A Joint Experimental and Theoretical Study on the Mechanisms of Methyl 2-Hydroxypropionate and Methyl 2-Hydroxyisobutyrate Decomposition in the Gas Phase

Article abstract of DOI:10.1021/jp030985h

The gas-phase decomposition kinetics of the title compounds have been examined over the temperature range of 369 9-439 4°C and pressure range of 67.5-209.0 Torr. The reactions were found to be homogeneous and unimolecular and to follow a first-order rate law The rate coefficients are expressed by the following Arrhenius equations: for methyl 2-hydroxypropionate (I), log k ₁ (s^-1) = (13 73 ± 0.19) - (219.8 ± 2.5) kJ·mol^-1 (2.303RT)^-1, and for methyl 2-hydroxyisobutyrate (II), log k₁ (s^-1) = (13.37 ± 0.39) - (217.1 ± 5.1) kJ·mol^-1 (2.303RT)^-1 The decomposition products of I are acetaldehyde, methanol, and carbon monoxide, while II yields mainly acetone, methanol, and carbon monoxide and very small amounts of methyl formate and methyl methacrylate The reaction mechanisms have been theoretically characterized at B3LYP/6-31+G**, MP2/6-31G**, and MP2/6-31++G** computing levels by characterizing the stationary points (reactants, products, intermediates, and transition structures) on the potential energy surface The transition-state theory has been used to obtain the rate coefficients, and a good agreement is found between theoretical and experimental results.

Full text of DOI:10.1021/jp030985h

996
J. Phys. Chem. A 2004, 108, 996-1007
A Joint Experimental and Theoretical Study on the Mechanisms of Methyl
2
-Hydroxypropionate and Methyl 2-Hydroxyisobutyrate Decomposition in the Gas Phase
Vicent S. Safont,* Juan Andr e´ s, and Raquel Castillo
Departament de Ci e` ncies Experimentals, UniVersitat Jaume I, Box 224, 12080 Castell o´ , Spain
Gabriel Chuchani, Alexandra Rotinov, Rosa M. Dom ´ı nguez, and Armando Herize
Centro de Qu ´ı mica, Instituto Venezolano de InVestigaciones Cient ´ı ficas, Apartado 21827,
Caracas 1020-A, Venezuela
ReceiVed: August 19, 2003; In Final Form: October 27, 2003
The gas-phase decomposition kinetics of the title compounds have been examined over the temperature range
of 369.9-439.4 °C and pressure range of 67.5-209.0 Torr. The reactions were found to be homogeneous
and unimolecular and to follow a first-order rate law. The rate coefficients are expressed by the following
-
1
Arrhenius equations: for methyl 2-hydroxypropionate (I), log k (s ) ) (13.73 ( 0.19) - (219.8 ( 2.5)
1
-
1
-1
-1
kJ‚mol (2.303RT) , and for methyl 2-hydroxyisobutyrate (II), log k
.1) kJ‚mol (2.303RT) . The decomposition products of I are acetaldehyde, methanol, and carbon monoxide,
1
(s ) ) (13.37 ( 0.39) - (217.1 (
-1
-1
5
while II yields mainly acetone, methanol, and carbon monoxide and very small amounts of methyl formate
and methyl methacrylate. The reaction mechanisms have been theoretically characterized at B3LYP/6-31+G**,
MP2/6-31G**, and MP2/6-31++G** computing levels by characterizing the stationary points (reactants,
products, intermediates, and transition structures) on the potential energy surface. The transition-state theory
has been used to obtain the rate coefficients, and a good agreement is found between theoretical and
experimental results.
1
. Introduction
SCHEME 1: Schematic Description of the Two-Step
Mechanism for the Decomposition of 2-Substituted
Carboxylic Acids
Gas-phase experiments provide the opportunity to obtain
valuable information on elementary reactions and mechanisms
in a controlled environment without disturbing factors such as
the presence of solvent molecules. In this context, the gas-phase
thermal decomposition of several carboxylic acids derivatives
was studied by some of us.1-8 From an experimental point of
view, explicit information on the elementary steps involved
along the whole reaction path is often difficult to obtain, and a
closer interaction between theory and experiment has turned
out to be very fruitful in this area of chemistry. The availability
of experimental data concerning the activation parameters, in
particular, rate coefficients and activation energies, made it
possible to check the reliability of quantum chemical tools in
the description of these processes. Therefore, the kinetics of
9
the gas-phase thermal decompositions of 2-chloropropionic,
decomposes to carbon monoxide and acetaldehyde (Scheme 1).
glycolic, lactic, 2-hydroxyisobutyric,10 mandelic, and meth-
oxyacetic, ethoxyacetic, and isopropoxyacetic1 acids was
theoretically studied. In addition, the gas-phase decompositions
of 2-methoxypropionic, 2-ethoxypropionic, 2-isopropoxypro-
pionic,13 and 3-chloropivalic acids were studied by means of
combined experimental and theoretical approaches.
The 2-chloropropionic acid decomposition1,9 takes place along
a two-step mechanism; in the first and rate-limiting step, the
hydrogen chloride is formed via a (3.1.0) bicyclic transition
structure (TS) with participation of the carbonylic oxygen of
the carboxyl group and the assitance of the acidic hydrogen,
thus yielding an R-propiolactone intermediate. This, in turn,
11
The same mechanism has been found to preferentially take
2
3,7,10,11
place if the 2-substituent is a hydroxyl group
or an
6
,12,13
alkoxy group
mechanism for other 2-chloroacids,
and has been proposed as the preferred
4
,15
2,5
2-bromoacids, and
14
8
2-phenoxyacids.
The assistance of the H of the COOH to the leaving L group
and the nucleophilic participation of the oxygen carbonyl for
the lactone formation may be derived from the results in the
pyrolyses of 2-chloro- and 2-bromopropionic acids as compared
with the results of the decomposition of their methyl esters.1
Since neighbor group participation in liquid media and in the
,2
1
6,17
gas phase has been reported,
it was thought that with
replacement of the H of the COOH by the methyl group in the
haloacids, the carbon-halogen bond polarization, in the sense
*
To whom correspondence should be addressed. E-mail: safont@
δ+
δ-
exp.uji.es. Telephone: 34 964728085. Fax: 34 964728066.
C
‚‚‚X , may first be assisted anchimerically by the carbo-
1
0.1021/jp030985h CCC: $27.50 © 2004 American Chemical Society
Published on Web 01/14/2004

A Joint Experimental and Theoretical Study
J. Phys. Chem. A, Vol. 108, No. 6, 2004 997
SCHEME 2: Schematic Description of the Expected
Two-Step Mechanism for the Decomposition of
DC-PS 25RT and an OMEGA solid-state relay, model SSR240
AC45, maintained within (0.20 °C and measured with a
calibrated platinum-platinum-13% rhodium thermocouple. No
temperature gradient was found along the reaction vessel. The
rate coefficients of methyl 2-hydroxypropionate were determined
by the unreacted amount of the substrate through chromato-
graphic analyses (OV 101-10% Gas Chrom. QI 80-100 mesh).
