Joint experimental and DFT study of the gas-phase unimolecular elimination kinetic of methyl trifluoropyruvate

Article abstract of DOI:10.1021/jp104238a

The elimination kinetics of methyl trifluoropyruvate in the gas phase was determined in a static system, where the reaction vessel was always deactivated with allyl bromide, and in the presence of at least a 3-fold excess of the free-radical chain inhibitor toluene. The working temperature range was 388.5-430.1 °C, and the pressure range was 38.6-65.8 Torr. The reaction was found to be homogeneous and unimolecular and to obey a first-order rate law. The products of the reaction are methyl trifluoroacetate and CO gas. The Arrhenius equation of this elimination was found to be as follows: log k₁ (s^-1) = (12.48 ± 0.32) - (204.2 ± 4.2) kJ mol ^-1(2.303RT)^-1 (r = 0.9994). The theoretical calculation of the kinetic and thermodynamic parameters and the mechanism of this reaction were carried out at the B3LYP/6-31G(d,p), B3LYP/6-31++G(d,p), MPW1PW91/6-31G(d,p), MPW1PW91/6-31++G(d,p), PBEPBE/6-31G(d,p), and PBEPBE/6-31G++(d,p) levels of theory. The theoretical study showed that the preferred reaction channel is a 1,2-migration of OCH₃ involving a three-membered cyclic transition state in the rate-determining step.

Full text of DOI:10.1021/jp104238a

7892
J. Phys. Chem. A 2010, 114, 7892–7897
Joint Experimental and DFT Study of the Gas-Phase Unimolecular Elimination Kinetic of
Methyl Trifluoropyruvate
Mar´ıa M. Tosta,† Jose´ R. Mora,† Tania Co´rdova,‡ and Gabriel Chuchani*,†
Centro de Qu´ımica, Instituto Venezolano de InVestigaciones Cient´ıficas (IVIC), Apartado 21827,
Caracas 1020A, Venezuela, Department of Medicinal Chemistry, College of Pharmacy, UniVersity of Florida,
P.O. Box 100485, GainesVille, Florida 32610, and UniVersidad Central, Caracas 1020, Venezuela
ReceiVed: May 10, 2010; ReVised Manuscript ReceiVed: June 15, 2010
The elimination kinetics of methyl trifluoropyruvate in the gas phase was determined in a static system,
where the reaction vessel was always deactivated with allyl bromide, and in the presence of at least a 3-fold
excess of the free-radical chain inhibitor toluene. The working temperature range was 388.5-430.1 °C, and
the pressure range was 38.6-65.8 Torr. The reaction was found to be homogeneous and unimolecular and to
obey a first-order rate law. The products of the reaction are methyl trifluoroacetate and CO gas. The Arrhenius
equation of this elimination was found to be as follows: log k1 (s-1) ) (12.48 ( 0.32) - (204.2 ( 4.2) kJ
mol-1(2.303RT)-1 (r ) 0.9994). The theoretical calculation of the kinetic and thermodynamic parameters
and the mechanism of this reaction were carried out at the B3LYP/6-31G(d,p), B3LYP/6-31++G(d,p),
MPW1PW91/6-31G(d,p), MPW1PW91/6-31++G(d,p), PBEPBE/6-31G(d,p), and PBEPBE/6-31G++(d,p)
levels of theory. The theoretical study showed that the preferred reaction channel is a 1,2-migration of OCH3
involving a three-membered cyclic transition state in the rate-determining step.
