Acceleration of the methanolysis of phosphate diesters promoted by La(OTf)3 - The analysis of non-integer s spH/rate profiles resulting from changes in metal ion speciation

Article abstract of DOI:10.1139/v05-065

In a previous publication (A.A. Neverov and R.S. Brown. Inorg. Chem. 40, 3588 (2001)) we reported very effective catalysis of the methanolysis of some phosphate diesters (methyl p-nitrophenyl phosphate (1), bis(p-nitrophenyl) phosphate (2), and diphenyl p

Full text of DOI:10.1139/v05-065

1268
Acceleration of the methanolysis of phosphate
diesters promoted by La(OTf)3 — The analysis of
s
non-integer pH/rate profiles resulting from
s
changes in metal ion speciation1
Graham T.T. Gibson, Alexei A. Neverov, Allen Chun-Tien Teng, and R.S. Brown
Abstract: In a previous publication (A.A. Neverov and R.S. Brown. Inorg. Chem. 40, 3588 (2001)) we reported very
effective catalysis of the methanolysis of some phosphate diesters (methyl p-nitrophenyl phosphate (1), bis(p-
nitrophenyl) phosphate (2), and diphenyl phosphate (3)) promoted by La3+, and noted a general observation that the
plots of logkcat vs. sspH had non-integer gradients. In this report the origins of that behaviour are studied and analyzed
through determination of the speciation of La3+(–OCH3)n, (La3+)2(–OCH3)m, (La3+)2:phosphate:(–OCH3)y forms in solu-
tion as a function of sspH. Potentiometric titrations of solutions of La(OTf)3 in methanol at low (<1 × 10–4 mol/L) and
high (>1 × 10–3 mol/L) concentration were analyzed through fits of the data to various models to provide speciation di-
agrams of the various La3+ forms in the absence of phosphate. Titrations of La3+ in the presence of diphenyl phosphate
were also analyzed to provide speciation diagrams for phosphate bound forms. The kinetic data for the La3+ catalyzed
methanolysis of 1 were analyzed through fitting the kinetic data at low and high [La3+] as a function of sspH to a linear
combination of the individual kinetic contributions of each species. Overall the data are best analyzed in the low
[La3+] domain as resulting from methoxide attack on a transient complex of phosphate bound to La3+(–OCH3)0,1. In the
high [La3+] domain the data fit two kinetically equivalent processes involving either a spontaneous decomposition of
(La3+)2:1–:(–OCH3)2,3,4,5 or external methoxide attack on (La3+)2:1–:(–OCH3)1,2,3,4
.
Key words: lanthanides, phosphate diester, methanolysis, kinetics, speciation, metal ion catalysis of methanolysis, DNA
model methanolysis.
Résumé : Dans une publication antérieure (A.A. Neverov et R.S. Brown. Inorg. Chem. 40, 3588 (2001)), nous avons
rapporté une catalyse très efficace de la méthanolyse de quelques esters de l’acide phosphorique (phosphate de méthyle
et de p-nitrophényle (1), phosphate de bis(p-nitrophényle) (2) et phosphate de diphényle (3)) sous l’influence du La3+
et nous avons noté que les gradients des courbes du logkcat vs. sspH n’étaient pas des nombres entiers. Dans ce travail,
nous avons étudié ce comportement et l’avons analysé par une détermination de la spéciation des formes La3+(–OCH3)n,
(La3+)2(–OCH3)m et (La3+)2:phosphate:(–OCH3)y en solution en fonction du sspH. Afin de pouvoir obtenir des diagram-
mes de spéciation des diverses formes de La3+ en l’absence de phosphate, nous avons analysé les résultats de titrages
potentiométriques de solutions de La(OTf)3 dans le méthanol, à des concentrations basses (<1 × 10–4 mol/L) et élevées
(>1 × 10–3 mol/L), en procédant à divers ajustements des données à divers modèles. Afin d’obtenir des diagrammes de
spéciation des formes liées du phosphate, nous avons aussi analysé les données des titrages du La3+ en présence de
phosphate de diphényle. Les données cinétiques pour la méthanolyse du 1 catalysée par le La3+ ont été analysées par le
biais d’un ajustement des données à des concentrations faibles et élevées de La3+ en fonction de sspH afin d’obtenir une
combinaison linéaire des contributions cinétiques individuelles de chaque espèce. Dans l’ensemble, la meilleure façon
d’expliquer les données dans le domaine de faible concentration de La3+ implique une attaque du méthanolate sur un
phosphate intermédiaire lié à un La3+(–OCH3)0,1. Dans le domaine de concentration élevée de La3+, les données peuvent
être expliquées par deux processus cinétiquement équivalents impliquant soit une décomposition spontanée d’un
complexe (La3+)2:1–:(–OCH3)2,3,4,5 ou une attaque externe d’un méthanolate sur un complexe (La3+)2:1–:(–OCH3)1,2,3,4
.
Mots clés : lanthanides, diester de l’acide phosphorique, méthanolyse, cinétique, spéciation, catalyse par un ion métal-
lique d’une méthanolyse, méthanolyse modèle de l’ADN.
[Traduit par la Rédaction] Gibson et al. 1276
Received 12 December 2004. Published on the NRC Research Press Web site at http://canjchem.nrc.ca on 18 October 2005.
G.T.T. Gibson, A.A. Neverov, A.C.-T. Teng, and R.S. Brown.2 Department of Chemistry, Queen’s University, Kingston,
ON K7L 3N6, Canada.
1This article is part of a Special Issue dedicated to organic reaction mechanisms.
2Corresponding author (e-mail: rsbrown@chem.queensu.ca).
Can. J. Chem. 83: 1268–1276 (2005)
doi: 10.1139/V05-065
© 2005 NRC Canada

Gibson et al.
