Kinetics and mechanisms of the unimolecular elimination of 2,2-diethoxypropane and 1,1-diethoxycyclohexane in the gas phase: Experimental and theoretical study

Article abstract of DOI:10.1021/jp209596p

The gas-phase thermal elimination of 2,2-diethoxypropane was found to give ethanol, acetone, and ethylene, while 1,1-diethoxycyclohexane yielded 1-ethoxycyclohexene and ethanol. The kinetics determinations were carried out, with the reaction vessels deactivated with allyl bromide, and the presence of the free radical suppressor cyclohexene and toluene. Temperature and pressure ranges were 240.1-358.3 °C and 38-102 Torr. The elimination reactions are homogeneous, unimolecular, and follow a first-order rate law. The rate coefficients are given by the following Arrhenius equations: for 2,2-diethoxypropane, log k₁ (s^-1) = (13.04 ± 0.07) - (186.6 ± 0.8) kJ mol^-1 (2.303RT)^-1; for the intermediate 2-ethoxypropene, log k₁ (s^-1) = (13.36 ± 0.33) - (188.8 ± 3.4) kJ mol^-1 (2.303RT) ^-1; and for 1,1-diethoxycyclohexane, log k = (14.02 ± 0.11) - (176.6 ± 1.1) kJ mol^-1 (2.303RT)^-1. Theoretical calculations of these reactions using DFT methods B3LYP, MPW1PW91, and PBEPBE, with 6-31G(d,p) and 6-31++G(d,p) basis set, demonstrated that the elimination of 2,2-diethoxypropane and 1,1-diethoxycyclohexane proceeds through a concerted nonsynchronous four-membered cyclic transition state type of mechanism. The rate-determining factor in these reactions is the elongation of the C-O bond. The intermediate product of 2,2-diethoxypropane elimination, that is, 2-ethoxypropene, further decomposes through a concerted cyclic six-membered cyclic transition state mechanism.

Full text of DOI:10.1021/jp209596p

ARTICLE
pubs.acs.org/JPCA
Kinetics and Mechanisms of the Unimolecular Elimination of 2,
2-Diethoxypropane and 1,1-Diethoxycyclohexane in the Gas Phase:
Experimental and Theoretical Study
Felix Rosas,† Alexis Maldonado,† Jesus Lezama,† Rosa M. Domínguez,† Josꢀe R. Mora,† 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
b
ABSTRACT: The gas-phase thermal elimination of 2,2-diethox-
ypropane was found to give ethanol, acetone, and ethylene, while
1,1-diethoxycyclohexane yielded 1-ethoxycyclohexene and etha-
nol. The kinetics determinations were carried out, with the
reaction vessels deactivated with allyl bromide, and the presence
of the free radical suppressor cyclohexene and toluene. Tem-
perature and pressure ranges were 240.1ꢀ358.3 °C and 38ꢀ102
Torr. The elimination reactions are homogeneous, unimolecu-
lar, and follow a first-order rate law. The rate coefficients are
given by the following Arrhenius equations: for 2,2-diethoxy-
propane, log k1 (sꢀ1) = (13.04 ( 0.07) ꢀ (186.6 ( 0.8) kJ molꢀ1 (2.303RT)ꢀ1; for the intermediate 2-ethoxypropene, log k1 (sꢀ1) =
(13.36(0.33) ꢀ (188.8 (3.4) kJ molꢀ1 (2.303RT)ꢀ1; and for 1,1-diethoxycyclohexane, log k=(14.02(0.11) ꢀ (176.6 (1.1) kJ molꢀ1
(2.303RT)ꢀ1. Theoretical calculations of these reactions using DFT methods B3LYP, MPW1PW91, and PBEPBE, with 6-31G(d,p)
and 6-31++G(d,p) basis set, demonstrated that the elimination of 2,2-diethoxypropane and 1,1-diethoxycyclohexane proceeds
through a concerted nonsynchronous four-membered cyclic transition state type of mechanism. The rate-determining factor in
these reactions is the elongation of the CꢀO bond. The intermediate product of 2,2-diethoxypropane elimination, that is,
2-ethoxypropene, further decomposes through a concerted cyclic six-membered cyclic transition state mechanism.
ethylene methylal and propylene methylal3 at 512ꢀ572 °C were
I. INTRODUCTION
Molera and co-workers1 were first to report the gas-phase
thermal decomposition of ethylal, dimethylacetal, and diethyla-
thought to proceed through a biradical mechanism as depicted in
reaction 2.
cetal, in a static system at 389ꢀ530 °C. Ethylal was believed to
decompose by a chain mechanism, whereas for dimethyl and
diethylacetals a rearrangement process was assumed to be im-
portant. Thus, dimethylacetal reaction was found to follow a first-
order rate law to yield the products as described in reaction 1.
A revisited investigation of methylal thermal decomposition in
a flow system4,5 showed again a complex radical reaction with
different results due to a higher working temperature than the
static system.
Years later, the gas-phase pyrolysis of a ketal without the
presence of a H at the carbon containing the two alkoxy group
Additional work on aliphatic ketals, for example, the gas-phase
pyrolysis kinetics of methylal,2 was carried out at 472ꢀ520 °C
and was found to be a free radical chain reaction. However,
Received: October 5, 2011
Revised: December 19, 2011
Published: December 20, 2011
r
2011 American Chemical Society
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Scheme 1
in reasonably good agreement with the experimental values using
the PBEPBE/6-31G(d,p) level of theory. Both experimental results
and theoretical calculations suggested a molecular mechanism
involving a concerted polar four-membered cyclic transition state.
