Kinetics and mechanisms of the elimination of ethyl and feit-butyl esters of carbazic acid in the gas phase: Experimental and theoretical studies

Article abstract of DOI:10.1002/poc.905

The kinetics of the gas-phase elimination of ethyl and tert-butyl carbazates were studied in a static system over the temperature range 220.3-341.7°C and pressure range 21.1-70.0 Torr (1 Torr = 133.3Pa). The reactions in seasoned vessels are homogeneous, unimolecular and obey a first-order rate law. The variation of the rate coefficients with temperature is given by the following Arrhenius equations: for ethyl carbazate log[k ₁(s^-1)] = (11.84±0.22)-[(176.2±2.5) kJ mol^-1](2.303 RT)^-1 and for tert-butyl carbazate log[k ₁, (s^-1)] = (12.34±0.29)-[(153.6±2.9) kJ mol^-1](2.303 RT)^-1. The theoretical examination indicates that the molecular mechanism corresponds to a concerted non-synchronous reaction giving the products. Bond order analysis and natural charges imply that polarization of the O(alkyl) - C(alkyl) bond of the ester is rate determining in these reactions. The rate coefficients from the experiments are in good agreement with the theoretical calculations. The mechanisms of these reactions and the role of the hydrazo group at the acid side of the ester are discussed. Copyright

Full text of DOI:10.1002/poc.905

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2005; 18: 616–624
Published online 11 February 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/poc.905
Kinetics and mechanisms of the elimination of ethyl and
tert-butyl esters of carbazic acid in the gas phase:
experimental and theoretical studies
1
1
2
1
Alexandra Rotinov, Rosa M. Dom ı´ nguez, Tania C o´ rdova and Gabriel Chuchani *
1
Centro de Qu ı´ mica, Instituto Venezolano de Investigaciones Cient ı´ ficas (IVIC), Apartado 21827, Caracas 1020-A, Venezuela
2
Laboratorio de F ı´ sico-Qu ı´ mica Org a´ nica, Escuela de Qu ı´ mica, Facultad de Ciencias, Universidad Central de Venezuela, Apartado 1020-A,
Caracas, Venezuela
Received 18 October 2004; revised 20 December 2004; accepted 4 January 2005
ABSTRACT: The kinetics of the gas-phase elimination of ethyl and tert-butyl carbazates were studied in a static
ꢀ
system over the temperature range 220.3–341.7 C and pressure range 21.1–70.0 Torr (1 Torr ¼ 133.3 Pa).
The reactions in seasoned vessels are homogeneous, unimolecular and obey a first-order rate law. The variation
of the rate coefficients with temperature is given by the following Arrhenius equations: for ethyl carbazate
ꢁ
1
ꢁ1
ꢁ1
ꢁ1
ꢁ1
log[k1ðs Þ] ¼ (11.84 ꢂ 0.22) – [(176.2 ꢂ 2.5) kJ mol ](2.303 RT) and for tert-butyl carbazate log[k (s )] ¼
1
ꢁ1
(
12.34 ꢂ 0.29) – [(153.6 ꢂ 2.9) kJ mol ](2.303 RT) . The theoretical examination indicates that the molecular
mechanism corresponds to a concerted non-synchronous reaction giving the products. Bond order analysis and
natural charges imply that polarization of the O(alkyl)—C(alkyl) bond of the ester is rate determining in these
reactions. The rate coefficients from the experiments are in good agreement with the theoretical calculations.
The mechanisms of these reactions and the role of the hydrazo group at the acid side of the ester are discussed.
Copyright # 2005 John Wiley & Sons, Ltd.
KEYWORDS: kinetics; unimolecular elimination; pyrolysis; ethyl carbazate; tert-butyl carbazate; ab initio calculations;
transition-state structure
ꢁ
INTRODUCTION
ꢁ ¼ ꢁ1.18 implied the interaction of the substituent
R
with an incipient negative reaction center and the abstrac-
tion of the ꢀ-hydrogen of the ethyl ester by the oxygen
The gas-phase elimination of esters of organic acids
proceed through a six-membered cyclic transition state
type of mechanism as described in reaction (1). For
molecular elimination, the presence of a C —H bond at
ꢀ
the alkyl side of the ester is necessary.
carbonyl. The polarizability or steric effect ꢁ ¼ ꢁ0.68
ꢂ
was believed to have a modest participation.
The presence of at least an H atom at the N in
carbamates has been found to give a different mechanistic
ð1Þ
2
According to the general elimination reaction of esters,
1
Herize et al. examined the kinetic parameters for the
pathway and product formation, as reported previously
[reaction (2)]. To avoid this type of elimination process,
most studies of the pyrolytic decomposition of carba-
mates have been carried out with the H of the amino
comparative rates of different substituents other than
carbon at the acid side of organic ethyl esters. These
1
organic esters gave a good Taft–Topsom correlation as
3–8
substituent replaced by a methyl or phenyl groups.
described in Scheme 1.
