D.J. Kennedy et al. / Inorganica Chimica Acta 436 (2015) 123–131
129
Table 7
simultaneously in Mathematica 9 (Wolfram Research, Champaign,
IL) using nonlinear least squares fitting approach. The
Second-order reaction rate constants k0 for Zn2+–[12]aneN3, Zn2+–cyclen, and Zn2+
–
a
cyclam. All values are calculated from the pseudo-first-order rate constants k in
Table and active catalyst concentrations determined using the Henderson–
Hasselbach equation and a nominal catalyst concentration of 1.36 mM.
resultant values of kDEP, kE4NPP, and S are given in Table 6. Graphs
of fit results are given in Supplementary Section S3 and
Supplementary Figs. S3–S7, and demonstrate that, while the effect
of decreased pH on / and reaction rates is ignored, the quality of
the fits is excellent.
This more detailed analysis yields values for paraoxon degrada-
tion that are strikingly similar to those calculated from the more
simplistic data analysis in Section 3.2 and summarized in
Table 1. Recall that estimates for sDEP (Table 2) only compared well
6
Catalyst
k0 (minꢁ1 mMꢁ1
)
Zn2+–[12]aneN3
Zn2+–cyclen
34.9 3.6
29.8 2.0
179 329
Zn2+–cyclam
[12]aneN3 catalyst. Reaction rates are relatively unaffected, how-
ever, because the pH changes are negligible at early times where
the magnitudes of k are more reliably determined.
with
duced DEP as the overwhelming product. A more thorough analysis
using Eqs. (2–4) reveals why values of sDEP diverge from when
s for paraoxon degradation for low pKa catalysts which pro-
s
These considerations also have an impact on the data described
in Fig. 6. There appears to be very little effect of buffer concentra-
tion on paraoxon degradation even for the highest buffer content of
0.5 M. The elevated temperature at which the experiments were
conducted lowered the pH of the samples. Acids generated as a
result of hydrolysis would further decrease this pH over time, cre-
ating sample conditions for which AMPSO no longer serves as an
effective buffer. Therefore, decreasing pH negates the effects of
increased buffer concentration on the observed rate of hydrolysis
for these samples.
considering the Zn2+–cyclam, Zn2+–[9]aneN3, and control samples:
for less effective catalysts with smaller initial /, E4NPP formation
becomes more important. However, the rate of formation of
E4NPP is largely invariant among samples, having an average value
of 0.596 0.056 ꢀ 10ꢁ4 minꢁ1. This strongly suggests that E4NPP
generation is due to background hydrolysis only and that product
selectivity depends primarily on catalyst activity. That is, all cata-
lysts overwhelmingly prefer the generation of DEP.
As discussed above, the fraction of catalyst in its active state is
dictated largely by the difference in pKa relative to the pH of the
medium. The Henderson–Hasselbalch equation dictates that a lar-
ger difference between sample pH and catalyst pKa produces a
3.9. Hydrolysis product distribution
higher fraction of catalyst in the active hydroxide state. For Zn2+
–
Phosphotriester hydrolysis under basic conditions proceeds via
nucleophilic attack of the phosphorus, which forms some degree of
associative intermediate with the more acidic leaving group ori-
ented apical to the nucleophile (Scheme 3) [31–33]. In the case
of paraoxon, the 4-nitrophenoxy moiety (with a low pKa of 7.0
compared to 16.0 for ethanol) [34] should occupy the apical posi-
tion and be preferentially hydrolyzed from the molecule, leaving
DEP as the dominant phosphorus-containing product.