1269
Fig. 1. Plot of pseudo-first-order rate constants for the
Introduction
methanolysis of 1 (2 × 10–5 mol/L) vs. [La(OTf)3] at 25 °C;
Various studies from these labs have shown that La3+,
along with 1 equiv. of methoxide in methanol, is an extraor-
dinarily active catalyst for the methanolysis of carboxylate
esters (1), β-lactams (2), and a variety of phosphates and
thiophosphates including phosphate di- and triesters (3). The
phosphate diester linkage is biologically important because
it is ideal for preserving genetic information in RNA and
DNA because of its kinetic robustness toward hydrolysis. To
facilitate what is otherwise a very slow hydrolytic process,
Nature provides various metallo-enzymes (4) such as the
RNAse from HIV reverse transcriptase (4a), 3′–5′ exonuclease
from DNA polymerase I (4b), and P1 nuclease (4c) to cleave
phosphate diesters so it is not surprising that a large number
of studies have been reported concerning metal-ion-promoted
sspH = 11.1 (0.02 mol/L triethylamine buffer). Based on data
1
1
from ref. 3a. The values of k2 and k1 are taken as the limiting
plateau value and initial gradient of the plots at given sspH val-
1
ues; double-headed arrows show the direction of change of k2
and k11 as a function of sspH.
1
k2
0.0002
–
hydrolysis of (RO)(R′O)PO2 species (5).
O
0.0001
R2O
P
OR1
1
k1
O-
1 R2O = OCH3, R1O = OC6H4NO2
2 R2O = R1O = OC6H4NO2
3 R2O = R1O = OC6H5
0.0000
0.0000
0.0005
0.0010
O
[La(OTf)3] (mol/L)
H
S
O2N
N
Scheme 1.
N
1-
1
S
O
k1
NO2
La3+(-OCH3)x
4
La3+:1-:(-OCH3)x
P
CO2H
CH3O-
Interestingly, metal-catalyzed alcoholysis of phosphate
diesters is, to our knowledge, a scarcely investigated area al-
though our own studies (3a) showed that the methanolyses
of methyl p-nitrophenyl phosphate (1), bis(p-nitrophenyl)
phosphate (2), and diphenyl phosphate (3) were accelerated
by as much as 1010-fold in the presence of La3+ compared to
the background methoxide promoted reaction. Unfortu-
nately, a comprehensive mathematical fit of the kinetic be-
1
1-
k2
(La3+)2:1-:(-OCH3)y
P
(La3+)2(-OCH3)y
CH3O-
1
At limiting low and high [La3+] we could define the k1
1
and k2 as the slope and plateau, respectively, of the kobs vs.
[La3+] plots at each pH, the values being reproduced in Ta-
s
s
1
haviour to a given mechanism that included all the species
ble 1S of the Supplemental material.3 Curiously, neither k1
s
1
responsible for catalysis as a function of pH was not possi-
nor k2 shows a unit linear dependence on [–OCH3], the
s
ble due to the complexity of the situation as revealed from
kinetic plots of the observed pseudo-first-order rate constant
(kobs) for the methanolysis of 1 as a function of [La3+] at var-
slopes being 0.35 and 0.5, respectively (3a): in the case of
1
s
the k1 plot there is a serious downturn at the highest pH
s
values.
s
s
ious pH values. Typically, the plots show (3a) two pH-
Typically, log plots of rate constant vs. [lyate], [lyoxide],
[catalyst], or [Mx+] have integer gradients of 0, 1, or 2,
which result from rate-limiting processes having zero-, first-,
or second-order dependencies on the concentration of the
species of interest. In some common cases such kinetic plots
exhibit “saturation” behaviour, with a domain of unit slope
evolving into a plateau of zero slope at higher concentration
indicative of a substrate associated with the catalytic entity
in a kinetically competent 1:1 complex. Non-integer kinetic
s
s
dependent domains of interest, which are illustrated sche-
matically in Fig. 1 (see Figs. 1S and 2S, Supplementary
material, for the appearance of these plots at two different
sspH values).3 On the basis of these plots, we rationalized the
kinetic behaviour in terms of the simplified process given in
Scheme 1, where monomeric and dimeric forms of La3+
s
associated with variable numbers of methoxides in a pH-
s
dependent way were responsible for the catalysis.
3 Supplementary data for this article are available on the Web site or may be purchased from the Depository of Unpublished Data, Document
Delivery, CISTI, National Research Council Canada, Ottawa, ON K1A 0S2, Canada. DUD 4014. For more information on obtaining mate-
rial refer to http://cisti-icist.nrc-cnrc.gc.ca/irm/unpub_e.shtml.
© 2005 NRC Canada

1270
Can. J. Chem. Vol. 83, 2005
plots are far less common for ionic reactions4 (6) although
square root dependencies are often observed for reactions
catalyzed by metal ions that dimerize to inactive forms such
as was found in our recent study of the Zn2+ promoted
methanolysis of p-nitrophenyl acetate and the phosphate
triester paraoxon (7), or the Cu2+ catalyzed hydrolysis of p-
nitrophenyl diethyl phosphate (8).
(swpH). This method was described by Bates and co-workers
(12b, 12c) for a molality scale (correction constant –2.34)
and later by Bosch and co-workers (13) for a molar correc-
tion constant of –2.24 units.
sspKa Determination
The potentiometric titrations of La(OTf)3 and diphenyl
phosphate in methanol were performed using a Metrohm
model 798 Titrino automatic titrator under anaerobic condi-
In cases where the speciation of a Mx+ catalyst changes as
a function of its concentration or as a function of pH, one
can envision an alteration of the catalytic properties in such
a way that the pH / log rate constant profiles can have non-
integer gradients or exhibit irregular upward or downward
curvature. This phenomenon is probably a general one, the
recognition and incorporation of which will prove particu-
larly applicable to studies of mono- and polymetal ion catal-
ysis as a function of pH where the pH / log rate constant
profiles do not vary in a regular way (9). Indeed, in a recent
analysis of the La3+ promoted methanolysis of the β-lactam
tions (Ar) at 25.0
0.1 °C. Methanolic La(OTf)3 and
diphenyl phosphate stock solutions (0.02 or 0.002 mol/L)
were diluted to the required concentrations by adding anhy-
drous methanol. The total sample volume in all cases was
20.0 mL. Sodium methoxide titrant, prepared from stock
0.5 mol/L NaOCH3 in a Sure Seal® bottle, was 0.021 or
0.0028 mol/L and was calibrated by titrating Fisher certified
standard HCl in water, with the endpoint taken to be wwpH 7.
After each titration the electrode was immersed in pH 4.00
aqueous buffer or a dilute aq. HCl solution for several min-
utes. The electrode was then rinsed with MeOH, dried with a
tissue, and used for the next titration. The electrode was
recalibrated often to ensure accurate readings.