1. Introduction
The elimination kinetics of ethyl esters of 2-oxocarboxylic
acids with nitrogen attached at the acid side, that is, ethyl
oxamate and ethyl oxanilinate,1 suggests that the first step of
An apparent interpretation from the above-reported investiga-
the reaction is a decarbonylation process by migration of the
tions (reaction 2) is that an electron-withdrawing substituent
amino substituent. Similarly, the gas-phase decomposition of
attached at the acid side of the 2-oxo-ester is liable to migrate
ethyl glyoxylate was shown to undergo a parallel and consecu-
to the adjacent carbonyl as CO gas is eliminated. Even if a
tive homogeneous elimination as described in reaction 1,2 where
hydrogen atom is included in this consideration (reaction 1, path
step 2 is also thought to comprise a decarbonylation followed
2), the result should not be surprising, as Taft’s polar substituent
by H migration.
constant σ* of H was defined with a value of +0.49,4 suggesting
a weak electron-withdrawing effect. The few examples reported
in the literature are not sufficient to establish a reasonable
generalization of the migration phenomenon. It is important to
consider the degree of polarization between the substituent at
the acid side and the carbon of the CdO. Therefore, the present
work was designed to study the CF3 substituent, which is
strongly electron-withdrawing but weakly polarizable, at the
2-oxo-ester. Consequently, the homogeneous, gas-phase elimi-
nation kinetics of methyl trifluoropyruvate (F3CCOCOOCH3)
in combination with theoretical calculations was examined. To
avoid parallel and consecutive elimination processes, the CH3
group is preferred at the alkyl side of the 2-oxo-ester.
2. Experimental Method
These mechanistic considerations were derived from experi-
mental and theoretical studies on the gas-phase elimination
kinetics of methyl oxalyl chloride.3 According to this work, a
concerted semipolar-type transition state was believed to occur
(reaction 2), where the Cl atom migrates to the adjacent carbonyl
group as CO gas is eliminated. Semiempirical PM3 and MP2/
6-31G* calculations were found to be in good agreement with
experiments.
Methyl trifluoropyruvate (Aldrich) was distilled several times
until the fraction had a purity of greater than 99%. The purity
of the substrates and products and their identifications were
determined by gas chromatography/mass spectrometry (GC/MS)
(Saturn 2000, Varian). Capillary column DB-5MS, 30 mm ×
0.250 mm i.d. × 0.25 µm, was used. The substrate was
quantitatively analyzed by GC (Varian Star 3600 CX) with a
thermal conductivity detector (column DB5, 30-m length and
0.53-mm i.d., helium gas carrier).
* To whom correspondence should be addressed. E-mail: chuchani@
ivic.gob.ve.
† Instituto Venezolano de Investigaciones Cient´ıficas (I.V.I.C.).
‡ University of Florida and Universidad Central de Venezuela.
Kinetics. The experiments were carried out in a static
system,5-7 and the reaction vessel was at all times deactivated
10.1021/jp104238a  2010 American Chemical Society
Published on Web 07/09/2010

J. Phys. Chem. A, Vol. 114, No. 30, 2010 7893
TABLE 1: Ratio of Final (Pf) to Initial (P0) Pressure of the
Substrate Methyl Trifluoropyruvate
by the product of allyl bromide decomposition. The kinetic
measurements were followed manometrically. The temperature
was controlled by a Shinko DC-PS resistance thermometer
controller, maintained (0.2 °C, and measured with iron-
constantan attached to a Digital Omega 3465B multimeter.
Different points along the reaction vessel showed no temperature
gradient. The pyruvate, dissolved in chlorobenzene (0.54 M),
was injected directly into the reaction vessel with a syringe
through a silicon rubber septum. The amount of substrate used
for each reaction was ∼0.02-0.1 mL.
a
temp (°C)
P0 (Torr)
Pf (Torr)
Pf/P0
398.6
408.8
420.4
430.1
41.4
51.6
57.0
55.1
82.0
99.1
112.5
109.1
2.0
1.9
2.0
2.0
a Average ) 2.0.