The little information on the homogeneous, unimolecular de-
composition of ketals in the gas phase led us to carry out addi-
tional experiments on the elimination kinetics of selected molecules,
but without an α-H at the carbon containing the two alkoxy groups.
In this work, we examined the thermal decomposition reactions of
2,2-diethoxypropane and 1,1-diethoxycyclohexane with theoretical
studies for a reasonable mechanistic interpretation. The theoretical
calculations aim to obtain the kinetic parameters and the character-
ization of the potential energy surface (PES) as a means to under-
stand the nature of the molecular mechanism of these reactions.
(geminal carbon), that is, 2,2-dimethoxypropane in the presence
of NO gas, yielded products as described in reaction 3.6
II. EXPERIMENTAL SECTION
The substrates 2,2-diethoxypropane (Aldrich) and1,1-diethoxy-
cyclohexane (Aldrich) were found better than of 98.0% purity
when analyzed by GCꢀMS Saturn 2000, Varian, with a DB-5MS
capillary column 30 m ꢁ 0.53 mm i.d., 0.53 μm film thickness. The
products ethanol and ethylene were identified in a GCꢀMS Saturn
2000, Varian with a DB-5MS capillary column 30 m ꢁ 0.25 mm
i.d., 0.25 μm. The impurities were traces, and their decomposition
products could not be identified. The reactant 2,2-diethoxypropane
was quantitatively analyzed with a capillary column VA-WAX,
30 m ꢁ 0.53 mm i.d., 1.0 μm film thickness using a Varian 3700 gas
chromatograph. For the quantitative analysis of the products,
ethanol was carried out by using a Varian 3700 gas chromatograph
with a Porapak R (80ꢀ100 mesh) column, while ethylene was done
by employing the same Varian 3700 with a Porapak S (80ꢀ100
mesh) column. Calibration for quantitative analysis of ethanol was
carried out using an internal standard of propanol, while propene
was the internal standard for ethene.
These investigations led the assumption that the CꢀOR bond
polarization may be rate determining, and because of this, a few
years ago, it was examined the importance of the hydrogen atom
present at the CβꢀH bond in the transition state mechanism of
ketals (Scheme 1). The work was on the gas-phase elimination
kinetics of 2,2-diethoxy ethylamine and 2,2-diethoxy-N,N-diethyl
ethylamine.7 The reactions undergoing two parallel processes
proved to be homogeneous, unimolecular, and obey a first-order
rate law [reaction 4]. According to these results, the H of the CβꢀH
bond was considered to be more favored in the elimination process.
Kinetics. The kinetic determinations were carried out in a
static reaction system as previously reported.10ꢀ13 The reaction
vessel was seasoned with the product of decomposition of allyl
bromide at 400ꢀ420 °C. At each temperature, several runs were
carried out in our experiments. The rate coefficients were cal-
culated from the pressure increase measured manometrically and
by the quantitative GC analysis. The temperature was maintained
within (0.2 °C through control with a Shinko DIC-PS 23TR
resistance thermometer and was measured with a calibrated
platinumꢀplatinumꢀ13% rhodium thermocouple. No tempera-
ture gradient was observed along the reaction vessel. The starting
materials were all injected directly into the reaction vessel with a
syringe through a silicone rubber septum. The amount of
substrate used for each reaction was ∼0.05ꢀ0.2 mL.
Along these line of works, the gas-phase elimination kinetics of
several β-substituted diethyl acetals were undertaken and dem-
onstrated to be homogeneous, unimolecular, and follow first-
order law kinetics [reaction 5].8 The decomposition processes
occur via two parallel reactions as depicted in reaction 5. The
comparative kinetic and thermodynamic parameters of the parallel
reactions suggested two different concerted polar four-membered
cyclic transition state types of mechanisms.
III. RESULTS AND DISCUSSION
The products of the gas-phase elimination of 2,2-diethoxypropane
and 1,1-diethoxycyclohexane, in vessels deactivated with the product
of decomposition of allyl bromide, are described in reactions 6 and 7.
Recently, the homogeneous, unimolecular gas-phase elimina-
tion kinetics of 1,1-dimethoxycyclohexane was found to give
1-methoxycyclohexene and methanol.9 Additional data in the
elucidation of the mechanism of this decomposition9 were the use
of theoretical calculations by using DFT methods. The calculated
values for energy of activation and enthalpy of activation were found
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Table 1. Homogeneity of the Reaction
To examine the effect of surface upon the rate of elimination,
several runs, in the presence of the free radical suppressor, were
carried out in a vessel with a surface-to-volume ratio of 6.0
relative to that of the normal vessel, which is equal to one. The
packed and unpacked clean Pyrex vessel had a marked effect on
the rates of decomposition of 2,2-diethoxypropane at 333.0 °C
and 1,1-diethoxycyclohexane at 270.1 °C. However, when the
packed and unpacked vessels are seasoned with allyl bromide, no
significant effect on the rate coefficient of these substrates was
obtained (Table 1).
a
b
c
compound
S/V (cmꢀ1
)
104 k1 (sꢀ1
)
104 k1 (sꢀ1
)
2,2-diethoxypropane
at 333.0 °C
1
6
1
6
33.00 ( 1.15 12.63 ( 0.33
50.09 ( 1.44 12.42 ( 0.46
54.89 ( 5.20 11.05 ( 0.13
1,1-diethoxycyclohexane
at 270.1 °C
65.30 ( 8.1
10.96 ( 0.17
a S = surface area; V = volume. b Clean Pyrex vessel. c Vessel deactivated
with allyl bromide.
