Joint theoretical and experimental study of the gas-phase elimination kinetics of tert-butyl ester of carbamic, N,N-dimethylcarbamic, N-hydroxycarbamic acids and 1-(tert-butoxycarbonyl)-imidazole

Article abstract of DOI:10.1002/poc.1248

The gas-phase elimination kinetics of the title compounds were carried out in a static reaction system and seasoned with allyl bromide. The working temperature and pressure ranges were 200-280°C and 22-201.5 Torr, respectively. The reactions are homogeneous, unimolecular, and follow a first-order rate law. These substrates produce isobutene and corresponding carbamic acid in the rate-determining step. The unstable carbamic acid intermediate rapidly decarboxylates through a four-membered cyclic transition state (TS) to give the corresponding organic nitrogen compound. The temperature dependence of the rate coefficients is expressed by the following Arrhenius equations: for tiert-butyl carbamate logk₁ (s^-1) = (13.02±0.46) - (161.6 ± 4.7)kJ/mol(2.303RT)^-1, for tert-butyl N-hydroxycarbamate logk₁ (s^-1) = (12.52 ± 0.11) - (147.8 ± 1.1) kJ/mol(2.303 RT)^-1, and for 1-(tert-butoxycarbonyl)-imidazole logk₁ (s^-11) = (11.63 ± 0.21)-(134.9 ± 2.0) kJ/mol (2.303 RT)^-1. Theoretical studies of these elimination were performed at Moller-Plesset MP2/6-31G and DFT B3LYP/6-31G(d), B3LYP/6-31G(d,p) levels of theory. The calculated bond orders, NBO charges, and synchronicity (Sy) indicate that these reactions are concerted, slightly asynchronous, and proceed through a six-membered cyclic TS type. Results for estimated kinetic and thermodynamic parameters are discussed in terms of the proposed reaction mechanism and TS structure. Copyright

Full text of DOI:10.1002/poc.1248

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2007; 20: 1021–1031
Published online 22 August 2007 in Wiley InterScience
(
www.interscience.wiley.com) DOI: 10.1002/poc.1248
Joint theoretical and experimental study of the
gas-phase elimination kinetics of tert-butyl ester of
carbamic, N,N-dimethylcarbamic, N-hydroxycarbamic
acids and 1-(tert-butoxycarbonyl)-imidazole
1
1
1
1
2
Jose R Mora, Mar ´ı a Tosta, Rosa M. Dom ı´ nguez, Armando Herize, Jenny Barroso,
2
1
Tania C o´ rdova and Gabriel Chuchani *
1
Centro de Qu ı´ mica, Instituto Venezolano de Investigaciones Cient ı´ ficas (I.V.I.C.), Apartado 21827, Caracas, Venezuela
Escuela de Qu ı´ mica, Facultad de Ciencias, Universidad Central de Venezuela, Apartado 1020-A, Caracas, Venezuela
2
Received 8 February 2007; revised 4 June 2007; accepted 27 June 2007
ABSTRACT: The gas-phase elimination kinetics of the title compounds were carried out in a static reaction system and
seasoned with allyl bromide. The working temperature and pressure ranges were 200–280 8C and 22–201.5 Torr,
respectively. The reactions are homogeneous, unimolecular, and follow a first-order rate law. These substrates
produce isobutene and corresponding carbamic acid in the rate-determining step. The unstable carbamic acid intermediate
rapidly decarboxylates through a four-membered cyclic transition state (TS) to give the corresponding organic nitrogen
compound. The temperature dependence of the rate coefficients is expressed by the following Arrhenius equations: for
ꢀ
1
ꢀ1
tert-butyl carbamate logk (s ) ¼ (13.02 ꢁ 0.46) – (161.6 ꢁ 4.7) kJ/mol(2.303 RT) , for tert-butyl N-hydroxycarbamate
1
ꢀ1
ꢀ1
ꢀ1
logk (s ) ¼ (12.52 ꢁ 0.11) – (147.8 ꢁ 1.1) kJ/mol(2.303 RT) , and for 1-(tert-butoxycarbonyl)-imidazole logk (s ) ¼
1
1
ꢀ
1
(
11.63 ꢁ 0.21)–(134.9 ꢁ 2.0) kJ/mol(2.303 RT) . Theoretical studies of these elimination were performed at Møller–
Plesset MP2/6-31G and DFT B3LYP/6-31G(d), B3LYP/6-31G(d,p) levels of theory. The calculated bond orders, NBO
charges, and synchronicity (Sy) indicate that these reactions are concerted, slightly asynchronous, and proceed through a
six-membered cyclic TS type. Results for estimated kinetic and thermodynamic parameters are discussed in terms of the
proposed reaction mechanism and TS structure. Copyright # 2007 John Wiley & Sons, Ltd.
KEYWORDS: tert-butyl carbamates; kinetics; gas-phase elimination; MP2/6-31G; B3LYP/6-31G(d); B3LYP/6-31G(d,p)
calculations; mechanism
INTRODUCTION
ism, similar to those described for acetates, carbo-
1
–7
nates, and xanthates
[reaction (1)]. A mechanism
8
The gas-phase elimination of esters of N,N-dimethyl-
carbamic acids with a C —H bond at the alkyl side is
generally considered to proceed through a six-
membered cyclic transition state (TS) type of mechan-
described in reaction (2) was thought to be possible.
However, the same authors considered the TS for
the b-H abstraction by nucleophilic nitrogen atom
improbable.
b
ð1Þ
ð2Þ
*
Correspondence to: G. Chuchani, Centro de Qu ´ı mica, Instituto Vene-
zolano de Investigaciones Cient ´ı ficas (I.V.I.C.), Apartado 21827, Car-
acas, Venezuela.
