Kinetics and mechanisms of the thermal decomposition of 2-methyl-1,3-dioxolane, 2,2-dimethyl-1,3-dioxolane, and cyclopentanone ethylene ketal in the gas phase. Combined experimental and DFT study

Article abstract of DOI:10.1021/jp305179n

The kinetics of the gas-phase thermal decomposition of 2-methyl-1,3- dioxolane, 2,2-dimethyl-1,3-dioxolane, and cyclopentanone ethylene ketal were determined in a static system and the reaction vessel deactivated with allyl bromide. The decomposition reactions, in the presence of the free radical suppressor propene, are homogeneous, are unimolecular, and follow first-order law kinetics. The products of these reactions are acetaldehyde and the corresponding ketone. The working temperature range was 459-490 °C, and the pressure range was 46-113 Torr. The rate coefficients are given by the following Arrhenius equations: for 2-methyl-1,3-dioxolane, log k = (13.61 ± 0.12) - (242.1 ± 1.0)(2.303RT)^-1, r = 0.9997; for 2,2-dimethyl-1,3-dioxolane, log k = (14.16 ± 0.14) - (253.7 ± 2.0)(2.303RT)^-1, r = 0.9998; for cyclopentanone ethylene ketal, log k = (14.16 ± 0.14) - (253.7 ± 2.0)(2.303RT)^-1, r = 0.9998. Electronic structure calculations using DFT methods B3LYP and MPW1PW91 with 6-31G(d,p), and 6-31++G(d,p) basis sets suggest that the decomposition of these substrates takes place through a stepwise mechanism. The rate-determining step proceeds through a concerted nonsynchronous four-centered cyclic transition state, and the elongation of the C-OCH₃ bond in the direction C _α^δ+...OCH₃^δ- is predominant. The intermediate products of these decompositions are unstable, at the working temperatures, decomposing rapidly through a concerted cyclic six-centered cyclic transition state type of mechanism.

Full text of DOI:10.1021/jp305179n

Article
pubs.acs.org/JPCA
Kinetics and Mechanisms of the Thermal Decomposition of 2‑Methyl-
1,3-dioxolane, 2,2-Dimethyl-1,3-dioxolane, and Cyclopentanone
Ethylene Ketal in the Gas Phase. Combined Experimental and DFT Study
Felix Rosas,† Jesus Lezama,† Jose R. Mora,† Alexis Maldonado,† Tania Cordova,‡ and Gabriel Chuchani*,†
́
†Centro de Química, Instituto Venezolano de Investigaciones Científicas (I.V.I.C.), Apartado 21827, Caracas 1020.A, Venezuela
‡Department of Medicinal Chemistry, College of Pharmacy, University of Florida, P.O. Box 100485, Gainesville, Florida 32610,
United States
S
* Supporting Information
ABSTRACT: The kinetics of the gas-phase thermal decom-
position of 2-methyl-1,3-dioxolane, 2,2-dimethyl-1,3-dioxolane,
and cyclopentanone ethylene ketal were determined in a static
system and the reaction vessel deactivated with allyl bromide.
The decomposition reactions, in the presence of the free
radical suppressor propene, are homogeneous, are uni-
molecular, and follow first-order law kinetics. The products
of these reactions are acetaldehyde and the corresponding
ketone. The working temperature range was 459−490 °C, and
the pressure range was 46−113 Torr. The rate coefficients are
given by the following Arrhenius equations: for 2-methyl-1,3-
dioxolane, log k = (13.61
0.12) − (242.1
1.0)-
(2.303RT)−1, r = 0.9997; for 2,2-dimethyl-1,3-dioxolane, log
k = (14.16 0.14) − (253.7 2.0)(2.303RT)−1, r = 0.9998;
for cyclopentanone ethylene ketal, log k = (14.16 0.14) −
(253.7
2.0)(2.303RT)−1, r = 0.9998. Electronic structure
calculations using DFT methods B3LYP and MPW1PW91
with 6-31G(d,p), and 6-31++G(d,p) basis sets suggest that the
decomposition of these substrates takes place through a stepwise mechanism. The rate-determining step proceeds through a
concerted nonsynchronous four-centered cyclic transition state, and the elongation of the C−OCH3 bond in the direction
δ−
Cαδ+...OCH3 is predominant. The intermediate products of these decompositions are unstable, at the working temperatures,
decomposing rapidly through a concerted cyclic six-centered cyclic transition state type of mechanism.