The parameter ꢁ ꢁ ¼ þ2.57 suggested the field or
F
electronic effect to be the most important influence in
the elimination process. Moreover, the resonance effect
ð2Þ
*
Correspondence to: G. Chuchani, Centro de Qu ´ı mica, Instituto
A substituent of interest to examine at the acid side of
an organic ethyl ester is the hydrazo group (NH NH), i.e.
ethyl carbazate, and possibly include it in the above
Venezolano de Investigaciones Cient ´ı ficas (IVIC), Apartado 21827,
Caracas 1020-A, Venezuela.
E-mail: chuchani@quimica.ivic.ve
2
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 616–624

GAS-PHASE ELIMINATION OF ETHYL AND tert-BUTYL CARBAZIC
617
Scheme 1
z
correlation (Scheme 1), or whether the presence of
hydrogens at the first or second nitrogen atom may lead
to the formation of other types of products. Consequently,
this work was aimed at examining the gas-phase elimina-
where ꢀG is the Gibbs free energy change between the
reactant and the transition state and K and h are the
Boltzman and Plank constants, respectively.
z
ꢀG was calculated using the relations
tion kinetics of the hydrazo substituent H NNH at the
2
z
z
z
ꢀ
G ¼ ꢀH ꢁ TꢀS
acid side of esters such as ethyl and tert-butyl carbazates.
Theoretical studies were also performed for an adequate
interpretation of the mechanisms of these elimination
reactions. The theoretical calculations aimed to procure
the kinetic parameters and the characterization of the
potential energy surface (PES) as a means to understand
the nature of the molecular mechanism of these reactions.
and
z
z
ꢀ
H ¼ V þ ꢀZPVE þ ꢀEðTÞ þ PV
z
where V is the potential energy barrier and ꢀZPVE and
ꢀE(T) are the differences in ZPVE and temperature
corrections between the transition state and the reactant,
respectively.
COMPUTATIONAL METHOD AND MODEL
The kinetics of the gas-phase elimination reaction of
ethyl and tert-butyl carbazates were studied using
ab initio RHF, MP2 and DFT/B3LYP methods with 6–
RESULTS AND DISCUSSION
Ethyl carbazate
3
1G, 3–21G* and 6–31G* basis sets as implemented in
9
Gaussian 98W. The Berny analytical gradient optimiza-
tion routines were used for optimization. A transition
states search was performed using the Quadratic Syn-
chronous Transit protocol as implemented in Gaussian
Complete kinetic studies of ethyl carbazate were difficult.
However, the products of elimination of this substrate, in
a vessel seasoned with allyl bromide and in the presence
of toluene inhibitor, are predominantly ethylamine, HNO
and CO, with traces amount of ethylene, hydrazine and
9
8W. The nature of stationary points was established by
calculating and diagonalizing the force constant matrix to
determine the number of imaginary frequencies. Intrinsic
reaction coordinate (IRC) calculations were performed to
verify transition-state structures. The unique imaginary
frequency associated with the transition vector (TV), i.e.
the eigenvector associated with the unique negative
eigenvalue of the force constant matrix, was character-
ized. Frequency calculations provided thermodynamic
quantities such as zero point vibrational energy (ZPVE),
temperature corrections and absolute entropies, and con-
sequently the rate coefficient can be estimated assuming
that the transmission coefficient is equal to 1. Tempera-
ture corrections and absolute entropies were obtained
assuming ideal gas behavior from the harmonic frequen-
CO . The stoichiometry based on the reaction (3)
2
ð3Þ
has to give a ratio of 3.0 for P /P , where P and P are the
final and initial pressures, respectively. Four measure-
f
0
f
0
ꢀ
ments in the temperature range 310–340 C with initial
pressures around 60 Torr (1 Torr ¼ 133.3 Pa) gave a mean
value of 2.91. The reaction was found to be homogeneous
in seasoned Pyrex vessels. However, some heterogeneous
effect on the rate, in clean packed and unpacked Pyrex
vessels, was obtained.
The effect of addition of different proportions of the
free radical inhibitor toluene can be seen from Table 1.
Nevertheless, the elimination reaction was carried out in
the presence of at least twice the amount of the inhibitor
in order to suppress any possible free radical chain
processes. No induction period was observed. The rate
coefficients were reproducible with a relative standard
deviation not greater than 5% at a given temperature.