The kinetic runs of 2,2-diethoxypropane were performed in
the presence of at least 3 times the amount of the chain inhibitor
toluene, while for 1,1-diethoxycyclohexane with at least twice the
amount of cyclohexene. Apparently, a low k-value of 1,1-diethox-
ycyclohexane in the absence of the inhibitor may be due to a
small polymerization of the product 1-ethoxycyclohexene. These
processes have been undertaken as a precaution, to inhibit any
possible radical chain processes. The effect of different propor-
tions of the chain suppressor on the reactions is shown in
Table 2.
The theoretical stoichiometry of reaction 6 suggests that the
final pressure Pf should be 3 times the initial pressure Po. The
average experimental results of Pf/Po values at five different
temperatures and 10 half-lives was 2.8 (Table 3). The fact that Pf/
Po < 3 for 2,2-diethoxypropane arises from the very small amount
of the undecomposed intermediate 2-ethoxypropene [reaction
6]. In the case for 1,1-diethoxycyclohexane [reaction 7], the
theoretical Pf/Po should be equal to 2, and the experimental
result was found in good agreement (Table 3). An additional
examination of the stoichiometry as depicted in reactions 6 and 7
is given in Table 4. In this respect, for both compounds, up to
76% reaction, there is a good agreement between the extent of
decomposition as predicted from pressure measurement and
from the chromatographic analyses of the reacted amount of the
diethoxy substrates.
Table 2. Effect of the Free Radical Chain Inhibitor on Rates
temp
Psa
Pib
104 k1
(sꢀ1
substrate
(°C)
(Torr) (Torr) Pi/Ps
)
2,2-diethoxypropanec
339.0
74
37.85
34.72
12.64
12.82
12.64
7.34
60
55
46
38
67
55
47
50
42
70
141
142
138
1.3
2.6
3.1
3.6
1,1-diethoxycyclohexaned
270.2
58
1.0
1.7
2.8
3.1
11.14
10.91
11.05
11.21
77.6
143
129
a Ps = pressure of substrate. b Pi = pressure of free radical inhibitor.
c Toluene inhibitor. d Cyclohexene inhibitor.
Table 3. Ratio of Final (Pf) to Initial Pressure (P0) of the
Substratea
substrate
temp (°C) Po (Torr) Pf (Torr) Pf/Po average
2,2-diethoxypropaneb
251.4
300.7
360.8
349.9
441.4
250.4
260.1
270.2
280.0
290.1
45
61
75
67
85
82
87
73
69
80
126
178
215
176
240
165
183
150
138
160.5
2.8
2.9
2.9
2.6
2.8
2.0
2.1
2.1
2.0
2.0
2.8
The rate coefficients were found to be independent of changes
in the initial pressure, Po, of the substrate (Table 5), and the first-
order plots are satisfactorily linear up to 70% decomposition
in both reactants. The variation of the rate coefficients with
temperature, in deactivated vessel with product of decomposi-
tion of allyl bromide and in the presence of the free radical
inhibitor, together with the corresponding Arrhenius expression
are given in Table 6 (90% confidence levels with a least-squares
method).
1,1-diethoxycyclohexanec
2.0
Analysis of the experimental results of the kinetic and thermo-
dynamic parameters of activation given in Table 7 suggests the
first step 1 of both substrate eliminations is to undergo a concerted
a Reaction vessels seasoned with allyl bromide. b In the presence of
toluene. c In the presence of cyclohexene inhibitor.
Table 4. Stoichiometry of the Reactiona
substrate
temp (°C)
parameters
time (min)
value
2,2-diethoxypropaneb
339.0
2
3
5
10
15
20
reaction (%) (pressure)
substrate (%) (GLC)
time (min)
14.3
13.0
5
20.8
16.9
10
31.3
33.3
15
53.8
55.6
20
67.2
67.3
76.9
76.6
2-diethoxypropeneb
339.0
270.0
reaction (%) (pressure)
ethylene (%) (GLC)
time (min)
31.3
17.6
2
53.8
20.3
5
67.2
33.9
8.3
76.9
46.0
10
1,1-diethoxycyclohexanec
11.7
52.6
52.2
13.3
76.4
76.2
reaction (%) (pressure)
substrate (%) (GLC)
17.8
18.0
20.3
20.2
24.8
25.4
31.0
30.8
a Reaction vessels seasoned with allyl bromide. b In the presence of toluene. c In the presence of cyclohexene inhibitor.
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Table 5. Invariability of the Rate Coefficients from Initial Pressure
substrate
temp (°C)
parameters
value
48
2,2-diethoxypropanea
339.0
P0 (Torr)
38
46
55
60
104 k1 (sꢀ1
)
12.64
48
12.82
60
12.16
77
12.64
88
12.53
102
1,1-diethoxycyclohexaneb
410.8
P0 (Torr)
104 k1 (sꢀ1
)
11.14
10.91
11.05
11.21
10.95
a Results from GLC analysis. b Results from manometric measurements.
