Dissociation kinetics of macrocyclic trivalent lanthanide complexes of 1-oxa-4,7,10-triazacyclododecane-4,10-diacetic acid (H2ODO2A)

Article abstract of DOI:10.1080/00958972.2014.945923

The dissociation rates of LnODO2A⁺ complexes (ODO2A^2- is the deprotonated dianion of the ligand H₂ODO2A, 1-oxa-4,7,10-triazacyclododecane-4,10-diacetic acid) are all faster than those of the corresponding LnDO2A⁺

Full text of DOI:10.1080/00958972.2014.945923

Journal of Coordination Chemistry, 2014
Vol. 67, No. 13, 2204–2216, http://dx.doi.org/10.1080/00958972.2014.945923
Dissociation kinetics of macrocyclic trivalent lanthanide
complexes of 1-oxa-4,7,10-triazacyclododecane-4,10-diacetic
acid (H ODO2A)
2
C. ALLEN CHANG*†‡§, CHIH-CHENG LIN‡¶ and CHIEN-HUNG KUO‡
†Department of Biomedical Imaging and Radiological Sciences, National Yang-Ming University,
Taipei, Taiwan, ROC
‡Department of Biological Science and Technology, National Chiao Tung University, Hsinchu,
Taiwan, ROC
§Biophotonics & Molecular Imaging Research Center (BMIRC), National Yang-Ming University,
Taipei, Taiwan
¶Department of Cosmetics Application, Asia-Pacific Institute of Creativity, Miaoli, Taiwan
(Received 20 December 2013; accepted 4 June 2014)
+
2−
The dissociation rates of LnODO2A complexes (ODO2A is the deprotonated dianion of the ligand
ODO2A, 1-oxa-4,7,10-triazacyclododecane-4,10-diacetic acid) are all faster than those of the corre-
H
2
+
2−
2
sponding LnDO2A complexes (DO2A is the deprotonated dianion of the ligand H DO2A, 1,4,7,10-
tetraazacyclododecane-1,7- diacetic acid), consistent with the fact that LnODO2A complexes are kineti-
cally more labile and thermodynamically less stable than the corresponding LnDO2A complexes, and
2 2
H ODO2A is not pre-organized for Ln ion complexation but H DO2A is.
+
+
3
+
3+
The dissociation kinetics of selected trivalent lanthanide (Ln , Ln=La, Pr, Eu, Er, Lu) complexes of
the macrocyclic ligand ODO2A (1-oxa-4,7,10-triazacyclododecane-4,10-diacetic acid),
H
2
+
+
−4
LnODO2A , were studied in the [H ] range (0.1–2.4) × 10 M in the temperature range 15–45 °C.
Excess Cu ions were used as the scavenger for the ligand in acetate–acetic acid buffer medium.
2+
2
+
The dissociation reactions are independent of [Cu ] and follow the rate law kobs = k
d
+ kAC[Acetate]
d
K′klim[H ]/(1 + K′[H ]), where k , kAC, and klim are the respective dissociation rate constants for
+
+
+
+
+
the [H ]-independent, acetate-assisted, and the [H ]-dependent limiting pathways; K′ is the equilib-
+
+
2+
rium constant for the protonation reaction LnODO2A + H $ LnODO2AH . The dissociation
+
+
rates of LnODO2A complexes are all faster than those of the corresponding LnDO2A complexes
2
−
(
1
DO2A is the fully deprotonated dianion of the ligand H DO2A, 1,4,7,10-tetrazacyclo-dodecane-
,7-diacetic acid), consistent with the notion that LnODO2A complexes are kinetically more labile
and thermodynamically less stable than the corresponding LnDO2A complexes, and H ODO2A is
2
2
+
+
3+
not pre-organized for Ln ion complexation but H
Keywords: Lanthanides; Macrocyclic ligands; ODO2A; DO2A; Dissociation kinetics
Corresponding author. Email: cachang@ym.edu.tw
2014 Taylor & Francis
2
DO2A is.