kinetics of 2,2-diethoxy ethylamine and 2,2-diethoxy-N,N-diethyl
ethylamine in the gas phase.7
I. INTRODUCTION
Several investigations of Molera et al.1−6 on the thermal
decomposition of ketals led to the idea that the C−OR bond
polarization may be rate-determining (Scheme 1). In addition,
The previous works led to the examination of the
homogeneous, unimolecular, gas-phase decomposition kinetics
of several β-substituted diethyl acetals (reaction 1).8 The
reactions were thought to proceed via two parallel reactions as
described in reaction 1. The kinetic and thermodynamic
parameters of the parallel reactions suggested two different
concerted polar four-membered cyclic transition state mecha-
nisms.
Scheme 1
Received: May 28, 2012
Revised: August 9, 2012
Published: August 10, 2012
the presence of a Cβ−H bond was believed to be important in the
transition state mechanism from the work on the decomposition
© 2012 American Chemical Society
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a
Scheme 2
a
The ketal functional group is depicted in grey shadow.
Further studies on ketals had been reported; for example,
the thermal decomposition kinetics of 1,1-dimethoxycyclo-
hexane yielded 1-methoxycyclohexene and methanol.9
Theoretical calculations about the elucidation of the mecha-
nism of this reaction9 were carried out using DFT methods.
The estimated values for the energy and enthalpy of activa-
tion showed reasonably good agreement with the experi-
mental values with a PBEPBE/6-31G (d,p) level of theory.
Experimental and theoretical results suggested a con-
certed polar four-membered cyclic transition state type of
mechanism.
Recently, a joint experimental and theoretical study on the
decomposition kinetics of ketals, but without an α−H at the
carbon containing the two alkoxy groups, 2,2-diethoxypro-
pane and 1,1-diethoxycyclohexane,10 was carried out. The
results of this work demonstrated that these reactions take
place through a concerted nonsynchronous four-centered
cyclic transition state type of mechanism as described in
reactions 2 and 3. The predicted rate-determining step is the
polarization of the C−O bond. The intermediate product of
the 2,2-diethoxypropane decomposition, 2-ethoxypropene,
further decomposes through a concerted cyclic six-centered
cyclic transition state mechanism, as reported for gas-phase
decomposition of alkyl vinyl ethers11,12 (reaction 2, step 2) to
a carbonyl compound.
the decomposition process and must be outside of the
heterocyclic geometry. In this respect, the substrates to be
examined are 2-methyl-1,3-dioxolane, 2,2-dimethyl-1,
3-dioxolane, and cyclopentanone ethylene ketal (Scheme 2).
For reasonable mechanistic interpretations, theoretical calcula-
tions were carried out along the minimum energy path, in
order to obtain the kinetic parameters as a means to
understand the nature of the molecular processes of these
reactions.
II. EXPERIMENTAL SECTION
The starting materials 2-methyl-1,3-dioxolane, 2,2-dimethyl-
1,3-dioxolane, and cyclopentanone ethylene ketal were
acquired from Aldrich and used after distillation to better
than 98.5% purity. Analyses of these substrates were con-
ducted using a GC/MS Saturn 2000, Varian instrument with
a DB-5MS capillary column of 30 m × 0.53 mm i.d. and
1.5 μm film thickness. The products were identified using a
GC/MS Saturn 2000, Varian instrument with a DB-5MS
capillary column of 30 m × 0.25 mm i.d. and 0.25 μm film
thickness. For quantitative analysis of the products, a Varian
3700 gas chromatograph with Porapak S (80−100 mesh)
4 m and Chromosorb 103 (80−100 mesh) 4 m columns was
used for acetone and cyclopentanone characterization,
respectively.
Kinetics. The kinetic measurements were carried out in a
static reaction system as previously described.13−16 The wall
of the reaction vessel was deactivated with the product of
decomposition of allyl bromide at approximately 400 °C. In
our experiments, several runs were performed at each
temperature. The rate coefficients were calculated from a
pressure increase measured manometrically and by the
quantitative GC analysis. The temperature was controlled
by a resistance thermometer controller, SHINKO DIC-PS
25RT, maintained within 0.2 °C and measured with a
calibrated 13% platinum−platinum rhodium thermocouple.
No temperature gradient was found along the reaction vessel.
The substrates were all injected directly into the reaction
vessel with a syringe through a silicone rubber septum.
The amount of reactant used for each kinetic run was ∼0.05−
0.2 mL.