Table 6. Temperature Dependence of the Rate Coefficients
2,2-Diethoxypropanea
temperature (°C)
104 k1 (sꢀ1
319.0
3.75
329.7
7.37
339.0
12.88
348.6
22.49
358.3
39.95
)
log k1 = (13.04 ( 0.07) ꢀ (186.6 ( 0.8) kJ molꢀ1 (2.303RT)ꢀ1; r = 0.9999
2-Ethoxypropenea,b
temperature (°C)
104 k1 (sꢀ1
319.0
5.12
329.7
10.09
339.0
16.61
348.6
31.73
358.3
55.61
)
log k1 = (13.36 ( 0.33) ꢀ (188.8 ( 3.4) kJ molꢀ1 (2.303RT)ꢀ1; r = 0.9990
1,1-Diethoxycyclohexanec
temperature (°C)
104 k1 (sꢀ1
240.1
1.12
250.3
2.53
260.2
5.30
270.0
11.10
280.5
22.27
290.0
44.80
)
log k1 = (14.02 ( 0.11) ꢀ (176.6 ( 1.1) kJ molꢀ1 (2.303RT)ꢀ1 ; r = 0.9998
a GLC analysis. b Decomposition of the intermediate. c Results from pressure measurements.
Table 7. Kinetic and Thermodynamic Parameters at 320 °C
Z
k1 ꢁ 104 (sꢀ1
)
Ea (kJ/mol)
log A (sꢀ1
)
ΔSq (J/mol K)
ΔHq (kJ/mol)
ΔGq (kJ/mol)
3
2,2-diethoxypropanea
2-ethoxypropenea,b
1,1-diethoxycyclohexanec
3.98
5.37
186.6 ( 0.8
188.8 ( 3.4
176.6 ( 1.1
13.04 ( 0.07
13.36 ( 0.33
14.02 ( 0.11
ꢀ9.23
ꢀ3.11
9.52
181.7
183.9
171.7
187.2
185.7
166.1
288.4
a GLC analysis. b Decomposition of the intermediate. c Results from pressure measurements.
polar four-membered cyclic transition state type of mechanism,
as shown in reactions 8 and 9.
(aldehyde or ketone) and the corresponding alkene as
depicted in reaction 10.
In the case of the intermediate product of 2,2-diethox-
ypropane, that is, 2-ethoxypropene, under the condition of
the temperature, proceeds as reported for the alkyl vinyl
ethers14a,b where the alkyl side contains at least a CβꢀH
bond, to further decompose through a six-membered cyclic
transition state, step 2 (reaction 8), to a carbonyl compound
To support or modify these interpretations derived from
experimental data, it was thought that a theoretical calculation
was a convenient method to elucidate a reasonable mechanism of
eliminations of both reactants.
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Figure 1. Structures of reactant (left), transition state TS (center), and products (right) of 2,2-diethoxypropane elimination reaction, optimized at
PBEPBE/6-31++G(d,p) level of theory.
Figure 2. Structures of reactant (left), transition state TS (center), and products (right) of 2-ethoxypropene elimination reaction optimized at
MPW1PW91/6-31G(d,p) level of theory.
IV. COMPUTATIONAL METHODS AND MODEL
is equal to 1, in the expression:
The reaction coordinates for the decomposition reactions of
2,2-diethoxypropane to yield products ethanol, ethylene and
acetone, and of 1,1-diethoxycyclohexane to products ethanol and
ethoxycyclohexene were studied. Theoretical calculations were
carried out using density functional theory (DFT) methods with
B3LYP, MPW1PW91, and PBEPBE methods with 6-31G(d,p),
and 6-31++G(d,p) basis sets in Gaussian 03W.15 The structures
of reactants and products were generated and optimized using
default parameters: Berny analytical gradient optimization algo-
rithm, requested convergence on the density matrix was 10ꢀ9
atomic units, the threshold value for maximum displacement
was 0.0018 Å, and maximum force 0.00045 hartree/bohr. The
Quadratic Synchronous Transit method was used to obtain the
transition state geometries. The stationary points were charac-
terized by means of normal-mode analysis; the transition state
structures had a unique imaginary frequency that is associated
with the transition vector (TV). Intrinsic reaction coordinate
(IRC) calculations were performed to verify that the transition
state structures connect the reactant and products in the reaction
path. Vibrational analysis allowed one to obtain thermodynamic
quantities such as zero-point vibrational energy (ZPVE), tem-
perature corrections [E(T)], and absolute entropies [S(T)].
Temperature corrections and absolute entropies were obtained
assuming ideal gas behavior from the harmonic frequencies and
moments of inertia by standard methods16 at average tempera-
ture and pressure values within the experimental range. Scaling
factors for frequencies and zero-point energies were taken from
the literature.17,18
kðTÞ ¼ ðkBT=hÞ expð ꢀ ΔG=RTÞ
whereΔGis the Gibbs free energychange between the reactant and
the transition state, and kB and h are the Boltzmann and Planck
constants, respectively.