The first-order rate coefficients of ethyl carbazate,
calculated from k ¼ (2.303/t)log[2P /(3P ꢁ P )], was
10
cies and moments of inertia by standard methods at
average temperature and pressure values within the
experimental range. Scaling factors for frequencies and
zero point energies for the HF, B3LYP and MP2 methods
11
used were taken from the literature.
The first-order rate coefficient k(T) was calculated
12
using the TST and assuming that the transmission
coefficient is equal to 1, as expressed in the following
relation:
1
0
0
t
found to be invariable of the initial pressure (Table 2).
A plot of log(3P ꢁ P ) against time t gave a good straight
0
t
z
kðTÞ ¼ ðKT=hÞexpðꢁꢀG =RTÞ
line up to 42% decomposition (Fig. 1). The variation of
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 616–624

6
18
A. ROTINOV ET AL.
Table 1. Effect of free radical inhibitor toluene on rates
tert-Butyl carbazate
4
Temperature Ps
ꢀ
Pi
(Torr) (Torr)
10 k
1
a
a
ꢁ1
Pi/Ps (s )
The elimination products of tert-butyl carbazate in a
vessel seasoned with allyl bromide are mainly isobutene,
Substrate
( C)
Ethyl carbazate
320.7
70
—
—
0.5
1.7
1.9
3.0
—
1.4 10.66
1.9 10.03
2.7 10.69
3.84
2.41
2.17
2.18
2.10
10.74
NH , HNO, and CO. The stoichiometry of the reaction
3
6
4
6
6
5.5
2
33
73.5
2.5 116.5
0
180.5
—
58
tert-Butyl carbazate 250.2
47
4
4
4
1.9
9.5
0.8 108.5
94
ð4Þ
a
was checked by measurements of the ratio P /P of final,
0
P
s
¼ pressure of the substrate; P
i
¼ pressure of the inhibitor.
f
to initial pressure. The average experimental result at four
ꢀ
Table 2. Variation of rate coefficients with initial pressure
different temperatures (230–260 C) and 10 half-lives
was 3.93. The theoretical stoichiometry of reaction (4)
Temperature
ꢀ
demands P ¼ 4P . To check the stoichiometry of this
f
0
Substrate
( C)
Parameter
Values
elimination, the percentage decomposition obtained from
pressure measurements was found to be in good agree-
ment with the quantitative chromatographic analyses of
isobutene formation (Table 4).
Ethyl
320.7
P (Torr)
0
42 50.5 62.5
2.27 2.10 2.18
4
10 k (s
ꢁ1
carbazate
tert-Butyl 250.2
)
1
P (Torr) 21.1 39.6 49.5 57.6
0
4
10 k (s
ꢁ1
carbazate
)
9.93 10.74 10.66 10.76
The homogeneity of reaction (4) was examined by
using vessels with a surface-to-volume ratio of 6.0,
greater than that of the unpacked vessels (1.0). The rates
were unaffected in seasoned vessels, yet a small effect
was found in clean packed and unpacked Pyrex vessels.
The lack of a free-radical chain process in this reaction
was examined by carrying out several runs in the pre-
sence of different proportions of the inhibitor toluene
1
(Table 1).
The rates of pyrolysis elimination calculated from
equation k ¼ (2.303/t)log[3P /(4P ꢁ P )] and also be
1
0
0
t
estimated from quantitative chromatographic analyses
of isobutene formation using the equation k ¼ (2.303/t)
1
log[P /(2P ꢁ P )] are independent of the initial pressure
0
0
t
of the carbazate, and the first-order plots of log(4P ꢁ P )
0
t
against time t are satisfactory up to 50% decomposition
Table 2, Fig. 2). The temperature dependence of the
(
reaction and the corresponding Arrhenius equation are
shown in Table 3. The rate coefficients are reproducible
with a relative standard deviation not greater than 5% at a
given temperature. The errors were estimated to 90%
confidence limits from a least-squares procedure.
Figure 1. Log(3P ꢁ P ) vs time (t) for ethyl carbazate at
0
t
ꢀ
20.7 C
3
In order to use the results shown in Table 5 to provide
reasonable mechanisms of elimination of ethyl and tert-
butyl carbazates, a theoretical examination was undertaken.
rate coefficients with temperature and the corresponding
Arrhenius equation are given in Table 3 (90% confidenc
limits from a least-squares procedure).