The values of the species formation constants in methanol
were calculated using the computer program Hyperquad
2000 (version 2.1 NT) (10), with the autoprotolysis constant
of pure methanol taken to be 10–16.77 (13) at 25 °C. The for-
mation constants for the species La3+2(–OMe)n (n = 1–5)
were determined from the analysis of the potentiometric ti-
tration of 1 × 10–3 mol/L La(OTf)3. Two such titrations were
analyzed separately and their respective species formation
constants averaged; the resulting values were used as con-
stants in the subsequent Hyperquad analysis of 2:1
La(OTf)3:phosphate titrations. Similarly, formation constants
for the species La3+(–OMe)n (n = 1–3) were determined from
the analysis of the titration of 1 × 10–4 mol/L La(OTf)3. Be-
cause the methanolysis of phosphates 1 and 2 in the pres-
ence of La(OTf)3 is too fast to perform the titrations of
nitrocefin (4) we demonstrated (2) that the nonunit slope for
s
the kinetic data as a function of pH could be accommodated
s
by two kinetically equivalent mechanisms: methoxide attack
on La3+2(4–)(–OCH3)n, n = 0–2, or spontaneous decomposi-
tion of the forms La3+2(4–)(–OCH3)n, n = 1–3.
In this report we analyze the previously obtained rate data
for the La3+ catalyzed methanolysis of 1 (3a) in terms of
models involving La3+ monomers and dimers with varying
numbers of methoxides, the speciation of which depends
upon [La3+] concentration and the pH. The speciation of
s
s
La3+ at low (<2 × 10–4 mol/L) and high (>1 × 10–3 mol/L)
metal ion concentrations is computed through analysis of the
potentiometric titration data using the program Hyperquad
2000 (10). At high concentrations of metal ion, where the ki-
netics are suggestive of the formation of La3+ bound phos-
phate, we have conducted the titrations on sol2utions of La3+
with a fixed 2:1 La3+ : diphenyl phosphate ratio, analyzing
these to determine the metal ion binding constants and
speciation. Finally, we have analyzed the kinetic data in
terms of the contributions of the various species present in
these, 3 was used as a model for all three phosphates studied
s
solution to develop an internally consistent explanation of
in the kinetics. The pKa of 3 was determined to be 3.47
s
s
the shapes of the pH/rate profiles.
0.01 from the average result of the Hyperquad analysis of
three separate titrations of 1 × 10–3 mol/L 3, and this value
was used in subsequent analyses as a constant. The forma-
tion constant for the species La3+2:3–, as a model for the
species La3+2:1–, was computed from fitting as were other
formation constants for species present in a solution of 2:1
La3+:diphenyl phosphate.
s
Experimental
Materials
Methanol (anhydrous, 99.8%), sodium methoxide (0.5 mol/L
in MeOH), lanthanum trifluoromethanesulfonate (99.999%),
bis(p-nitrophenyl) phosphate (2, 99%), and diphenyl phos-
phate (3, 99%) were all purchased from Aldrich and used
without any further purification.
Kinetic measurements
The rate of appearance of p-nitrophenol accompanying the
methanolysis of 2 was followed by monitoring the increase
in absorbance of buffered methanol solutions at 311 nm and
25.0 0.1 °C with a Varian Cary 100 Bio UV–vis spectro-
photometer. Its extinction coefficient at 311 nm was deter-
mined to be 10 878 479 (mol/L)–1 cm–1 by averaging the
slopes of 17 independent plots of Abs. vs. added [p-
nitrophenol] over 5 × 10–5 mol/L < [La3+] < 1 × 10–3 mol/L
and 2.5 × 10–5 mol/L < [p-nitrophenol] < 2.25 × 10–4 mol/L.
Due to the slow rate of reaction at low [La3+], all reactions
sspH Measurements
+
The CH3OH2 concentration was determined for kinetic
and titration measurements using a Radiometer pHC4000-8
or an Accumet model 13-620-292 combination glass elec-
trode calibrated with Fisher certified standard aqueous buff-
ers (pH = 4.00 and 10.00) as described in our recent papers
s
(11). Values of pH were calculated by subtracting a correc-
tion constant ofs –2.24 from the experimental meter reading
4 Of course, the kinetics of free-radical-initiated chain reactions such as H2 + Br2 → 2HBr, where the first step requires a dissociation of the
Br2 into 2Br radicals, are well-known to follow a square root dependence in [Br2] (for a discussion of this mechanism see ref. 6).
© 2005 NRC Canada

Gibson et al.
1271
Fig. 2. Potentiometric titration data for 0.001 mol/L La(OTf)3
in this study were followed to 10% completion and kobs was
(᭹), 0.001 mol/L diphenyl phosphate (᭿), and a mixture of
0.001 mol/L La(OTf)3 and 0.0005 mol/L diphenyl phosphate (᭞)
determined in methanol at 25 °C.
determined in triplicate using the initial rates method. All re-
s
actions were performed at pH 9.21 0.10 (measured after
s
the kinetic run) using a methanol buffer solution of 1.75 ×
10–2 mol/L N-ethylmorpholine (sspKa = 8.60 (measured by
half neutralization (3a)) partially neutralized with 70%
HClO4 (BDH). The solutions prepared in this way contain a
small, but kinetically insignificant quantity (<0.1%) of water
stemming from that present in the MeOH and what is de-
rived from buffer neutralization. To avoid any chloride ion
contamination from the glass electrode that might affect the
s
metal ion reactions, the pH of the reaction solutions was al-
s
ways determined after kinetic measurements.
To investigate whether the kinetics in the low [La3+] do-
main result from a 1:1 or a 2:2 La3+:2– complex at a given
sspH (9.21), it was first necessary to establish the point of
transition between the ascending and descending wings of
the kobs vs. [La3+] plot (see Fig. 1S, Supplemental informa-
tion).3 This kinetic experiment was done using [2] = 5 ×
10–5 mol/L and varying [La3+] between 2.5 × 10–5 and 4 ×
10–3 mol/L; the point of transition was determined to occur
at 2 × 10–4 mol/L [La3+]. To determine if the kinetically ac-
tive species was a monomeric 1:1 La3+:phosphate complex
or a dimeric 2:2 La3+:phosphate complex, [La3+] and [total
phosphate] were varied together such that [total phosphate] =
[La3+] = 2 × 10–4 to 1.2 × 10–3 mol/L. Phosphate 2 had poor
solubility in the presence of La3+ at concentrations higher
than 3 × 10–4 mol/L, and so its concentration was held con-
stant at 2 × 10–4 mol/L in each case, and the far more solu-
ble phosphate 3 was used make up the [total phosphate]
throughout the rest of the concentration range.5
combination of the contribution of various kinetically active
species.