*
©

Kinetics of trivalent lanthanides
2205
Introduction
Over the last 30 years we have been interested in the study of the coordination chemistry
(
[
i.e. thermodynamic stabilities [1], kinetics of complex formation and dissociation reactions
2], solid and solution state structures [3], and spectroscopic properties [4]) of trivalent lan-
3
+
thanide (Ln ) complexes of macrocyclic ligands and their potential applications as ion
selective reagents [1], solvent extraction reagents [5], magnetic resonance imaging contrast
enhancement agents [6], nuclear medicine [7], molecular imaging agents [8], luminescent
anion sensors [9], and artificial nucleases, peptidases and hydrolases [10]. In a previous
paper [11], we reported the trivalent lanthanide complex formation constants (log K ) of the
f
macrocyclic ligand H ODO2A (1-oxa-4,7,10-triazacyclododecane-4,10-diacetic acid,
2
scheme 1) determined by pH titration techniques to be in the range 10.84–12.62 which are
smaller than those of the structurally related H DO2A (1,4,7,10-tetraazacyclododecane-1,7-
2
diacetic acid, scheme 1) complexes (log K range 10.94–13.31). Starting at pH > 7, the
f
+
equilibrium formation of the dinuclear hydrolysis species, e.g. Ln (ODO2A) (μ-OH) and
2
2
Ln (ODO2A) (μ-OH) , dominates over the mononuclear species, e.g. LnODO2A(OH)
2
2
2
−
and LnODO2A(OH) . Mass spectrometry confirmed the presence of both the mononuclear
2
and dinuclear species at pH > 7. Density function theory (DFT)-calculated structures of the
+
+
EuODO2A(H O)
and EuDO2A(H O)
3
complexes indicate that three inner-sphere
2
3
2
coordinated water molecules are arranged in a meridional configuration, i.e. the three water
molecules are on the same plane perpendicular to that of the basal N O or N atoms of the
3
4
+
macrocyclic ligand. However, luminescence lifetime studies reveal that the EuODO2A and
TbODO2A complexes have 4.1 and 2.9 inner-sphere coordinated water molecules,
respectively, indicating that other equilibrium species are also present for the EuODO2A
+
+
complex. Additional DFT calculations by using Y(III) ion to substitute Eu(III) ion show
that each Y(III) ion is eight-coordinated in the two lowest energy possible cis-
+
[
Y (ODO2A) (μ-OH)(H O) ] and [Y (ODO2A) (μ-OH) ] dinuclear complex structures.
2
2
2
2
2
2
2
2
−
The former includes six-coordination by the ligand ODO2A , one by the bridged μ-OH ion
and one by a water molecule. The second includes six-coordination by the ligand ODO2A
2
−
and two by the bridged μ-OH ions. However, to confine the length of the paper, the studies
of the dissociation kinetics of these Ln complexes were excluded from that publication.
Previously, we have also reported the results of our studies on the formation
stability, dissociation kinetics, and structures of a number of Ln(III) complexes of
macrocyclic ligands, including H K21DA (dapda, 1,7-diaza-4,10,13-trioxacyclopenta-dec-
2
ane-N,N′-diacetic acid [1(b), 2(a) and (b)], scheme 1), H K22DA (dacda, 1,10-diaza-
2
4
,7,13,16-tetraoxacyclo-octadecane-N,N′-diacetic acid [1(a), 2(c)], scheme 1), H DO3A
3
(
1,4,7,10-tetraazacyclododecane-1,4,7-triacetic acid [2(d), 3(c)]), H DOTA (1,4,7,10-tetraaz-
4
acyclododecane-1,4,7,10-tetraacetic acid [2(e)]), and their structural analogs [3(e), 12]. The
cavity sizes, basicities, steric factors, and conformations of the macrocyclic ligands all affect
the physicochemical properties of their Ln(III) complexes, in particular, the formation sta-
bilities and dissociation rates. In this paper, we report the results of the studies of dissocia-
+
tion kinetics of selected LnODO2A complexes. These kinetic data fill in the gap of those
+
of two sets of trivalent lanthanide macrocyclic complexes, namely the LnK21DA /
+
+
−
LnK22DA complexes and the LnDO2A /LnDO3A/LnDOTA complexes, and would be
useful for future quantitative comparisons.

2
206
C.A. Chang et al.
Scheme 1. Structural formulas of H
2 2 2 2
DO2A, H ODO2A, H K21DA, and H K22DA.
Results and discussion
+
Dissociation kinetics of LnODO2A
Lanthanide complex solutions were carefully prepared at pH range of 6.3–6.7 to ensure
complete complex formation before dissociation studies. As the lanthanide complexes do
not show appreciable absorption in the near-ultraviolet region, Cu(II) ion was used as the
scavenger of free ligand and the reaction kinetics were followed by monitoring the growth
in absorbance due to the CuODO2A complex formation at 264 nm. Since the stability of
+
CuODO2A [13] (log K = 17.85) is much greater than those of all LnODO2A complexes
f
(
log K = 10.84–12.62) [11], the following exchange reaction (1) will be complete under the
f
2
+
experimental conditions (20-fold excess of Cu ):
LnODO2A þ Cu ! CuODO2A þ Ln3þ
þ
2þ
(1)
2
+
Independence of kobs on [Cu ]
The rates of the exchange reactions are zero order in copper(II) concentration at both pH
4
0
.50 and 3.80 (table S1, see online supplementary material at http://dx.doi.org/10.1080/
0958972.2014.945923), suggesting no copper attack on the LnODO2A complex to form
+
a rate-determining intermediate due to the steric constraint of the macrocyclic complex.
