some were estimated using NIST-
Standard Reference Data Base #25 (Structure and Properties
program (SP)). As has been mentioned before, the thermody-
namic properties of the radical intermediates and of several other
species (Table 2) were calculated using quantum chemical
methods at the QCISD(T)// B3LYP level of theory.
Figure 5 shows the overall disappearance of the reactant
2-methylindene, and Figure 6 shows experimental and calculated
yields of twelve products found in the post-shock mixtures. The
symbols (•) in the figures are the experimental yields in mole
percent and the lines are best fits to the calculated points using
the scheme shown in Table 3. The calculations were done at
25 K intervals in the temperature range 1050-1300 K and are
shown as (+) on the lines. The agreement between the model
prediction and the experimental results is reasonable for most
of the products. The model underestimates the yield of benzene,
styrene, and ethylene at the low-temperature end. Using the
sensitivity analysis we tried to change rate parameters within
the limits of their uncertainties but were unable to improve the
overall agreement between the calculations and the experimental
results.
SensitiVity Analysis. Table 4 shows the sensitivity of the
system to variation of specific reactions in the kinetic scheme,

Thermal Reactions of 2-Methylindene in Argon
J. Phys. Chem. A, Vol. 108, No. 16, 2004 3437
calculated at 1100 and 1250 K, respectively. The table gives
the percent change in the yield of a particular product for a
factor of 3 increase in the rate constant of a particular reaction.
The calculations correspond to a dwell time of 2 ms. Reactions
that show an effect of less than 10%, both at 1100 K and at
1200 K, are not included in the table.
We have run also sensitivity analyses with respect to
variations (or rather uncertainties) in the ∆fH° of species whose
thermodynamic properties were estimated or calculated. Note
that incorrect values of the thermodynamic properties result in
erroneous values for the rate constants of the back reactions
for a given value of the forward rate constant. The sensitivity
spectrum calculated at 1100 and 1250 K is shown in Table 5.
It gives the effect of an increase of 5 kcal/mol in the ∆fH° of
the species on the product yields. As can be seen, there is a
significant effect on some of the products. Special attention
should be paid to the effect caused by variation in the ∆fH° of
the calculated radical intermediates.
It should be mentioned that whereas ring expansion (produc-
tion of naphthalene) depends on the concentrations of the radical
intermediates (as expansion does not take place from the
molecules), the contribution of the radical reactions to isomer-
ization is practically negligible since the molecules do interi-
somerize. Since their concentrations are much higher than those
of the radicals, their contribution to the isomerization process
is significantly greater.
Conclusions
Methylindene undergoes decompositions, isomerizations (meth-
yl group shifts), and ring expansion to hydronaphthalene when
elevated to high temperatures. Both aliphatic and new aromatic
compounds are formed in the process.
Ring expansion takes place only from radical intermediates
that have a methylene group connected to the five-membered
ring. Ring expansion from mindene(R4)• (see Table 2), where
the methylene group is connected, an sp3 carbon is much faster
than ring expansion from mindene(R1)• and mindene(R7)•, in
which the methylene group is connected to an sp2 carbon.
The rate constant of the isomerization 1-methylindene f
3-methylindene is much higher than the rate constants for both
1-methylindene f 2-methylindene and 2-methylindene f
3-methylindene isomerizations as 1-methylindene f 3-meth-
ylindene isomerization involves H-atom shifts (double 1,2-shifts)
only, whereas the other two involve methyl group migration
with considerably higher barriers.
A model containing 71 elementary steps and 34 species, both
stable and unstable, was constructed. The model prediction is
satisfactory except for the yields of benzene, styrene, and
ethylene at the low-temperature end of the range where the
yields are underestimated.
Acknowledgment. This work was supported by a grant from
the Israel Science Foundation (ISF) #34/01.
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