Titration analysis
Electrospray MS
High [La3+] domain (>10–3 mol/L)
Mass spectra were determined in methanol using a
Waters/Micromass ZQ (Manchester, UK) single quadrupole
mass spectrometer equipped with an electospray source op-
erating at cone voltages between 30 and 70 V. The solutions
contained [3] = 2 × 10–4 mol/L, along with equimolar
La(OTf)3 and 4 × 10–4 mol/L Bu4NOCH3, the latter to create
3– and add 1 equiv. of methoxide to the metal ion. Samples
were infused at a flow rate of 10 µL/min; the spectrometer
was externally calibrated and run in positive mode.
In the high [La3+] domain of the kobs vs. [La3+] plots for
s
methanolysis of 1 at each pH the saturation signifies that
s
the active species comprise two metal ions and one phos-
phate substrate, the latter most likely bridging the two La3+
ions to employ double activation (3a, 3b). Depending on the
sspH, the active (La3+)2:1– species are also proposed to
contain a variable number of methoxides from zero to five
(3a). The six (La3+)2:1–:(–OCH3)0–5 forms serve as a starting
model to fit the potentiometric titration data for 2:1
La2+:phosphate in methanol at 1 × 10–3 mol/L La3+, a con-
1
centration within the k2 domain. Since 1 is too reactive to
Results and discussion
survive titration in the presence of La3+, the less reactive
phosphate 3 was used in the present study as a structural
model. While we recognize that the substitution of 3 for 1
might alter the phosphate binding constants and all forma-
tion constants for the associated methoxide containing species,
the structural variations should not seriously alter the overall
conclusions concerning stoichiometry and formation constants.
The titration data for representative titrations of (La3+)2:3–,
as well as La3+ alone and 3 alone for comparison are illus-
trated in Fig. 2. The formation constants for the background
unbound (La3+)2 with one to five methoxides were estab-
lished first by Hyperquad fitting of a (La3+)2(–OCH3)1–5
model to the titration data for 1 × 10–3 mol/L La(OTf)3 in
The methodology for fitting the kinetic data as a function
of varying [La3+] and pH involves analyzing the speciation
s
of the metal ion alones at low and high concentrations as a
s
function of pH and then determining the speciation of the
s
phosphate bound forms of the metal ion. All these data can
be gleaned from potentiometric titrations under the appropri-
ate conditions. Following analysis of the speciation, one can
then fit the kinetic data (Table 1S, Supplemental material)3
1
pertaining to k1 (the second-order rate constant for La3+
promoted methanolysis of 1 at low [La3+] as a function of
1
sspH) and k2 (the plateaued pseudo-first-order rate constant
for (La3+)2:1– methanolysis as a function of pH) as a linear
s
s
5 In previous work (ref. 3b) we showed that the effect of a second phosphate diester was to act as a bridge between the two La3+ ions to facil-
itate formation of catalytically active dimers, and that a nonreactive or less-reactive phosphate diester can be used to structurally maximize
the formation of active (La3+)(reactive phosphate)(surrogate phosphate) dimers.
© 2005 NRC Canada

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Can. J. Chem. Vol. 83, 2005
Table 1. Formation constants for La3+2(–OCH3)n and La3+2:3–:(–OCH3)n species in methanol at [La3+] =
1 × 10–3 mol/L (25.0 °C).
logssKa
Microscopic sspKa
b
Equilibrium
[La2(–OCH3)1]/[La]2[–OCH3]
12.79 0.01c
22.33 0.22c
29.64 0.60c
36.71 0.39c
42.68 1.08c
10.47 0.47d
20.15 0.51d
29.48 0.51d
36.12 0.42d
42.32 0.52d
47.07 0.03d
[La2(–OCH3)2]/[La]2[–OCH3]2
[La2(–OCH3)3]/[La]2[–OCH3]3
[La2(–OCH3)4]/[La]2[–OCH3]4
[La2(–OCH3)5]/[La]2[–OCH3]5
[La2(3–)]/[La]2[3–]
sspKa = 7.23 0.21c
2
sspKa = 9.46 0.38c
3
sspKa = 9.70 0.22c
4
sspKa = 10.80 0.69c
5
[La2(3–)(–OCH3)1]/[La]2[3–][–OCH3]
[La2(3–)(–OCH3)2]/[La]2[3–][–OCH3]2
[La2(3–)(–OCH3)3]/[La]2[3–][–OCH3]3
[La2(3–)(–OCH3)4]/[La]2[3–][–OCH3]4
[La2(3-)(–OCH3)5]/[La]2[3–][–OCH3]5
sspKa = 7.09 0.04d
1
sspKa = 7.44 0.01d
2
sspKa = 10.13 0.10d
3
sspKa = 10.57 0.11d
4
sspKa = 12.02 0.50d
5
aDerived from fits of the potentiometric titration data using the program Hyperquad (10).
bDefined as –logssKa for La3+2:3–:(–OCH3)n(HOCH3)x ꢀ La3+2:3–:(–OCH3)n+1(HOCH3)y + H+, calculated from data in
column 2 as 16.77 – (sspKan
–
sspKan–1) where 16.77 is the –log of the autoprotolysis constant for pure methanol.
cAverages of duplicate titrations of La(OTf)3 (1 × 10–3 mol/L). Errors are calculated as the standard deviation of the
mean.
dAverages of duplicate titrations of La(OTf)3 (1 × 10–3 mol/L) in the presence of 3 (5 × 10–4 mol/L). Errors calcu-
lated as the standard deviation of the mean.
Fig. 3. Speciation diagram for La3+2:1–:(–OCH3)n forms as
a function of sspH computed from the formation constants given
in Table 1 for the titration of diphenyl phosphate (2 × 10–5 mol/L)
and 2 × 10–3 mol/L La3+. Captions of 2:1:n refer to La3+2:1–:
(–OCH3)n forms with a variable number of methoxides,
(— — —) La3+2:1–:(–OCH3)1, (- - - - -) La3+2:1–:(–OCH3)3,
(—·—·) La3+2:1–:(–OCH3)4. Data superimposed on the figure as
(᭿) are first-order rate constants (k2) for the La3+ catalyzed
methanolysis of methyl (4-nitrophenyl) phosphate (1) from
ref. 3a.
methanol. In Table 1 are presented the average of the log
formation constants (log β or logssK) for three separate deter-
minations that were used as constants for all subsequent
s
analyses of the titrations in the presence of 3. The pKa of 3
s
(3.47 0.01) was also used as an experimentally determined
constant, and the autoprotolysis constant for pure methanol
(10–16.77) (13) was included as the last constant for the fits.