This has been seen for a number of linear and macrocyclic lanthanide complexes with steric
+
+
+
−
constraints, i.e. LnDO2A [11], LnK21DA [2(b)], LnK22DA [2(c)], LnCyDTA [14],
and LnMEDTA [15], and the obtained rate data can be regarded as those of the dissociation
+
reactions of the LnODO2A complexes. For a given lanthanide ion in the solution pH stud-
ied, the rate constants and the kinetic labilities are in the order LnK21DA > LnK22DA >
LnODO2A > LnDO2A , even though the thermodynamic stability is not the same trend.
For example, the thermodynamic stability trend for the Nd complexes is NdDO2A
+
+
+
+
3
+
+
>

Kinetics of trivalent lanthanides
2207
+
+
+
+
NdK22DA > NdODO2A > NdK21DA [11]. However, for the LnODO2A complexes,
the trend of kinetic stability is the same as that of their thermodynamic stabilities, i.e. the
thermodynamically more stable dissociates more slowly.
Acetate catalysis
+
The LnODO2A dissociation rates are influenced by the presence of acetate ions. Table 1
+
lists the kobs data for five selected LnODO2A complexes at [Acetate] = 1.0−5.0 mM. Lin-
ear least squares regression analyses of the plots of the kobs values versus [Acetate] give
2
slope values kAC (acetate-assisted dissociation rate constant) and intercept values k with r
0
values close or equal to 1 at both pH 4.50 and 3.80 (equation (2)).
kobs ¼ k þ kAC½Acetateꢀ
(2)
0
The effect of acetate ion on k could be explained by acetate complexation on the posi-
obs
+
tively charged LnODO2A , leading to a neutral, more labilized intermediate for hydrogen
ion attack and dissociation. Usually, the number of inner-sphere coordinated water mole-
cules, their easiness by acetate displacement, and the thermodynamic stability of the com-
plex may all be important to account for the absolute and relative strength of acetate
catalysis. The higher the number of inner-sphere coordinated water molecules, the greater
+
the chance for acetate to replace them. The kAC and k values of the LnODO2A complexes
0
+
are in most cases greater than those of the corresponding ones of the LnDO2A complexes
+
except for the k value for the LaODO2A complex, indicating that the kinetic lability of
the LnODO2A complex is greater than that of the corresponding LnDO2A complex.
Similar to DO2A , ODO2A offers six coordination donor sites, the remaining inner-
sphere coordination water molecules on the lanthanide ions are possibly 4 for LaODO2A ,
–4 for PrODO2A and EuODO2A , 2–3 for ErODO2A , and 2 for LuODO2A . Thus,
under the experimental conditions, the observed k value is the highest for LaODO2A
and it decreases as the atomic number of Ln is increased until Eu , the value then
AC
+
+
2
−
2−
+
+
+
+
+
3
+
AC
3
+
3+
increases slightly with increasing atomic number. On the other hand, among the five
+
+
LnODO2A complexes studied, the relative acetate catalysis of the LnODO2A complex
3
+
dissociation is the greatest for Lu . At 25 °C, pH 4.61, and [Acetate] = 5.0 mM, acetate
catalysis constitutes 20, 41, 30, 43, and 75% for the La, Pr, Eu, Er, and Lu complex dissoci-
ation pathways, respectively.
The acetate catalysis is found to be greater at pH 3.80 than at pH 4.61 for the
+
EuODO2A complex. Specifically, at pH 3.80, acetate catalysis at 1.0 and 5.0 mM
+
constitutes the respective 71 and 90% of the EuODO2A complex dissociation pathway.
+
−1
Table 1. Effect of acetate concentration on LnODO2A dissociation kinetics, kobs (s ). pH 4.61 and 3.80
(
2+
−3
+
−5
Eu only), [Cu ] = 1.0 × 10 M, [LnODO2A ] = 5.0 × 10 M, T = 25 °C, μ = 0.10.
3+
[
Acetate]\Ln
La
Pr
Eu
Er
Lu
Eu (pH 3.80)
−
−
−
−
−
3
3
3
3
3
−4
−4
−4
−4
−4
−2
−4
−5
−5
−5
−5
−5
−3
−5
−5
−5
−5
−5
−5
−3
−5
−5
−5
−5
−5
−5
−3
−5
−4
1
2
3
4
5
.0 mM
.0 mM
.0 mM
.0 mM
.0 mM−
1.35 × 10
1.39 × 10
1.43 × 10
1.55 × 10
1.59 × 10
6.40 × 10
1.27 × 10
0.9998
1.57 × 10
1.75 × 10
1.97 × 10
2.15 × 10
2.31 × 10
1.88 × 10
1.39 × 10
1.000
4.59 × 10
5.19 × 10
5.35 × 10
5.71 × 10
6.14 × 10
3.62 × 10
4.31 × 10
0.9998
4.01 × 10
4.92 × 10
5.58 × 10
5.77 × 10
6.28 × 10
5.39 × 10
3.70 × 10
0.9989
1.81 × 10
2.70 × 10
3.33 × 10
3.96 × 10
4.66 × 10
6.96 × 10
1.20 × 10
0.9996
1.17 × 10
−4
2.02 × 10
−4
2.84 × 10
−4
3.50 × 10
−4
4.61 × 10
1 −1
−2
−3
−2
kAC (M
s
)
8.34 × 10
−
1
−5
k
r
0
(s
)
3.26 × 10
2
0.9943

2
208
C.A. Chang et al.