Table 3. Variation of rate coefficients with temperature
Substrate
Parameter
Temperature ( C)
Values
ꢀ
Ethyl carbazate
310.0
1.12
320.7
2.18
329.3
3.70
341.7
7.26
4
0 k (s
ꢁ1
1
)
1
Rate equation: log[k (s )] ¼ (11.84 ꢂ 0.22) – [(176.2 ꢂ 2.5) kJ mol ](2.303RT)ꢁ1; r ¼ 0.9998
ꢁ
1
ꢁ1
1
ꢀ
tert-Butyl carbazate
Temperature ( C)
1
220.3
1.18
230.2
2.51
240.1
5.22
250.2
10.18
260.8
20.23
4
0 k (s )
1
1
Rate equation: log[k (s )] ¼ (12.34 ꢂ 0.29) – [(153.6 ꢂ 2.9) kJ molꢁ1] (2.303RT)ꢁ1; r ¼ 0.9999
ꢁ
1
1
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 616–624

GAS-PHASE ELIMINATION OF ETHYL AND tert-BUTYL CARBAZIC
619
Table 4. Stoichiometry of the reaction
Geometries for the reactant, transition state (TS)
and products for the rate-determining step were opti-
mized using ab initio RHF, MP2 and DFT/B3LYP
methods with 6–31G, 3–21G* and 6–31G* basis sets.
Frequency calculations at the average experimental tem-
perature and pressure (598.57 K and 0.09917 atm) were
carried out.
Temperature
ꢀ
Substrate
( C)
Parameter
Values
8
tert-Butyl 250.2 Time (min)
carbazate
4
6
10 12
Reaction (%) 21.9 31.1 38.1 44.9 50.1
pressure)
Isobutene (%) 21.1 29.7 40.7 46.7 51.7
GC)
(
Even though theoretical calculations of transition-state
structures have been a useful tool for reasonable mechan-
istic interpretations of organic reactions, the results have
usually been limited to enthalpy of activation, and con-
sequently to energy of activation. Reasonable entropy
values are rarely obtained directly from frequency calcu-
lations. This was the case for the thermal decomposition
of ethyl carbazate. It is our experience in true gas-phase
reactions that the difference in values between experi-
(
exp
mental energy of activation (Ea ) and the free energy of
activation (ꢀG ) gives an idea of the magnitude of the
zexp
entropy of activation.
In view of the above considerations, entropy values are
estimated as follows. If
zexp
ztheo
ꢀ
H
ꢃ ꢀH
consequently
exp
theo
Figure 2. Log(4P ꢁ P ) vs time (t) for tert-butyl carbazate at
Ea ꢃ Ea
0
t
ꢀ
50.2 C
2
and therefore we expect that
THEORETICAL RESULTS
Ethyl carbazate
zexp
ztheo
ꢀG
ꢃ ꢀG
From the experimental observation that ethyl carbazate
undergoes thermal decomposition to give ethylamine,
HNO and CO, the theoretical studies on the mechanism
of elimination of this ester were carried out based on the
assumption that the reaction occurs in a two-step process.
In a first rate-determining step, ethyl carbazate eliminates
ethylamine and an unstable cyclic intermediate oxazir-
idinone COONH, which rapidly decomposes to give
HNO and CO as shown in Eqn (5).
We may define
to obtain
zexp
exp
ꢁ Ea ¼ C
exp
ꢀ
G
ztheo
theo
¼ Ea þ C
exp
ꢀG
where the superscripts exp and theo refer to experimental
and theoretical values, respectively, and the parameter
exp
C
is
ð5Þ
exp
zexp
C
¼ nRT ꢁ TꢀS
n ¼ 1, unimolecular reaction.
ꢀ
Table 5. Kinetic and thermodynamic parameters at 280 C
4
10 k (s
ꢁ1
ꢁ1
ꢁ1
6
ꢁ1 ꢁ1
6
ꢁ1
6
ꢁ1
)
Substrate
)
Ea (kJ mol
)
Log [A (s )] ꢀS (J mol
K
) ꢀH (kJ mol ) ꢀG (kJ mol
1
Ethyl carbazate
tert-Butyl carbazate
0.16
68.0
176.2 ꢂ 2.5
153.6 ꢂ 2.9
11.84 ꢂ 0.22
12.34 ꢂ 0.29
ꢁ31.6
ꢁ22.1
171.6 189.1
149.0 161.2
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 616–624

6
20
A. ROTINOV ET AL.
Structural parameters for ethyl carbazate and for the TS
at the B3LYP/6–31G level at 598.15 K and 0.09917 atm
are given in Table 7. The TS configuration is a quasi-
cyclic structure similar to the proposed intermediate
oxaziridinone (atoms C1, O2 and N11 are positioned in
a three-membered-like ring), where the O2—N11 dis-
˚
tance is too large for a formal bond (1.77 A in the TS) and
˚
C1—O2 has double bond character (1.216 A). In the TS
˚
O3—C4 breaking is complete (3.57 A in the TS) and
substantial progress is also observed in N11—N13 bond
˚
breaking (2.59 A in the TS). Analysis of NBO charges
shows an increase in partial charge on C4 (from ꢁ0.068
to ꢁ0.253 in the TS, that is, C4 becomes more positive)
and also on N13 (from ꢁ0.758 to ꢁ0.992 in the TS, i.e.