In association with the ketal functional group, it seemed
interesting to investigate the thermal decomposition kinetics
when both oxygen atoms attached to a carbon atom are
members of a heterocyclic structure. In addition to this
fact, the presence of a hydrogen atom of the adjacent C−H
bond to the −C(O)2− is required in the assistance of
III. RESULTS AND DISCUSSION
The products' formation in the molecular decomposition
of 2-methyl-1,3-dioxolane, 2,2-dimethyl-1,3-dioxolane, and
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cyclopentanone ethylene ketal, in vessels deactivated with
Table 2. Effect of the Free Radical Chain Inhibitor on Rates
allyl bromide, are described in reactions 4−6.
a
b
temp
(°C)
Ps
Pi
(Torr) Pi/Ps
104k1
(s−1
substrate
(Torr)
)
2-methyl-1,3-dioxolane
469.8
49
63
54
52
66
54
−
70
−
1.1
6.64
5.33
3.96
3.78
3.90
1.59
81
1.5
1.9
2.4
100
158
−
2,2-dimethyl-1,3-
dioxolane
480.3
−
41
64
56
68
56
37
90
0.9
1.4
2.2
3.3
3.36
3.78
3.56
3.62
3.27
123
224
−
cyclopentanone ethylene
ketal
470.1
−
46
58
44
62
93
140
170
285
1.0
2.4
3.4
4.6
5.04
5.86
5.70
5.96
a
b
Ps, pressure of substrate. Pi, pressure of free radical inhibitor
propene.
The homogeneity of these reactions was examined by carrying
out several runs in a vessel with a surface-to-volume ratio of
6.0, relative to that of the normal vessel which is equal to 1.0
(Table 1). The packed and unpacked Pyrex vessel, seasoned with
together, with the corresponding Arrhenius equation, are given
in Table 5. The errors were estimated to 90% confidence limits
from a least-squares procedure.
Table 1. Homogeneity of the Reaction
The values of log A from 13.61 to 14.16, listed in Table 6, are
reasonable values for a four-membered cyclic transition state
type of mechanism, as suggested by Benson.17 According
to product formations and the kinetic and thermodynamic
parameters, the mechanisms of these reactions may be con-
sidered to proceed via a concerted four-membered cyclic
transition state in the rate-determining step, as described in
reactions 7−9.
S/V
a
b
c
substrate
2-methyl-1,3-dioxolane 469.8
T (°C) (cm−1
)
104 k1 s−1
104 k1 s−1
1
15.83 4.60
35.40 6.34
12.89 3.80
3.96 0.07
3.90 0.09
3.74 0.07
6.22
1
2,2-dimethyl-1,3-
dioxolane
480.3
470.1
6.22
1
37.11 5.66
8.95 2.53
3.81 0.12
5.82 0.14
cyclopentanone
ethylene ketal
The proposed mechanism for product formation from
2-methyl-1,3-dioxolane is shown below.
6.22
32.23 4.41
5.71 0.10
a
b
c
S, surface area; V, volume. A clean Pyrex vessel was used. The
vessel was deactivated with allyl bromide.
allyl bromide, had no effect on rates. However, the packed and
unpacked clean Pyrex vessel resulted in a very significant
heterogeneous effect in the rate coefficients.
The thermal decomposition experiments were carried out in
the presence of the free radical suppressor propene in order to
prevent any possible chain reactions. The effect of different
proportions of propene in this process is shown in Table 2. No
induction period was observed. The rate coefficient was
reproducible with a relative deviation of less than 5% at a given
temperature.
The stoichiometries of reactions 4−6, up to a 75% reaction,
were verified by comparing the extent of decomposition of the
substrates from pressure measurements to that obtained from
quantitative gas liquid chromatographic (GLC) analyses of the
starting material and/or the corresponding products' formation
(Table 3).
The rates of decomposition were found to be invariable with
changes in the initial pressure of the substrates (Table 4), and the
first-order plots are satisfactorily linear, up to 75% decomposition
of the reactants. The temperature dependence of the reaction in
the deactivated vessel with the product of decomposition of allyl
bromide and in the presence of the free radical inhibitor propene
As described above for the decomposition of 2,2-diethox-
ypropane,10 the intermediate formed in 2-methyl-1,3-dioxolane
undergoes further decomposition at the high-temperature
condition. This type of reaction has been reported for alkyl
vinyl ethers.11,12 The proposed mechanism proceeds through a
six-centered cyclic transition state as shown in step 2 (reaction 7).