Because the buffer solutions were prepared using the acetic acid (pKa 4.76)/acetate ion
stock solution, the acetic acid concentration at pH 3.80 is ~9-fold of that of [Acetate] and a
general acid catalysis by acetic acid cannot be ruled out. However, it is difficult to com-
pletely separate the general acid catalysis from the acetate catalysis at present (vide infra).
+
+
[
H ]-independent and [H ]-dependent pathways
The observed rate constants for reaction 1, the temperature at which they were measured,
+
and the concentration of hydrogen ion for selected LnODO2A complexes (Ln = La, Pr, Eu,
Er and Lu) are given in table S2 (Supplemental data). Selected absorbance versus time data
plots at 15, 25, and 35 °C are shown in figures S1–S8 (Supplemental data). When the
+
observed rate constants are plotted against [H ] (e.g. figure 1), all five lanthanide complexes
+
show saturation curves with limiting rate constants at higher [H ]. And in all plots, appre-
+
ciable intercepts are obtained that correspond to [H ]-independent or self-dissociation rate
constants (k ). The simplified proposed dissociation mechanisms are shown in scheme 2,
d
+
which is similar to that of the LnDO2A complexes.
+
2+
+
The species [LnL ]*, [LnL(Ac)], and [LnLH ]* are the respective distorted LnL com-
plex, acetate ternary complex, and distorted protonated complex. The rate law consistent
with the proposed mechanisms is:
0
þ
0
þ
kobs ¼ kd þ kAC½Acetateꢀ þ K klim½H ꢀ=ð1 þ K ½H ꢀÞ
(3)
0.0008
0.0006
0.0004
0.0002
0.0000
0.00000
0.00005
0.00010
0.00015
0.00020
0.00025
+
[
H ], M
+
+
Figure 1. Plots of observed rate constants (kobs) vs. [H ] for the LuODO2A complex dissociation reactions at
different temperatures 15 ~ 45 °C. ●: 15 °C; ○: 25 °C; ▼: 35 °C; Δ: 45 °C.

Kinetics of trivalent lanthanides
2209
+
+
Scheme 2. The simplified proposed mechanisms for the dissociation of LnODO2A complexes in the [H ] range
−4
(
0.1–2.4) × 10 M.
+
where k is the [H ]-independent direct dissociation rate constant, K′ (= k /k ′) is the
d
H H
equilibrium constant for the formation of the monoprotonated complex (equation (4)), and
klim is the limiting rate constant for the protonated lanthanide complex.
þ
þ
2þ
LnL þ H $ LnLH
(4)
+
+
Note that k in equation (2) is equal to k + K′k [H ]/(1 + K′[H ]) in equation (3).
0
d
lim
2
+
Strictly speaking, in the pH range 3.6–5.0 studied, there is a small fraction of LnLH pres-
ent for the lighter lanthanide if equilibrium is reached [11], and the acetate anion could form
+
+
the LnLH(Ac) species. However, the amount of the LnLH(Ac) species is likely small
compared to that of LnL(Ac). Thus, assuming that the term (k + kAC[Acetate]) does not
d
+
vary with [H ] very much, equation (3) can be written as:
0
þ
0
þ
kobs ¼ kd
0
þ K klim½H ꢀ=ð1 þ K ½H ꢀÞ
(5)
+
Table 2. Resolved rate constants for the dissociation of selected LnODO2A complexes.