N13 becomes more negative) and a decrease in the
negative partial charge on N11 (from ꢁ0.605 to ꢁ0.366
in the TS), resulting in marked polarization of the O3—
C4 and N11—N13 bonds in the TS.
Figure 3. Thermal decomposition of ethyl carbazate (left)
and TS structure (right) at 598.57 K and 0.09917 atm
(
B3LYP/6–31G). Schematic drawings with atom numbers
are shown at the bottom
exp
C includes the contribution of collisional entropy,
which has not been considered in frequency calculations
Bond order analysis. To investigate further the nature
of the TS along the reaction pathway, NBO bond order
(
isolated molecules). Using
13–15
calculations were performed.
16
Wiberg bond indexes
17
ztheo
ztheo
ztheo
were computed using the NBO program as imple-
mented in Gaussian 98W. Bond breaking and making
processes involved in the reaction mechanism can be
monitored by means of the synchronicity (Sy) concept
ꢀG
¼ ꢀH
ꢁ TꢀS
ztheo
the rate coefficients can be calculated.
ztheo
theo
and Ea , logA and
ꢀS
was obtained. From ꢀS
18
proposed by Moyano et al., defined by the expression
Several low-energy conformations of the reactant were
found. At the working temperature there is enough
thermal energy for these conformations to interconvert
"
#
ꢀ
n
X
ꢁ
1
[
4
barriers ranging from 1.2 to 8.2 kcal mol ) (1 kcal ¼
Sy ¼ 1 ꢁ
jꢃB ꢁ ꢃB j=ꢃB
2n ꢁ 2
i
av
av
.184 kJ)]. The conformation shown in Fig. 3 is a local
i¼1
minimum showing an orientation close to the TS struc-
ture or reactive conformation.
where n is the number of bonds directly involved in the
reaction and the relative variation of the bond index is
obtained from
Calculation results for the RHF, B3LYP and MP2
methods are given in Table 6. Rate coefficients and
Arrhenius pre-exponential factors were determined and
compared with the experimental values. The results show
the best agreement for the B3LYP/6–31G method for all
activation parameters (Table 6), within 2.2, 2.0, 1.9, 0.7%
ꢁ
ꢂ ꢁ
ꢂ
TS
i
R
i
P
i
R
i
ꢃB ¼ B ꢁ B = B ꢁ B
i
z
z
z
of error for ꢀH , E , ꢀG and ꢀS , respectively. The
where the superscripts R, TS and P, represent reactant,
transition state and product, respectively.
The evolution in bond change is calculated as
a
first-order rate coefficient is of the same order of magni-
tude as the experimental value. The best calculated values
were use to select the TS geometry for further analysis
(
Fig. 3).
%Ev ¼ ꢃB ꢄ 100
i
ꢀ
a
Table 6. Ethyl carbazate activation parameters for the thermal decomposition at 325.0 C and 0.09917 atm
6
ꢁ1
ꢁ1
6
ꢁ1
6
ꢁ1 ꢁ1
ꢁ1
4
10 k (s
ꢁ1
Level of theory
ꢀH (kJ mol
)
Ea (kJ mol
)
ꢀG (kJ mol
)
ꢀS (J mol
K
)
Log [A (s )]
)
1
ꢁ
6
RHF/6–31G
B3LYP/6–31G
MP2/6–31G
MP2/3–21G*
MP2/6–31G*
Experimental
246.9
174.9
150.9
165.6
163.8
171.6
251.3
179.8
155.9
170.5
168.8
176.2
264.2
192.7
168.8
183.4
181.7
189.1
ꢁ28.9
ꢁ29.7
ꢁ29.9
ꢁ29.7
ꢁ29.9
ꢁ29.9
12.02
11.97
11.97
11.97
11.97
11.97
1.06 ꢄ 10
1.85
226.6
12.02
16.90
3.82
a
exp
ꢁ1
6¼
Free energy values were calculated using the parameter C (12.9 kJ mol ). From these and ꢀH from frequency calculations, entropy values were
obtained.