TABLE 2: Stoichiometry of the Reactiona
substrate
decomposition
(%) (GC)
3. Computational Method and Model
time
(min)
reaction (%)
(pressure)
Theoretical calculations on the kinetics and mechanisms for
the gas-phase elimination reaction of methyl trifluoropyruvate
were carried out using density functional theory (DFT) with
Becke’s three-parameter formulation from functional Lee, Yang,
and Parr [B3LYP/6-31G(d,p), B3LYP/6-31++G(d,p)]:8-10 the
Perdew-Wang 1991 correlation functional [MPW1PW91/6-
31G(d,p), MPW1PW91/6-31++G(d,p)];11 and the Perdew,
Burke, and Ernserhof [PBE/6-31G(d,p), PBE/6-31++G(d,p)]12
methods, as implemented in Gaussian 03.13
The default options for convergence in the Berny analytical
gradient optimization routines were used; that is, convergence
on the density matrix was 10-9 atomic units, the threshold value
for maximum displacement was 0.0018 Å, and the maximum
force was 0.00045 hartree/Bohr. Stationary points, minimum-
energy states, and transition states were verified using frequency
calculations. Transition state (TS) structures were located using
the quadratic synchronous transit (QST) protocol. The TS
structures were identified by means of normal-mode analysis
by having a single imaginary frequency and the corresponding
transition vector (TV). Intrinsic reaction coordinate (IRC)
calculations were performed to confirm that the transition state
structures connected the reactant and products along the
minimum-energy path.
8.6
20.2
23.3
27
34.2
59.8
67.8
70.8
79.1
37.0
61.2
66.8
74.3
79.4
34
a Substrate ) methyl trifluoropyruvate, temperature ) 408.5 °C.
TABLE 3: Homogeneity of the Reactiona
104 k1 (s-1
)
clean Pyrex
vessel
vessel seasoned with
allyl bromide
S/V (cm-1
)
b
1
6
24.76 ( 5.01
59.90 ( 9.56
12.45 ( 0.44
12.49 ( 0.55
a Substrate ) methyl trifluoropyruvate, temperature ) 420.4 °C.
b S ) surface area (cm2), V ) volume (cm3).
where V‡ is the potential energy barrier and ∆ZPVE and ∆E(T)
are the differences in ZPVEs and temperature corrections,
respectively, between the TS and the reactant. Entropy values
were estimated from vibrational analysis.
Thermodynamic quantities such as zero-point vibrational
energy (ZPVE), temperature corrections [E(T)], and absolute
entropies [S(T)] were obtained from frequency calculations.
Temperature corrections and absolute entropies were obtained
assuming ideal gas behavior from the harmonic frequencies and
moments of inertia by standard methods14 at average temperature
and pressure values within the experimental range. Scaling
factors for frequencies and zero-point energies were taken from
the literature.15,16
4. Results and Discussion
4.1. Experimental Results. The gas-phase elimination of
methyl trifluoropyruvate (reaction 3), in vessels deactivated with
the product of decomposition of allyl bromide, was found to
produce methyl trifluoroacetate and CO gas.
F3CCOCOOCH3 f F3CCOOCH3 + CO
(3)
The first-order rate coefficient, k(T), was calculated using
transition state theory (TST)17 and assuming that the transmis-
sion coefficient is equal to 1, as expressed in the equation
The stoichiometry of reaction 3 demands Pf ) 2P0, where Pf
and P0 are the final and initial pressures, respectively. The
average experimental result for Pf/P0 at four different temper-
atures and 10 half-lives was 2.0 (Table 1). An additional
verification of the stoichiometry in reaction (3), up to 80%
reaction progress, is that the percentage decomposition of the
substrate calculated from pressure measurements was in good
agreement with the chromatographic analyses of the unreacted
pyruvate (Table 2).
The homogeneity of the reaction was tested by using a vessel
with a surface-to-volume ratio 6.0 times greater than that of
the unpacked vessel (Table 3). The packed and unpacked clean
Pyrex vessels had a very significant heterogeneous effect on
the substrate. However, when the vessels were seasoned with
allyl bromide, no significant effect of the rate coefficients on
elimination of the methyl trifluoropyruvate was obtained.