In the case of methyl 2-hydroxyisobutyrate, the kinetics was
followed by quantitative analyses of acetone formation in the
column of Porapak R 80-100 mesh. The substrates were
injected with a syringe through a silicone rubber septum directly
into the reaction vessel.
2
-Substituted Methyl Esters
nylic oxygen. Therefore, the leaving X group, through an
intramolecular solvation or autosolvation, may uptake the methyl
group of the ester to give CH3X as described in Scheme 2.
However, the products of direct elimination, that is, the
corresponding alkene and HX, are obtained.2 This fact
suggests that the assistance of the H of the COOH to the leaving
group is necessary in the process of elimination to yield the
lactone intermediate.
3
. Computing Methods
,18
The transition state theory (TST)21,22 was devised to facilitate
the interpretation of rate coefficients and is used almost
universally by chemists interested in reaction mechanisms. Other
theories have been developed to calculate the rate coefficients
The OH group of aliphatic alcohols is known to be a very
poor leaving group, especially in dehydration processes; there-
fore, it is interesting to determine the gas-phase elimination
kinetics of 2-hydroxycarboxylic acids with the H of the COOH
replaced by the methyl group, that is, primary, secondary, and
tertiary methyl esters of 2-hydroxycarboxylic acids. This type
of compound may provide information as to whether the oxygen
carbonyl provides anchimeric assistance or some other type of
mechanism may occur during the pyrolytic decomposition. In
addition to the experiments, theoretical calculations have been
done to obtain a more adequate interpretation about the
mechanistic pathways of these reactions.
The aim of the present study is to extend our work on this
type of compound, and here we report the experimental
kinetics of the decomposition processes of methyl hydroxy-
acetate, methyl 2-hydroxypopionate (I), and methyl 2-hydroxy-
isobutyrate (II). We also report a detailed theoretical study of
the corresponding reaction pathways for the decomposition of
I and II. A comparison between experimental and theoretical
values of activation parameters has been carried out.
2
3
for chemical processes, such as the Rice-Ramsperger-Kassel-
2
4,25
Marcus (RRKM)
or the variational transition-state theory
2
6,27
(VTST);
however the mechanism of a given chemical
reaction can be described by the transition structure associated
with the chemical interconversion step in the sense proposed
2
8,29
by Tapia and Andr e´ s.
We have selected this method to
calculate the kinetic parameters in the present study.
Calculations at the MP2 level of theory with the 6-31G**
and 6-31++G** basis sets have been performed with the
30
Gaussian 98 program. In addition, the B3LYP/6-31+G** level
has also been used. The Berny analytical gradient optimization
3
1,32
routines
were used for optimization. The requested conver-
-9
gence on the density matrix was 10 atomic units; the threshold
value of maximum displacement was 0.0018 Å, and that of
maximum force was 0.000 45 hartree/bohr. The nature of each
stationary point was established by calculating and diagonalizing
the Hessian matrix (force constant matrix). The TSs were
characterized by means of a normal-mode analysis. The unique
imaginary frequency associated with the transition vector (TV),33
that is, the eigenvector associated with the unique negative
eigenvalue of the force constant matrix, has been characterized.
2
. Experimental Section
3
4
The intrinsic reaction coordinate (IRC) path was traced to
check and obtain the energy profiles connecting each transition
structure to the two associated minima of the proposed mech-
anism by using the second-order Gonz a´ lez-Schlegel integration
Methyl 2-Hydroxyacetate (Methyl Glycolate). This com-
pound was bought from Aldrich of 98% purity (GLC, FFAP-
% Chromosorb AW DMCS 80-100 mesh). The decomposition
7
products are acetaldehyde (Aldrich), methanol (Aldrich), CO2,
and CO. The analyses were irreproducible and could not be
estimated quantitatively in the same FFAP or any other column.
Methyl 2-Hydroxypropionate (Methyl Lactate). This sub-
strate (Aldrich) of 99.9% purity determined by GLC (FFAP-
35,36
method.
Each stationary point in the potential energy surface (PES)
is characterized by an index that is equal to the number of
negative eigenvalues of the Hessian matrix (0 for a minimum,
1
for a saddle point). This index is also the number of imaginary
7
% Chromosorb AW DMCS 80-100 mesh) was used. The
wavenumbers obtained in a normal-mode analysis of the
corresponding molecular structure. This analysis also provides
thermodynamic quantities such as zero-point vibrational energy
products acetaldehyde (Aldrich) and methanol (Aldrich) were
quantitatively analyzed in the same FFAP column.
Methyl 2-Hydroxyisobutyrate. Methyl 2-hydroxyisobutyrate
was found to be of 98.7% purity (GLC, Porapak R 80-100
mesh). The pyrolysis product acetone (Merck) was quantitatively
analyzed in the Porapak R column. The identities of the
substrates and products were additionally verified by mass
spectrometry and nuclear magnetic resonance spectroscopy.
Kinetics. The kinetic experiments were carried out in a static
(
ZPVE), temperature corrections (E(T)), and the absolute entropy
37
(S(T)), and consequently, the rate coefficient can be estimated.
Temperature corrections and absolute entropies were obtained
assuming ideal gas behavior from the harmonic frequencies and
3
8
moments of inertia by standard methods. A temperature of
73.15 K (400 °C), inside the experimental range, was taken in
6
the calculations.
19,20
reaction apparatus as described before
but with some
The first-order rate coefficient (k(T)) was computed using
modifications and additions of modern electronic and electrical
devices. The reaction vessel was seasoned with allyl bromide,
and the pyrolysis was performed in the presence of cyclohexene
or toluene as a free radical chain inhibitor. The temperature was
controlled by a resistance thermometer controller type SHINKO
2
1,39
the TST
and assuming that the transmission coefficient is
equal to 1, as expressed by the following relation:
q
k(T) ) (kT/h) exp(-∆G /(RT))
(1)

998 J. Phys. Chem. A, Vol. 108, No. 6, 2004
Safont et al.