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 616–624

GAS-PHASE ELIMINATION OF ETHYL AND tert-BUTYL CARBAZIC
621
Table 7. Structural parameters for ethyl carbazate and the TS for thermal decomposition at 598.57 K and 0.09917 atm (B3LYP/
˚
6–31G method) (atom distances in A and dihedral angles in degrees)
Structure
C1—O3
O3—N11
O3—C4
N11—N13
C4—N13
Ethyl carbazate
TS
Product
1.373
1.216
1.380
2.370
2.470
1.710
1.480
3.570
3.510
1.390
2.590
2.710
2.890
1.480
1.490
N11—C1—O3
O2—C1—O3
O2—C1—N11
Ethyl carbazate
TS
Product
118.41
141.06
76.61
120.91
139.18
137.72
120.67
79.71
144.97
Atomic charges from NBO analysis for ethyl carbazate and the TS for thermal decomposition (B3LYP/6–31G method):
Structure
C1
O2
O3
C4
N11
N13
Ethyl carbazate
TS
1.090
1.018
ꢁ0.710
ꢁ0.530
ꢁ0.666
ꢁ0.633
ꢁ0.068
ꢁ0.253
ꢁ0.605
ꢁ0.367
ꢁ0.758
ꢁ0.992
The average value is calculated from
the intermediate NH NHCOOH proceeds to give NH
2 3
and the unstable oxaziridinone COONH is believed to
decompose rapidly to HNO and CO gas [reaction (6)].
ꢀ
n
X
ꢃBav ¼ 1
n
ꢃBi
i¼1
Bonds indexes were calculated for those bonds involved
in the reaction changes, i.e. O3—N11 (B3–11), O3—C4
(B3–4), C4—N13 (B4–13) and N11—N13 (B11–13). The
C1—O2 and C1—O3 bonds remain practically unaltered
during the process.
NBO analysis results are given in Table 8. The syn-
chronicity parameter Sy ¼ 0.731 suggest a concerted non-
synchronous mechanism, where the breaking of the O3—
C4 bond plays an important role.
ð6Þ
Geometries of the reactant tert-butyl carbazate and the
intermediate products isobutylene and H NNCOOH were
2
optimized using ab initio RHF, MP2 and DFT/B3LYP
methods with 6–31G, 3–21G* and 6–31G* basis sets.
Quadratic Synchronous Transit calculations were per-
formed to obtain TS structures.
Frequency calculations at the average experimental
temperature and pressure (513.45 K and 0.055197 atm)
were carried out for the reactant tert-butyl carbazate, the
TS and products of the rate-determining step. Calculation
tert-Butyl carbazate
Theoretical studies on the mechanism of elimination of
tert-butyl carbazate were based on the hypothesis that the
reaction occurs in a two-step process, the first step giving
isobutylene and H NNCOOH being rate determining, as
2
shown in Eqn (4). Under the conditions of the reaction,
results for RHF, B3LYP and MP2 methods are given in
z
Table 8. NBO analysis for ethyl carbazate thermal decom-
position at 598.57 K and 0.09917 atm (B3LYP/6–31G level):
Table 9. The best agreement in E and ꢀH were found
for both the MP2/6–31G and MP2/6–31G* levels of
theory. Agreement with experimental values is within
a
Wiberg bond indexes (B ), % evolution through the reaction
i
coordinate (%Ev), average bond index variation (ꢃB ) and
av
z
z
z
respectively. As for ethyl carbazate, entropies for tert-
synchronicity parameter (Sy)
2.4, 1.4, 1.4 and 5.0% error for ꢀH , E , ꢀG and ꢀS ,
a
exp
butyl carbazate were obtained using the C parameter to
estimate ꢀG . The best calculated values were used to
Parameter O3—N11 O3—C4 C4—N13 N11—N13
z
R
Bi
ꢁ0.0378
ꢁ0.5440 ꢁ0.0003
0.6768 0.0006
70.83 100.15
0.5707
ꢁ0.0010
0.7743
0.7511
103.08
0.9499
0.0194
ꢁ0.2040
19.36
TS
select the best TS geometry for further analysis (Fig. 4).
The TS structure for tert-butyl carbazate thermal
decomposition is an almost planar six-membered ring
where the hydrogen being transferred is half way between
O2 and C5, and there is partial double bond character of
Bi
Bi
%
P
Ev
ꢃBav
Sy
0.283
0.731
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 616–624