E-mail: chuchani@ivic.ve
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 1021–1031

1
022
J. R. MORA ET AL.
The carbamate esters were also thought to decompose
through an intermediate whose structure lies between a
semi-concerted six-membered cyclic TS and an intimate
7
,9
ion-pair type of mechanism.
nation kinetics of 2-substituted alkyl ethyl N,N-diethyl
Moreover, the elimi-
10
carbamates showed a difference in the elimination
rates of olefin formation in the order tert-butyl >
isopropyl > ethyl. A similar sequence for the correspond-
ing 2-substituted alkyl ethyl N,N-dimethyl carbamates
was obtained. The mechanism of these reactions was
Scheme 1.
11
Recently, work related to the heterocyclic carbamates
described above was examined theoretically at the MP2/
1
8
explained in terms of C —O bond polarization, in the
a
6-31G level of theory. The theoretical thermodynamic
and kinetic parameters were found to be in good
agreement with the experimental values. TS structures
are described as six-membered rings with some departure
from planarity.
dþ
dꢀ
direction C —O , as a determining factor to proceed
according to reaction (1).
a
Phenyl and bulky groups attached to the N atoms of
ethyl carbamates were found to decrease the elimination
1
2
rates due to steric factors.
The use of several
correlation methods, such as the steric parameters of
The previous investigations of comparable reactions
have led to the examination of both experimental
and theoretical elimination kinetics of tert-butyl carba-
mates with different substituents directly attached to the
N atom, such as tert-butyl carbamate and tert-butyl
N,N-dimethyl carbamate. These substrates may be
useful to use for related or comparative study on the
gas-phase decomposition of tert-butyl carbamates com-
pounds. In the present paper, the kinetic work on the
gas-phase elimination of tert-butyl N-hydroxycarbamate
and 1-(tert-butoxycarbonyl)-imidazole is included.
13
c
Hancock’s E , Taft’s E , Charton’s y, the inductive s
I
s
values, and the Taft–Topsom equation, for a large num-
s
14
ber of 2-substituted-ethyl N,N-dimethylcarbamates,
CH ) NCOOCH CH Z, gave random points with no
(
3
2
2
2
meaning for a reasonable mechanistic interpretation.
However, the plot of the logk /k against the original
Z
CH3
14
Taft s( values gave rise at the origin [s((CH ) ¼ 0.00] to
3
three approximately straight lines. Such results suggested
that small alterations in the polarity of the TS may be due
to changes of electronic transmission at the reaction
center. This means that a simultaneous effect may be
operating during the process of elimination. A reasonable
mechanism was proposed according to each slope of
the straight lines. In the case of the point position of
COMPUTATIONAL METHODS
AND MODELS
—
Z ¼ phenyl (C H ) and isopropenyl [CH —C(CH )],
Electronic structure calculations were carried out
using Møller–Plesset perturbation method MP2/6-31G
and DFT B3LYP/6-31G(d), B3LYP/6-31G(d,p) as imple-
6
5
2
3
substituents falling far above the three lines were found to
enhance the rate of elimination due to the acidity of the
15
19
benzylic and allylic C —H bond.
b
mented in Gaussian 98W.
The Berny analytical
gradient optimization routines were used. The requested
A theoretical study using the Møller–Plesset MP2/
-31G method for the gas-phase elimination of
-substituted alkyl ethyl N,N-dimethyl carbamate gave
ꢀ9
6
2
convergence on the density matrix was 10
units, the threshold value for maximum displacement
atomic
16
˚
was 0.0018 A, and that for the maximum force was
additional support for the concerted, non-synchronous
six-membered cyclic TS mechanism. Correlation of the
logarithm of the theoretical rate coefficients against Taft
0.00045 Hartree/Bohr. The nature of stationary points was
established by calculating and diagonalizing the Hessian
matrix (force constant matrix). TS structures were
characterized by means of normal-mode analysis. The
transition vector (TV) associated with the unique
imaginary frequency, that is, the eigenvector associated
with the unique negative eigenvalue of the force constant
matrix, has been characterized.
ꢂ
(
( values gave an approximate straight line of r ¼ ꢀ1.39,
16
r ¼ 0.956 at 360 8C in comparison of the experimental
ꢂ
correlation of r ¼ ꢀ1.94, r ¼ 0.976 at 360 8C. It is
interesting to note that the experimental logk versus the
rel.
theoretical logkrel. of these alkyl substituted carbamates
16
gave a straight line (r ¼ 0.9919 at 360 8C), implying
similar mechanism.
Frequency calculations were carried out to obtain
thermodynamic quantities such as zero point vibrational
energy (ZPVE), temperature 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
17
Saturated heterocyclic carbamates showed a dec-
rease in elimination rates due to electronic factors. The
nitrogen atom of heterocyclic carbamates has its electrons
delocalized through the pi bonds, causing a rate enhan-
cement from the resonance interactions (Scheme 1).
The elimination products of these carbamates are the
corresponding carbamic acids and isobutylene. The
intermediate acids are unstable and decarboxylate at
the reaction temperature.
20
inertia by standard methods at the average temperature
and pressure values within the experimental range.
Scaling factors for frequencies and zero point energies
21
were taken from the literature.
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 1021–1031
DOI: 10.1002/poc

GAS PHASE ELIMINATION KINETICS
1023
demands that P /P ¼ 3.0, where the P and P are the
f
0
f
0
Method
fVIB
fZPE
final and initial pressures, respectively. The average
experimental results of P /P values at four different
f
0
HF/6-31G(D)
0.8929
0.9613
0.97
0.9135
0.9804
0.99
temperatures and 10 half-lives were: 2.8 for tert-butyl
carbamate, 2.9 for tert-butyl N-hydroxy carbamate, and
2.8 for 1-(tert-butoxycarbonyl)-imidazole (Table 1).