−
1
−1
lim (s
−1
3
Ln
La
T (°C)
kd′ (s
)
k
)
K′ (M dm )
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
−
4
3
3
3
5
4
4
4
5
5
4
4
5
5
5
4
6
5
5
5
−3
−3
−3
−3
−4
−4
−3
−3
−5
−4
−4
−4
4
15
(6.37 ± 0.35) × 10
(1.29 ± 0.13) × 10
(3.15 ± 0.23) × 10
(6.33 ± 0.39) × 10
(8.28 ± 1.69) × 10
(1.75 ± 0.23) × 10
(3.91 ± 0.21) × 10
(8.69 ± 0.58) × 10
(1.41 ± 0.49) × 10
(4.58 ± 0.25) × 10
(1.13 ± 0.12) × 10
(2.56 ± 0.21) × 10
(1.72 ± 0.35) × 10
(3.46 ± 0.60) × 10
(8.22 ± 1.42) × 10
(1.67 ± 0.31) × 10
(3.91 ± 5.07) × 10
(2.01 ± 0.57) × 10
(4.65 ± 1.12) × 10
(9.68 ± 2.49) × 10
(1.39 ± 0.05) × 10
(2.58 ± 0.22) × 10
(7.28 ± 3.71) × 10
(9.92 ± 0.56) × 10
(2.89 ± 0.64) × 10
(6.68 ± 2.28) × 10
(1.00 ± 0.07) × 10
(2.33 ± 0.84) × 10
(7.21 ± 0.90) × 10
(1.76 ± 0.31) × 10
(3.61 ± 0.97) × 10
(5.82 ± 0.71) × 10
(1.53 ± 0.25) × 10
(1.08 ± 0.39) × 10
(2.93 ± 2.60) × 10
(1.21 ± 0.31) × 10
(6.81 ± 4.33) × 10
(3.88 ± 2.65) × 10
(7.58 ± 1.31) × 10
(3.14 ± 2.03) × 10
(1.04 ± 0.52) × 10
(3.42 ± 1.14) × 10
(4.32 ± 2.46) × 10
(7.34 ± 2.71) × 10
(8.80 ± 8.35) × 10
(1.03 ± 0.70) × 10
(2.56 ± 0.95) × 10
(1.68 ± 1.16) × 10
(1.73 ± 1.77) × 10
(3.19 ± 1.34) × 10
(2.34 ± 1.12) × 10
(3.97 ± 1.64) × 10
4
3
4
3
3
3
3
4
3
3
3
2
3
3
3
3
3
3
3
2
3
4
5
5
5
Pr
15
2
3
4
5
5
5
Eu
Er
Lu
15
2
3
4
5
5
5
−4
15
(6.48 ± 5.06) × 10
−3
2
3
4
5
5
5
(1.19 ± 0.64) × 10
(1.29 ± 0.29) × 10
(2.76 ± 1.35) × 10
(2.96 ± 2.12) × 10
(3.48 ± 0.80) × 10
(9.03 ± 2.72) × 10
(1.18 ± 0.24) × 10
−3
−3
−4
−4
−4
−3
15
2
3
4
5
5
5

2
210
C.A. Chang et al.
+
Figure 2. Plots of log kd′(◆) and log klim(◇) values against log K
f
values for selected LnODO2A and
+
LnDO2A [2(f)] complexes at 25 °C (Ln = La, Pr, Eu, Er, Lu).
where k = k + k [Acetate]. The values of k , k and K′ are resolved by an unweighted
d′
d
AC
d′ lim
least squares analysis using equation (5) and are listed in table 2.
+
The values of [H ]-independent rate constants (k ) are in the order La > Pr > Eu > Er > Lu
d′
in most temperatures studied, which is in the same trend as the thermodynamic stability
(
figure 2). This trend is different from that of the limiting rate constants (kIim) which is in
+
the order La > Er > Pr > Eu > Lu. The observation that the ErODO2A complex is much
more sensitive to proton-assisted dissociation remains to be understood. The fitted log K′
values are in the range 2.94–4.18 which is similar to that determined by pH titration, i.e.
+
3
.28–3.98 [11], and to those of the LnDO2A complex, i.e. 3.20–3.98 [2(f)], and the
+
LnK21DA complex, i.e. 3.47–4.24 [2(c)].
Effects of temperature
+
+
The activation parameters for the [H ]-independent and [H ]-dependent pathways have been
obtained from the temperature dependence of rate constants. According to the Eyring
equation [16],
ꢂ
ꢂ
Lnðk=TÞ ¼ lnðkB=hÞ ꢁ ðDH =RTÞ þ ðDS =RÞ
(6)
the activation parameters of these dissociation reactions can be obtained by plotting of ln
−
1
−1
(
k/T) versus (1/T), where k is the rate constant, R is the gas constant (1.987 cal M K ),
−
23
−1
kB is the Boltzmann’s constant (1.381 × 10 J K ), h is the Planck’s constant
6.626 × 10 Js) and T is the absolute temperature, K. The slope and intercept values of
−
34
(
these plots yield the activation enthalpy (ΔH*) and entropy (ΔS*) data:
ꢂ
Slope ¼ ðꢁDH =RÞ
(7)

Kinetics of trivalent lanthanides
2211
Table 3. Activation parameters for self-and acetate-catalyzed dissociation and proton-catalyzed dissociation
+
a
reactions of selected LnODO2A complexes . ΔG* values are calculated at 25 °C.
ꢂ
ꢂ
ꢂ
ꢂ
ꢂ
ꢂ
DG
lim
DH
DS
DG
DH
DS
d
d
d
lim
lim
Ln
kcal (M)
cal/(deg M)
kcal (M)
kcal (M)
cal/(deg M)
kcal (M)
+
+
LaODO2A
PrODO2A
EuODO2A
13.6(0.6)
13.7(0.4)
16.9(0.9)
13.4(0.5)
18.6(2.4)
−26.1(1.9)
−29.7(1.5)
−21.8(2.4)
−33.9(1.7)
−18.4(7.9)
21.3
22.5
23.4
23.5
24.0
12.1(1.6)
11.5(1.2)
12.2(0.9)
7.4(1.7)
8.7(2.0)
−29.7(5.3)
−34.6(3.8)
−35.1(3.1)
−47.2(5.5)
−44.7(6.5)
20.9
21.8
22.6
21.5
22.0
+
+
ErODO2A
LuODO2A
+
a
Values in parentheses are standard deviations.