ΔG# was calculated using the following relations:
ΔG ¼ ΔH ꢀ TΔS
and
ΔH ¼ V þ ΔZPVE þ ΔEðTÞ
where V is the potential energy barrier, ΔZPVE accounts for the
differences of ZPVE between the transition state TS and the re-
actant, and ΔE(T) represents the contribution of thermal energy
at a given temperature.
Theoretical Results. Kinetic and Thermodynamic Para-
meters. The gas-phase elimination reactions of 2,2-diethoxypro-
pane and 1,1-diethoxycyclohexane [reactions 6 and 7] were
studied using quantum chemical calculations to predict plausible
mechanism of these molecular decomposition. The minimum
energy path for the elimination reaction of 2,2-diethoxypropane
and 1,1-diethoxycycloehane to give 2-ethoxypropene, plus etha-
nol, and 1-ethoxycyclohexene, respectively, was characterized.
The TS connecting reactant and products has four-centered geo-
metry with elongation of the CꢀO bond (Figures 1 and 3). For
the decomposition reaction of 2-ethoxypropene, the TS is six-
centered geometry (Figure 2).
Results from theoretical calculations in these elimination re-
actions are given in Table 8. We found reasonable agreement with
the experimental values for enthalpy and energy of activations for
The TST19 used to estimate the first-order rate coefficients k(T)
was calculated using assuming that the transmission coefficient
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Table 8. Calculated Kinetic and Thermodynamic Parameters of Activation at 270.0 °C
method
Ea (kJ molꢀ1
)
log(A)
ΔSq (J molꢀ1 Kꢀ1
)
ΔHq (kJ molꢀ1
)
ΔGq (kJ molꢀ1
)
104k1 (s ꢀ1
)
2,2-Diethoxypropane
experimental
186.6
221.0
212.8
235.3
229.6
192.9
187.8
13.04
14.36
14.21
14.41
14.97
14.42
14.91
ꢀ8.50
16.70
13.80
17.70
28.40
17.80
27.20
182.1
216.5
208.3
230.8
225.1
188.4
183.3
186.7
207.4
198.5
221.2
209.7
178.8
168.5
0.12
B3LYP/6-31G(d,p)
0.0013
0.0054
0.00006
0.00076
0.72
B3LYP/6-31++G(d,p)
MPW1PW91/6-31G(d,p)
MPW1PW91/6-31++G(d,p)
PBEPBE/6-31G(d,p)
PBEPBE/6-31++G(d,p)
6.92
2-Ethoxypropenea
ꢀ2.40
experimental
188.8
182.6
178.5
186.5
183.9
152.3
148.8
13.36
13.29
13.36
13.18
13.20
13.29
13.30
184.3
178.1
174.0
181.9
179.4
147.8
144.3
185.6
182.6
175.7
185.2
182.4
149.9
146.2
0.16
0.53
B3LYP/6-31G(d,p)
ꢀ3.80
B3LYP/6-31++G(d,p)
MPW1PW91/6-31G(d,p)
MPW1PW91/6-31++G(d,p)
PBEPBE/6-31G(d,p)
PBEPBE/6-31++G(d,p)
ꢀ2.40
1.53
ꢀ5.90
0.17
ꢀ5.40
0.32
ꢀ3.70
432.4
960.9
ꢀ3.60
1,1-Diethoxycyclohexane
experimental
176.6
218.6
213.2
232.6
223.7
193.8
184.5
14.02
13.77
14.73
14.49
13.96
14.48
14.13
10.23
5.48
172.1
214.1
208.7
228.1
219.1
189.3
180.0
167.3
211.1
195.8
217.6
211.8
178.9
173.3
10.66
B3LYP/6-31G(d,p)
0.00055
0.0165
0.00013
0.00027
0.68
B3LYP/6-31G++(d,p)
MPW1PW91/6-31G(d,p)
MPW1PW91/6-31++G(d,p)
PBEPBE/6-31G(d,p)
23.80
19.21
8.98
19.07
12.35
PBEPBE/6-31++G(d,p)
a Intermediate decomposition.
2.39
Scheme 2
Scheme 3
the elimination reactions of 2,2-diethoxypropane and 1,1-diethox-
ycyclohexane, through four-membered TS, at the PBEPBE/
6-31++G(d,p) level of theory. For the decomposition reaction
of the intermediate 2-ethoxypropene, occurring through six-
centered TS geometry, better accord between experimental and
calculated enthalpy and, consequently, energy of activation was
found using MPW1PW91/6-31G(d,p) method. For the elimina-
tion reactions occurring through four-centered TS, deviations in
the entropy of activation and consequently the free energy of acti-
vation and log A values are observed, for all methods used. Typically,
calculated entropies were more positive; however, for the decom-
position reaction of 2-ethoxypropene, calculated entropies of activa-
tion were within an order of magnitude of experimental values.
Calculated entropies of activation for these reactions were closer to
the experimental values when using B3LYP functional. The perfor-
mance of different electronic structure methods varies, depending
on the nature of the transition state for unimolecular reaction.20ꢀ22
The above results are in accord with previous works23 where
the elimination reaction through four-centered TS producing
ethanol gave good results using PBE functional, in contrast with
the six-centered TS elimination reaction, which gave better agre-
ement between experimental and calculated parameters using
MPW1PW91.