Similar decomposition occurs with the intermediates of 2,2-
dimethyl-1,3-dioxolane and cyclopentanone ethylene ketal
shown below.
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a
Table 3. Stoichiometry of the Reaction
substrate
temp (°C)
parameters
time (min)
value
b
2-methyl-1,3-dioxolane
469.8
5
10
15
20
40
60
reaction (%) (pressure)
substrate (%) (GLC)
time (min)
10.3
11.0
5
18.5
19.4
10
28.4
28.1
15
35.4
35.3
20
58.3
59.3
40
72.9
72.5
60
b
2,2-dimethyl-1,3-dioxolane
480.3
470.1
reaction (%) (pressure)
substrate (%) (GLC)
acetone (%) (GLC)
time (min)
10.1
8.8
9.7
2.5
8.3
8.0
8.4
20.1
19.5
20.3
5
28.8
28.0
28.8
10
35.9
35.3
36.0
15
60.6
59.5
60.4
20
76.1
75.4
75.2
40
b
cyclopentanone ethylene ketal
reaction (%) (pressure)
substrate (%) (GLC)
17.4
16.2
16.4
29.3
29.0
29.7
40.7
39.9
40.1
50.4
48.3
48.4
76.2
75.5
75.0
cyclopentanone (%) (GLC)
a
b
Reaction vessels were seasoned with allyl bromide. Values determined in the presence of the propene inhibitor.
a
Table 4. Invariability of the Rate Coefficients from the Initial Pressure
substrate
temp (°C)
parameters
value
2-methyl-1,3-dioxolane
469.8
P0 (Torr)
46
57
69
86.5
3.94
72
113
3.96
85
104k1 (s−1
P0 (Torr)
104k1 (s−1
P0 (Torr)
104k1 (s−1
)
)
)
4.09
51
4.01
53
3.90
67
2,2-dimethyl-1,3-dioxolane
480.3
470.1
3.71
55
3.95
52
3.51
69.5
5.83
3.78
86
3.77
88
cyclopentanone ethylene ketal
5.75
5.86
5.96
5.71
a
The results are from the GLC analyses.
a
The mechanism suggested for product formation from
cyclopentanone ethylene ketal is as follows:
Table 5. Variation of the Rate Coefficients with Temperature
2-Methyl-1,3-dioxolane
temperature (°C)
104k1 (s−1
459.7
2.26
465.1
3.00
469.8
3.84
475.0
5.05
479.7
6.50
)
log k1 = (13.61 0.12) − (242.1 1.0) kJ mol−1 (2.303RT)−1; r = 0.9997
2,2-Dimethyl-1,3-dioxolane
temperature (°C)
104k1 (s−1
470.2
2.17
475.1
2.83
480.3
3.71
485.0
4.86
490.0
6.40
)
log k1 = (14.16 0.14) − (253.7 2.0) kJ mol−1 (2.303RT)−1; r = 0.9998
Cyclopentanone Ethylene Ketal
temperature (°C)
104k1 (s−1
460.0
3.40
465.6
4.50
470.1
5.84
475.3
7.60
480.4
9.80
)
log k1 = (13.48 0.11) − (238.0 1.6) kJ mol−1 (2.303RT)−1; r = 0.9998
a
Obtained by GLC analysis.
The proposed mechanism for product formation from 2,2-
dimethyl-1,3-dioxolane is shown below.
In order to support or modify the proposed mechanisms
described in reactions 7−9, a theoretical study of these decomposi-
tion reactions in the present work was additionally carried out.
IV. COMPUTATIONAL METHODS AND MODEL
The electronic structure calculations were performed using
density functional theory (DFT) methods: Becke’s three-
parameter formulation from functional Lee, Yang, and Parr
[B3LYP/6-31G(d,p) and B3LYP/6-31++G(d,p)],18−20 and
Perdew−Wang 1991 correlation functional [MPW1PW9/
6-31G(d,p) and MPW1PW91/6-31++G(d,p)].21 The calcu-
lations have been performed with Gaussian 03.22 Default
parameters were used for convergence (e.g., Berny analytical
gradient optimization routine, convergence on the density
matrix, 10−9 atomic unit; threshold value for maximum
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Table 6. Kinetic and Thermodynamic Parameters at 480.0°C
substrate
104k1 (s−1
)
Ea (kJ/mol)
log A (s−1
)
ΔS⧧ ( J mol−1 K−1
)
ΔH⧧ (kJ/mol)
ΔG⧧ (kJ/mol)
2-methyl-1,3-dioxolane
6.46
3.63
9.32
242.1 1.0
253.7 2.0
238.0 1.6
13.61 0.12
14.16 0.14
13.48 0.11
−0.43
10.10
−2.92
235.8
247.4
231.7
236.1
239.8
233.9
2,2-dimethyl-1,3-dioxolane
cyclopentanone ethylene ketal
displacement, 0.0018 Å; and maximum force, 0.00045
hartree/bohr. Location of transition state (TS) structures
was performed using the Quadratic Synchronous Transit
(QST) protocol. All structures were fully optimized, and
frequency calculations were performed to ensure the absence
of any imaginary frequencies on local minima and the pre-
sence of a single imaginary frequency on TSs. Intrinsic reaction
coordinate (IRC) calculations were carried out to confirm the
reaction pathways (Supporting Information).