The small departure from P ¼ 3P may be due to slight
B3LYP/6-31G(d)
B3LYP/6-311G(d,p)
MP2(Full)/6-31G(d)
0.9427
0.9676
f
0
The first-order rate coefficient k(T) was calculated
using the TST assuming that the transmission coeffi-
cient is equal to 1, as expressed in the following relation:
polymerization of the product isobutene. Additional
examination of the stoichiometry of reaction (3), up to
22
65–80% decomposition, was possible by comparing the
ꢀ
ꢁ
percentage decomposition of the substrate calculated
from pressure measurements with that obtained from the
chromatographic analyses of the olefin product isobutene
(Table 2).
To examine the influence of the surface area on the
rate of elimination, several runs were carried out in
a vessel with a surface-to-volume ratio 6.0 times
greater than that normal which is equal to 1.0. The
packed and unpacked clean Pyrex vessels, except
6¼
kðTÞ ¼ ðKT=hÞ exp ꢀDG =RT
where is the Gibbs free energy change between the
reactants and the TS and K and h are the Boltzmann and
Planck constants, respectively. was calculated using the
following relations:
6
6
6¼
DG ¼ DH ꢀ TDS
and
1
-(tert-butoxycarbonyl)-imidazole had a significant effect
6
¼
6¼
DH ¼ V þ DZPVE þ DE ðTÞ
on the rates. However, the packed and unpacked vessels
seasoned with allyl bromide showed no marked effect on
the rate coefficients of these carbamates (Table 3). The
pyrolysis of these carbamates, in seasoned vessels, had to
be carried out in the presence of at least twice the amount
of the inhibitor cyclohexene and/or toluene (Table 4). No
induction period was obtained. The rate coefficients are
reproducible with a relative standard deviation not greater
than 5% at a given temperature.
where is the potential energy barrier and and are the
differences of ZPVE and temperature corrections
between the TS and the reactant, respectively.
RESULTS AND DISCUSSION
The rate coefficient of these eliminations has been
found to be independent of initial pressures (Table 5), and
the first-order rate coefficient was calculated from . A plot
of log(3P ꢀ P ) against time (t) gave a good straight line
The molecular elimination of the carbamates described by
reaction (3), in a static system,
0
t
up to 65–80% decomposition (Fig. 1). The variation of the
rate coefficient with temperature and the corresponding
Arrhenius equations are given in Table 6 (90% confidence
coefficient from least-squares procedure).
(3)
To provide a reasonable mechanism from the
calculated results of Table 7 describing the elimination
kinetics tert-butyl carbamates, a theoretical examination
was carried out.
with vessels seasoned with allyl bromide and in the
presence of cyclohexene and/or toluene inhibitors,
Table 1. Ratio of final (P ) to initial pressure (P ) of the substrate
f
0
Substrate
Temperature (8C)
249.0
P0 (Torr)
Pf (Torr)
Pf/P0
Aver.
2.8
tert-Butyl carbamate
35
33
26
39
76
49
67.5
68
20.3
16.8
26.2
27.9
96.5
90.5
72
107.5
222.5
144
199.5
200
53.6
46.8
74.2
76.7
2.8
2.7
2.8
2.8
2.9
3.0
2.9
2.9
2.6
2.8
2.8
2.8
2
2
2
61.5
70.8
80.9
tert-Butyl N-hydroxy carbamate
219.0
2.9
2.8
2
2
2
30.4
40.3
50.3
1
-(tert-Butoxycarbonyl)-imidazole
198.3
2
2
2
16.7
26.6
38.1
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 1021–1031
DOI: 10.1002/poc

1
024
J. R. MORA ET AL.
Table 2. Stoichiometry of the reaction
Substrate
Temperature (8C)
Parameters
Time (min)
Reaction (%) (pressure)
Isobutene (%) (GLC)
Time (min)
Reaction (%) (pressure)
Isobutene (%) (GLC)
Time (min)
Reaction (%) (pressure)
Isobutene (%) (GLC)
Value
tert-Butyl carbamate
261.5
229.3
216.7
3
4
8
12
26.8
27.6
1
7.9
7.1
3.6
27.6
24.8
34.2
33.2
3
19.1
18.8
7
56.6
53.5
7
42.7
41.9
8.5
71.1
75.0
10
tert-Butyl N-hydroxy carbamate
14
56.2
56.8
12
78.4
75.7
67.4
69.9
18.5
86.7
83.0
1
-(tert-Butoxycarbonyl)-imidazole
45.7
42.5
58.7
55.2
Table 3. Homogeneity of the reactions
Compound
ꢀ
1
)
4
10 k (s
ꢀ1 a
4
10 k (s
ꢀ1 b
S/V (cm
)
)
1
1
tert-Butyl carbamate at 249.0 8C
tert-Butyl N-hydroxy carbamate at 219.4 8C
1
6
1
6
1
6
14.15
13.79
11.43
13.39
18.00
16.77
7.93
7.42
7.03
7.15
17.74
17.23
1
-(tert-Butoxycarbonyl)-imidazole at 216.4 8C
S ¼ surface area; V ¼ Volume.
a
Clean Pyrex vessel.
Vessel seasoned with allyl bromide.
b
Table 4. Effect of the free radical inhibitor on rates
4
10 k (s
ꢀ1
Substrate
Temperature (8C)
Ps (Torr)
Pi (Torr)
Pi/Ps
)
1
c
tert-Butyl carbamate
249.0
34.5
—
51
61.5
100.5
101
—
—
1.0
1.8
4.4
5.2
—
0.8
1.4
2.0
—
7.97
7.65
8.08
7.96
5
3
2
1
1.5
5
3
9
8.00
a
tert-Butyl N-hydroxy carbamate
219.3
216.6
55
10.93
7.68
7.77
5
8
5
8.3
0.3
3
44
115
106.5
—
59
86
7.87
b
1
-(tert-Butoxycarbonyl)-imidazole
74
15.21
19.21
18.00
19.16
4
4
4
1.5
2
2
1.4
2.1
3.0
126
P
s
¼ pressure of the substrate.
¼ Pressure of the inhibitor.
P
i
a
Toluene inhibitor.
