P.H. Abram, et al.
InorganicaChimicaActa499(2020)119178
to 12.7 M−1 in 3-methyl-2-buten-1-ol. For the same four allylic alcohols
the K1 values for the analogous Mn(III)-substituted Dawson anion range
from 14.2 to 10.4 M−1 [15]. These values do not involve deprotonation
of the –OH group, and hence any formation of an M(n+)-alcoholate
type species.
systems. The average values are given in both tables. In general, the
rate constants for the concentration dependence studies are fairly
constant for both the Ni and Co trimetallic systems. Thus k4 is relatively
constant, while some slight variations are observed for k5 and k10 for
the [catalyst] and [H2O2] (Ni3 system) and [catalyst] (Co3 system)
dependence studies. The variations may have several possible causes.
Note that the studies were carried out in 1,2-dichloroethane solvent,
and involved significant concentrations of ionic species (both catalyst
and Aliquat 336, although the latter is actually constant throughout all
studies), and high concentrations of neutral species (3-methyl-2-buten-
1-ol, H2O2 and product hydroxy epoxide) in 1,2-dichloroethane. No
activity coefficients could be applied during the numerical fitting pro-
cess so that no account could be made for ionic strength which will vary
in the [catalyst] studies or for the actual activities of the neutral solvent
in all studies. This will likely have some effect on the fitted values of the
rate constants and are likely the cause of the observed variations. Si-
milar variations were observed previously for the related [WZn{Mn
(OH2)}2(B-ZnW9O34)2]12− catalyst system. While k4 and k5 are fairly
similar for both the Ni3 and Co3 catalyst systems, even allowing for the
temperature difference, k10 is much faster in the Co3 system. This likely
arises from the ease of formation of the transition state in the auto-
catalytic pathway. Further comparisons are evident from the enthalpies
of activation (ΔH≠), entropies of activation (ΔS≠) and free energies of
activation at 25 °C (ΔG≠), see below.
For the [Ni3(OH2)3(B-PW9O34){WO5(H2O)}]7− ion, we have chosen to
use a value of K1 = 17.7 M−1 (i.e. log K1 = 1.25) for a Ni(II) site co-
ordinating a 3-methyl-2-buten-1-ol molecule at 25 °C in 1,2-dichloroethane
for the present study, which was evaluated by taking the stability constant
value for complexation of 3-methyl-2-buten-1-ol to Co(II) in the (structu-
rally similar) Co(II)-substituted Dawson anion and scaling it upwards by
40%, so as to account for the natural order of stability constants (the Irving-
Williams series). The scaling was based on relative stability constants for
coordination of a neutral O donor (in this case H2O) to Ni(II) relative to Co
(II), made with the same experimental techniques and under the same
experimental conditions [45,46]. This generates the value for K1. However,
it is unlikely that K1, K2 and K3 are equal for all three Ni(II) sites, given that
the Ni···Ni distances average only 3.176 Å in the [Ni3(OH2)3(B-PW9O34
)
{WO5(H2O)}]7− ion [29,30]. Some reduction in Kn values for successive
complexation would likely arise from steric effects between the co-
ordinating allylic alcohol molecules. Moreover, in the case of the two-site
species [Co4(OH2)2(B-PW9O34)2]10−, for the N-donor N-methylimidazole,
which has much greater stability constant values than the O-donor 3-me-
thyl-2-buten-1-ol used in the present study, two ligand complexation steps
have been observed with K2 < K1 [47]. We have thus chosen to succes-
sively decrease a Kn+1 value relative to Kn by the factor 0.5, giving values
of K2 = 8.9 M−1 and K3 = 4.4 M−1 for complexation of the three 3-me-
thyl-2-buten-1-ol molecules to Ni(II). Using the same approach for
[Co3(OH2)6(A-PW9O34)2]12− (despite the fact that the Co⋯Co distance is
certain to be larger, see above) the initial K1 value was assumed to be the
same as that for complexation of 3-methyl-2-buten-1-ol to Co(II) in the Co
(II)-substituted Dawson anion, i.e. K1 = 12.7 M−1, with K2 = 6.4 M−1 and
K3 = 3.2 M−1. In the case of the Co(II) trimetallic system, no attempt was
made to account for the difference in temperature at which the kinetic
dependence on the catalyst concentration was determined and the stability
constant data. However, this temperature difference should only lead to a
small effect on the value of the stability constants [48]. While the final
values of K1, K2 and K3 in both trimetallic systems may be approximate in
each case, some variation in their magnitudes will be discussed below. No
analogous stability constants for complexation of the product hydroxy
epoxide to Ni(II) or Co(II) are known (i.e. K6, K9, K11, K14, K18 and K21), but
these are likely to be similar to the analogous values for 3-methyl-2-buten-
1-ol, so that the stability constants for 3-methyl-2-buten-1-ol and its ep-
oxide were assumed equivalent for the respective values of K1, K2 and K3
for both trimetallic systems. This is the same procedure that was used in the
case of our previous study of the kinetics of the epoxidation of 3-methyl-2-
buten-1-ol by H2O2 under biphasic conditions with [WZn{Mn(OH2)}2(B-
ZnW9O34)2]12− as the catalyst [14].