ꢂ
Intercept ¼ ðDS =RÞ þ lnðkB=hÞ
(8)
The free energy of activation, ΔG*, can then be calculated according to the following
equation:
DG ¼ DHꢂ ꢁ TDSꢂ
ꢂ
(9)
+
+
Table 3 lists the values of ΔH*, ΔS*, and ΔG* for the [H ]-independent and [H ]-depen-
+
dent dissociation reaction pathways of selected LnODO2A complexes.
The observed k values of the LuODO2A and EuODO2A complexes have larger tem-
+
+
d′
ꢂ
perature variations, leading to the highest and second highest DH values among the five
d
+
ꢂ
selected EuODO2A complexes. On the other hand, the DS values of the two complexes
d
ꢂ
are the least and second least negative (i.e. isokinetic behavior [17]), and the trend of DG
values is LuODO2A > ErODO2A > EuODO2A > PrODO2A > LaODO2A . This
trend is similar to that of their complex formation stability and that of the LnDO2A com-
d
+
+
+
+
+
+
plexes. Note that the k values have both k and k components, no attempt was made to
d′
d
AC
separate them for the present temperature variation studies.
For the proton-catalyzed dissociation pathway, the obtained DH values are in the order
ꢂ
lim
+
+
+
+
+
EuODO2A ≥ LaODO2A ≥ PrODO2A > LuODO2A > ErODO2A . With the isokinet-
ic compensation of the DS barriers, the trend for the DG values is EuODO2A
LuODO2A > PrODO2A > ErODO2A > LaODO2A which is quite different from that
of their complex formation stability and that of the LnDO2A complexes.
ꢂ
ꢂ
+
>
lim
lim
+
+
+
+
+
+
Comparisons of the dissociation kinetic and thermodynamic data of LnODO2A
complexes with other Ln(III) macrocyclic complexes
From our current and previously reported data, the thermodynamic formation stability con-
stants for a number of cyclen-based macrocyclic Ln(III) complexes are in the order
−
+
+
LnDOTA > LnDO3A > LnDO2A > LnODO2A [2(f), 11]. For the macrocyclic dicarbox-
ylic acetate ligands with the respective 12, 15, and 18-membered rings, the stability order is
+
+
+
+
LnDO2A > LnODO2A > LnK22DA > LnK21DA , with a few exceptions. For exam-
+
+
+
ple, for Ln = La, Ce, and Pr, the stability trend is LnK22DA > LnDO2A > LnODO2A >
+
LnK21DA , due to better metal ionic radius and macrocycle cavity size fit of the
+
+
LnK22DA complexes. Thus, except for the LnK22DA complexes where Ln = La, Ce, and
Pr, the other Ln(III) complexes of the macrocyclic K22DA and K21DA ligands with larger
cavity sizes are more flexible than those of the smaller 12-membered ring DO2A and
ODO2A ligands, and result in faster dissociation rates. At a given pH, the expected ascending

2
212
C.A. Chang et al.
Table 4. Various kinetic rate and equilibrium constants of selected macrocyclic Ln(III) complexes at
25 °C.
−
1
−1
lim, s
−1
3
k
d′, s
k
K′, M dm
+
,a
−3
−4
−5
−5
−5
−4
−5
−6
−6
−7
−3
−2
−3
−4
−4
−3
−4
−3
−4
−4
−4
−5
−2
−2
4
3
3
3
3
3
3
3
3
3
3
LaODO2A
(1.29 ± 0.13) × 10
(1.75 ± 0.23) × 10
(4.58 ± 0.25) × 10
(3.46 ± 0.60) × 10
(2.01 ± 0.57) × 10
(3.09 ± 0.79) × 10
(1.94 ± 0.40) × 10
(7.83 ± 2.68) × 10
(3.05 ± 0.94) × 10
(4.99 ± 1.34) × 10
(3.32 ± 0.13) × 10
(1.08 ± 0.06) × 10
(2.58 ± 0.22) × 10
(6.68 ± 2.28) × 10
(1.76 ± 0.31) × 10
(1.19 ± 0.64) × 10
(3.48 ± 0.80) × 10
(2.70 ± 0.53) × 10
(2.29 ± 0.11) × 10
(1.14 ± 0.15) × 10
(1.80 ± 0.46) × 10
(3.20 ± 0.33) × 10
(1.04 ± 0.12) × 10
(4.11 ± 0.36) × 10
(1.08 ± 0.39) × 10
(3.88 ± 2.65) × 10
(3.42 ± 1.14) × 10
(1.03 ± 0.70) × 10
(3.19 ± 1.34) × 10
(4.91 ± 2.20) × 10
(8.06 ± 1.30) × 10
(5.48 ± 1.76) × 10
(1.58 ± 0.56) × 10
(2.31 ± 0.38) × 10
(6.64 ± 0.85) × 10
+,a
PrODO2A
EuODO2A
+
,a
+,a
ErODO2A
LuODO2A
+
,a
+
,b
LaDO2A
+
,b
PrDO2A
EuDO2A
+
,b
+
,b
ErDO2A
LuDO2A
ErK21DA
+
,b
,c
,c
+
+
4
LuK21DA
(1.22 ± 0.11) × 10
a
−3
d
This work. kd′ = k + kAC[Acetate = 0.005 M dm ].