Thermodynamic parameters were calculated from frequency
calculations {i.e., zero-point vibrational energy (ZPVE), tempera-
ture corrections [E(T)], and absolute entropies [S(T)]}, assum-
ing ideal gas behavior from the harmonic frequencies and
moments of inertia by standard methods.23 Frequency values,
moments of inertia, and thermochemistry results are included as
Supporting Information. We used average temperature and
pressure within the experimental range. Scaling factors for
frequencies and zero-point energies were taken from the
literature24,25 (Table 7)
method. In all cases, the calculated entropy of activation was
more negative than the experimental value. The divergences
observed are possibly due to the use of the harmonic approxi-
mation and the existence of low-frequency modes. These vibra-
tional modes are highly unharmonic and may contribute
significantly to the entropy. Anharmonic frequency calculations,
hindered-rotor and free-rotor models, have been used for this
purpose; however, we have found that enthalpies of activation
and consequently energies of activation can be used to explain
the preferred reaction path.
To further study the nature of these reactions and the TS
involved in the processes, we studied the geometrical parameters,
NBO charges, and bond orders as described in the following
sections.
For the analysis of geometrical parameters, NBO charges, and
bond orders, we have selected the B3LYP/6-31++G(d,p)
method for 2-methyl-1,3-dioxolane and the MPW1PW91/
6-31G(d,p) method for 2,2-dimethyl-1,3-dioxolane and cyclo-
pentanone ethylene ketal.
Transition State and Mechanism. The quadratic synchro-
nous transit method allowed us to locate the transition state
structures of the above reactions. The optimized structures
for reactants, the TS, and products of the thermal decom-
position of 2-methyl-1,3-dixolane, 2,2-1,3-dimethyldioxo-
lane, and cyclopentanone ethylene ketal are displayed in
Figures 4−6.
The structures of the transition states are four-centered
geometries comprising atoms C1, C2, O3, and H4. Structural
parameters of reactant, TS, and product of these reactions
are reported in Tables 9−11; atom numbers are shown in
Schemes 3−5.
Table 7. Scaling Factors for Frequency Calculations at
753.15 K (480 °C)
method
T (K)
P (atm)
scaling factors
2-Methyl-1,3-dioxolane
753.15
B3LYP/6-31++G(d,p)
0.11
0.964
0.952
0.952
2,2-Dimethyl-1,3-dioxolane
MPW1PW91/6-31G(d,p) 753.15 0.11
Cyclopentanone Ethylene Ketal
MPW1PW91/6-31G(d,p) 753.15 0.11
In the thermal decomposition of 2-methyl-1,3-dioxolane, 2,2-
dimethyl-1,3-dioxolane, and cyclopentanone ethylene ketal, the
most significant geometrical change is the elongation of the
C2−O3 bond from 1.43 to 2.39 Å in the TS for 2-methyl-1,3-
dioxolane and from 1.42 to 2.25 Å in the TS for both 2,2-
dimethyl-1,3-dioxolane and cyclopentanone ethylene ketal. The
elongation of the H4−C1 bond is also important as this distance
changes from 1.09 to 1.24 Å in the TS for 2-methyl-1,3-dioxolane
and cyclopentanone ethylene ketal; this change is greater for 2,2-
dimethyl-1,3-dioxolane (from 1.09 to 1.28 Å). The C1−C2
distance shortens from 1.51−1.54 to 1.43−1.44 Å reflecting
the change from a single to a double bond. For all substrates, the
four atoms involved in the TS lie in a plane, as seen in the
dihedrals.
