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details, see the Supporting Information). Differentiating the re-
maining isomers is more challenging. Most likely, a mixture of
the B1Cp*, B2Cp*, and B3Cp* isomers exist after styrene associa-
tion, with B1Cp* having the highest concentration. However,
the free energy needed to overcome the TS1 barrier is smaller
for B3Cp* than for B1Cp*, which would ultimately result in for-
mation of a greater amount of 3aa, contradicting experimental
findings. Because the energetic picture surrounding the pre-
liminary steps does not clearly indicate a preferred isomer, the
later intermediates and TS barriers must be analyzed in more
detail to uncover the preference for production of 4aa.
Indeed, the lower barrier height of TS2-B1Cp* (corresponding
to separation of the final product from the O-Boc group) in
comparison to TS2-B3Cp* may be the origin of the preferred
formation of 4aa. The TS3 barrier height could also further dif-
ferentiate product formation in favor of the B1Cp* isomer and
4aa. However, this preference contrasts the final reaction step
(TS3!I7) that indicates B1Cp* as the least stable conformer.
Clearly, in the case of the Cp* ligand, even predicting the
major and minor products based on reaction pathway thermo-
dynamics alone is an extremely difficult task. As such, more re-
fined techniques are needed to uncover the desired informa-
tion about preferred product formation.
and styrene (0.4m), while concentrations of all intermediates
and products were set to zero. The movement between differ-
ent reaction intermediates is always associated with overcom-
ing a transition state barrier. However, only certain TS barriers
differ sufficiently between the various isomers and are large
enough to affect the ratio of final products. For the two ligand
systems studied here, TS1 (migratory olefin insertion), TS2 (Nꢀ
O cleavage), and TS3 (reductive CꢀN elimination) have been
identified as important TS barriers. All other transition states,
including the association of styrene to I1, and the steps involv-
ing isomerization of the seven-membered ring, were found to
minimally effect the final product ratios and, therefore, have
each been set to a constant value (4.0 kcalmolꢀ1 for barrier
heights not reported earlier) for each of the four isomers. The
results of the kinetic simulations displaying final product infor-
mation are shown in Figure 3. For the Cp* ligand (Figure 3a),
4aa is favorably produced at the reaction’s onset, with 3aa be-
coming dominant at intermediary times, and finally reaching
a 4aa/3aa ratio of 49:51 (Figure 3b). The origin of the initial
favorability of 4aa can be traced to the thermodynamically
preferred binding of styrene in a manner that produces more
4aa and less 3aa (I1-B1Cp*!I2-B1Cp*). However, the lower TS1
barrier height that leads to formation of 3aa (I2-B3Cp*!TS1-
B3Cp*) becomes more important as the reaction proceeds. Fi-
nally, the near equivalence in the 3aa and 4aa products likely
results from the relatively similar TS barrier heights (particularly
TS1) for the B1Cp* and B3Cp* isomers, each of which are ex-
pected to be the major contributors to their respective final
products (Figure 2).
Owing to the murky picture surrounding the thermodynam-
ics and kinetics of the Cp* ligand, it is desirable to proceed
beyond the free-energy reaction pathway modeling exempli-
fied in Figure 1 and Figure 2, and directly access kinetic infor-
mation that reveals the final product ratios. The coupling of
thermodynamic data derived from either quantum chemical
methods or experiment and transition state theory (TST) is
a tool that has been employed to access kinetic information in
various domains traditionally associated with chemical engi-
neering. When used together, these methods provide a means
to estimate the concentrations of different product and inter-
mediate species over time. For example, approaches based on
TST have assisted in the modeling of combustion[24] and poly-
merization[25] processes. Their use in catalysis and organometal-
lic chemistry, however, is scarce. Reiher and co-workers recent-
ly used TST to determine the kinetics of various [Fe]-hydroge-
nase model compounds,[26] whereas ligand addition reactions
to an iron carbonyl complex have been examined by George,
Harvey and co-workers.[27] Moreover, Kozuch and Shaik used
TST to develop a new model to calculate turnover frequency
of catalytic cycles.[28] Applying a TST model to the cases involv-
ing the CpCy and Cp* ligands should provide direct access to
crucial information concerning the final product ratios.
For the CpCy ligand (Figure 3c), the kinetic picture confirms
predictions made through examination of the reaction free
energy profile. The B3Cy pathway is consistently seen to have
intermediates amongst the most thermodynamically stable
and the lowest TS barrier heights (Figure 1). As expected, these
favorable thermodynamics translate directly into a clear prefer-
ence for the production of 3aa when the CpCy ligand is used.
Our simulations estimate the final 4aa/3aa ratio to be 24:76
(Figure 3d).
Immediately evident from the use of these kinetic models is
the distinct advantage of directly accessing major and minor
product ratios that arise during the catalytic process. This mir-
rored the experimentally observed trend in selectivity. Howev-
er, an exact quantitative reproduction of the observed product
ratios was not anticipated as even minimal changes in the re-
action free-energy profile (in the sub-kcalmolꢀ1 range) enor-
mously impact the final product ratios. For instance, decreas-
ing the height of the TS1 barriers along 4aa-forming pathways
(Figure 2, green and black lines) while increasing the same bar-
rier along the 3aa-forming pathways (Figure 2, purple and
blue lines) by only 0.1 kcalmolꢀ1 shifts the major product from
3aa to 4aa, which qualitatively matches experimental observa-
tion (4aa/3aa ratio of 57:43). Moving the same barrier heights
by 0.5 kcalmolꢀ1 reproduces, nearly exactly (83:17), the experi-
mentally observed 84:16 ratio in methanol. This dramatic de-
pendence and sensitivity of the final product ratios on the TS1
barrier height is further illustrated in Table S7 (see the Support-
ing Information). Thus computational treatments, capable of
The first step in evaluating the kinetic data involves defining
the rate constants and establishing the systems of ordinary dif-
ferential equations that govern the concentrations of all spe-
cies present in the reaction scheme. Forty-four rate constants
are defined for the transitions between starting, intermediate,
and final products (see the Supporting Information). Based on
these rate constants, a series of 24 ordinary differential equa-
tions can be constructed (see the Supporting Information) that
measure the change in concentration of the 24 chemical spe-
cies potentially present in a reaction mixture over time. Our ki-
netic simulations initially set concentrations for I1 (0.001m)
Chem. Eur. J. 2014, 20, 1 – 11
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