The effect of the addition of different proportions of toluene,
a free-radical inhibitor, is described in Table 4. The experiments
on the pyruvate were always carried out in seasoned vessels
and in the presence of at least 3 times the amount of toluene in
k(T) ) (kBT/h) exp(-∆G‡/RT)
where ∆G‡ is the Gibbs free energy change between the reactant
and the transition state and kB and h are the Boltzmann and
Planck constants, respectively.
∆G‡ was calculated using the following relations
∆G‡ ) ∆H‡ - T∆S‡
and
∆H‡ ) V‡ + ∆ZPVE + ∆E(T)

7894 J. Phys. Chem. A, Vol. 114, No. 30, 2010
Tosta et al.
TABLE 4: Effect of the Inhibitor Toluene on the Ratea
The results given in Table 6 lead to the consideration of two
possible mechanisms for the elimination of methyl trifluoro-
pyruvate as described in reactions 4 and 5. In this respect, a
theoretical study was carried out to elucidate which is the most
probable and reasonable mechanism according to the experi-
mental data.
Psb (Torr)
Pic (Torr)
Pi/Ps
104 k1 (s-1
)
60
63
42
52
48
-
65
86
176
206
-
18.73 ( 5.01
17.81 ( 4.16
14.12 ( 4.01
12.45 ( 0.44
12.43 ( 0.40
1.0
2.1
3.4
4.3
a Substrate ) methyl trifluoropyruvate, temperature ) 420.2 °C.
Vessel seasoned with allyl bromide. b Ps ) pressure of the substrate.
c Pi ) pressure of the inhibitor.
TABLE 5: Invariability of the Rate Coefficient with the
Initial Pressurea
P0 (Torr)
104 k1 (s-1
)
38.6
47.0
56.0
65.8
11.93 ( 0.41
11.67 ( 0.55
11.49 ( 0.27
11.57 ( 0.72
a Substrate ) methyl trifluoropyruvate, temperature ) 420.2 °C.
Vessel seasoned with allyl bromide. In the presence of the inhibitor
toluene.
4.2. Theoretical Results. 4.2.1. Kinetic and Thermody-
namic Parameters. Theoretical calculations were performed in
order to consider a reasonable mechanism for the gas-phase
decarbonylation of methyl trifluoropyruvate. Two possible
mechanisms were examined, as depicted in reactions 4 and 5.
Mechanism A shown in reaction 4 implies the migration of CF3
to the neighboring carbonyl carbon with loss of CO. Conversely,
mechanism B shown in reaction 5 implies the migration of
OCH3 with loss of CO. Both processes proceed in concerted
fashion and account for the products formed, methyl trifluoro-
acetate and carbon monoxide.
Thermodynamic quantities obtained from frequency calcula-
tions and the estimated activation parameters were compared
with the experimental values. Calculated parameters are given
in Table 7. Temperature corrections were carried out at the
average experimental conditions (T ) 410 °C).
TABLE 6: Temperature Dependence of the Rate
Coefficienta,b
temperature (°C)
104 k1 (s-1
)
388.5
398.6
408.8
420.4
430.1
2.31 ( 0.08
4.16 ( 0.19
7.32 ( 0.24
12.45 ( 0.44
20.40 ( 0.82
a Substrate ) methyl trifluoropyruvate. b Rate equation: log k1
(s-1) ) (12.48 ( 0.32) - (204.2 ( 4.2) kJ mol-1(2.303RT)-1; r )
0.9994.
For mechanism A, the calculated enthalpies of activation and
energies of activation were overestimated by all DFT methods
used by 34-87 kJ/mol when compared to the experimental
value. Deviations were also found for the entropy of activation
and free energy of activation.