NBO Charges. The changes in electronic structure along
the reaction pathway may be followed by NBO charges. The
NBO charges of atoms involved in the reaction changes in the
reactant, TS, and products of the compounds in this study are
reported in Tables 12−14. Atom numbers are shown in
Schemes 3−5.
The rate constants were obtained using the canonical TST.
The experimental enthalpy, entropy, and free energy of
activation are obtained from the energy of activation and log A
using the Arrhenius and Eyring equations.26 Theoretical energies
of activation, log A, and rate coefficients are derived from the
enthalpy and entropy of activation obtained in the frequency
calculations. Detailed description and equations are described in
previous works.27,28
Theoretical Results. Kinetic and Thermodynamic Param-
eters. Calculated activation parameters for the rate-determining
step of the thermal decomposition of 2-methyl-1,3-dioxolane,
2,2-dimethyl-1,3-dioxolane, and cyclopentanone ethylene ketal
are presented in Table 8. The second step in all cases has a
lower energy of activation, thereby confirming that the first
step is rate-determining, derived from the B3LYP/6-31++G(d,p)
and MPW1PW91/6-31G(d,p) level of theory, as shown in
Figures 1−3.
Comparing calculated parameters to the experimental values,
we obtain good agreement for energies of activation and, con-
sequently, for enthalpies of activation at B3LYP/6-31++G(d,p)
for the decomposition reaction of 2-methyl-1,3-dioxolane.
Conversely, for 2,2-dimethyl-1,3-dioxolane and cyclopentanone
ethylene ketal, B3LYP/6-31++G(d,p) underestimates the en-
thalpy and energies of activation. The calculated values were closer
to the experimental values with the MPW1PW91/6-31G(d,p)
For the three substrates, there is an increase in electron density
at O3 of an ∼0.18 negative charge increase for 2-methyl-1,3-
dioxolane and 2,2-dimethyl-1,3-dioxolane, and a 0.2 negative
charge increase for cyclopentanone ethylene ketal. At C2 the
changes are very small in the TS for the three substrates. There is
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Table 8. Calculated Kinetic and Thermodynamic Parameters of Activation at 480.0 °C
method
Ea (kJ/mol)
log A
ΔS⧧ ( J mol−1 K−1
)
ΔH⧧ (kJ/mol)
ΔG⧧ (kJ/mol)
2-Methyl-1,3-dioxolane
experimental
242.1
253.7
247.1
269.2
265.2
172.3
13.61
−0.43
−15.23
−15.52
−14.81
−16.23
−34.61
235.8
247.5
240.8
263.8
258.9
166.1
236.1
259.0
252.5
274.1
271.1
192.13
B3LYP/6-31G(d,p)
12.83
B3LYP/6-31++G(d,p)
12.82
MPW1PW91/6-31G(d,p)
MPW1PW91/6-31++G(d,p)
Fast step (B3LYP/6-31++G(d,p))
12.86
12.78
11.82
2,2-Dimethyl-1,3-dioxolane
experimental
253.7
235.1
225.0
246.2
239.3
163.1
14.16
10.10
−6.56
−3.98
−8.72
−5.65
−20.23
247.4
228.8
218.8
239.9
233.1
156.8
239.8
B3LYP/6-31G(d,p)
13.29
233.75
221.76
246.47
237.33
172.05
B3LYP/6-31++G(d,p)
MPW1PW91/6-31G(d,p)
MPW1PW91/6-31++G(d,p)
fast step (MPW1PW91/6-31G(d,p))
13.42
13.17
13.33
12.57
Cyclopentanone Ethylene Ketal
experimental
238.0
229.6
217.8
242.2
233.6
162.7
13.48
12.92
12.73
12.91
12.94
12.02
−2.92
−13.57
−17.27
−13.81
−13.23
−30.89
232.4
223.3
211.6
236.0
227.3
156.4
233.9
B3LYP/6-31G(d,p)
233.52
224.57
246.36
237.30
179.66
B3LYP/6-31G++(d,p)
MPW1PW91/6-31G(d,p)
MPW1PW91/6-31++G(d,p)
fast step (MPW1PW91/6-31G(d,p))
Figure 1. Reaction profile for the thermal decomposition of 2-methyl-1,3-dioxolane at the B3LYP/6-31++G(d,p) level of theory.
a similar increase in positive charge at H4 in the TS by 0.15, 0.16,
and 0.15 for 2-methyl-1,3-dioxolane, 2,2-dimethyl-1,3-dioxolane,
and cyclopentanone ethylene ketal, respectively, as C1 becomes
more electron-rich, increasing the negative charge by 0.15, 0.10,
and 0.13 for 2-methyl-1,3-dioxolane, 2,2-dimethyl-1,3-dioxolane,
and cyclopentanone ethylene ketal, respectively. These changes
reflect the C1−H4 and C2−O3 bond breaking in the TS, described
in the proposed mechanism.