Cyclohexene inhibitor.
b
Table 5. Invariability of the rate coefficients with initial pressure
Substrate
Temperature (8C)
249.0
Parameters
Value
tert-Butyl carbamate
tert-Butyl N-hydroxy carbamate
P (Torr)
0
19
8.00
53
7.87
22.9
34.29
24
34.5
7.97
94
7.67
46
33.42
51.5
7.60
127
7.45
56
33.71
4
0 k (s
ꢀ1
1
)
7.86
80.3
7.77
36.2
33.12
1
219.3
P (Torr)
0
4
ꢀ1
1
0 k (s
)
)
1
1
-(tert-Butoxycarbonyl)-imidazole
226.6
P (Torr)
0
64
34.04
4
0 k (s
ꢀ1
1
1
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 1021–1031
DOI: 10.1002/poc

GAS PHASE ELIMINATION KINETICS
1025
Geometries for reactants, TS, and products for the
reactions under study were optimized using Møller–
Plesset perturbation MP2/6-31G and DFT B3LYP/
6-31G(d), B3LYP/6-31G(d,p). Frequency calculations
were carried out at the average experimental conditions
for this series of N-substituted carbamates (T ¼ 230 8C).
Thermodynamic quantities such as ZPVE, temperature
corrections (H(T)), energy, enthalpy, and free energies
were obtained from vibrational analysis. Entropy values
were calculated from vibrational analysis and using
exp
the empirical parameter C
suggested by Chuchani–
23
Cordova. This parameter is obtained from the exper-
imental free energy of activation for each reaction and
serves as scaling factor. The calculation results for the rate
controlling step are shown in Table 8.
Figure 1. A representative plot of log(3P ꢀ P ) versus time
Analysis of calculated parameters at MP2/6-31G,
B3LYP/6-31G(d), and B3LYP/6-31G(d,p) levels of
theory shows that calculated activation energies are in
reasonable agreement to the experimental counterparts
for the two step mechanism at B3LYP/6-31G(d,p) level of
theory [reaction (1)]. In all cases, MP2/6-31G over-
estimates the activation parameters, while DFT B3LYP/
0
t
for carbamates (tert-butyl carbamate at 261.5 8C). This
figure is available in colour online at www.interscience.
wiley.com/journal/poc
Calculated kinetic and thermodynamic
parameters
6-31G underestimates; however, the inclusion of polar-
The gas-phase thermal decomposition of N-substituted
t-butyl carbamates yields isobutylene and the correspond-
ing carbamic acid in a slow step according to Scheme 2.
The carbamic acids are unstable under the reaction
conditions and decarboxylate rapidly to give carbon
dioxide and the corresponding amine. The kinetics of
the rate-determining step in the decomposition of
N-substituted t-butyl carbamates as well as the dec-
arboxylation of the corresponding carbamic acids were
examined using electronic structure calculations.
ization functions significantly improves the results as
expected. Rate coefficients are within the same order of
magnitude compared to experimental values. Experimen-
tally, it is observed that the reaction is faster for the
imidazole substituent followed by that of —NHOH,
dimethylamine, and amine, that is: N C H > NHOH >
2
3 3
N(CH ) > NH . Calculated energies of activation follow
3
2
2
the same trend.
Calculated values of entropies of activation for the
rate-determining step vary from ꢀ35 to ꢀ9 J/mol K. It
Table 6. Variation of rate coefficients with temperature
Substrate
Parameters
Value
tert-Butyl carbamate
Temp. (8C)
235.6
2.41
240.1
3.71
249.0
7.93
261.5
17.31
270.8
29.55
280.8
59.55
4
0 k (s
ꢀ1
)
1
1
Rate equation logk (s ) ¼ (13.02 ꢁ 0.46) ꢀ (161.6 ꢁ 4.7) kJ/mol(2.303 RT)ꢀ1r ¼ 0.9983
ꢀ1
1
tert-Butyl N-hydroxy carbamate
Temp. (8C)
220.3
1.67
210.3
3.52
219.4
7.03
230.4
16.03
239.8
30.36
250.3
58.38
4
0 k (s
ꢀ1
)
1
1
Rate equation logk (s ) ¼ (12.52 ꢁ 0.11) ꢀ (147.8 ꢁ 1.1) kJ/mol(2.303 RT)ꢀ1r ¼ 0.9999
ꢀ1
1
1
-(tert-Butoxycarbonyl)-imidazole
Temp. (8C)
198.3
4.84
207.5
9.26
216.7
18.00
226.6
34.12
238.1
64.10
4
0 k (s
ꢀ1
)
1
1
Rate equation logk (s ) ¼ (11.63 ꢁ 0.21) ꢀ (134.9 ꢁ 2.0) kJ/mol (2.303 RT)ꢀ1r ¼ 0.9998
ꢀ1
1
Table 7. Kinetic and thermodynamics parameters for pyrolysis of ZCOOC(CH ) at 230.0 8C
3
3
k1 ꢃ 10ꢀ (s
4
ꢀ1
)
Ea (kJ/mol)
ꢀ1
logA (s )
DS (J/mol K)
6
DH (kJ/mol)
6
DG (kJ/mol)
6
Ref.
Z
NH2
(CH ) N
1.74
2.95
14.79
41.89
161.6 ꢁ 4.7
157.9
13.02 ꢁ 0.46
12.87
ꢀ8.28
ꢀ11.15
ꢀ17.85
ꢀ34.89
157.4
153.7
143.6
130.7
161.6
159.3
152.6
148.3
This work
11
This work
This work
3 2
HONH
C H N
3 2
147.8 ꢁ 1.1
12.52 ꢁ 0.11
134.9 ꢁ 2.0
11.63 ꢁ 0.21
3
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 1021–1031
DOI: 10.1002/poc

1
026
J. R. MORA ET AL.
Scheme 2.