Interestingly, theoretical calculations gave reasonable enthal-
pies of activation and energies of activation for mechanism B,
particularly when using B3LYP/6-31G++(d,p), MPW1PW91/
6-31G(d,p), and MPW1PW91/6-31++G(d,p). We found that
the PBEPBE method gave underestimated parameters when
compared to the experimental values. Regarding the entropy of
activation, better results were obtained using MPW1PW91/6-
31G(d,p), MPW1PW91/6-31++G(d,p), PBEPBE/6-31G(d,p),
and PBEPBE/6-31++G(d,p). However, in considering all
calculated parameters, the best agreement with experimental
values was obtained with the MPW1PW91 functional. The
entropy of activation of about -20 J/(mol K) implies a loss of
degrees of freedom corresponding to cyclic transition state
structures.
The calculation results are in agreement with mechanism B,
suggesting that the gas-phase decarbonylation of methyl trif-
luoropyruvate is likely to proceed by this reaction channel
involving the 1,2-migration of the OCH3 group to the next
carbonyl carbon.
Characterization of the TS structure and a detailed description
of the changes in geometrical parameters, charges, and bond
orders for mechanism B are provided in the following sections.
4.2.2. Transition State and Mechanism. The optimized
structures for reactants, TSs, and products of the reactions
Figure 1. Arrhenius plot for the elimination kinetic of methyl
trifluoropyruvate in the gas phase.
order to suppress any possible free-radical chain reaction. No
induction period was observed, and the rates were reproducible
with a relative standard deviation not greater than 5% at a given
temperature.
The first-order rate coefficients of this reaction calculated from
k1 ) -(2.303/t) log[(2P0 - Pt)/P0 were found to be independent
of the initial pressures (Table 5). The logarithmic plot of log(2P0
- Pt) against time t gave a good straight line up to 75% extent
of reaction. The temperature dependence of the rate coefficients
and the corresponding Arrhenius equation are given in Table 6
and Figure 1 (90% confidence coefficient obtained from the
least-squares procedure).

J. Phys. Chem. A, Vol. 114, No. 30, 2010 7895
TABLE 7: Thermodynamic and Arrhenius Parameters of Methyl Trifluoropyruvate (CF3COCOOCH3) at 410 °C
method
Ea (kJ/mol)
log A (s-1
Mechanism A
12.48
13.9
13.8
13.6
13.5
13.4
13.3
)
∆H‡ (kJ/mol)
∆S‡ [J/(mol K)]
∆G‡ (kJ/mol)
experimental
B3LYP/6-31G(d,p)
B3LYP/6-31++G(d,p)
MPW1PW91/6-31G(d,p)
MPW1PW91/6-31++G(d,p)
PBEPBE/6-31G(d,p)
204.22
278.8
269.4
291.2
282.6
246.0
237.6
198.5
273.2
263.7
285.5
277.0
240.4
231.9
-21.2
6.8
213.0
268.5
261.1
285.6
277.7
243.1
236.1
3.9
-0.9
-1.1
-4.0
-6.2
PBEPBE/6-31++G(d,p)
Mechanism B
B3LYP/6-31G(d,p)
197.9
205.6
206.7
209.1
168.1
172.7
13.0
12.8
12.6
12.5
12.5
12.5
192.2
199.9
201.1
203.4
162.4
167.0
-12.2
-15.7
-19.7
-20.6
-21.4
-21.5
200.6
210.7
214.5
217.5
177.0
181.7
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)
SCHEME 1
involved in mechanisms A and B are shown in Figures 2 and
3, respectively. The structures of the transition state in the
decarbonylation of trifluoropyruvate proceeding through a 1,2-
migration correspond to a cyclic three-membered ring. In
mechanism A, the migrant group is CF3, whereas in mechanism
B, the migrating group is OCH3, where the lone pair of electrons
on the O atom in OCH3 moves toward C2. Because a reasonably
good agreement was found between the calculated parameters
(Table 7) and the experimental values for mechanism B, in
contrast with large deviations found for mechanism A, the data
for the geometrical parameters, charges, and bond orders for
mechanism B are presented. The atom numbering is shown in
Scheme 1.