Table 1 shows the results for the formation constants of all
the species used as the model in the Hyperquad fitting. The
concentrations of the various (La3+)2:1–:(–OCH3)0–5 species
s
were subsequently computed as a function of pH from these
s
0.00003
0.00002
0.00001
0.00000
0.00100
0.00075
0.00050
0.00025
0.00000
formation constants using HySS, another program in the
Hyperquad 2000 suite. The speciation diagram shown in
Fig. 3 was constructed using conditions relevant to the kinet-
ics where [La3+] = 2 × 10–3 mol/L and [3] = 2 × 10–5 mol/L.
2:1:0
1
Also superimposed on Fig. 3 are the kinetic data for k2 in
2:1:5
2:1:2
units of s–1 from Table 1S3 (3a) as a function of pH to indi-
s
s
cate possible species that may contribute to the rate constant.
From the appearance of the latter plot, it is clear that no sin-
gle species is responsible for the kinetic behaviour, and thus
a more detailed analysis is required.
Low [La3+] domain (<2 × 10–4 mol/L)
Due to the fact that the overall behaviour is a composite
of two independent pathways, we analyze the kobs vs. [La3+]
data at the limits of two concentration domains. In the low
[La3+] domain, the kobs vs. [La3+] plots for the La3+ catalyzed
methanolysis of 1 show a linear increase corresponding to an
apparent second-order process, with the gradient taken to be
4
5
6
7
8
9
10 11 12 13
s
s
pH
1
k1 in units of (mol/L)–1 s–1. The active form is believed to
(–OCH3)n or to the second-order rate constant for the attack
of external methoxide on La3+:1–:(–OCH3)n–1
be a transiently formed La3+ bound phosphate, formulated
.
preliminarily as La3+:1–:(–OCH3)n, where the number of
s
[1]
La3+(–OCH3)n + 1–
La3+:1–:(–OCH3)n
methoxides is zero to two depending on the pH. Since not
s
kcat
all the substrate is bound in this region, the apparent second-
order kinetics could also be accommodated by the process
depicted in eq. [1], where k11 = kcat/KB ((mol/L)–1 s–1), where
kcat refers either to the spontaneous decomposition of La3+:1–:
⎯⎯⎯→ P
There is some ambiguity as to whether the reaction proceeds
through the above monomeric form, or through a double
© 2005 NRC Canada

Gibson et al.
1273
Table 2. Formation constants for various La3+ containing species in methanol at [La3+] = 1 ×
10–4 mol/L (25.0 °C).
logssKa
Microscopic sspKa
b
Equilibrium
[La(–OCH3)1]/[La][–OCH3]
[La2(–OCH3)3]/[La]2[–OCH3]3
[La2(–OCH3)4]/[La]2[–OCH3]4
[La2(–OCH3)5]/[La]2[–OCH3]5
9.09 0.08c
28.35 0.38c
34.66 0.23c
41.55 0.09c
sspKa = 10.45 0.61c
3
sspKa = 9.88 0.32c
4
aDerived from fits of the potentiometric titration data using the program Hyperquad (10).
bDefined as –log ssKa for La3+(–OCH3)n(HOCH3)x ꢀ La3+(–OCH3)n+1(HOCH3)y + H+, calculated from data in
column 2 as 16.77 – (sspKn – sspKn–1) where 16.77 is the –log of the autoprotolysis constant for pure methanol.
cAverages of duplicate titrations of La(OTf)3 (1 × 10–4 mol/L). Errors are calculated as the standard deviation
of the mean.
phosphate bridged dimer formulated as (La3+)2:(phosphate–)2:
(–OCH3)m as was determined to be the case in the La3+ pro-
moted methanolysis of 2-hydroxypropyl p-nitrophenyl phos-
phate (3b). To cast light on this question, two independent
sets of experiments were performed. In the first, the electro-
spray mass spectrum of a methanol solution containing 2 ×
10–4 mol/L of both La3+(–OTf)3 and phosphate diester 3
(chosen because it is kinetically stable during the experi-
mental measurement while 1 is not) displayed masses at m/z
419.12 and 451.15 indicative of La3+:3–:(–OCH3)(HOCH3)0,1,
but no masses indicative of any dimeric forms. In the second
set of experiments, the kinetics for methanolysis of 2 in the
presence of equimolar La3+ were determined at an initial
concentration corresponding to the point of transition (2 ×
10–4 mol/L) between the low and high [La3+] domains ob-
served in the kobs vs. [La3+] plot for the methanolysis of 2.
This same trend and point of transition was previously ob-
served in the methanolysis of 1 ((3a), see Fig. 1S, Supple-
mental material).3 The kinetics of the methanolysis of 2
were then determined as a function of varying [La3+] con-
centration, but maintaining the [La3+]:[phosphate]total ratio at
1.0. Under these conditions, one anticipates shifting a puta-
tive 2(La3+:phosphate) ꢁ (La3+:phosphate)2 equilibrium to
the right so that if the dimeric species is active, an increase
in observed rate constant, with possible saturation, will ac-
company the increase in [La3+:phosphate]. This phenomenon
was previously observed with the La3+ : 2-hydroxypropyl p-
nitrophenyl phosphate system (3b). Above a concentration
of 2 × 10–4 mol/L, the complex of phosphate 2 is poorly sol-
uble in this medium so the additional phosphate concentra-
tion was made up with the more soluble 3, but this change
will not alter significantly the kinetic result since the ob-
served reaction concerns the decomposition of 2 (2). The
kobs for methanolysis of 2 determined under these conditions
is invariant to increasing [La3+] within experimental error
(kobs = (2.43 0.12) × 10–4 s–1, Table 2S, Supplemental ma-
terial)3 as expected if the reactive species is the monomeric
form La3+:2: (–OCH3)n.
consuming 1 equiv. of methoxide per La3+ followed by a
much steeper profile for the consumption of additional
methoxides. The steeper profile corresponding to the addi-
–
tion of more than 1 equiv. of OCH3 per La3+ suggests that
dimers or higher order aggregates are formed in that region.