TABLE 1: Stoichiometry of the Decomposition Reactiona
TABLE 2: Homogeneity of the Reaction
S/V
T
T
(°C) (cm 1)a
-
104k
(s-1)b
104k (s-1)c
1
substrate
(°C)
params
value
substrate
1
methyl 2-hydroxy- 399.4 time (min)
5
10 15 20 25
methyl 2-hydroxy- 399.4
propionate
1
6
8.18d
4.45 ( 0.15
4.26 ( 0.12
b
12.84d
propionate
reaction (%) 11.9 21.7 30.3 39.2 56.4
pressure)
substrate (%) 12.0 22.2 32.4 39.7 57.3
(
methyl 2-hydroxy- 409.9
isobutyrate
1
6
7.51 ( 0.19 6.01 ( 0.11
8.67 ( 0.32 6.19 ( 0.15
d
(GLC)
a
2
3
b
S ) surface area (cm ); V ) volume (cm ). Clean Pyrex vessel.
Vessel seasoned with allyl bromide. d Average k-values.
methyl 2-hydroxy- 419.7 time (min)
4
5
6.5
reaction (%) 26.0 24.2 33.4 38.0 43.5
pressure)
substrate (%) 26.2 29.1 33.5 37.3 42.7
GLC)
8
10
c
c
isobutyrate
(
TABLE 3: Effect of the Free Radical Inhibitor on Ratesa
(
substrate
T (°C)
P
s
(Torr)
P
i
(Torr)
P
i
/P
s
104k (s-1
1
)
a
Vessel seasoned with allyl bromide. b In the presence of toluene
Ib
399.4
130
91
126.5
4.06 ( 0.16
4.20 ( 0.10
4.50 ( 0.19
4.45 ( 0.15
4.81 ( 0.21
c
d
157.5
208
355
0.6
1.6
2.5
3.2
inhibitor. In the presence of cyclohexene inhibitor. GLC ) gas-
liquid chromatography.
1
82
35
q
267.5
in which ∆G is the Gibbs free energy change between the
reactant and its corresponding transition structure and k and h
are the Boltzmann and Planck constants, respectively. ∆G was
calculated as usually:
IIc
409.9
105.5
114.0
6.66 ( 0.31
6.41 ( 0.22
6.70 ( 0.28
6.82 ( 0.25
6.49 ( 0.27
q
83.5
174
150
0.7
1.2
1.4
3.0
1
1
7
44
04
8
140
q
q
q
∆
G ) ∆H - T∆S
(2)
a
P
s
) pressure of the substrate; P ) pressure of the inhibitor. Vessel
i
b
c
and
seasoned with allyl bromide. Inhibitor toluene. Inhibitor cyclohexene.
q
∆
H ) PEB + ∆ZPVE + ∆E(T)
(3)
runs had to be carried out with at least an equal amount of
cyclohexene to suppress any possible free radical process of
the starting material or product or both. No induction period
was observed: when the substrate was introduced into the
reaction vessel, the process of elimination immediately took
place. Moreover, drawing the graph of total pressure (mmHg)
versus time (min), we obtained a curve characteristic of a
unimolecular reaction. Also, the presence of different propor-
tions of free radical inhibitors (Table 3) did not affect the rate
coefficient. The k-values are reproducible with a standard
deviation not greater than 5% at a given temperature.
The experimental stoichiometry for the pyrolytic elimination
of II in the gas phase (eq 5) was made by comparing, up to
50% reaction, the percentage decomposition of the substrate
from pressure measurements with that obtained from the
quantitative chromatographic analyses of the unreacted starting
material (Table 1).
q
where ∆H is the activation enthalpy, PEB is the potential
energy barrier, and ∆ZPVE and ∆E(T) are the differences of
ZPVE and temperature corrections between the TS and the
q
corresponding reactant, respectively. ∆S is obtained directly
as the entropy (taken from the normal mode Gaussian 98
outputs) difference between the TS and its corresponding
reactant.
4
. Results and Discussion
.1. Experimental Results. The gas-phase elimination of
methyl 2-hydroxyacetate (methyl glycolate) in a vessel seasoned
with allyl bromide and in the presence of the free radical
inhibitor toluene was found to be difficult for complete kinetic
mesurements. At two different temperatures, it was possible to
determine approximately the overall rate coefficients: k ) 0.68
4
-
4
-1
-4 -1
×
10
s
(420.0 °C) and k ) 2.16 × 10
s
(439.7 °C).
Moreover, yields of products CH3OH, CH2O, CO, CO2, and
CH4 were erratic and irreproducible. This elimination process
showed to be rather complex with concurrent molecular and
radical reactions.
(CH ) C(OH)COOCH f CH COCH + CH OH + CO (5)
3
2
3
3
3
3
4
0
CH COCH + HCOOCH (2%)
3
3
3
CH dC(CH )COOCH + H O (1%)
2
3
3
2
The pyrolysis products of I in a vessel seasoned with allyl
bromide and in the presence of the inhibitor toluene were
acetaldehyde, methanol, and carbon monoxide:
The homogeneity of this reaction was established by carrying
out several runs in a vessel with a surface-to-volume ratio of
6.0 relative to that of the normal vessel, which is equal to 1.0
CH CH(OH)COOCH f CH CHO + CH OH + CO (4)
3
3
3
3
(Table 2). The packed and unpacked vessels seasoned with allyl
The stoichiometry of reaction 4 was made by comparing, up to
0% decomposition, the percentage decomposition of the
substrate from pressure measurements with those obtained from
the quantitative chromatographic analyses of the reacted amount
of the ester (Table 1).
The homogeneity of the reaction was examined by using a
vessel with a surface-to-volume ratio of 6.0 times greater than
that of the unpacked vessel (Table 2). The rates were found to
be unaffected by the packed and unpacked seasoned vessels,
while a significant heterogeneous effect was obtained in the
packed and unpacked clean Pyrex vessels. The effect of the free
radical inhibitor cyclohexene is shown in Table 3. The kinetic
bromide had no effects on rates. However, the packed and
unpacked clean Pyrex vessel gave a significant heterogeneous
effect in the rate coefficients. The free radical inhibitor toluene
had no effect on the rates of elimination (Table 3). No induction
period was observed. The rate coeffcients were reproducible
with a relative standard deviation of 5% at a given temperature.