As discussed previously [14], the autocatalysis is caused by an in-
crease in the rate of formation of a peroxo site that is adjacent to a co-
ordinated hydroxy epoxide (k10 and k13) relative to one adjacent to a
coordinated allylic alcohol (k4 and k7). The steps that are involved in the
autocatalysis (k5, k10, K11, K12, k8, k13, K14 and K15) result in the accel-
eration of the overall rate with time following the induction period, as
shown in Figs. 4–6, S5 and S6 and the increase in k10 (and k13) relative to
k4 (and k7), respectively, may again be attributed to an electronic (pos-
sibly inductive) effect from the coordinated hydroxy epoxide. Alter-
natively, the increase may be steric in nature, with the coordinated hy-
droxy epoxide actually directing formation of the adjacent peroxo group.
The latter might be expected to depend on the environment surrounding
the site where the allylic alcohol coordinates to the M(II), but no firm
conclusions can be made considering the significantly different en-
vironments of the [Co3(OH2)6(A-PW9O34)2]12−, [Ni3(OH2)3(B-PW9O34
)
{WO5(H2O)}]7− and [WZn{Mn(OH2)}2(B-ZnW9O34)2]12− ions.
Variation of the K1 value (and thus K2, K3, K6, K9, K11, K12, K14, K15, K18
and K21) for the eleven equilibria by increasing its value (×2) or decreasing
its value (×0.5) produced only relatively small changes in the values of k4,
k5 and k10. For example, for the trimetallic Ni(II) system with [catalyst] =
1.00 mM, [3-methyl-2-buten-1-ol] = 1.000 M, [H2O2] = 4.50 M and
T = 25 °C, increasing and decreasing K1 (and K2 and K3) by the above
factors gave variations for k4 of −6 and +19%, respectively, k5 of +9 and
−15%, respectively, and k10 of +1 and −12%, respectively. Likewise, for
the trimetallic Co(II) system with [catalyst] = 1.00 mM, [3-methyl-2-buten-
1-ol] = 1.000 M, [H2O2] = 2.125 M and T = 5 °C, the variations were for
k4 of −2 and −3%, respectively, k5 of +6 and −23%, respectively, and k10
of +15 and −6%, respectively. In each case the choice made for K1 does
not have a strong bearing on the fitted rate constants.
With these simplifications in place, this leaves just k4, k5 and k10 to
be determined for each trimetallic system. The results of the fitting of
the GC data for both the catalyst and H2O2 concentration dependence
)
[Co3(OH2)6(A-PW9O34)2]12−, respectively. Also included in Tables 2
For [Ni3(OH2)3(B-PW9O34){WO5(H2O)}]7− a typical fitting of the cal-
culated and experimental data for [catalyst] = 1.50 mM, [H2O2] =
4.50 M and [3-methyl-2-buten-1-ol] = 1.000 M at 25.0 °C is shown in
Fig. 7. The sum of the differences squared between the experimental
and fitted data points (ssq) is 0.0008. The ssq values for the reactions in
Table 2 varied from 0.0001 to 0.0010, and for the reactions in Table 3
Setting the three values of K1, K2 and K3 equal within each of the
trimetallic systems, with values for all log Kn = 1.25 for the Ni(II)
system and all log Kn = 1.10 for the Co(II) system resulted in variations
for k4 of −9%, k5 of +14% and k10 of +6%, for the former, and k4 of
−5% k5 of +11% and k10 of +16% for the latter. Again the variations
are not large, indicating that the choice of K1 does not have a strong
influence on the fitted rate constants. Attempts to fit the values of K1, K2
and K3 along with the rate constants were unsuccessful, giving incon-
sistent results. It is assumed that the data are not sensitive (or extensive)
enough to be able to refine both the equilibrium and rate constants.
For the temperature dependence data for both trimetallic systems
(Tables 2 and 3) no variations in the values of K1 (and K2 and K3) were
The three unique rate constants k4, k5 and k10 reported in Tables 2
and 3 for the eight [catalyst] and [H2O2] dependence studies in Table 2
stant, with differences evident between the Ni and Co trimetallic
8