Ref. [2(f)].
Ref. [2(c)].
b
c
−
+
+
dissociation rate trend would be LnDOTA < LnDO3A < LnDO2A < LnODO2A
<
+
+
LnK22DA < LnK21DA .
Table 4 lists various kinetic rate and equilibrium constants of selected macrocyclic
Ln(III) complexes of ODO2A , DO2A , and K21DA with similar proposed dissocia-
2
−
2 −
2−
tion mechanisms at 25 °C. In general, the dissociation rate constants k and k follow the
d′
lim
inverse trend of their complex thermodynamic formation stability.
Implications on the effects of ligand structures on Ln(III) complex dissociation and
formation reactions
In another paper, we reported the prediction of conformations and protonation sites for the
macrocyclic ligands H DO2A and H ODO2A employing the simulated annealing (SA)
2
2
method and DFT calculations using the B3LYP/6–31G* method in vacuum and aqueous
solution [18]. These SA method/DFT calculations reveal that, in contrast to the H ODO2A
2
ligand system, the H DO2A ligand system is (1) pre-organized for trivalent lanthanide (Ln)
2
and other metal ion complexation, (2) structurally more symmetrical and slightly more com-
pact in aqueous solution (i.e. more and/or shorter intra-molecular hydrogen bonds), and (3)
with greater degree of partial positive charge accumulation on the hydrogen atoms bonded
to macrocyclic ring nitrogen atoms when protonated. The H ODO2A ligand system is not
2
pre-organized. These observations are in accord with the present experimental findings that
+
the LnODO2A complexes are less thermodynamically stable and kinetically more labile as
+
compared to the corresponding LnDO2A complexes.
According to the principle of microscopic reversibility [2(b), 19] (i.e. corresponding to
every individual process there is a reverse process, and in a state of equilibrium the average
rate of every process is equal to the average rate of its reverse process), the possible dissoci-
ation reaction mechanisms are the reverse of the formation reaction mechanisms. Thus, the
+
formation of the LnODO2A complex is likely going through the following simplified three
steps [2(k), 12(i)]: (1) an initial interaction of the aquated Ln(III) ion with one carboxylate
group of the non-pre-organized H ODO2A, (2) followed by a Ln(III) ion induced ligand
2
reorganization [3(e)] to form an intermediate in which the Ln(III) ion is either coordinated
to the two carboxylate groups in a syn-configuration [12(h)] or partially coordinated by

Kinetics of trivalent lanthanides
2213
(
2−n)−
H ODO2A
(n = 1–2), and (3) the Ln(III) ion moves into the macrocycle cavity and is
n
2
−
+
fully coordinated by all six donating atoms of ODO2A to form the LnODO2A complex.
Step 3 is most likely the rate-determining step. It has been well documented that the
formation reactions are usually catalyzed by OH ions [2(d)] and the dissociation reactions
−
+
by H ions.
If the reactions are slow enough, the formation intermediates in step 2 could be observed
by luminescence spectroscopy such as those of the Ln(III)DOTA-like complexes [2(k),
1
2(h), 12(i)]. Unfortunately, luminescence spectroscopy is not appropriate for our present
+
kinetic studies because the formation and dissociation reactions of LnODO2A are much
faster than those of the Ln(III)DOTA-like complexes. The lifetime measurements by lumi-
nescence spectroscopy could not confirm the presence of the reaction intermediate(s). How-
ever, we have used the technique to measure the inner-sphere coordinated number of water
+
+
molecules (q = 3–4) for the respective TbODO2A and EuODO2A complexes and have
reported the results previously [11].