As discussed in Section 3.2, however, there are samples where
E4NPP is generated in significant quantities. For pseudo-first order
kinetics, the ratio of the products (or selectivity, S ¼ ½DEPꢂ=½E4NPPꢂ
is expected to be time-invariant; however, the data in this study
yield a range of S values due to fluctuations in experimental condi-
tions, poor NMR signal-to-noise, and measurement error. To
extract additional reaction rate information and more accurately
calculate product selectivity, simultaneous nonlinear regression
was performed for all phosphorus-containing species for each cat-
alyst. Maintaining that the hydrolysis is pseudo-first-order, the
one-reactant, two-product reaction scheme can be analyzed
straightforwardly. Note, however, that for the present purposes
the effect of pH (i.e. time-dependent reaction rates, as discussed
in Section 3.7) has been ignored. The time-dependent normalized
concentrations [P](t), [DEP](t), and [E4NPP](t) of paraoxon, DEP,
and E4NPP, respectively, are described by a series of coupled, linear
differential equations whose solutions are:
[12]aneN3, Zn2+–cyclen, and Zn2+–cyclam, the pseudo-first order
reaction rates correlate well with the active catalyst fraction (linear
fit, R2 = 0.986). We can further quantify this by examining second-
order rate constants k0, calculated according to k0 ¼ kcat=½catꢂ where
[cat] is the active catalyst concentration. Second-order rate con-
stants accounting for the fraction of active catalyst / are shown
in Table 7. We do not provide data for Zn2+–[9]ane–N3, as its struc-
ture is still under debate, or for the buffer. In addition, the uncer-
tainty in the second-order rate constant for Zn2+–cyclam is quite
large. This is a result of the very small value and high uncertainty
in / for this species; the low value results from the catalyst having
a pKa of 10.02, much larger than the starting pH of 8.1, while the
high uncertainty results from the presence of multiple catalyst
conformers. Given this large uncertainty, we do not place much
weight on the apparently high but statistically insignificant sec-
ond-order rate constant for Zn2+–cyclam presented in Table 7.
Zinc–azamacrocyclic catalyst preference for DEP generation
warrants additional discussion. Hydrolysis of phosphotriesters
has been discussed in regards to both electrostatic and steric
effects on the reaction free energy barrier [35,36]. For ester groups
of like pKa, it has been shown that larger side groups increase this
barrier, making reaction rates subsequently smaller. Despite the
size of the 4-NP group of paraoxon, its low pKa makes it the over-
whelmingly likely leaving group. For the buffer control, however,
there is very little favorability for DEP formation at 50 °C. At this
elevated temperature, thermodynamic determinants like pKa no
longer matter, and roughly equimolar amounts of DEP and
E4NPP are observed to form (S = 1.5 0.2). In none of the samples
was generation of E4NPP dominant. Moreover, DEP formation far
outweighs E4NPP formation for additional experiments performed
at reduced temperatures, a regime in which relative pKa values
strongly dictate product formation. For these data, see
Supplementary Section S4, Supplementary Figs. S8–S9, and
Supplementary Table S1.
½PꢂðtÞ
½ðꢁkDEPꢁkE4NPPÞtꢂ
¼ e
ð2Þ
ð3Þ
ð4Þ
½P0ꢂ
À
Á
½DEPꢂðtÞ
½P0ꢂ
kDEP
½ðꢁkDEPꢁkE4NPPÞtꢂ
¼
1 ꢁ e
kDEPþk
E4NPP
À
Á
½E4NPPꢂðtÞ
½P0ꢂ
kE4NPP
kDEPþk
½ðꢁkDEPꢁkE4NPPÞtꢂ
¼
1 ꢁ e
E4NPP
This is consistent with the observation of preferential cleavage
of 4-NP from diphenyl (4-nitrophenol) phosphate (phenol
pKa = 9.99 relative to 4-NP pKa = 7.15) for both catalytic and
alkaline hydrolysis [31]. In that work, however, selectivity
where kDEP and kE4NPP are the formation rates of DEP and E4NPP,
respectively, and [P0] is the initial concentration of paraoxon. The
exponential terms in Eqs. (2) and (3) go to zero at long times, leav-
ing the long-time selectivity S ¼ kDEP=kE4NPP. Eqs. (1–3) were fit