Table 8. Kinetic and thermodynamic parameters for the gas-phase elimination of tert-butyl carbamates Z-COO-C(CH3)3
6
6
6
ꢀ1
4
ꢀ1
)
Z
DH (kJ/mol)
Ea (kJ/mol)
DG (kJ/mol)
DS (J/mol K)
logA (s
)
k ꢃ 10 (s
a
a
a
a
a
a
–
–
–
–
NH2
161.6
179.5
138.5
155.6
157.9
166.6
134.8
152.9
147.8
160.5
130.4
145.2
134.9
151.1
124.9
139.1
13.02
1.74
0.07
439
7.41
2.95
0.42
759
10.0
14.8
0.74
964
28.0
41.89
0.96
460
b
b
b
b
b
b
75.3
34.3
51.5
1.19
13.51c
13.02
c
d
a
b
c
d
a
b
c
d
a
b
c
d
c
c
c
d
d
d
d
d
13.03a
12.87
a
a
a
N(CH3)2
NHOH
N C H
b
b
b
b
b
62.3
30.6
48.7
12.91c
12.88
c
c
c
d
d
d
d
d
12.87a
12.52
a
a
a
b
b
b
b
b
56.4
26.2
41.0
12.53c
12.52
c
c
c
d
d
d
d
d
12.52a
11.63
a
a
a
2
3
3
b
b
b
b
b
47.0
20.7
34.9
11.63c
11.63
11.63
c
c
c
d
d
d
d
d
15.4
Z ¼ NH
2
, N(CH
3
)
2
, NHOH, and N
2
C
3
H
3
calculated at 230 8C
a
Experimental.
MP2/6-31G.
B3LYP/6-31G.
b
c
d
B3LYP/6-31G(d,p).
is interesting that the more constrained TS corresponds
to the fastest reaction: N C H > NHOH > N(CH ) >
Parameters for decarboxylation of the intermediate
N-substituted carbamic acids were also calculated at the
B3LYP/6-31G level of theory. Experimentally, this was
not possible due to instability of the acids under the
reaction conditions. Calculated energies of activation and
rate coefficients for this step are shown in Table 9. The TS
for this step is shown in Fig. 3. Calculated energies of
activation and rate coefficients demonstrate that dec-
arboxylation of the carbamic acids is significantly faster
than the previous step for all substrates.
2
3
3
3 2
NH2; that is, the loss of degrees of freedom in the TS is
compensated by activation energies which vary in the
sense N C H < NHOH < N(CH ) < NH The negative
2
3
3
3 2
2.
activation entropies are indicative of a concerted process
and a cyclic TS geometry (Scheme 3, Fig. 2). The TS for
the gas-phase thermal decomposition of N-substituted
t-butyl carbamates is a cyclic six-membered structure, in
24
accord to logA values between 11.63 and 13.02.
An alternate pathway [reaction (2)] was also investi-
gated. This mechanism is unlikely because the lone
electron pair on the nitrogen is involved in a partial double
bond with the carbonyl oxygen in the carbamates, as seen
on optimized carbamate structures. Even though the
electron density on the nitrogen is significant, proton
affinity on amides shows that the carbonyl oxygen is more
likely to be protonated than the nitrogen, thereby
suggesting that the abstraction is carried out by the
carbonyl oxygen. Previous theoretical studies on similar
substrates support the mechanism shown in reaction (1),
1
6,18
Scheme 2.
the mechanism in reaction (2) for t-butyl carbamate
Calculated activation parameters for
6¼
(
2
Z ¼ NH ) calculated at B3LYP/6-31G(d) are: DH ¼
2
6
07.67 kJ/mol, Ea ¼ 211.85 kJ/ml, DG ¼ 203.84 kJ/mol,
6¼
Scheme 3.
DS ¼ 7.61 J/K mol. Activation parameters for the
J. Phys. Org. Chem. 2007; 20: 1021–1031
Copyright # 2007 John Wiley & Sons, Ltd.
DOI: 10.1002/poc

GAS PHASE ELIMINATION KINETICS
1027
Figure 2. Two views of the optimized structures for the TS in the rate-determining step are shown for Z ¼ imidazole. TS
geometries are a six-membered ring for all carbamates in this series. The six atoms involved in are almost in the same plane
(O–C–O–C–C–H). The imaginary frequency is associated with the transfer of the hydrogen from Cb at the ester side of the
carbamate to the carbonyl oxygen. This figure is available in colour online at www.interscience.wiley.com/journal/poc
Table 9. Energies of activation and rate coefficients for
N-substituted carbamic acids decarboxylation step from
B3LYP/6-31G(d) calculations
some departure from planarity was observed in the
dihedral angles.
Comparison of TS structure for the carbamates of this
series showed similarity in bond distances. However,
some differences were observed; for example, the
progress in H1—O2 bond forming is more advanced
ꢀ4
ꢀ1
s )
Z
k2 (10
Ea (kJ/mol)
N(CH3)2
NH2
HONH
1995931.7
481115.4
54795.0
98.3
102.6
116.0
121.2
for carbamate Z ¼ NH . The O4—C5 bond is more
2
elongated for the TS of carbamate Z ¼ N C H in the TS.
2
2 3
N C H
2 3 3
16582.3
Some changes are observed also in C6—H1 bond
breaking, indicating differences in the electronic density
distribution in the TS for this series of carbamates. The TS
N-substituted carbamic acids are intermediates in the thermal decompo-
sition of tert-butyl carbamates Z-COO-C(CH at 230 8C.
3 3
)
˚
C6—H1 bond breaking distance is longer (1.270 A) for
carbamates Z ¼ NH and Z ¼ N(CH ) compared to
2
3 2
˚
1
.230 A for carbamates Z ¼ NHOH and Z ¼ N C H .