Because the above results show better agreement between the
experimental and calculated energy of activation using PBEPBE/
6-31++G(d,p) for the elimination reactions of 2,2-diethoxypro-
pane and 1,1-diethoxycyclohexane and MPW1PW91 for the de-
composition of 2-ethoxypropene, we expect that the description
of the TS geometry in terms of bond formation and bond break-
ing can be obtained from these methods. We have selected these
methods, PBEPBE/6-31G(d,p) in the case of four-membered
cyclic TS eliminations and MPW1PW91/6-31G(d,p) for the six-
membered cyclic TS mechanism, to study the geometrical para-
meters, charges, and bond orders in the transition state, and to
learn about the progress in the reaction path connecting the
reactant and products.
The TS nature is described by the geometrical parameters and
NBO charges indicated in the following sections.
851
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The Journal of Physical Chemistry A
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Figure 3. Structures of reactant (left), transition state (center), and products (right) of 1,1-diethoxycyclohexane elimination reaction optimized at
PBEPBE/6-31++G(d,p) level of theory.
Scheme 4
Table 9. Structural Parameters for Optimized Reactant (R),
Transition State (TS), and Products (P) from 2,2-Diethox-
ypropane Decomposition with PBEPBE/6-31++G(d,p)
Method
Atomic Lengths (Å)
C1ꢀC2
C2ꢀO3
O3ꢀH4
H4ꢀC1
R
1.532
1.448
1.354
1.419
2.386
4.090
2.529
1.489
0.974
1.100
1.206
4.119
TS
P
Transition State and Mechanism. The transition state struc-
tures for the elimination reaction of 2,2-ethoxypropane and 1,
1-diethoxycyclohexane are four-centered geometry comprising
the atoms C1, C2, O3, and H4 (Schemes 2, 4). The decomposi-
tion reaction of 2-ethoxypropene occurs through six-centered
TS, including atoms C1, C2, O5, C6, C7, and H8 (Scheme 3). The
TS were verified by IRC calculations, demonstrating the TS con-
nected to reactant and products in the minimum energy path
(MEP). IRC plots are available in the Supporting Information,
Figures 4ꢀ6.
Dihedral Angles (deg)
C1ꢀC2ꢀO3ꢀH4 C2ꢀO3ꢀH4ꢀC1 O3ꢀH4ꢀC1ꢀC2 H4ꢀC1ꢀC2ꢀO3
TS
TS
1.264
ꢀ2.013
2.747
ꢀ1.292
Imaginary Frequency (cmꢀ1
)
523.45
calculations. The NBO charges of atoms involved in the reaction
changes in the reactant, transition state TS, and products for 2,
2-diethoxypropane, 2-ethoxypropene, and 1,1-diethoxycyclohex-
ane elimination reactions are shown in Tables 12ꢀ14, respec-
tively. Atom numbering corresponds to Schemes 2ꢀ4. For 2,
2-diethoxypropane and 1,1-diethoxycyclohexane 1,2-elimination
reactions (Tables 12 and 14), there is an important increase in
electron density at the oxygen atom O3 of the leaving ethoxy
group, from ꢀ0.6 to ꢀ0.8 in the TS. The hydrogen H4 becomes
more positive, from 0.26 to 0.24 to 0.38ꢀ0.39 in the TS; the
change is more significant for 1,1-diethoxycyclohexane. Also sig-
nificant is the increase in negative charge in C1, from ꢀ0.72
toꢀ0.82in the TSfor 2,2-diethoxypropane and from ꢀ0.5 toꢀ06
in the TS for 1,1-diethoxycyclohexane. Atom C2 is almost un-
changed for 2,2-diethoxypropane and undergoes small changes,
from 0.54 to 0.56 in the TS in the case of 1,1-diethoxycyclohexane.
The NBO charges in the elimination reaction of the inter-
mediate in the decomposition of 2,2-diethoxypropane, that is,
2-ethoxypropene, are reported in Table 13. There is an increase
in negative charge at oxygen O5 from ꢀ0.55 to ꢀ0.59, however,
smaller than that observed of the 1,2-elimination reactions
described above. Hydrogen H8 develops more positive charge,
from 0.25 to 0.29 in the TS. A significant change is observed for
C6 (C6ꢀO5 bond breaking) and C2 (C2dO5 double bond
formation), from ꢀ0.13 to ꢀ0.26 and from 0.34 to 0.46 in the
TS, respectively. Atom C1 becomes more negative as the hydro-
gen is transferred to C7, from ꢀ0.61 to ꢀ0.69 in the TS.
For 2,2-ethoxypropane and 1,1-diethoxycyclohexane, the un-
ique imaginary frequency of the TS is associated with the hydro-
gen H4 migration from the carbon C1 to O3 to produce ethanol
(Scheme 2, Figure 1, and Scheme 4, Figure 3). Structural param-
eters for the elimination reaction of 2,2-diethoxypropane (R),
the transition state (TS), and products (P) are given in Table 9.
Table 10 summarizes the geometrical parameters for 2-ethoxypro-
pene decomposition, and Table 11 shows the geometrical para-
meters for the elimination reaction of 1,1-diethoxycyclohexane.