The first-order rate coefficients for the pyrolytic elimina-
tion of these 2-hydroxyesters, calculated from k1 ) (2.303/t)
log[P0/(2P0 - Pt)], were invariant of their initial pressure (Table
4). Plotting log[P0/(2P0 - Pt)] vs time t gave a good straight
line up to 60% decomposition for I and up to 50% for II. The
temperature dependence of the rate coefficients and their
6

A Joint Experimental and Theoretical Study
J. Phys. Chem. A, Vol. 108, No. 6, 2004 999
TABLE 4: Independence of the Rate Coefficients with Initial Pressure
substrate
T (°C)
params
value
I
399.9
P
0
(Torr)
67.5
4.24 ( 0.14
82.5
4.81 ( 0.21
126.5
4.50 ( 0.19
157.5
4.20 ( 0.10
209
4.34 ( 0.13
4
-1
10 k
1
(s
)
II
409.9
P
0
(Torr)
76
104
6.82 ( 0.25
114
6.41 ( 0.22
149
6.10 ( 0.14
4
-1
10 k
1
(s
)
6.49 ( 0.17
TABLE 5: Variation of Rate Coefficients with Temperaturea
substrate
parameters
value
399.4
4.45 ( 0.12
I
T (°C)
369.9
0.76 ( 0.03
380.0
1.41 ( 0.04
390.2
2.55 ( 0.09
410.0
8.31 ( 0.31
419.3
14.13 ( 0.51
429.9
25.12 ( 0.65
4
(s-1
1
0 k
1
)
rate equation log k
(s-1) ) (13.73 ( 0.19) - (219.8 ( 2.5) kJ‚mol-1 (2.303RT)-1; r ) 0.999 92
1
II
T (°C)
380.4
1.09 ( 0.03
390.7
1.85 ( 0.06
399.8
3.39 ( 0.14
409.9
6.01 ( 0.21
419.7
10.19 ( 0.30
430.2
17.32 ( 0.62
439.4
29.46 ( 0.77
4
(s-1
1
0 k
1
)
rate equation log k
(s-1) ) (13.37 ( 0.39) - (217.1 ( 5.1) kJ‚mol-1 (2.303RT)-1; r ) 0.99963
1
a
Vessel seasoned with allyl bromide and in the presence of cyclohexene or toluene inhibitor.
TABLE 6: Kinetic Parameters at 400.0 °C from the Experimental Results
104k
(s-1
)
log A (s-1
)
E
(kJ/mol)
∆S (J/(mol‚K))
q
∆H (kJ/mol)
q
∆G (kJ/mol)
q
substrate
1
a
I
II
4.79 ( 0.55
3.39 ( 0.77
13.73 ( 0.19
13.37 ( 0.39
219.8 ( 2.5
217.1 ( 5.1
2.85 ( 0.12
-4.04 ( 0.24
214.2 ( 2.5
211.5 ( 5.1
212.3 ( 2.6
214.2 ( 5.3
corresponding Arrhenius equations are given in Table 5 (90%
confidence coefficient from least-squares procedure).
Once the values for the activation energy (Ea) and the
preexponential Arrhenius factor (A) are obtained, the activation
enthalpies can be calculated from the equation
thalpy, entropy, and Gibbs free energy differences are -6.67
-1
-1
-1
-1
kJ‚mol , 0.08 J‚mol ‚K , and -6.72 kJ‚mol , respectively.
Finally, at B3LYP/6-31+G** level, the values are -7.44
-1
-1
-1
-1
kJ‚mol , 2.82 J‚mol ‚K , and -9.34 kJ‚mol , respectively,
and hence the second conformation is described as more stable
at the two last levels.
q
∆
H ) E - mRT
(6)
An exhaustive exploration of the PESs associated with the
decomposition processes of I and II has been conducted, and
the possible mechanisms have been characterized. In the case
of I, we have found the TS related with the process experi-
mentally described, TS1 (Figure 2). The corresponding TV is
mainly controlled by the simultaneous C2-C3, C3-O4, and
O2-H2 breaking bonds, thus yielding directly the products in
one step.
a
where m is the molecularity of the reaction, that is, the number
of molecules of reactant per molecule of TS; in this case, m is
equal to 1. On the other hand, the activation entropy is deduced
from the relationship
m
q
A ) (e kT/h) exp(∆S /R)
(7)
In the case of II, the equivalent TS has been characterized
(TS2, Figure 2). In addition, other decomposition mechanisms
have been found that can explain the paths yielding the
byproducts experimentally observed. The acetone and methyl
formate products can be reached in a two-step process: a first
TS (TS3, Figure 3) yields acetone and a zwiterionic species,
which in turn, through a second TS (TS4, Figure 3), renders
methylformate. On the other hand, the methyl methacrylate can
be obtained via the TS describing the direct water elimination
from reactants (TS5, Figure 3).
q
With the use of eq 2, the ∆G value is obtained. Hence,
q
q
q
the activation parameters ∆G , ∆H , and ∆S can be obtained
from two independent sources: either from the experimental
measurements with eqs 6, 7, and 2 or from the theoretical
calculations as explained before. The kinetic data obtained
from the experimental data of the hydroxyesters are included
in Table 6.
4
.2. Theoretical Results. The gas-phase decomposition of
methyl glycolate was not theoretically studied because it was
not possible to obtain a complete experimental kinetic study,
as explained before.
4.2.1. Energetics and the Kinetic Parameters. The thermo-
chemical data of products and byproducts relative to the
reactants (∆H, ∆S, and ∆G), obtained from the normal mode
Gaussian 98 outputs as explained, are reported in Table 7. The
The pyrolitic eliminations of I and II in the gas phase were
studied from a theoretical point of view to obtain a complete
picture and a deeper insight into the molecular mechanisms of
the decompositions. The equilibrium geometries of I and II are
depicted in Figure 1, including atom numbering. For II, two
geometries are depicted, the first one related with TS2 and TS5
and the other related with TS3 (see below). It is not clear which
is the most stable conformation at the temperature used in the
calculations (400 °C), although the differences are small. At
MP2/6-31G** level, the first conformation is described as more
stable (the Gibbs free energy difference between the two
q
q
q
activation parameters (∆H , ∆S , and ∆G ), together with the
calculated elementary first-order rate coefficients, corresponding
to the decomposition reactions of I through TS1 and of II
through TS2, TS3 and TS4, and TS5, are also included in
Table 7.
The decompositions of the two compounds are endothermic
processes; ∆H values are positive. But the entropy increments
are large, and the global processes are favorable; ∆G values
are always negative. The decomposition of II, to yield CO,
CH3OH, and CH3COCH3 is found to be themodynamically
more favorable than the corresponding processes that yield
either HCOOCH3 and CH3COCH3 or H2O and CH2CH(CH3)-
COOCH3.
-1
conformations is equal to 7.13 kJ‚mol ); the second conformer
has lower enthalpy than the first one by 12.23 kJ‚mol , but
the entropic term is also lower by 28.76 J‚mol ‚K . However,
at MP2/6-31++G** level, the corresponding values for en-
-
1
-1
-1

1000 J. Phys. Chem. A, Vol. 108, No. 6, 2004
Safont et al.