2
2 3
mechanism in reaction (2) deviate significantly from
experimental values; the energy of activation is about
Conversely, the breaking of O4—C5 bond is more
advanced for carbamate Z ¼ N C H . The progress of the
2
2 3
5
suggest that the thermal decomposition of t-butyl
0 kJ/mol higher than experimental. These findings
reaction in the TS shows that O4—C5 and C6—H1 bond
distances increase implying breaking of these bonds
˚
(1.47–1.48 to 2.15–2.90 A in TS and 1.08–1.09 to
˚
1.23–1.27 A in TS, respectively). The C5—C6 and
C3—O4 bond distances reveal changes from single to
carbamates proceeds through the mechanism in reaction
(
16,18
1) as proposed in previous investigations.
˚
double bond character (1.53 to 1.41 A in TS and
˚
.33–1.35 to 1.25–1.27 A in TS, respectively) as
1
3
2
TS structure and mechanism
hybridization changes from sp to sp . The transition
vector TV shows that the process is dominated by the
elongation of O4—C5 bond.
Geometrical parameters for reactants and TSs of the
rate-determining step for mechanism in reaction (1) are
shown in Table 10. Distances and angles between the
atoms involved in the reaction (H1, O2, C3, O4, C5, and
C6) show that the TS geometry is a six-membered ring
with the hydrogen being transferred (H1) midway
between the carbon (C6) and the oxygen (O2)
TSs for the rate-determining step were characterized by
unique imaginary frequencies: ꢀ1061.1, ꢀ1047.5,
ꢀ
1
ꢀ748.6, and ꢀ705.4 cm
for Z ¼ NH , N(CH ) ,
2
3 2
NHOH, and N C H respectively, and it is associated
3 3
2
with the displacement of hydrogen H1 from C6 to the
carbonyl oxygen O2. It is interesting that the imaginary
frequency is much lower for carbamates Z ¼ NHOH
and N C H
(
Scheme 3, Fig. 2). The TS structure is almost planar
for all carbamates, except when Z ¼ —NHOH, for which
2
3 3.
Figure 3. Decarboxylation reaction of the unstable N-substituted carbamic acids. The TS structure is a four-membered ring
N–C–O–H) and the imaginary frequency is associated with the hydrogen transfer. This figure is available in colour online at
www.interscience.wiley.com/journal/poc
(
Copyright # 2007 John Wiley & Sons, Ltd.
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DOI: 10.1002/poc

1
028
J. R. MORA ET AL.
Table 10. Structural parameters reactants (R), TS, and products (P) for tert-butyl carbamates Z-COO-C(CH ) ;
3
3
˚
Atom distances (A)
H –O
1
O –C
2
C –O
3
O –C
4
C –C
5
C –H
6
C –N7
3
2
3
4
5
6
1
Z ¼ –NH
1.470
2.150
2
R
TS
P
2.414
1.278
0.979
1.210
1.280
1.350
1.350
1.270
1.220
1.530
1.410
1.340
1.090
1.270
2.310
1.365
1.377
1.360
3.400
Z ¼ –N(CH )
3
2
R
TS
P
2.397
1.351
0.979
1.220
1.280
1.350
1.350
1.270
1.220
1.470
2.140
3.390
1.530
1.410
1.340
1.080
1.270
2.310
1.372
1.377
1.365
Z ¼ –NHOH
R
TS
P
3.503
1.419
0.983
1.210
1.270
1.330
1.330
1.270
1.220
1.470
2.230
1.530
1.410
1.340
1.090
1.230
2.220
1.396
1.393
1.373
3.410
Z ¼ –N C H
2
1.480
3 3
R
TS
P
2.445
1.434
0.986
1.210
1.260
1.330
1.330
1.250
1.210
1.530
1.410
1.340
1.090
1.230
2.180
1.410
1.426
1.403
2.290
3.410
Dihedral angles (degrees)
O –C –O –C C –O –C –C
H –O –C –O
1
O –C –C –H
1
2
3
4
2
3
4
5
3
4
5
6
4
5
6
Z ¼ –NH2
Z ¼ –N(CH3)2
Z ¼ –NHOH
Z ¼ –N C H
TS
TS
TS
TS
ꢀ5.699
1.300
7.210
ꢀ1.530
16.390
0.300
ꢀ3.820
0.680
ꢀ0.050
0.130
ꢀ14.480
ꢀ0.260
ꢀ6.590
ꢀ0.060
ꢀ1.540
ꢀ0.120
2
3 3
ꢀ
1
Imaginary frequency (cm
N(CH3)2
ꢀ1047.5
)
NH2
NHOH
N C H
2 3 3
TS
ꢀ1061.1
2 3 2 2 3 3
, N(CH ) , NHOH, and N C H .
ꢀ748.6
ꢀ705.4
Z ¼ NH
´
˚
Atom distances are in A and dihedral angles are in degrees from B3LYP/6-31G(d,p) calculations.
NBO charges in Table 11 show the changes in electron
density for each substrate, from the reactant structure (R)
to the TS of the rate-determining step (TS) to products
that of carbamates Z ¼ NHOH and N C H . The
2
3 3
observation on NBO charges together with rate coeffi-
cients implies that the alkyl oxygen–carbon bond
dꢀ
dþ
(
P). In all substrates there is an important charge
polarization in the sense O —Ca , dominates the
decomposition process. Charge density plots of the TS
(Fig. 4) show the polarization towards the substituents
—NHOH and N C H .
separation in atoms C3—O2 (carbonyl moiety),
C3—O4, and O4—C5.
The analysis illustrates that O4—C5 bond is highly
polarized in the reactants and the charge separation
2
3 3
dꢀ
dþ
increases in the TS structures, in the sense O4 —C5 .
Following the reaction coordinate from reactant to TS, the
following changes in partial charges occur: an increase in
positive charge dþ in hydrogen H1 (from 0.11–1.45 to
Bond order analysis
2
5–27
0
.331, 0.344 in TS), a small increase in negative charge in
Bond order calculations NBO were performed.