The 1,2-elimination reactions from 2,2-diethoxypropane
(Table 9) and 1,1-diethoxy cyclohexane (Table 11), proceeding
through concerted four-membered cyclic TS mechanism, show
important elongation of C2ꢀO3 bond in the TS (from 1.4 to
2.4 Å in the TS), while a moderate increase in H4ꢀC1 distance is
observed (from 1.1 to 1.2 Å in the TS). The alkene formation is
observed in the decrease in C1ꢀC2 distance from 1.53 to 1.54 to
1.45 Å in the TS. The four atoms involved in the TS are approxi-
mately in plane for 2,2-diethoxypropane, as shown by the small
dihedrals in Tables 9; in the case of 2,2-diethoxycyclohexane,
deviations from planarity are observed, as seen in the dihedrals in
Table 11.
The geometrical parameters for the elimination of 2-ethoxy-
propene, Table 10, show an important increase in O5ꢀC6 distance
(from 1.42 to 1.98 Å in the TS) and also an increase in C7ꢀH8
distance(from1.09to1.34 Å intheTS) accompaniedbya decrease
in C6ꢀC7 and C3ꢀO5 distances as the double bonds form to give
acetone and ethylene. The TS is a semichair configuration.
NBO Charges. The changes in electron distributions through-
out the reaction were studied by means of NBO charges
Bond Order Analysis. Bond orders can be used to describe
the changes in the reaction coordinate.24ꢀ26 Wiberg bond
852
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ARTICLE
Table 10. Structural Parameters for Optimized Reactant (R), Transition State (TS), and Products (P) from 2-Ethoxypropene
Decomposition with MPW1PW91/6-31G(d,p) Method
Atomic Lengths (Å)
C1ꢀC2
C2ꢀO5
O5ꢀC6
C6ꢀC7
C7ꢀH8
H8ꢀC1
R
1.338
1.401
1.510
1.358
1.272
1.214
1.416
1.979
3.527
1.512
1.402
1.329
1.092
1.339
5.049
4.709
1.451
1.095
TS
P
Dihedral Angles (deg)
C1ꢀC2ꢀO5ꢀC6
C2ꢀO5ꢀC6ꢀC7
ꢀ24.340
O5ꢀC6ꢀC7ꢀH8
0.773
C6ꢀC7ꢀH8ꢀC1
C7ꢀH8ꢀC1ꢀC2
H8ꢀC1ꢀC2ꢀO5
ꢀ60.613
TS
TS
63.313
ꢀ22.289
49.145
Imaginary Frequency (cmꢀ1
)
1145.45
Table 11. Structural Parameters for Optimized Reactant (R),
Transition State (TS), and Products (P) from 1,1-Diethox-
ycyclohexane Decomposition with PBEPBE/6-31++G(d,p)
Method
Table 12. NBO Charges of the Atoms Involved in 2,
2-Diethoxypropane Thermal Decomposition from PBEPBE/
6-31++G(d,p) Calculations
C1
C2
O3
H4
Atomic Lengths (Å)
R
ꢀ0.717
ꢀ0.817
ꢀ0.611
0.541
0.542
0.308
ꢀ0.580
ꢀ0.804
ꢀ0.769
0.262
0.380
0.494
C1ꢀC2
C2ꢀO3
O3ꢀH4
H4ꢀC1
TS
P
R
1.547
1.451
1.359
1.439
2.351
3.428
2.774
1.494
0.983
1.103
1.202
2.494
TS
P
Table 13. NBO Charges of the Atoms Involved in 2-Ethoxy-
propene Thermal Decomposition from MPW1PW91/
6-31G(d,p) Calculations
Dihedral Angles (deg)
C1ꢀC2ꢀO3ꢀH4 C2ꢀO3ꢀH4ꢀC1 O3ꢀH4ꢀC1ꢀC2 H4ꢀC1ꢀC2ꢀO3
C1
C2
O5
C6
C7
H8
TS
TS
ꢀ5.913
9.409
ꢀ12.770
6.088
R
ꢀ0.606
ꢀ0.691
ꢀ0.812
0.337
0.463
0.596
ꢀ0.547
ꢀ0.589
ꢀ0.552
ꢀ0.129
ꢀ0.259
ꢀ0.455
ꢀ0.734
ꢀ0.742
ꢀ0.461
0.249
0.292
0.261
Imaginary Frequency (cmꢀ1
)
TS
P
489.8
indexes27 were calculated using the natural bond orbital NBO
program28 in Gaussian 03W. Bond order indexes estimate bond
orders from population analysis. Bond breaking and bond
making process involved in the reaction mechanism are mon-
itored by means of the synchronicity (Sy) concept proposed by
Moyano et al.29 defined by the expression:
Table 14. NBO Charges of the Atoms Involved in 1,
1-Diethoxycyclohexane Thermal Decomposition from
PBEPBE/6-31G(d,p)++ Calculations
C1
C2
O3
H4
R
ꢀ0.523
ꢀ0.611
ꢀ0.392
0.541
0.561
0,307
ꢀ0.594
ꢀ0.806
ꢀ0.775
0.244
0.390
0.497
"
#
n
TS
P
Sy ¼ 1 ꢀ
jδBi ꢀ δBavj=δBav =2n ꢀ 2
∑
i¼1
where n is the number of bonds directly involved in the
reaction, and the relative variation of the bond index is given
by:
δBi ¼ ½BiTS ꢀ BiRꢂ=½BiP ꢀ BiRꢂ
Also, the superscripts R, TS, and P denote reactant, transition
state, and product, respectively.