6
22
A. ROTINOV ET AL.
ꢀ
a
Table 9. tert-Butyl carbazate activation parameters for the thermal decomposition at 240.3 C and 0.055197 atm
6
ꢁ1
ꢁ1
6
ꢁ1
6
ꢁ1 ꢁ1
ꢁ1
4
10 k (s )
ꢁ1
Level of theory
ꢀH (kJ mol
)
Ea (kJ mol
)
ꢀG (kJ mol
)
ꢀS (J mol
K
)
Log [A (s )]
1
RHF/6–31G
B3LYP/6–31G
MP2/6–31G
MP2/3–21G*
MP2/6–31G*
Experimental
142.2
115.7
151.8
170.6
148.5
149.0
146.0
120.0
155.8
174.6
152.5
153.6
153.6
127.6
163.4
182.2
160.1
161.2
ꢁ22.2
ꢁ23.2
ꢁ22.6
ꢁ22.6
ꢁ22.6
ꢁ23.8
12.30
11.09
12.28
12.28
12.28
12.22
24.4
1120.0
2.55
0.031
5.52
4.27
a
exp
ꢁ1
6¼
Free energy values were calculated using the parameter C (7.6 kJ mol ). From these and ꢀH from frequency calculations, entropy values were obtained.
of NBO charges shows an increase in partial charge on
C4 (from 0.325 to 0.456 in the TS), an increase in partial
charge on O3 (from ꢁ0.691 to ꢁ0.846 in the TS), an
increase in partial charge on C5 (from ꢁ0.713 to ꢁ0.883
in the TS) and an increase in positive partial charge on H8
(from 0.270 to 0.469 in the TS), resulting in polarization
of the O3—C4 and C4—C5 bonds in the TS. The bond
3
angles show progress in hybridization change from sp to
2
sp in C4; both C5—C4—C14 and C5—C4—C18 are
ꢀ
close to 120 in the TS.
Bond order analysis. NBO bond order calculations
1
3–15
were performed
the TS along the reaction pathway. Wiberg bond in-
to investigate further the nature of
Figure 4. Thermal decomposition of tert-butyl carbazate
(
(
left) and TS structure (right) at 513.47 K and 0.055197 atm
MP2/6–31G). Schematic drawings with atom numbers are
16
17
dexes were computed using the NBO program as
shown at the bottom
implemented in Gaussian 98W. Synchronicity (Sy), ꢃBi,
%
Ev and ꢃBav values were determined as described
above.
Bonds indexes were calculated for those bonds being
modified during the reaction, i.e. C1—O2 (B1–2), C1—
O3 (B1–3), O3—C4 (B3–4), C4—C5 (B4–5), C5—H8 (B5–8
both the C1—O3 and C1—O2 bonds (Fig. 2). Structural
parameters for tert-butyl carbazate and the TS are given
in Table 10. In the TS structure there is substantial
)
˚
progress in O3—C4 bond breaking (2.17 A) and O2—
and O2—H8 (B2–8). NBO results are given in Table 11.
The greatest progress in the reaction coordinate is the
breaking of the O3—C4 bond. The synchronicity para-
meter Sy ¼ 0.882 and partial charges in the TS suggest a
˚
H8 bond formation (1.35 A), an important double bond
˚
character of C1—O3 (1.30 A) and intermediate progress
˚
in double bond formation for C4—C5 (1.42 A). Analysis
Table 10. Structural parameters for tert-butyl carbazate and the TS for thermal decomposition at 513.47 K and 0.055197 atm
˚
MP2/6–31G method) (atom distances in A and dihedral angles in degrees)
(
Structures
C1—O2
C1—O3
O3—C4
C4—C5
C5—H8
O2—H8
tert-Butyl carbazate
TS
Product
1.258
1.390
1.520
1.390
1.300
1.250
1.520
2.170
3.470
1.537
1.420
1.354
1.090
1.300
2.310
2.450
1.350
0.980
O2—C1—O3
C5—C4—C14
C5—C4—C18
tert-Butyl carbazate
TS
Product
126.69
124.62
124.20
112.87
119.96
122.19
111.63
120.14
122.19
Atomic charges from NBO analysis for tert-Butyl carbazate and the TS for thermal decomposition (MP2/6–31G method):
Structure
C1
O2
O3
C4
C5
H8
N9
tert-Butyl carbazate
TS
1.075
1.082
ꢁ0.764
ꢁ0.859
ꢁ0.691
ꢁ0.846
0.325
0.456
ꢁ0.713
ꢁ0.883
0.270
0.469
ꢁ0.588
ꢁ0.593
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 616–624

GAS-PHASE ELIMINATION OF ETHYL AND tert-BUTYL CARBAZIC
623
Table 11. NBO analysis for tert-butyl carbazate thermal
decomposition at 513.45 K and 0.055197 atm (MP2/6–
synchronicity parameters for ethyl and tert-butyl
carbazate implies a more polarized asynchronous me-
chanism for ethyl carbazate (Sy ¼ 0.731) compared with
tert-butyl carbazate (Sy ¼ 0.882).