Bond Order Analysis. NBO calculations were used to
calculate bond orders aimed at describing the progress along
different reaction coordinates.29−31 Wiberg bond indexes32 were
calculated using the Natural Bond Orbital (NBO) program33
with Gaussian 03. The reaction mechanism involving bond
breaking and making may be identified by the synchronicity (Sy)
concept proposed by Moyano et al.34 as described in the
following equations:
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Figure 2. Reaction profile for the thermal decomposition of 2,2-dimethyl-1,3-dioxolane at the MPW1PW91/6-31G(d,p) level of theory.
Figure 3. Reaction profile for the thermal decomposition of cyclopentanone ethylene ketal at the MPW1PW91/6-31G(d,p) level of theory.
n
⎡
⎢
⎤
⎥
process in which all bonds are formed and broken in the same
way in the TS.
δBi indicates change in i bond order, and n is the number of
bonds directly involved in the reaction. The relative variation of
the bond index is obtained from
Sy = 1 −
δB − δB |/δB
2n − 2
∑
i
av
av
⎢
⎣
⎥
⎦
i=1
The synchronicity parameter in concerted reactions varies
from 0 to 1; the value 1 represents a synchronic concerted
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Figure 4. Structures of reactant (left), transition state (TS) (center), and products (right) of the gas-phase decomposition of 2-methyl-1,3-dioxolane,
optimized at the B3LYP/6-31++G(d,p) level of theory.
Figure 5. Structures of reactant (left), transition state (TS) (center), and products (right) of the gas-phase decomposition of 2,2-dimethyl-1,3-
dioxolane, optimized at the MPW1PW91/6-31G(d,p) level of theory.
Figure 6. Structures of reactant (left), transition state (TS) (center), and products (right) of the gas-phase decomposition of cyclopentanone ethylene
ketal, optimized at the MPW1PW91/6-31G(d,p) level of theory.
Table 9. Structural Parameters for the Optimized Reactant
(R), Transition State (TS), and Products (P) from the
2-Methyl-1,3-dioxolane Decomposition with the B3LYP/
6-31++G(d,p) Method
Table 10. Structural Parameters for the Optimized Reactant
(R), Transition State (TS), and Products (P) from the 2,2-
Dimethyl-1,3-dioxolane Decomposition with the
MPW1PW91/6-31G(d,p) Method
Atomic distances (Å)
Atomic Distance (Å)
C1−C2
C2−O3
O3−H4
H4−C1
C1−C2
C2−O3
O3−H4
H4−C1
R
1.510
1.433
1.336
1.429
2.391
2.680
1.463
0.967
1.093
1.239
3.318
R
1.523
1.432
1.339
1.417
2.248
2.704
1.381
0.963
1.092
1.275
2.523
TS
P
TS
P
3.171
3.345
Dihedral (deg)
Dihedral (deg)
C1−C2−O3−
C2−O3−H4−
O3−H4−C1−
H4−C1−C2−
C1−C2−O3−
C2−O3−H4−
O3−H4−C1−
H4−C1−C2−
H4
C1
C2
O3
H4
C1
C2
O3
TS
−2.522
4.369
−5.771
2.356
TS
−1.504
2.518
−3.238
1.334
Imaginary Frequency (cm−1
)
Imaginary Frequency (cm−1
)
TS
1459.7
TS
1653.2
δB = [B TS − B R]/[B P − B R]
Bond orders were estimated using Wiberg bond
indexes Bi, calculated for the bonds involved in the reac-
tion changes (i.e., C1−C2, C2−O3, O3−H4, and H4−C1;
Tables 15−17).
i
i
i
i
i
The superscripts R, TS, and P indicate reactant, transition
state, and product, respectively.