Figure 2. Structures of TS1 and TS2.
obtained for TS1 are 231.6 (MP2/6-31G**), 231.2 (MP2/6-
-
1
3
1++G**), and 219.6 kJ‚mol (B3LYP/6-31+G**), while for
-
1
TS2 they are 228.1, 227.3, and 211.1 kJ‚mol . The B3LYP
results agree better with the experiment than the MP2 values:
the experimental values are 219.8 and 217.1 kJ‚mol for TS1
and TS2, respectively.
-
1
One can then conclude in the present case that the DFT
method describes very well the activation enthalpy and,
consequently, the Arrhenius activation energy, Ea, and quite
poorly the activation entropy. The MP2 methods, while describ-
ing poorly either the enthalpic or the entropic term, compensate
these two errors, and a good value is obtained for the activation
Gibbs free energy and rate coefficient. This seems to be a quite
general trend, and we have tested that MP2 approaches render
Figure 1. Structures of reactants, methyl lactate and methyl 2-hydroxy-
isobutyrate. For the last species, two conformations are shown.
When comparing the results obtained with the three different
theoretical approaches used, we see significative differences in
the values of the increments of enthalpy and entropy. In general,
∆H values are lower with the DFT approach than with MP2,
q
and the same can be observed with respect to the ∆S values.
However, the ∆G values in the main processes are found to be
roughly independent of the theoretical level used. This is not
observed in the case of the obtainment of the byproducts, for
very good values for ∆G and k values in the gas-phase
9
-14
decompositions of different systems.
In Figure 4, the experimental and theoretical Arrhenius plots
for the main processes are presented. The values for log k were
calculated by means of the corresponding frequency calculations
of TSs and reactants at the same temperatures used for the
experimental plot, as well as by using the theoretically obtained
a
-
1
which differences rounding 30 kJ‚mol are obtained.
A comparison between the experimental and the theoretical
q
values of ∆G for TS1 and TS2, listed in Tables 6 and 7,
respectively, shows that the best approach is the MP2/6-
values for E and A, eqs 6 and 7, and the Arrhenius equation:
3
1++G** level, for which the differences between the experi-
-
1
mental and theoretical values are ∼3 kJ‚mol . The worst one
log k ) log A - E /(2.303RT)
(8)
a
q
is B3LYP/6-31+G**, for which the ∆G is clearly understi-
mated for TS2. Therefore, the rate coefficient values obtained
at the first level show quite a good agreement with experiment,
while the values obtained with the last level are 1 order of
magnitude larger than the experimental ones. For MP2/6-31G**,
the results obtained agree quite well with experiment for TS2
and slightly differ for TS1.
The same results were obtained, as expected. For the I
decomposition (Figure 4a), it can be seen that the four lines are
roughly parallel, due to the good agreement in the Arrhenius
activation energies between experimental and theoretical values,
specially for the B3LYP/6-31+G** level. The lines do not
coincide, thus reflecting the differences in the Arrhenius
preexponential factor, A: the experimental value for log A is
13.73, and the MP2/6-31G**, MP2/6-31++G**, and B3LYP/
6-31+G** values are, respectively, 14.04, 14.35, and 14.14. In
By using eq 6, one can obtain the Arrhenius activation energy,
q
Ea, from the theoretical ∆H values and compare it with the
experimental ones. For the three levels used, the Ea values

A Joint Experimental and Theoretical Study
J. Phys. Chem. A, Vol. 108, No. 6, 2004 1001
TABLE 7: Relative Enthalpies (∆H, kJ/mol), Entropies
(
∆S, J/(mol‚K)), and Gibbs Free Energies (∆G, kJ/mol)
to the Corresponding Reactants in Their Most Stable
q
Conformations, Activation Enthalpies (∆H , kJ/mol),
q
Entropies (∆S , J/mol‚K), and Gibbs Free Energies
q
(
∆G , kJ/mol) to the Corresponding Reactants or
-
1 a
Intermediates, and First-Order Rate Coefficients (k, s
)
∆
H
∆S
∆G
products from I,
CO + CH OH + CH
107.8
353.4
-130.1
3
3
3
CHO
(
[
99.3)
97.4]
(353.9)
[337.9]
369.2
(-138.9)
[-130.1]
-146.3
products from II,
CO + CH OH + CH
102.2
3
COCH
3
(
[
88.5)
71.6]
59.2
(344.8)
[328.0]
227.4
(-143.6)
[-149.2]
-93.9
byproducts from II,
3 3
HCOOCH + CH COCH
3
(
[
50.7)
14.4]
73.2
(174.0)
[168.1]
175.3
(-66.5)
[-98.8]
-44.8
byproducts from II,
H
2
O + CH
2
CH(CH
3
)COOCH
3
(
[
59.0)
38.7]
(182.4)
[170.4]
(-63.8)
[-76.0]
q
q
q
∆
H
∆S
∆G
k
-
-
-
4
4
3
TS1
TS2
TS3
TS4
226.1
225.6)
214.0]
8.9
(14.7)
[10.7]
220.1
(215.7)
[206.8]
1.18 × 10
(
[
(2.57 × 10
[1.25 × 10
)
]
-
-
-
4
4
3
222.5
221.7)
205.6]
8.1
(14.6)
[12.2]
217.0
(211.9)
[197.4]
2.02 × 10
(5.03 × 10
[6.79 × 10
(
[
)
]
-
-
-
5
6
3
243.2
237.1)
193.9]
23.1
(-5.2)
[-11.6]
227.6
(240.6)
[201.7]
3.05 × 10
(2.99 × 10
[3.13 × 10
(
[
)
]
3
3
121.8
123.9)
132.1]
3.4
(3.4)
[5.6]
119.5
(121.6)
[128.4]
7.48 × 10
(
[
(5.14 × 10 )
3
[1.53 × 10 ]
Figure 3. Structures of TS3, TS4, and TS5.
-
10
TS5
296.8
284.0)
257.9]
0.3
(6.3)
[8.9]
296.6
(279.8)
[251.9]
1.36 × 10
-
9
(
[
(2.75 × 10
)
Figure 4b, the corresponding Arrhenius plots for the decomposi-
tion of II to give CO, methanol, and acetone are presented. As
before, the lines are roughly parallel, while the corresponding
values for log A are 13.37 (experimental), 14.00 (MP2/6-31G**),
[3.97 × 10-7]
a
All values in this table have been theoretically calculated at MP2/
-31G**, at MP2/6-31++G** (in parentheses), and at B3LYP/6-
1+G** (in brackets).
6
3
14.34 (MP2/6-31++G**), and 14.22 (B3LYP/6-31+G**).