28
carbonyl oxygen O2 (ꢀ0.488, ꢀ0.539 to ꢀ0.563, ꢀ0.594
in TS), and an increase in negative charge in O4 (ꢀ0.495,
Wiberg bond indexes were computed using the natural
29
bond orbital NBO program as implemented in Gaussian
98W, to further investigate the nature of the TS along the
reaction pathway. Bond breaking and making processes
involved in the reaction mechanism can be monitored by
means of the Synchronicity (Sy) concept proposed by
ꢀ
0.535 to ꢀ0.561, ꢀ0.597 in TS). There is also an
increase in the polarization at the O4—C5 bond, with
charge separation increasing from 0.77, 0.76 in the
reactants to 0.82, 0.85 in the TS. The more polarized TS is
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 1021–1031
DOI: 10.1002/poc

GAS PHASE ELIMINATION KINETICS
Table 11. NBO charges for reactants (R), TS, and products (P) for tert-butyl carbamates Z-COO-C(CH3)3
NBO charges
1029
R
TS
P
R
TS
P
Z ¼ –NH2
Z ¼ –N(CH3)2
H1
O2
C3
O4
C5
C6
N7
0.145
ꢀ0.520
0.776
0.342
ꢀ0.572
0.731
0.330
ꢀ0.519
0.710
0.145
ꢀ0.539
0.814
0.344
ꢀ0.594
0.784
0.329
ꢀ0.534
0.745
ꢀ0.521
ꢀ0.566
ꢀ0.513
ꢀ0.535
ꢀ0.586
ꢀ0.533
0.272
ꢀ0.321
ꢀ0.620
0.254
ꢀ0.463
ꢀ0.479
0.159
ꢀ0.319
ꢀ0.483
0.275
ꢀ0.321
ꢀ0.467
0.255
ꢀ0.463
ꢀ0.448
0.160
ꢀ0.319
ꢀ0.440
Z ¼ –NHOH
Z ¼ –N C H
2
3 3
H1
O2
C3
O4
C5
C6
N7
0.110
ꢀ0.510
0.788
0.331
ꢀ0.571
0.744
0.334
ꢀ0.514
0.728
0.146
ꢀ0.488
0.331
ꢀ0.563
0.773
0.336
ꢀ0.506
0.756
0.823
ꢀ0.511
0.258
ꢀ0.495
ꢀ0.597
ꢀ0.529
ꢀ0.561
ꢀ0.479
0.263
0.257
0.157
0.258
ꢀ0.455
ꢀ0.473
0.156
ꢀ0.332
ꢀ0.463
ꢀ0.323 ꢀ0.454 ꢀ0.328
ꢀ0.334 ꢀ0.278 ꢀ0.256
2 3 2 2 2 3 3
, N(CH ) , NH OH, and N C H from B3LYP/6-31G(d,p) calculations.
ꢀ0.324
ꢀ0.505
Z ¼ NH
3
0
Moyano et al. defined by the expression:
from:
n
P
TS
R
i
R
jdB ꢀ dB j=dB
½Bi ꢀ B ꢄ
i
av
av
dB ¼
i
i¼1
P
Sy ¼ 1 ꢀ
n is the number of bonds directly involved in the reaction
and the relative variation of the bond index is obtained
½B ꢀ B ꢄ
i
i
2n ꢀ 2
where the superscripts R, TS, P, represent reactant, TS,
and product, respectively.
Figure 4. Charge density plots the TS in carbamate Z-COO-C(CH ) ; Z ¼ NH , N(CH ) , NHOH, and N C H . Polarization of the
3
electron density toward the substituents NHOH and N C H is observed. This figure is available in colour online at
3
2
3 2
2 3 3
2
3 3
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Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 1021–1031
DOI: 10.1002/poc

1
030
J. R. MORA ET AL.
The evolution in bond change is calculated as:
oxygen–carbon (O4—C5) bond leading to its breaking
as the reaction proceeds, for all carbamates in the series.
Sy parameters tell a concerted asynchronic, semipolar
process, with Sy values ranging from 0.85 (most
asynchronic, imidazole substituent) to 0.89 (less asyn-
chronic, Z ¼ —NH , N(CH ) ). The bond order analysis
%
E ¼ dB ꢃ 100
The average value is calculated from:
v
i
n
X
1
2
3 2
dBave ¼ n
dBi
is in accord with the TS structure, both in distances,
angles, and NBO charges as analyzed above. The TS
structure shows more progress in O3—C4 bond breaking
compared to other reaction changes. This finding suggests
i¼1
Bonds indexes were calculated for those bonds that
change as the reaction proceeds, that is: H1—O2,
O2—C3, C3—O4, O4—C5, C5—C6, C6—H1
dꢀ
that the polarization of this bond in the sense O3
dþ
(
Scheme 3, Fig. 2); all other bonds remain practically
—C4 is a determining factor in the gas-phase
elimination of N-substituted t-butyl carbamates.
unaffected. C3—N7 bond order was also included to
investigate the possible participation in the reaction
coordinate.
EXPERIMENTAL
Calculated Wiberg indexes B for reactant, TS, and
i
products for N-substituted t-butyl carbamates (Z ¼
Tert-butyl carbamate, tert-butyl N-hydroxycarbamate,
and 1-(tert-butoxycarbonyl)-imidazole were bought
from Aldrich. The purity and identity of the
substrates and products were determined by GLC/MS
—
NH , —N(CH ) , —NHOH, —N C H ) allow inspec-
2 3 2 2 3 3
tion of the progress of the reaction and the position of the
TS between reactant and product (Table 12). Wiberg
indexes show that for all carbamates in this series the most
advanced reaction coordinate is O4—C5 bond breaking
(
3
Saturn 2000, Varian). Capillary column DB-5MS,
0 mm ꢃ 0.250 mm., i.d. 0.25 mm. The olefin product
isobutylene was analyzed using a chromatograph Varian
700 with a flame ionization detector and a two meter
(
68–76%), followed by C3—O4 bond change from single
to double (55–61%). The O2—C3 change from double to
single bond is intermediate (50–53%) indicating that
hydrogen being transferred is halfway between O2 and
C6. The advancement in other reaction coordinates is less
important C6—H1 (43–48%), C5—C6 bond changes
from single to double (35–37%) and H1—O2 (35–40%).