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Table 11. Structural Parameters for the Optimized Reactant
(R), Transition State (TS), and Products (P) from the
Cyclopentanone Ethylene Ketal Decomposition with the
MPW1PW91/6-31G (d,p) Method
Table 13. NBO Charges of the Atoms Involved in the 2,2-
Dimethyl-1,3-dioxolane Thermal Decomposition from the
MPW1PW91/6-31G(d,p) Calculations
R
TS
P
Atomic Distance (Å)
C1
C2
O3
H4
−0.76
0.59
−0.86
0.58
−0.77
0.31
C1−C2
C2−O3
O3−H4
H4−C1
−0.59
0.25
−0.77
0.41
−0.76
0.27
R
1.539
1.441
1.336
1.418
2.365
2.482
1.443
0.960
1.092
1.237
6.613
TS
P
4.704
Table 14. NBO Charges of the Atoms Involved in the
Cyclopentanone Ethylene Ketal Thermal Decomposition
from the MPW1PW91/6-31G(d,p) Calculations
Dihedral (deg)
C1−C2−O3−
C2−O3−H4−
O3−H4−C1−
H4−C1−C2−
H4
C1
C2
O3
TS
0.827
−1.475
1.920
−0.765
R
TS
P
Imaginary Frequency (cm−1
)
C1
C2
O3
H4
−0.53
0.59
−0.66
0.61
−0.31
0.32
TS
1445.85
−0.59
0.26
−0.79
0.41
−0.77
0.49
Scheme 3
Table 15. Wiberg Bond Index of the Reactant (R), Transition
State (TS), and Products (P) for the 2-Methyl-1,3-dioxolane
Thermal Decomposition from the B3LYP/6-31++G(d,p)
Calculation
C1−C2
C2−O3
O3−H4
H4−C1
Sy
δBav
BiR
BiTS
BiP
1.02
1.23
1.90
24.31
0.90
0.25
0.01
72.23
0.00
0.22
0.74
30.09
0.92
0.57
0.00
38.67
0.75
0.41
Scheme 4
%Ev
Table 16. Wiberg Bond Index of the Reactant (R), Transition
State (TS), and Products (P) for the 2,2-Dimethyl-1,3-
dioxolane Thermal Decomposition from the MPW1PW91/
6-31G(d,p) Calculation
C1−C2
C2−O3
O3−H4
H4−C1
Sy
δBav
BiR
BiTS
BiP
0.99
1.23
1.87
26.81
0.89
0.27
0.00
70.19
0.00
0.26
0.74
34.81
0.92
0.51
0.00
44.74
0.80
0.44
Scheme 5
%Ev
Table 17. Wiberg Bond Index of the Reactant (R), Transition
State (TS), and Products (P) for the Cyclopentanone
Ethylene Ketal Thermal Decomposition from the
MPW1PW91/6-31G(d,p) Calculation
C1−C2
C2−O3
O3−H4
H4−C1
Sy
δBav
Table 12. NBO Charges of the Atoms Involved in the
2-Methyl-1,3-dioxolane Thermal Decomposition from the
B3LYP/6-31++G(d,p) Calculations
BiR
BiTS
BiP
0.98
1.19
1.81
25.30
0.90
0.22
0.00
75.56
0.00
0.23
0.75
30.67
0.90
0.53
0.00
41.11
0.75
0.43
R
TS
P
%Ev
C1
C2
O3
H4
−0.69
0.39
−0.84
0.41
−0.54
0.11
2-methyl-1,3-dioxolane, 2,2-dimethyl-dioxolane, and cyclopen-
tanone ethylene ketal, repectively.
−0.61
0.24
−0.79
0.39
−0.77
0.50
V. CONCLUSIONS
Bond order indexes describing the bond formation and
breaking in the thermal decomposition reactions of 2-methyl-
1,3-dioxolane, 2,2-dimethyl-dioxolane, and cyclopentanone
ethylene ketal are shown in Tables 15−17. In comparison
with the other bonds in the TS, the breaking of the C2−O3
bond is more complete at 72%, 70%, and 76% for
In the present joint experimental and theoretical work, we have
studied the thermal decomposition reactions in the gas phase of a
series of dioxolanes (i.e., 2-methyl-1,3-dioxolane, 2,2-dimethyl-1,3-
dioxolane, and cyclopentanone ethylene ketal) and aimed to propose
a reasonable mechanism in accordance with product formation and
experimental and calculated kinetic and thermodynamic parameters.
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ASSOCIATED CONTENT
* Supporting Information
■
S
IRC obtained from gas-phase thermal decomposition kinetics of
2-methyl-1,3-dioxolane, 2,2-dimethyl-1,3-dioxolane, and cyclo-
pentanone ethylene ketal. This material is available free of charge
via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION
Corresponding Author
*E-mail: chuchani@ivic.gob.ve.
■
Notes
The authors declare no competing financial interest.
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