Therefore, for the low [La3+] titrations we analyzed the data
in terms of a model comprising La3+, La3+(–OCH3)0,1, and
(La3+)2(–OCH3)3,4,5. The goodness-of-fit of this model to the
titration profile up to pH 11 is shown in Fig. 3S,3 and in
s
s
Table 2 are presented the computed formation constants for
all the species in this model. These were then used to com-
pute the speciation diagram using HySS for the kinetically
relevant conditions where [La3+] = 1 × 10–4 mol/L. This
speciation diagram is represented in Fig. 4 along with the
1
overlaid kinetic data that refer to k1 in (mol/L)–1 s–1 for the
La3+ catalyzed methanolysis of 1 as a function of pH.
s
s
Kinetic analysis
High [La3+] domain (>10–3 mol/L)
The fits of the titration data to the models previously de-
scribed provide the concentration of all the participating
species as a function of pH in the low and high [La3+] do-
s
s
mains. In each domain we can fit the observed rate constants
1
1
s
(k1 or k2 ) at the various pH values for the La3+ catalyzed
s
methanolysis of 1 (3a) as linear combinations of the contri-
1
s
butions of the individual species. For k2 vs. pH in the high
[La3+] domain, the appropriate linear combisnation is given
as eq. [2], where each of the (La3+)2:1–:(–OCH3)n species
contributes its own first-order rate constant (k22:1:n) for reac-
tion.
5
1
[2]
k2
=
k22:1:n[(La3+)2:1–:(–OCH3)n]/[1]total
∑
n=1
This equation is appropriate for spontaneous breakdown of
the substrate-bound species to methanolyzed product via an
internal La3+ coordinated methoxide mechanism, the transi-
tion structure of which is not implied other than it probably
contains a dual role for the metal ion as a Lewis acid and
deliverer of nucleophilic methoxide. An alternative, and
kinetically equivalent, mechanism requires external
methoxide attack on the (La3+)2:1– bound species having one
less methoxide than in the internal methoxide model, the ap-
propriate kinetic equation being shown as eq. [3] where
Having established that La3+ monomers are active in the
low [La3+] domain, we turned our attention to the analysis of
the titration data in this concentration range. Shown in
Fig. 3S, Supplementary material3 is the titration curve for a
1 × 10–4 mol/L solution of La(OTf)3 in methanol. The gen-
eral appearance of this curve is quite different from the pro-
file obtained at 1 × 10–3 mol/L (see Fig. 2) in that the first
consumption of methoxide follows a regular titration profile
© 2005 NRC Canada

1274
Can. J. Chem. Vol. 83, 2005
Fig. 4. Speciation diagram for La3+ species as a function of sspH
computed from the formation constants given in Table 2 for the
titration of 1 × 10–4 mol/L La3+. Data superimposed on the fig-
Table 3. Computed k′2
or k2
rate constants for various
2:1:n
2:1:n
species for the La3+ catalyzed methanolysis of 1 computed from
fits of k2 vs. sspH data to eq. [2] and [1].
ure as (᭿) are second-order rate constants (k1 ) for the La3+ cat-
1
[La3+2:1–:(–OCH3)n]
k′2
or k2
2:1:n
2:1:n
alyzed methanolysis of methyl (4-nitrophenyl) phosphate (1)
from ref. 3a.
External methoxide model (eq. [3])
La3+2:1–:(–OCH3)1
2:1:1
2:1:2
2:1:3
2:1:4
k′2
k′2
k′2
k′2
= (1.5 0.2)×104a
= (3.7 0.6)×102a
= (2.5 0.4)×102a
= (3.3 0.5)×101a
3.0
La3+(HOCH3)n
0.00010
La3+2:1–:(–OCH3)2
La3+2:1–:(–OCH3)3
La3+(-OCH3)
2.5
La3+2:1–:(–OCH3)4
0.00008
Internal methoxide model (eq. [2])
2.0
La3+2:1–:(–OCH3)2
k2
k2
k2
k2
= (6.3 0.9)×10–6b
= (9.8 1.5)×10–5b
= (1.4 0.2)×10–4b
= (1.3 0.2)×10–3b
2:1:2
2:1:3
2:1:4
2:1:5
La3+2:1–:(–OCH3)3
La3+2:1–:(–OCH3)4
La3+2:1–:(–OCH3)5
0.00006
(La3+)2(-OCH3)5
1.5
0.00004
1.0
Note: Errors computed from the avg. % deviation in the fitted numbers
calculated by eq. [2] or [3] from the actual kinetic data. Data fit under the
assumption that the various La3+:3–:(–OCH3)n formation constants from Ta-
ble 1 are realistic approximations for those for the La3+:1–:(–OCH3)
system.
(La3+)2(-OCH3)3
(La3+)2(-OCH3)4
0.00002
0.5
aValues of k′22:1:n are actually second-order rate constants in units of
(mol/L)–1 s–1 after accounting for the OCH3 concentration.
–
0.00000
0.0
2:1:n
bValues of k2
in units of s–1.
5
6
7
8
9
10
11
12
13
sspH
Fig. 5. Plot of k2 vs. sspH for the La3+ catalyzed methanolysis
1
2
of 1 and the contributionsof each active species. Lines come
from the fit of the kinetic data to eq. [2]. Solid line, composite
of all contributions; (—··—··), contribution of La3+2(1–)(–OCH3)2;
(— — —), contribution of La3+2(1–)(–OCH3)3; (···), contribution
of La3+2(1–)(–OCH3)4; (—·—·), contribution of La3+2(1–)(–OCH3)5.
2:1:n
k′2
is a second-order rate constant for methoxide attack
on each species.