The C3—N7 bond order shows very small changes. These
results show that the most important event in the
decomposition reaction is the polarization of alkyl
3
packed column Porapak Q column (80–100 meshes).
Kinetics
The kinetics determinations were carried out in a static
reaction system as described before.
31–33
The reaction
Table 12. Wiberg bond index from NBO B3LYP/6-31G(d,p) calculations for reactant (R), TS, and products (P) for the thermal
decomposition of tert-butyl carbamates Z-COO-C(CH3)3
H –O
1
O –C
2
C –O
3
O –C
4
C –C
5
C –H
6
C –N
3 7
dBav
Sy
2
3
4
5
6
1
Z ¼ –NH
2
1.0049
BiR
0.0056
0.2762
0.6725
40.58
1.647
1.3182
1.0274
53.07
0.9947
1.3659
1.6327
58.18
0.8215
0.2649
0.0014
67.87
0.9096
0.4854
0.0226
47.82
1.1643
1.1342
1.1679
0.5071
0.8935
ET
Bi
1.3294
1.8882
36.74
P
Bi
%Ev
Z ¼ –N(CH )
3
2
BiR
0.0057
0.274
0.6692
40.44
1.6165
1.2985
1.0218
53.47
0.9905
1.3405
1.6012
57.31
0.8196
0.2676
0.0014
67.47
1.0046
1.3272
1.8888
36.48
0.909
0.4863
0.0221
47.66
1.1408
1.1220
1.1465
0.5047
0.4922
0.5061
0.8937
0.8718
0.8550
ET
Bi
P
Bi
%Ev
Z ¼ –NHOH
BiR
0.0001
0.2383
0.6558
36.33
1.6547
1.3522
1.058
1.0365
1.3422
1.5926
54.97
0.8113
0.2156
0.0012
73.53
1.0062
1.3165
0.9255
0.5287
0.0297
44.30
1.0878
1.1047
1.1472
ET
Bi
P
Bi
1.8805
35.49
%Ev
50.70
Z ¼ –N C H
2
3 3
BiR
0.0044
0.2322
0.6471
35.44
1.7033
1.3793
1.0754
51.60
1.055
1.4463
1.6994
60.72
0.7962
0.1902
0.0012
76.23
1.0082
1.324
0.9108
0.5304
0.0332
43.35
0.9799
0.8492
0.9896
ET
Bi
P
Bi
1.8771
36.34
%Ev
Z ¼ NH
2
, N(CH
Wiberg bond indexes (B
3
)
2
, NHOH, and N
2 3 3
C H .
i
), % evolution through the reaction coordinate (%E
v
), average bond index variation (dBav), and synchronicity parameter (Sy) are shown.
Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 1021–1031
DOI: 10.1002/poc

GAS PHASE ELIMINATION KINETICS
1031
vessel was seasoned with the product of decomposition of
allyl bromide at high temperature to produce a polymeric
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to be within ꢁ0.2 8C when controlled by a SHINKO
DIC-PS 23TR resistance thermometer controller with a
calibrated iron–constantan thermocouple. Then, the
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thermopar of iron–constantan attached to a Digital
Multimeter Omega 3465B. The reaction vessel showed
no temperature gradient at different points, and the
substrate was injected directly into the reaction vessel
through a silicone rubber septum.
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PMW, Johnson B, Chen W, Wong MW, Andres JL, Head-Gordon
M, Replogle ES, Pople JA. Gaussian 98, Revision A.3, Gaussian,
Inc., Pittsburgh, PA, 1998.
CONCLUSIONS
1
The experimental data show that the elimination process
of N-substituted tert-butyl carbamates in the gas-phase is
homogeneous, unimolecular, and follows a first-order rate
law.
1
1
1
1
1
Theoretical calculations of these reactions suggest it
proceeds through a concerted asynchronous mechanism.
The TS structure of the rate-determining step for the
gas-phase elimination of N-substituted t-butyl carbamates
is a six-member ring geometry with some departure from
planarity when the nitrogen of the carbamates bears bulky
substituents. We demonstrate that the hydrogen is
abstracted by the carbonyl oxygen, not by the amide
nitrogen. In the TS structure the hydrogen is located
halfway between the carbonyl oxygen and alkyl beta
carbon. Calculated activation parameters are in good
agreement with experimental values at B3LYP/
6
and bond orders suggests that the polarization of alkyl
-31G(d,p) level of theory. Analysis of NBO charges
dꢀ
dþ
20. McQuarrie D. Statistical Mechanics. Harper & Row: New York,
986.
21. Foresman JB, Frish Æ. Exploring Chemistry With Electronic
Methods (2nd edn). Gaussian, Inc.: Pittsburg, PA, 1996.
2. Benson SW. The Foundations of Chemical Kinetics.
Mc-Graw-Hill: New York, 1960.
oxygen–carbon bond, in the sense O —Ca , is the
determining factor in the decomposition process, with this
reaction coordinate being the most advanced for all
substrates in the TS. The presence of an aromatic system
and electron withdrawing groups in the carbamate
nitrogen facilitates the decomposition process by
polarizing the alkyl carbon–oxygen bond; nonetheless
other factors such as steric constraints and loss of entropy
may also be important, in view of the fact that the more
constrained TS correspond to the fastest reaction.
1
2
23. Rotinov A, Dominguez RM, C o´ rdova T, Chuchani G. J. Phys.
Org. Chem. 2005; 18: 616–624.
2
4. (a) O’Neal HE, Benson SW. J. Phys. Chem. 1967; 71: 2903–2921;
b) Benson SW. Thermochemical Kinetics. John Wiley & Sons:
New York, 1968.
(
2
2
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8
3(2): 735–746.
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99–926.
2
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Copyright # 2007 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2007; 20: 1021–1031
DOI: 10.1002/poc