Interatomic distances reported in Table 8 show a significant
elongation of the C3-O4 bond in the transition state from 1.33
to 1.85 Å, indicating significant bond breaking. Also, the O4-C2
distance decreases considerably from 2.38 to 1.67 Å as the
methoxy group migrates from C3 to C2. However, the formation
of CO is not yet apparent, as indicated by the small change in
the C2-C3 distance in the TS. The transition vector is associated
with a rocking vibration showing the migration of OCH3 from
C3 to C2
The TS of mechanism B described above was verified by
means of IRC calculations. The corresponding plot is given as
Supporting Information (Figure 4). To better describe the
changes occurring in the proposed reaction channel, further
analysis of NBO charges and bond indexes was carried out.
The results are discussed in the next two sections.
4.2.3. NBO Charge Analysis. NBO charges have been used
to describe the changes in electron distribution occurring in a
reaction. Table 9 lists the NBO charges for the relevant atoms
Figure 2. Optimized structures for reactant R, transition state TS, and products P in the gas-phase elimination of CF3COCOOCH3 at the B3LYP/
6-31++G(d,p) level. Mechanism A.
Figure 3. Optimized structures for reactant R, transition state TS, and products P in the gas-phase elimination of CF3COCOOCH3 at the B3LYP/
6-31++G(d,p) level. Mechanism B.

7896 J. Phys. Chem. A, Vol. 114, No. 30, 2010
Tosta et al.
n
TABLE 8: Structural Parameters of Reactant (R),
Transition State (TS), and Products (P) of Methyl
Trifluoropyruvate, in Gas-Phase Elimination at 410 °C,
Obtained from B3LYP/6-31++G(d,p) Calculations
1
δBav
)
δB
i
∑
n i)1
Interatomic Distances (Å)
Wiberg bonds indexes, Bi, were calculated for those bonds
involved in the changes in the methyl trifluoropyruvate decar-
bonylation reaction: C2-C3, C3-O4, and O4-C2. (See Table
10.) Other reaction coordinates undergo negligible changes and
were not considered.
C2-C3
C3-O4
O4-C2
R
1.547
1.567
4.457
1.335
1.847
4.499
2.380
1.669
1.329
TS
P
Calculated parameters show that the single bond order C3-O4
was changed from 1.01 to 0.39 in the TS. This coordinate is
the most advanced at 63%. Formation of the new single bond
O4-C2 has an intermediate progress of 47%, whereas breaking
of C2-C3 shows very little advancement of 8.5%. The syn-
chronicity parameter has been used to describe whether a
reaction occurring in a concerted fashion shows equal progress
along the different reaction coordinates or not. This parameter
varies from 1, in the case of concerted synchronic reaction, to
0 in the case of asynchronous process. Although global
synchronicity is a general concept, analysis of bond order in
the different reaction coordinates describe the extension to which
any particular bond involved in the reaction is formed or broken
in the TS. In this sense, the reaction can be described as more
advanced in some reaction coordinates than others.
For the elimination of carbon monoxide from methyl tri-
fluoropyruvate, the analysis of bond orders given as Wiberg
indexes showed that the process is dominated by the breaking
of C3-O4 (63%) compared to the other reaction coordinates,
and as a result, the reaction is considered asynchronous to a
significant extent (Sy ) 0.61).
Angles (deg)
C2-C3-O4
C3-O4-C2
O4-C2-C3
TS
57.86
52.65
69.49
Imaginary Frequency (cm-1
)
TS
473.83
TABLE 9: NBO Charges of Reactant (R), Transition State
(TS) and Products (P) of Methyl Trifluoropyruvate, in
Gas-Phase Elimination at 410 °C, Obtained from B3LYP/
6-31++G(d,p) Calculations
C2
C3
O4
R
TS
P
0.416
0.415
0.733
0.733
0.760
0.509
-0.533
-0.583
-0.527
of the reactant, TS, and products in the decarbonylation reaction
of methyl trifuoropyruvate. Atom numbers are given in
Scheme 1.