1
[3]
k2
=
4
k′2 2:1:n[(La3+)2:1–:(–OCH3)n][–OCH3]/[1]total
0.001
∑
n=0
Given in Table 3 are the rate constants derived from fitting
1
the k2 data to eqs. [2] and [3] with the results being dis-
played in Fig. 5, which includes the individual contributions
for all species found to have activity. Their sum generates
the overall best fit curve, which is remarkably good given
the inherent assumptions of approximating the La3+:1– sta-
bility constants through the use of 3. Although the caption
for Fig. 5 is specific for the internal methoxide model, the fit
is obviously identical for the kinetically equivalent external
methoxide model where the (La3+)2:1–:(–OCH3)n species re-
sponsible for catalysis have one less associated methoxide
than in the internal model. The kinetically active forms for
0.0001
0.00001
the internal methoxide process are (La3+)2:1–:(–OCH3)2,3,4,5
,
while for the external methoxide process, the reaction
is computed to proceed via methoxide attack on (La3+)2:1–:
0.000001
7
8
9
10
11
12
13
14
(–OCH3)1,2,3,4
.
sspH
There is nothing by way of argument that might allow one
to prefer one or the other of the described two mechanisms.
The computed rate constants for internal methoxide sponta-
neous decomposition of (La3+)2:1–:(–OCH3)2,3,4,5 are 6.3 ×
10–6, 9.8 × 10–5, 1.4 × 10–4, and 1.3 × 10–3 s–1, respectively,
consistent with the expectation that the species having the
highest basicity for its associated methoxide will react the
fastest. For the external methoxide process, the computed
second-order rate constants for methoxide on the bound
forms with one to four associated methoxides are 1.5 × 104,
3.7 × 102, 2.5 × 102, and 3.3 × 101 (mol/L)–1 s–1, respec-
tively, but are well below the limit of ~1010 (mol/L)–1 s–1,
which would be appropriate for a diffusion-limited process
involving reaction of an anion and a positively charged spe-
cies (14). Nevertheless, the rate constants for the external
methoxide model are considerably larger than the experi-
mental second-order rate constant for methoxide attack on 1
alone of (7.9 0.6) × 10–7 (mol/L)–1 s–1 at 25 °C (3a), indi-
cating that complexation of 1 to the (La3+)2(–OCH3)1,2,3,4
© 2005 NRC Canada

Gibson et al.
1275
1:n
1:n
Table 4. Computed k′1 or k1 rate constants for various spe-
cies for the La3+ catalyzed methanolysis of 1 computed from fits
system provides a catalytic enhancement varying from 1.9 ×
1010-fold to 4 × 107-fold, with the least catalysis being ob-
served for methoxide attack on the least positively charged
complex.
1
of k1 vs. sspH data to eq. [4].
[La3+(–OCH3)n]
k′1
1:n
Low [La3+] domain
External methoxide model (eq. [4])
La3+(–OCH3)0
k′1 = (3.0 0.6)×108a
1:0
As stated previously, in the low [La3+] domain the kinetics
are linearly dependent on the metal ion. Thus, the preferred
La3+(–OCH3)1
k′1 = (5.1 0.9)×106a
1:1
1
fitting procedure considers that the k1 rate constants at each
Note: Errors computed from the avg. % deviation in the fitted numbers
calculated by eq. [4] from the actual kinetic data.
sspH can be described as a linear combination of second-
s
aValues of k′11:n are third-order rate constants in units of (mol/L)–2 s–1
order rate constants (equivalent to kcat/KB at each pH) for
s
–
each of the contributing (La3+)(–OCH3)n species for the in-
ternal methoxide model. For the external methoxide model
(eq. [4]), the rate constants are now third-order to accommo-
date the methoxide concentration that has been factored out.
At low [La3+] the only monomeric species available in so-
lution, as revealed by fits of the potentiometric curve, are
La3+(–OCH3)0,1 and it immediately becomes clear that:
(1) each species is required to provide a satisfactory fit to
after accounting for the OCH3 concentration.
Fig. 6. Plot of k1 vs. sspH for the La3+ catalyzed methanolysis
1
of 1 and the contributions of each active species. Lines come
from the fit of the kinetic data to the external methoxide model
given in eq. [4]. Solid line, composite of all contributions;
(— — —), contribution of La3+(–OCH3)0; (···), contribution of
La3+(–OCH3)1.
1
the kinetic k1 data; and (2) that an additional methoxide is
1.0
required to explain the activity seen where La3+(–OCH3)1 is
the dominant species to accommodate the increase in rate
s
with pH. Thus, the internal methoxide mechanism is ren-
deredsunlikely because, if operative, the kinetic data would
have to track the concentration behaviour of La3+(–OCH3)1
s
as a function of pH, which it does not: correspondingly, the
external methoxisde mechanism is favoured. Given in Table 4
are the best-fit rate constants from the application of eq. [4],
which generate the species contributions to the overall fitted
1
s
curve presented in Fig. 6 for k1 as a function of pH. The
overall fit displayed in Fig. 6, while not as good assobtained
1
for the k2 data vs. the (La3+)2:1–:(–OCH3)n species, is still
considered satisfactory in view of the inherent errors in de-
s
termining the linear region of the kobs vs. pH profile and the
s
0.1
assumed speciation to fit the titration data. The computed
constants of 3 × 108 and 5.1 × 106 (mol/L)–2 s–1 refer to the
apparent termolecular processes corresponding to CH3O– +
1– + La3+(–OCH3)0,1 respectively, the reduction by a factor of
~60-fold in rate constant between the two resulting from
Lewis acidity differences attributable to the methoxide con-
tent of the respective complexes.
7
8
9
10
11
12
13
sspH
1
1
[4]
k1
=
k11:n[La3+(–OCH3)n][–OCH3]/[La3+]total
′
∑
mental second-order rate constant for methoxide attack on 1–
alone of (7.9 0.6) × 10–7 (mol/L)–1 s–1 at 25 °C (3a), coor-
dination to La3+(–OCH3)0,1 provides a rate enhancement of at
least 1011- to 109-fold depending on the overall charge of the
metal:substrate complex.
n=0
While the fitting provides the apparent third-order rate constant
for the process involving CH3O– + 1– + La3+(–OCH3)0,1, it is
difficult to envision any mechanism where there is not a
preequilibrium binding of the substrate to the metal ion fol-
lowed by attack of methoxide on that complex as in eq. [1].