Bi values represent bond order, and δBi represents its change in
the reaction coordinate from the reactant (BiR), to the transition
state TS (BiTS), and to products (BiP). The percent evolution %
Ev is used to show the relative advance of the different reaction
coordinates studied. The parameter Sy, or synchronicity, varies
between 0 and 1 for concerted reactions; the closer is the Sy value
to unity, the more synchronic is the process.
Wiberg bond indexes were calculated for those bonds in-
volved in the reaction changes, that is, C1ꢀC2, C2ꢀO3, O3ꢀH4,
and H4ꢀC1 for the elimination reaction of 2,2-diethoxy-
propane and 2,2-diethoxy cyclohexane (Schemes 2 and 4,
Tables 15ꢀ17), and for bonds C1ꢀC2, C2ꢀO5, O5ꢀC6,
C6ꢀC7, C7ꢀH8, and H8ꢀC1 for the decomposition reaction
for 2-ethoxypropene.
The evolution in bond change is calculated as:
ꢃ
%Ev ¼ δBi 100
The average bond order change is calculated from:
n
δBav ¼ 1=n
δBi
∑
i¼1
853
dx.doi.org/10.1021/jp209596p |J. Phys. Chem. A 2012, 116, 846–854

The Journal of Physical Chemistry A
ARTICLE
Table 15. Wiberg Bond Index of Reactant (R), Transition
State (TS), and Products (P) for 2,2-Diethoxypropane Ther-
mal Decomposition from PBEPBE/6-31++G(d,p)
’ ASSOCIATED CONTENT
S
Supporting Information. IRC obtained from gas-phase
b
elimination reaction kinetics of 2,2-diethoxypropane and 1,
1-diethoxy-cyclohexane. This material is available free of charge
via the Internet at http://pubs.acs.org.
C1ꢀC2
C2ꢀO3
O3ꢀH4
H4ꢀC1
Sy
BiR
0.9995
1.2058
1.8099
25.46
0.9338
0.2809
0.0004
69.95
0.0021
0.2010
0.7442
26.80
0.9133
0.6067
0.0001
33.57
0.735
BiTS
BiP
’ AUTHOR INFORMATION
%Ev
Corresponding Author
*E-mail: chuchani@ivic.gob.ve.
Table 16. Wiberg Bond Index of Reactant (R), Transition
State (TS), and Products (P) for 2-Ethoxypropene Thermal
Decomposition from MPW1PW91/6-31G(d,p)
’ REFERENCES
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C1ꢀC2 C2ꢀO5 O5ꢀC6 C6ꢀC7 C7ꢀH8 H8ꢀC1
Sy
BiR
1.8306 1.0011 0.8848 1.0337 0.9200 0.0001
0.931
BiTS 1.3870 1.3947 0.3843 1.4203 0.4771 0.3675
BiP
1.0139 1.8169 0.0049 2.0364 0.0000 0.9054
%Ev 54.32 48.25 56.88 38.56 48.14 40.58
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Table 17. Wiberg Bond Index of Reactant (R), Transition
State (TS), and Products (P) for 1,1-Diethoxycyclohexane
Thermal Decomposition from PBEPBE/6-31G(d,p)
C1ꢀC2
C2ꢀO3
O3ꢀH4
H4ꢀC1
Sy
BiR
BiTS
BiP
0.9762
1.1888
1.7433
27.71
0.8958
0.2830
0.0082
69.04
0.0023
0.2037
0.7120
28.38
0.9049
0.5886
0.0203
35.76
0.761
%Ev
Calculated bond orders indicate that the most advanced re-
action coordinate is the breaking of CꢀO bond, being more
important for the 1,2-elimination processes of 2,2-diethoxypro-
pane and 2,2-diethoxycyclohexane, 69ꢀ70%, than the decomposi-
tion of 2-ethoxypropene, 57%. In the 1,2-elimination reaction,
the other reaction coordinates are less advanced as compared to
the CꢀO bond breaking, indicating a nonsynchronous process,
Sy values 0.74ꢀ0.76. Conversely, in the 2-ethoxypropene decom-
position, the progress is intermediate in reaction coordinates
C1ꢀC2, C2ꢀO3, O5ꢀC6, and C7ꢀH8 and somewhat less ad-
vanced for C6ꢀC7 and H8ꢀC1; overall, the process is more
synchronic, Sy = 0.93.
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V. CONCLUSIONS
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573–582.
The thermal decomposition reactions of 2,2-diethoxypropane
and 1,1-diethoxy-cyclohexane have been studied by experimental
and theoretical methods to propose a reasonable mechanism.
These reactions were demonstrated to be unimolecular, homo-
geneous, and follow first-order kinetics under the experimental
conditions used. These compounds undergo 1,2-elimination
reactions through nonsynchronous four-membered cyclic TS
processes. The 2,2-diethoxypropane gives ethanol and the inter-
mediate compound 2-ethoxypropene, which further decomposes
through a concerted six-membered cyclic TS mechanism to give
acetone and ethylene. The 2-ethoxypropene decomposition is
more synchronic than the 1,2-elimination reactions. The rate-
determining step of these elimination reactions is the polariza-
tion of the CꢀO bond, in the sense of Cδ+
Oδꢀ, in the
3 3 3 3
transition state.
854
dx.doi.org/10.1021/jp209596p |J. Phys. Chem. A 2012, 116, 846–854