Several byproducts have been found in the decomposition
formate can be afforded through TS6 (depicted in Figure 6)
followed by TS4, the barrier over TS6 being 30.9 kJ/mol greater
than the barrier associated with TS1. At the same theoretical
level, for II, the difference between the barriers through TS3
and TS2 is only 10.6 kJ/mol, and therefore, it is more probable
to obtain the byproducts in the last case than in the first one, in
which, in fact, the putative byproducts are not experimentally
detected. The second alternative path, in the case of I, would
lead to water and methyl propionate via TS7 (Figure 6). The
barrier is 76.2 kJ/mol greater than the corresponding TS1 barrier,
a similar value to that obtained at the same theoretical level for
the decomposition of II via TS5 (79.5 kJ/mol). Experimentally
the formation methyl propionate is not detected, although
experimental confirmation exists of the obtainment of methyl
methacrylate. This trend could not be explained on theoretical
grounds, based on the energetic values.
process of II, and we have characterized possible mechanistic
paths leading to such byproducts. In Figure 5a, a schematic
representation of the Gibbs free energy values for all stationary
points found, relative to reactants, for the decomposition process
of II is presented at MP2/6-31++G** and at B3LYP/6-31+G**
levels. The MP2/6-31G** level renders results similar to that
at MP2/6-31++G** and the results are not shown.
Starting from the reactant in its first conformation, the
pathway through TS2 to yield the main products is the more
favorable, as expected. The alternative paths to the byproducts
are kinetically unfavored: the first alternative path would pass
through TS3, the intermediate zwitterionic species, and TS4 to
give methyl formate plus acetone. The barrier to pass over TS3
(the limiting step) is 28.7 kJ/mol greater than the barrier to pass
over TS2 at MP2/6-31++G** level. This alternative path would
explain the minority observation of methyl formate as byproduct.
On the other hand, the passage through TS5 to yield water
and methyl methacrylate is even less favorable, the barrier being
4.2.2. Geometries and Transition Vectors. TVs and geometries
for the transition structures corresponding to the decomposition
processes (TS1 and TS2), as well as those related with the
byproduct appearance (TS3, TS4, and TS5) and with the
putative byproducts of methyl lactate (TS6 and TS7), are
reported in Table 8. Further information on TSs (the whole set
of geometric parameters, the force constants, all positive
6
7.8 kJ/mol greater than the TS2 barrier at MP2/6-31++G**
level.
For the sake of completeness, we have also studied analogous
alternative mechanisms for the decomposition of I, at MP2/6-
1G** level (Figure 5b). In this case, the obtainment of methyl
3

1002 J. Phys. Chem. A, Vol. 108, No. 6, 2004
Safont et al.
Figure 4. Arrhenius plots obtained from experimental and theoretical data, log k (s-1) versus 1000/T (K-1): (a) decomposition of I through TS1;
b) decomposition of II through TS2.
(

A Joint Experimental and Theoretical Study
J. Phys. Chem. A, Vol. 108, No. 6, 2004 1003
Figure 5. Gibbs free energy profiles at 673.15 K relative to reactants: (a) decomposition of II relative to reactants in its first conformation (see
Figure 1); (b) decomposition of I relative to reactants in the conformation shown in Figure 1.
eigenvalues, or all vibrational frequencies) is available from the
authors on request (andres@exp.uji.es; safont@exp.uji.es).
For TS1 and TS2 (see Table 8 and Figure 2), the main
components of TV are the C2-C3, O2-H2, and C3-O4
distances. These components correspond to the decomposition
processes. In addition, the O4-C3-C2 and O3-C3-C2 bond
angles also have a significant participation in the TV, due to
the separation of the three resulting molecules. The C2-O2
motion slightly participates in the TV; this bond evolves from
single to double while the elimination process takes place.
The geometric parameters for TS1 and TS2 displayed in
Table 8 correspond with a concerted molecular mechanism, and
the TSs are late, closer to the products than to the reactant. Thus,
the distances for the breaking bonds C2-C3, O2-H2, and C3-
O4 are ca. 1.8, 1.5, and 1.97 Å, respectively, while the H2-O4
forming bond distance (data not shown in Table 8) is 1.03 Å.
The distance for the bond that evolves from single to double,
C2-O2, is ca. 1.3 Å. The simultaneity of the breaking and
forming bonds can be better analyzed by using the bond order
evolution and the synchronicity values (see below).

1004 J. Phys. Chem. A, Vol. 108, No. 6, 2004
Safont et al.
4
.2.3. Bond Order Analysis. To better analyze the extent of
bond breaking or bond forming along the characterized reaction
4
1-43
pathways, the bond order (B) concept has been used.
The
44
Wiberg bond indices have been computed by using the natural
analysis as implemented in Gaussian
8. Several breaking/forming bond processes are involved in
4
5,46
bond orbital (NBO)
3
0
9
the mechanisms, and the nature of each step can be monitored
by means of the synchronicity (Sy) concept proposed by
4
7
Moyano et al., using the following expression:
n
|δB - δB |
i
av
∑
i)1
δBav
Sy ) 1 -
(9)
2
n - 2
In eq 9, n is the number of bonds directly involved in the
reaction, and the relative variation of the bond index is obtained
from
TS
R
Bi - Bi
δB )
(10)
i
P
i
R
i
B - B
where the superscripts TS, R, and P refer to the TS, reactant,
and product of each step, respectively. The average value is
therefore
Figure 6. Structures of TS6 and TS7.
n
-
1
δB ) n
δBi
(11)
av
∑
i)1
For TS3 and TS6 (see Table 8 and Figures 3 and 6), the
bond distances that participate significantly in the TV are the
C2-C3 and O2-H2 breaking bonds, as well as the O4-C3-
C2 bond angle. This reaction pathway corresponds to the
formation of acetone or acetaldehyde and a zwitterionic species
HOCOCH3. An analysis of the geometric parameters values
shows a concerted and late character for these TSs. The H2-
O3 bond distance (data not shown in Table 8) is 1.02 Å.
The imaginary frequency values are between 500i and 620i
cm- for TS1 and TS2, depending on the computing level, and
between 230i and 272i cm for TS3 and TS6, indicating that
these stationary points are mainly associated with the heavy
atom motions. It must be noted that the qualitative description
of the decomposition processes is independent of the computing
method used and also that the geometric values are not affected
by the theoretical level. This fact points out that all theoretical
approaches used are adequate for an accurate description of the
processes in what refers to TVs and geometries.
TS4 is associated with the conversion of the intermediate to
formaldehyde (see Figure 3 and Table 8). The TV is mainly
controlled by the H2-O3 bond distance, as well as the H2-
O3-C3 bond angle. The fluctuation pattern describes the H2
motion; the imaginary frequency value is high because the H
motion dominates the process.