3
1G level): Wiberg bond indexes (B ), % evolution through
i
the reaction coordinate (%Ev), average bond index variation
ꢃB ) and synchronicity parameter (Sy)
(
av
With regard to the methods used, ethyl carbazate gave
the best results with the B3LYP/6–31G method whereas
for tert-butyl carbazate the best parameters were obtained
with both the MP2/6–31G and MP2/6–31G* methods.
For ethyl carbazate, the electronic distribution in the TS
structure is more polarized and there is more charge
separation. For this molecular system, a different level
of electron correlation energy may be involved. The MP4
perturbation method accounts for ꢅ95% of electron
correlation energy or more, compared with multilevel
correlated methods such as CC and CI theories. MP2,
being a lower level of calculation, does not account for
the total correlation energy. In this case DFT methods
using hybrid ACM functionals such as B3LYP give better
results.
Parameter C1—O2 C1—O3 O3—C4 C4—C5 C5—H8 O2—H8
R
Bi
Bi
Bi
%
ꢃBav
Sy
1.1810 0.6997 0.5362 0.9820 0.7229 0.0017
0.8919 0.9881 0.1207 1.1986 0.3341 0.1576
0.701 1.1801 0.0001 1.8361 0.0155 0.4221
TS
P
Ev
60.23 60.03 77.50
0.568
0.882
25.36 54.96
concerted non-synchronous mechanism, where the polar-
ization of O3—C4 is rate determining.
CONCLUSIONS
Ethyl carbazate
For the thermal decomposition of tert-butyl carbazate,
entropy values were obtained directly from frequency
calculations whereas for ethyl carbazate decomposition,
entropy values were estimated using the empirical para-
Theoretical calculations on ethyl carbazate thermal de-
composition were based on the assumption that the
reaction occurs in a two step-process [reaction (5)],
involving an unstable three-membered ring intermediate,
oxaziridinone. The TS structure obtained supports the
mechanistic hypothesis and the formation of the inter-
mediate oxaziridinone, because the TS found is similar
to this intermediate as shown in Fig. 3. The results there-
fore suggest that the reaction proceeds by a concerted
non-synchronous mechanism, through a quasi-three-
membered ring transition state. Structural parameters,
partial charges and NBO analysis suggest that polariza-
tion of O3—C4 bond is the determining factor in the
decomposition process. The synchronicity parameter
Sy ¼ 0.731 is in accord with a concerted non-synchronous
polar type of mechanism. Reasonable agreement of the
activation parameters with the experimental parameters
was found for the B3LYP/6–31G method.
exp
meter C described above.
EXPERIMENTAL
Ethyl carbazate (Aldrich) after several distillations and
tert-butyl carbazate (Aldrich) both, with >99.0% purity
[GC/MS (Saturn 2000, Varian), DB-5MS capillary col-
umn, 30 m ꢄ 0.250 mm i.d., 0.25 mm film thickness] were
used. The product isobutene was quantitatively analyzed
in a column of Porapak Q (80–100 mesh). The
CH CH NH product, when collected from the reaction
3
2
2
vessel in the trap, reacts with the HNO to form a solid,
þ
ꢁ
CH CH NH NO . This salt was identified by mass
3
2
3
spectrometry. The free amine was obtained through a
column of soda lime.
Kinetics
tert-Butyl carbazate
Kinetic studies were carried out in a static system as
with an Omega DP41-TC/
19–21
described previously
Theoretical calculations suggest that the reaction pro-
ceeds via a concerted non-synchronous mechanism. The
TS structure for tert-butyl carbazate thermal decomposi-
tion is an almost planar six-membered ring with the
hydrogen being transferred located half way between
O2 and C5. The activation parameters are in agreement
with the experimental values for both the MP2/6–31G
and MP2/6–31G* levels of theory and the first-order
reaction rate coefficient of in the same order of
magnitude.
DP41-RTD high-performance digital temperature indica-
tor. The rate coefficients were calculated from pressure
increase and from chromatographic analyses. The tem-
perature was controlled by a resistance thermometer
controller and an Omega Model SSR280A45 solid-state
ꢀ
relay, maintained within ꢂ 0.2 C and measured with a
calibrated platinum–platinum–13% rhodium thermocou-
ple. No temperature gradient was detected along the
reaction vessel. Both carbazate esters were dissolved in
dioxane and injected directly into the reaction vessel with
a syringe through a silicone rubber septum. The amount
of substrates used for each run was ꢅ0.05–0.1 ml.
Results from calculations and the agreement with
experiment suggest the validity of the methods and
mechanistic assumption proposed. Comparison of the
Copyright # 2005 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2005; 18: 616–624

6
24
A. ROTINOV ET AL.
Cioslowski J, Ortiz JV, Stefanov BB, Liu G, Liashenko A, Piskorz
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