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more or less to Ea in case of an Arrhenius evaluation of
temperature dependent reaction rates, whereas the overall
Gibbs free energy G to overcome for epoxide ring opening is
around 100 kJmolꢁ1. The immediately resulting bridged
alkoxide species III is computed to be about as stable as II.
Another rather stable alkoxide species (see Supporting
Information) which has a m2-oxo bridge could be identified,
but needs no further consideration owing to a higher relative
G if compared to I and III. Addition of CO2 to III leads to IV,
which by a nucleophilic attack of the alkoxide at the carbonyl
carbon atom, TS(b), regenerates the propagated carbonato
species I + 1. Altogether, all the alkoxide species are signifi-
cantly higher in G than I, therefore it is concluded that,
independent of the rate-limiting step, the resting state is this
dicarbonato species. Thus, for the incorporation of CO2, the
effective activation barriers have to be calculated with respect
to I, this gives a computed H which suggests an Ea of around
20 kJmolꢁ1, whereas the relative barrier with respect to G is
again around 100 kJmolꢁ1 and depends on the applied CO2
pressure. This striking similarity in the computed G value of
both potentially highest lying transition states means that
both transition states are similarly difficult to overcome
(considering potential sources of error from the quantum
chemical energy method as well as the solvation treatment),
which is in line with the observed change in rate-limiting step
upon variation of the CO2 pressure: Whereas in the first part
of the catalytic cycle CO2 is not involved (TS(a)), increasing
or decreasing the CO2 pressure will shift the second (TS(b))
part downwards or upward, respectively. For high CO2
pressures as high as the 50 bar considered in Figure 4, the
epoxide ring opening TS(a) with its Ga of 101.0 kJmolꢁ1 is the
highest point of the G profile compared to the Ga of
95.3 kJmolꢁ1 for the CO2 insertion TS(b); at lower CO2
pressure (e.g. 5 bar), alkoxides are formed in a pre-equilib-
rium and undergo the rate-limiting CO2 insertion, with for
example, a Ga of 102.4 kJmolꢁ1 for TS(b) (Figure 4). The
point where TS(b) is identical to the Ga of 101.0 kJmolꢁ1 of
TS(a) is computed to be at a CO2 pressure of around 8 bar,
which is somewhat below the experimental 25 bar where both
elementary reactions are “equally rate limiting”; at 25 bar,
a Ga of 97.4 kJmolꢁ1 is obtained for TS(b). This means
however still a remarkably good agreement between experi-
ment and theory considering typical errors of quantum
chemical calculations for larger molecules in solution.
species into the catalyst-bound polymer chain. On the other
hand, CO2 addition is effectively a trimolecular reaction,
which consumes both one liquid epoxide and one gaseous
CO2. Consequently, the Gibbs free energy G for epoxide ring
opening is higher than the corresponding enthalpy H (around
50 kJmolꢁ1), but the difference between G and H for CO2
insertion is even larger (around 80 kJmolꢁ1). This, of course
means that Arrhenius prefactors are significantly smaller for
CO2 insertion than for epoxide ring opening (for the
measured Ea, a ratio of around 5000 in prefactors would be
required at 1008C to obtain similar rate coefficients at
standard concentrations of all reactants).
The flexibility of the tether between the two b-diketimi-
nato zinc centers is also supported by the calculations:
Whereas for the bis[bis(trimethylsilyl)amido] precursor com-
plex a Zn–Zn distance of 7.77 ꢁ is computed, all the Zn–Zn
distances within the actual catalytic cycle are significantly
smaller but also exhibit a variation of more than 1 ꢁ (the
following distances are computed for the presented inter-
mediates and transition states: I 4.50 ꢁ, II 5.66 ꢁ, TS(a)
5.31 ꢁ, III 5.29 ꢁ, IV 5.40 ꢁ and TS(b) 4.92 ꢁ).
It can be assumed that the accessibility of such a large
range of Zn–Zn distances allows every transition state to
adopt optimal structures and thus avoids additional barriers
from catalyst rigidity, which means that the entropic benefit
from not having to group two b-diketiminato zinc units
together is fully exploited. The acceleration of the epoxide
ring-opening step leads to the high copolymerization activ-
ities of the catalyst (Table 1).
With decreasing catalyst loading the activity slightly
increases, which can be attributed to better diffusion
(Table 1, entries 1–3). The dependence of the activity on
CO2 pressure is also documented (entries 3–6). The results for
the selectivity for polycarbonate over cyclic carbonate are in
accordance with those in the literature.[12,21,39] The selectivity
increases with higher CO2 pressure. The catalyst shows an
unusual temperature dependence. The temperature of 1008C
seems to be the optimum with regard to polymerization
activity and selectivity. The decreased activity at 1208C could
be explained by catalyst decomposition and a higher proba-
bility for side reactions (Table 1, entry 7). This catalyst
exhibits a turnover frequency (TOF) of 9130 hꢁ1 at 1008C
and 40 bar CO2 pressure, a result of a good balance in
activation barriers for the two potentially rate-determining
steps.
Kinetic studies at various temperatures were performed to
further probe this mechanistic picture (Figure S16–S19).
Experimental activation energies at 10 and 30 bar are found
to be 8.8 and 35.9 kJmolꢁ1, respectively. The computationally
estimated values demonstrate the same trend. For low
pressure (5 bar) the CO2 insertion step is rate limiting with
an activation energy of 19.2 kJmolꢁ1, at higher pressure
(50 bar) the epoxide ring opening becomes rate limiting with
52.3 kJmolꢁ1. At a first glance, it appears surprising that
elementary steps with such dissimilar activation energies can
both be rate limiting. However, this is a consequence of Gibbs
free activation energies depending on both activation enthal-
pies and activation entropies. As the resting state is in all cases
the dicarbonato complex I, epoxide ring opening is a bimo-
lecular reaction, that is, the incorporation of one solution
In summary we report the first dinuclear zinc catalyst
which shows a shift in the rate-determining step from ring
opening of the epoxide to carbon dioxide insertion for the
copolymerization of cyclohexene oxide and carbon dioxide.
The reason for this behavior is the similarity of the activation
barriers of the ring opening and insertion reactions, which is
achieved by linking the two active centers with a flexible
tether. These attributes lead to very high activities for the
copolymerization reaction. To achieve even higher activities,
according to our study, an additional decrease of the
activation energy of the ring-opening step is necessary. The
match between experimental and theoretical results delivers
a tool for further catalyst development. Currently, modifica-
tion of these catalysts is under investigation.
ꢀ 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Angew. Chem. Int. Ed. 2013, 52, 9821 –9826