Furan-Maleic Anhydride and Furan-Maleimide Diels-Alder Reactions
Initial molar concentrations were determined from the
known volumes of reactants provided that the mixing was ideal
(i.e., no volume contraction or expansion was assumed). The
obtained data were used for a detailed analysis of the kinetic
of the both reactions using Bayesian fits for a constructed
kinetic model.29,30 To estimate parameters, the time depend-
ences of the molar concentrations of isomers were included only
in the objective function because of the linear dependence of
the responses of reactants.
among all four components involved in the first reaction
system
A1 + A2 T A4
A1 + A2 T A5
A4 T A5
(1)
(2)
(3)
Computational Details. The calculations were performed
with MOLPRO31,32 (coupled clustersCCSD(T)ssingle point
energies) and Gaussian 9833 (all the remaining calculations)
programs. Three basis sets were used throughout the calcula-
tions: 6-31+G(d),34 6-311++G(2p,d),35 and aug-cc-pVDZ.36 The
optimization of molecular geometries was carried out at the
B3LYP/6-31+G(d) and MP2/6-31+G(d) levels. The single-point
electronic energies were computed at the CCSD(T)/aug-cc-
pVDZ level, using MP2/6-31+G(d) optimized geometries. Vi-
brational analyses were carried out at the B3LYP/6-31+G(d)
level and the computed frequencies used for the subsequent
thermochemistry calculations, using the standard formulas of
statistical thermodynamics in the ideal gas approximation. In
this way, ∆Ggas values were obtained for each adduct and
transition state. Solvation Gibbs energies, ∆Gsolv, for all species
concerned have been computed in the framework of the PCM
reaction field model of Tomasi and co-workers.37,38 The
standard dielectric constants for three solvents were used:
(ꢀr (H2O) ) 78.39, ꢀr (CH3CN) ) 36.64, ꢀr (benzene) ) 2.247).
as well as among all the components involved in the
second reaction system:
A1 + A3 T A6
A1 + A3 T A7
A6 T A7
(4)
(5)
(6)
For the first reaction system, rates of reaction steps,
rj, were defined as
rI ) kfIc1c2 - kbIc4
rII ) kfIIc1c2 - kbIIc5
rIII ) kfIIIc4 - kIbIIc5
(7)
(8)
(9)
3. Results and Discussion
provided that these reaction steps are elementary. Molar
concentrations of individual components A1-A7 are de-
noted ci, and rate constants (kinetic parameters) are
denoted kfj and kfb for forward and backward steps,
respectively. Similar equations for the rates of elemen-
tary steps, rIV, rV, and rVI were derived for the second
system characterized by rate constants of kfIV-VI and
3.1. Kinetic Experiments. Model Development.
The first system comprised 1, 2, 4, and 5; the second
system, 1, 3, 6, and 7. To formulate a model more easily,
reaction components were denoted in agreement with
Scheme 1 as Ax where x stands for the compound
numbers.
Acetonitrile-d3 did not react under conditions used in
this work and thus does not appear in the list of
components involved in mass balance considerations. We
assumed that three reversible reactions were possible
kbIV-VI
.
Kinetics. Reaction mechanisms proposed for both
reaction systems consisted of three reversible elementary
reaction steps. To elucidate the role of direct conversion
of endo-adduct to exo-adduct (reaction steps III and VI)
in the reaction mechanism, several preliminary kinetic
experiments were performed. Specifically, we focused on
the conversion of the thermodynamically less stable 4 and
6 to the thermodynamically more stable 5 and 7 isomers.
After injecting a known amount of 6 into the NMR tube
with CD3CN, we observed a time lag in the increase of
the concentration of 7; see Figure 1. Similar time lags
were found for other temperatures as well as for the
decomposition of 4. The absence of the direct conversion
of the endo- to exo-adduct is strongly supported by the
results of the quantum-chemical calculations. The direct
conversion barrier (reaction steps III and VI) was found
to be significantly larger than the energy barrier of the
endo/exo-adduct formation and/or decomposition. (In fact,
the estimate of a barrier height of more than 220 kJ/mol
was made from the linearly interpolated structure of
endo/exo adducts, whose geometry optimization has
ended up in its dissociation into the reactants, i.e., in one
of the transition states reported throughout this paper.
This fact makes the definition of a barrier height for the
direct conversion physically unsound.) We recognized
these facts to be sufficient for excluding the reaction steps
(III) and (VI) from the next data treatment and discus-
sion, i.e., kfIII ) kbIII ) kVf I ) kVb I ) 0. This contradicts the
conclusions of Zhulin et al.,39 who found the irreversible
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