Finally, TS5 and TS7 (see Figures 3 and 6 and Table 8) are
related with the dehydration of the starting reactant to give the
corresponding alkene. The main TV components are the C-C
distance that evolves from single to double (C2-C5 in TS5;
C2-C1 in TS7) in antiphase with the O2-C2 bond breaking
distance, as well as with the H-C5 (or H-C1 in TS7) distance,
where H refers to the hydrogen atom leaving the methyl carbon
at C5 (or C1). Also, the O2-C2-C5 and the H-C5-C2 bond
angles have significant contributions to the TV for TS5 and
the same for the O2-C2-C1 and H-C1-C2 bond angles for
TS7. The imaginary frequency values are very high, thus
indicating that the fluctuation pattern is associated with the water
elimination, particularly with the H motions.
Synchronicities calculated from expression 9 and the Wiberg
bond indices of the breaking/making bond processes, obtained
at MP2/6-31++G** level, are reported in Table 9. The
percentage of evolution of the bond order through each chemical
step has been calculated by using
44
%Ev ) δB × 100
(12)
i
1
-
1
The results are also included in Table 9.
For TS1, the percentages of evolution of the bond orders are
within a range of 29%-80%, thus describing a somewhat
asynchronous TS. The displacement of H2 atom is the more
advanced motion (80.4% evolution), while the C2-C3 breaking
bond and the C2-O2 bond, which evolves from single to
double, are late, displaying a small evolution percentage. Then,
the extension of the O2-H2 bond with initial migration of the
hydrogen atom to O4 and the C3-O4 breaking bond with a
high evolution percentage value (74.4%) can be seen as the
driving forces for the decomposition process. The synchronicity
value of 0.777 shows that the reaction pathway can be described
as concerted and slightly asynchronous.
A very similar analysis can be made in what refers to TS2,
thus showing that the decompositions of either I or II take place
via the same mechanisms, through equivalent TSs. The similar
values obtained for the rate coefficients for the two systems
can be explained on the basis of the present bond order analysis.
On the other hand, TS3 has a larger synchronous character
than TS2; the corresponding Sy value is 0.93. The C2-O2
evolution from single to double bond and the C2-C3 breaking
bond processes are the latest for this TS with 58.3% and 66.4%
evolution, respectively. The more advanced bond order evolution
corresponds to the O2-H2 breaking, 86.1% evolution. All
percentages of evolution are within a narrow range of 58.3%-
86.1%, reflecting the highly synchronous character or this TS.
The next TS of this path, TS4, also shows a highly synchronous

A Joint Experimental and Theoretical Study
J. Phys. Chem. A, Vol. 108, No. 6, 2004 1005
TABLE 8: Imaginary Frequency (freq, cm-1), Main Components of the TV (C, au), and Corresponding Geometric Parameters
(
G, bonds in Å, Angles and Dihedrals in deg) for the Indicated TSs, MP2/6-31G** Valuesa
TS1
TS2
freq
566.30i (532.04i) [508.78i]
599.42i (555.53i) [619.66 i]
C
G
C
G
C2-C3
0.556 (0.645) [0.646]
-0.153 (-0.154) [-0.151] 1.296 (1.298) [1.291]
0.504 (0.419) [0.406]
0.455 (0.469) [0.462]
0.106 (0.099) [0.113]
-0.193 (-0.137) [-0.145] 91.19 (91.92) [92.90]
0.294 (0.102) [0.162] 149.34 (151.64) [151.52]
1.758 (1.771) [1.821]
0.653 (0.657) [0.666]
-0.154 (-0.160) [-0.146] 1.303 (1.305) [1.299]
0.405 (0.423) [0.388]
0.451 (0.453) [0.441]
0.095 (0.094) [0.091]
-0.141 (-0.139) [-0.150] 91.42 (91.92) [92.41]
0.079 (0.098) [0.214] 147.87 (150.72) [152.20]
1.768 (1.780) [1.866]
C2-O2
O2-H2
C3-O4
H2-O2-C2
O4-C3-C2
O3-C3-C2
1.456 (1.499) [1.445]
1.963 (1.969) [1.918]
96.52 (98.13) [100.79]
1.429 (1.469) [1.377]
1.954 (1.960) [1.878]
96.99 (98.24) [101.32]
O2-C2-C1-H5 -0.195 (-0.221) [-0.213] -141.39 (-141.28) [-141.97] -0.251 (-0.225) [-0.229] -139.22 (-139.31) [-141.27]
O3-C3-C2-O2 -0.066 (-0.185) [-0.233] 107.84 (122.02) [140.19]
-0.220 (-0.156) [-0.122] 104.20 (116.71) [139.40]
TS3
TS6
freq
264.87i (272.36i) [235.43i]
230.58i
C
G
C
G
C2-C3
0.821 (0.818) [0.801]
0.230 (0.370) [0.423]
0.115 (0.092) [0.083]
0.301 (0.236) [0.219]
-0.162 (-0.125) [-0.117]
-0.288 (-0.266) [-0.265]
0.126 (0.115) [0.120]
2.202 (2.192) [2.218]
1.553 (1.576) [1.506]
99.88 (100.13) [101.50]
147.89 (146.76) [146.76]
98.20 (99.06) [97.81]
-154.44 (-153.78) [-153.51]
-103.19 (-103.52) [-103.64]
0.791
0.438
0.073
0.222
-0.111
-0.263
0.124
2.224
1.603
99.33
148.72
97.81
-159.06
-95.76
O2-H2
H2-O2-C2
O4-C3-C2
O3-C3-C2
O2-C2-C1-C5
C3-C2-O2-C5
b
b
TS4
freq
1897.21i (1893.95i) [1934.28i]
C
G
O3-C3
-0.242 (-0.236) [-0.255]
0.708 (0.716) [0.696]
0.245 (0.231) [0.232]
1.315 (1.316) [1.303]
1.209 (1.215) [1.222]
118.32 (118.90) [119.66]
58.64 (58.94) [59.17]
H2-O3
O3-C3-O4
H2-O3-C3
-0.613 (-0.612) [-0.626]
TS5
TS7
freq
2201.73i (2061.01i) [1466.86i]
2219.61i
C
G
C
G
c
C2-C5
-0.259 (-0.317) [-0.252]
0.441 (0.359) [0.360]
0.639 (0.568) [0.662]
-0.300 (-0.455) [-0.277]
0.192 (0.094) [0.393]
-0.312 (-0.444) [-0.302]
-0.120 (-0.107) [-0.124]
0.246 (0.077) [0.017]
1.416 (1.412) [1.416]
1.891 (1.959) [2.102]
1.395 (1.348) [1.276]
92.38 (89.56) [83.77]
113.15 (127.60) [151.69]
74.94 (78.50) [86.33]
107.54 (106.56) [101.07]
129.53 (115.36) [62.13]
-0.320
0.353
0.552
-0.489
0.087
-0.439
-0.088
0.076
1.413
1.846
1.423
94.12
110.45
73.90
104.37
130.72
O2-C2
c
H-C5
c
O2-C2-C5
H2-O2-C2
c
H-C5-C2
d
O2-C2-C5-C1
H2-O2-C2-C3
a
MP2/6-31++G** and B3LYP/6-31+G** values are given in parentheses and brackets, respectively. H5 instead of C5 in TS6. c C1 instead
b
d
of C5 in TS7. C1 instead of C5 and H5 instead of C1 in TS7.
character with a Sy value of 0.923, and the percentages of
evolution of the main bonds breaking or forming stand in a
range of 47%-64%; the TS has an intermediate character
between its reactant and product.