Calculated NBO charges for the atoms involved in the
reaction show augmentation of the negative charge at oxygen
O4 from -0.53 to -0.58 in the TS as the O4-C3 bond breaks,
accompanied by an increase in the positive charge at carbon C3
from 0.73 to 0.76. The charge at C2 is practically unaltered.
The electron distribution in the TS (Table 9) implies the
polarization of the O4-C3 bond, suggesting that the TS is
reactant-like.
4.2.4. Bond Order Analysis. The changes along the reaction
coordinatescanbestudiedusingNBObondordercalculations.18-20
For this purpose, Wiberg bond indexes21 were computed using
the natural bond orbital (NBO) program22 as implemented in
Gaussian 03. These indexes can be used to estimate bond orders
from population analysis. The bond breaking and making
process involved in the reaction mechanism are described by
means of the synchronicity (Sy) concept proposed by Moyano
et al.,23 defined by the expression
5. Conclusions
The gas-phase decarbonylation reaction of methyl trifuoro-
pyruvate has been studied in a static system with reactor walls
deactivated with pyrolysis products with allyl bromide and in
the presence of the free-radical inhibitor toluene. The reaction
was found to be homogeneous and unimolecular and to obey a
first-order rate law. The reaction products are methyl trifluo-
roacetate and carbon monoxide. The Arrhenius equation of this
elimination was found to be log k1 (s-1) ) (12.48 ( 0.32) -
(204.2 ( 4.2) kJ mol-1(2.303RT)-1 (r ) 0.9994). Two mech-
anisms were studied to account for product formation. Mech-
anism A proposes CF3 1,2-migration through a three-membered
cyclic transition state, and mechanism B engages OCH3 1,2-
migration also through a cyclic three-membered transition state
structure. Theoretical calculations of the potential energy surface
encompassing the reactant and products were carried out using
different DFT levels with the aim of proposing a reasonable
reaction mechanism. The results are in good agreement with
the experimental values for migration of a methoxy group rather
than a trifluoromethyl group. Comparison of the calculated
parameters with experimental values indicates that better results
were obtained when using the MPW1PW91 functional and
including diffuse functions in the basis set. The suggested
n
Sy ) 1 -
|δB - δB |/δB /(2n - 2)
∑
i
av
av
[
]
i)1
n is the number of bonds directly involved in the reaction, and
the relative variation of the bond index is obtained from
δBi ) (BTi S - BRi )/(BiP - BRi )
TABLE 10: Wiberg Bond Indexes of Reactant (R),
Transition State (TS), and Products (P) of Methyl
Trifluoropyruvate, in Gas-Phase Elimination at 410 °C,
Obtained from B3LYP/6-31++G(d,p) Calculations
where the superscripts R, TS, and P represent the reactant,
transition state, and products, respectively.
The evolution in bond change is calculated as
C2-C3
C3-O4
O4-C2
Sy
BiR
0.9027
0.8264
0.0004
8.5
1.0717
0.3941
0.0004
63.3
0.0179
0.5245
1.0867
47.4
0.605
Ev (%) ) δBi × 100
BTi S
BiP
and the average value is calculated from
Ev(%)

J. Phys. Chem. A, Vol. 114, No. 30, 2010 7897
Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.;
Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.;
Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li,
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reaction channel for this reaction thereby involves OCH3 1,2-
migration. These results imply that, in this type of gas-phase
reaction, the OCH3 group has a better migratory aptitude than
the CF3 group.
Acknowledgment. T.C. is grateful to the Consejo de Desar-
rollo Cient´ıfico y Human´ıstico of Universidad Central de
Venezuela (C.D.C.H.) for Grant PG-03-00-6499-2006.
Supporting Information Available: Plot of the IRC de-
scribing the energy profile versus the reaction coordinate of the
reactant, TS, and products. This information is available free
of charge via Internet at http://pubs.acs.org.
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