On the basis of the experimental kinetic saturation plots of
kobs vs. [La3+] (3a), we estimate the complex between an
oppositely charged phosphate and metal ion to have a disso-
ciation constant (Kdis) between 2 × 10–4 and 10–3 mol/L de-
pending on the metal ion charge as controlled by the number
of metal bound methoxides (n = 0, 1). Accordingly, one can
calculate the second-order rate constant for methoxide attack
on the transiently bound substrate as being between 6 × 104
and 3 × 105 (mol/L)–1 s–1 in the case of the complex with
n = 0, and 103 to 5 × 103 (mol/L)–1 s–1 for the attack of
methoxide on the complex with n = 1. Relative to the experi-
Conclusions
In this paper we have presented a detailed analysis of the
kinetic contributions of various La3+ species catalyzing the
methanolysis of the phosphate diester 1 for which kinetic
data were presented previously (3a), but only qualitatively
analyzed within the framework of Scheme 1. By coupling
the rate data to an analysis of the speciation of the La3+ con-
s
taining complexes present in solution as a function of pH
one can provide a simplified, but satisfactory, model tosex-
plain the kinetic behaviour in the high and low [La3+] do-
mains. We anticipate that such an approach will prove
© 2005 NRC Canada

1276
Can. J. Chem. Vol. 83, 2005
Sunderland, and R.S. Brown. Org. Biomol. Chem. 3, 65
(2005).
2. P.J. Montoya-Pelaez, G.T.T. Gibson, A.A. Neverov, and R.S.
beneficial to explain the origins of nonunit, or irregular de-
pendencies of kinetic profiles of many other metal-ion-
catalyzed reactions where the metal ion undergoes changes
s
Brown. Inorg. Chem. 42, 8624 (2003).
in speciation as a function of pH.
s
3. (a) A.A. Neverov and R.S. Brown. Inorg. Chem. 40, 3588
(2001); (b) J.S.W. Tsang, A.A. Neverov, and R.S. Brown. J.
Am. Chem. Soc. 125, 1559 (2003); (c) J.S.W. Tsang, A.A.
Neverov, and R.S. Brown. Org. Biomol. Chem. 2, 3457
(2004); (d) J.S. Tsang, A.A. Neverov, and R.S. Brown. J. Am.
Chem. Soc. 125, 7602 (2003).
4. (a) J.F. Davies, Z. Hostomska, Z. Hostomsky, S.R. Jordan, and
D.A. Mathews. Science (Washington, D.C.), 252, 88 (1991);
(b) L.S. Beese and T.A. Steitz. EMBO J. 10, 25 (1991); (c) A.
Lahm, S. Volbeda, and D. Suck. J. Mol. Biol. 215, 207 (1990).
5. R.S. Brown and A.A. Neverov. J. Chem. Soc. Perkin Trans. 2,
1039 (2002), and refs. 2 and 31 therein.
6. A.A. Frost and R.G. Pearson. Kinetics and mechanism: A
study of homogeneous chemical reactions. 2nd ed. John Wiley
and Sons, New York. 1965. pp. 236–261.
7. W. Desloges, A.A. Neverov, and R.S. Brown. Inorg. Chem. 43,
6752 (2004).
8. (a) J.R. Morrow and W.C. Trogler. Inorg. Chem. 28, 2330
(1988); (b) (erratum to ref. 8a): J.R. Morrow and W.C.
Trogler. Inorg. Chem. 31, 1544 (1992).
9. J. Suh and S.H. Hong. J. Am. Chem. Soc. 120, 12 545 (1998).
10. Hyperquad 2000 is a computer program that applies nonlinear
curve fitting to a titration by adjusting a series of formation
constants (log β) for species input to a model, published in: P.
Gans, A. Sabatini, and A. Vacca. Talanta, 43, 1739 (1996).
11. G. Gibson, A.A. Neverov, and R.S. Brown. Can. J. Chem. 81,
495 (2003).
There is an interesting observation revealed by comparing
these analyses with those previously reported for the La3+
promoted catalysis of the methanolysis of neutral substrates
such as phosphate triesters (3c, 3d) and carboxylate esters
(1). In those cases, the pH/rate profiles are bell-shaped or
distorted bell-shaped and best accommodated by mechanisms
involving a dual role for the metal ion as a Lewis acid and
deliverer of a metal-coordinated methoxide on a transiently
bound neutral substrate. However, in the present cases where
there is stronger binding of the anionic phosphate to the
metal ion to produce a thermodynamically more stable com-
plex, the pH/rate profiles for both the La3+ monomer and
dimer cases show gradual increases with non-integral slopes.
The preferred analysis involves attack of external methoxide
on the relatively stable complex where the main apparent
role of the metal ion is to act as a Lewis acid or electrostatic
stabilizer of the developing negative charge in the TS. While
we offer no detailed explanation of the difference in behav-
iour between neutral and anionic substrates at this time, it
must be related to a counterbalancing of the effects of coor-
dination geometry, Lewis acid activation, relative nucleo-
philicity of metal-bound and external nucleophiles, and
geometry of the activated complexes for each mode of catal-
ysis.
12. (a) C.L. deLigny and M. Rehbach. Recl. Trav. Chim. 79, 727
(1960); (b) R.G. Bates, M. Paabo, and R.A. Robinson. J. Phys.
Chem. 67, 1833 (1963); (c) R.G. Bates. Determination of pH:
Theory and practice. 2nd ed. John Wiley and Sons, New York.
1964. p. 245.
13. (a) I. Canals, J.A. Portal, E. Bosch, and M. Rosés. Anal.
Chem. 72, 1802 (2000); (b) E. Bosch, F. Rived, M. Roses, and
J. Sales. J. Chem. Soc. Perkin Trans. 2, 1953 (1999); (c) F.
Rived, M. Rosés, and E. Bosch. Anal. Chim. Acta, 374, 309
(1998); (d) E. Bosch, P. Bou, H. Allemann, and M. Roses.
Anal. Chem. 68, 3651 (1996).
Acknowledgements
The authors gratefully acknowledge the financial assis-
tance of Queen’s University and the Natural Sciences and
Engineering Research Council of Canada (NSERC) to which
G.T.T. Gibson is particularly thankful for the award of a
Canada Graduate Scholarship–D. A.C.T. Teng is also in-
debted to NSERC for the award of an Undergraduate Sum-
mer Research Award.
14. (a) A. Fersht. Enzyme structure and mechanism. W.H. Free-
man and Co., New York. 1985. pp. 147 to 148; (b) M. Eigen
and L.Z. De Maeyer. Electrochemistry, 59, 986 (1955).
References
1. (a) A.A. Neverov, T. McDonald, G. Gibson, and R.S. Brown.
Can. J. Chem. 79, 1704 (2001); (b) A.A. Neverov, N.E.
© 2005 NRC Canada