TS5, corresponding to the obtainment of water and methyl
methacrylate, also shows a very synchronous character and an
intermediate nature between reactant and products, Sy value of
tively. The largest variation between reactant and TS atomic
charges corresponds to the positive charge on C2, which evolves
from 0.04 at reactant to 0.28 at TS. The smooth charge
redistribution between reactant and TS indicates that the
breaking and forming bond processes are coupled, hence
supporting the conclusion that the process can be described as
concerted. The slight asynchrony is mainly reflected in the
positive charge increment on H2, in the negative charge
increment on O2, and in the C2 charge variation.
0
.835; the percentages of evolution of the main bond orders in
a range of 34%-61.4%.
Finally, an analysis of the NBO charges for I shows a large
negative charge at C1 (-0.62) and at O2, O3, and O4 (-0.81,
A very similar analysis can be done for II, first conformation,
and the corresponding TS2: At reactant, large negative charges
are found at C1 and C5 (-0.61 and -0.62, respectively), as
well as at the oxygen atoms O2, O3, and O4 (-0.81, -0.70
and -0.68, respectively), and also at C4 (-0.21). At C2, a
positive charge can be sensed (0.20). The main positive charges
are located on C3 (0.97) and H2 (0.51). At TS2, the charges
have been slightly modified: a small increment in the negative
charges on C1 (-0.65), C5 (-0.65), O2 (-0.91), and O4
(-0.85) is found. The charge on C4 has been maintained
-
0.70 and -0.67, respectively). C4 bears also a negative charge
(
(
-0.21). Positive charges mainly appear at C3 (0.96) and H2
0.51) centers. At TS1, the negative charge at C1 has been
slightly increased to -0.66; the charge on O2 and O4 has also
been increased to -0.90 and -0.85, respectively, while the
negative charge on O3 has somewhat been decreased to -0.57.
The charge on C4 is maintained. The positive charges on C3
and H2 have been slightly modified to 0.89 and 0.58, respec-

1006 J. Phys. Chem. A, Vol. 108, No. 6, 2004
Safont et al.
TABLE 9: Wiberg Bond Indices (B ) and Percentage of
i
lecular, and follow first-order rate laws, which have been
determined. (2) The decomposition processes, via five-
membered cyclic transition structures, TS1 and TS2, yield the
corresponding products in one step. The molecular mechanisms
can be described as concerted and slightly asynchronous. (3)
An analysis of bond orders and NBO charges suggests that the
extension of the O2-H2 bond with initial migration of the
hydrogen atom to O4 seems to be the driving force for the
decomposition processes, either at TS1 or at TS2. (4) Alternative
mechanisms have been found that can explain the byproduct
formation in the case of the methyl 2-hydroxyisobutyrate
decomposition. A two-step mechanism via TS3 and TS4 would
explain the acetone and methyl formate formation. This path is
calculated to be unfavored with respect to the main path,
explaining the very small formation of the corresponding
byproducts. On the other hand, a one-step mechanism via the
four-center TS5 has been found that can explain the water and
methyl methacrylate formation. This mechanism is even less
favored, which explains the even smaller byproduct formation.
Evolution through the Chemical Process (%Ev) of the Bond
Indices at the Indicated TSs Calculated by Means of Eq 12
and the Synchronicity Value (Sy) Obtained from Eq 9a
TS1
C2-C3
C3-O4
O4-H2
O2-H2
C2-O2
R
Bi
0.96
0.68
28.9
0.99
0.25
74.4
0.01
0.51
68.5
0.777
0.72
0.14
80.4
0.92
1.23
34.6
TS
Bi
%Ev
Sy
TS2
C2-C3
C3-O4
O4-H2
O2-H2
C2-O2
R
Bi
0.95
0.67
29.8
0.99
0.26
73.3
0.01
0.50
66.3
0.785
0.72
0.15
78.6
0.91
1.21
34.8
TS
Bi
%Ev
Sy
TS3
(5) An equivalent theoretical study has been made on the
C2-C3
C3-O3
O3-H2
O2-H2
C2-O2
possibility of analogous byproduct formation for the methyl
2-hydroxypropionate decomposition. This study, based on
energetic grounds, renders that the obtainment of methyl formate
plus acetone from methyl 2-hydroxyisobutyrate is more probable
than the obtainment of methyl formate and acetaldehyde from
methyl 2-hydroxypropionate. However, it is not explained why
methyl 2-hydroxyisobutyrate dehydrates to yield methyl meth-
acrylate, while water and methyl propionate are not experimen-
tally detected in the decomposition of methyl 2-hydroxypropi-
onate. (6) For the main processes, the analysis and comparison
of the calculated and experimental kinetic parameters and
Arrhenius plots point out the validity of the theoretical ap-
proaches. A good agreement is achieved between the theoretical
and experimental results.
R
Bi
0.95
0.32
66.4
1.68
1.20
75.1
0.01
0.55
77.0
0.930
0.70
0.10
86.1
0.92
1.42
58.3
TS
Bi
%Ev
Sy
TS4
H2-O3
O3-C3
H2-C3
R
Bi
0.70
0.28
63.9
1.04
1.42
55.3
0.00
0.43
46.9
TS
Bi
%Ev
Sy
0.923
TS5
C2-C5
C5-H
H-O2
C2-O2
Acknowledgment. We are grateful for financial support to
DGI (Project BQU2000-1425-C03-02), as well as to Fundacio´
Caixa Castell o´ -Bancaixa (Project P1 1A2002-04). Computer
facilities of the Servei d'Inform a` tica of the Universitat Jaume I
are also acknowledged.
R
Bi
0.99
1.31
35.0
0.93
0.44
53.1
0.00
0.26
34.0
0.92
0.36
61.4
TS
Bi
%Ev
Sy
0.835
a
The results obtained at MP2/6-31++G** level are reported.
References and Notes
(
-0.21), and the charge on O3 has been reduced (-0.57). The
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1
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