Conclusion
+
The dissociation kinetics of these LnODO2A complexes exhibit certain different features
from those of the open chain and macrocyclic polyaminopolycarboxylate complexes
reported previously that might be attributed to the replacement of a nitrogen by an oxygen
+
in the rigid macrocyclic ring structure of the ligand. The dissociation rates of LnODO2A
+
complexes are all faster than those of the corresponding LnDO2A complexes which are
consistent with the notion that LnODO2A complexes are thermodynamically less stable
+
+
and kinetically more labile than the corresponding LnDO2A complexes, and H ODO2A is
2
3
+
+
not pre-organized for Ln ion complexation but H DO2A is. In particular, the EuODO2A
2
+
+
and ErODO2A complexes have relatively unusual [H ] and temperature-dependent behav-
iors and the exact reasons remain to be explored. Overall, the trend of thermodynamic sta-
bility is LnDOTA > LnDO3A > LnDO2A > LnK22DA ~ LnODO2A > LnK21DA ; the
trend of kinetic lability is roughly the reverse of it. These results will be useful for the
design of ligands that form mono- and di-nuclear Ln(III) complexes for various analytical
and biomedical applications.
−
+
+
+
+
Experimental
Materials and standard solutions
Analytical reagent grade chemicals and buffers, unless otherwise stated, were purchased
from Sigma (St. Louis, MO, USA), Aldrich (Milwaukee, Wl, USA) or Merck (Darmstadt,
Germany) and were used as received without further purification. Disodium ethylenedi-
aminetetraacetic acid (Na H EDTA) was purchased from Fisher. The ligand ODO2A was
2
2
prepared and purified as described below. Carbonate-free deionized water was used for all
solution preparations.
The concentration of the ODO2A stock solution (ca. 0.01 M) was determined by pH titra-
tion using a standard tetramethylammonium hydroxide solution (0.1 M), and was also
checked by complexometric back titration. The concentrations of the lanthanide nitrate
stock solutions were ca. 0.01 M and were standardized by EDTA titration using xylenol

2
214
C.A. Chang et al.
orange as indicator. The EDTA solution was standardized by titrating a calcium carbonate
primary standard solution (first dissolved in HCl solution) at pH 10 using calmagite as the
indicator.
The 0.1 M tetramethylammonium hydroxide solution was prepared by diluting a 20%
(
(
CH ) NOH-methanol solution obtained from Aldrich (carbonate-free). The aqueous
3 4
CH ) NOH solution was standardized by using reagent grade primary standard potassium
3
4
hydrogen phthalate. A 0.1 M HCl solution was prepared by diluting a reagent grade HCl
solution and standardized by using the standard (CH ) NOH solution. A 1.0 M stock solu-
3
4
tion of tetramethylammonium chloride (Aldrich) was prepared and diluted to 0.1 M for each
titration to maintain a constant ionic strength (0.1 M).
Synthesis of ODO2A
The compound was synthesized according to a published method with minor modification
[
11, 20]. 4,10-Dicarboxymethyl-1-oxa-4,7,10-triazacyclododecane (H ODO2A) in the
2
hydrochloride form was obtained by carboxymethylation of 1-oxa-4,7,10-triazacyclodode-
cane with bromoacetate and recrystallization in ethanolic HCl solution (yield 35%). Anal.
Calcd for ODO2A.2.7HCl.H O (C H N O .2.7HCl.H O): C, 35.51; H, 6.88; N, 10.36.
2
12 23
3
5
2
1
3
Found: C, 35.53; H, 6.89; N, 10.12. NMR (D O-DSS), C: δ42.05, δ50.35, δ52.59, δ55.58,
δ66.29, δ170.0 ppm; H: δ3.26, 3.27, 3.28, δ3.34, 3.35, δ3.68, 3.69, 3.70, δ3.89 ppm. ESI
2
1
(+)-MS, m/z 290.1.
Kinetic measurements
All lanthanide complex solutions were freshly prepared by mixing 1.00 : 1.02 metal salts to
ligand molar ratio solutions. Stoichiometric amounts of (CH ) NOH solution were slowly
3
4
added into each metal–ligand mixture to neutralize the protons expelled from the ligand
after metal ion complexation. The final pH of each complex solution was carefully adjusted
to be in the pH range 6.3–6.7 (i.e. guided from the titration curves of figure S2 in [11]) to
ensure complete metal complex formation and the solution was allowed to stand for at least
+
one hour before use. Luminescence spectrum of the EuODO2A complex was found to be
similar to that previously published at pH 6.0 and 7.0 ([cf 11], figure 7). For kinetic mea-
surements, the pH of each solution was adjusted by using acetic acid/lithium acetate buffer.
+
−5
The final [LnODO2A ] is 5.0 × 10 M. The acetate anion concentrations were carefully
adjusted to be 1.0–5.0 mM for acetate catalysis studies. As the lanthanide complexes do not
show appreciable absorption in the near-ultraviolet region, Cu(II) ion was used as the scav-
enger of free ligand and the reaction kinetics were followed by monitoring the growth in
absorbance due to the CuODO2A complex formation at 264 nm, using a HP 8453 UV–vis
diode-array spectrophotometer equipped with a thermostatted cell holder with a constant
temperature circulating bath (FIRSTEK SCIENTIFIC B403). The solution temperature was
2
+
controlled to ±0.1 °C. Although the rates observed are independent of [Cu ], a pseudo-
2
+
−3
first-order (20-fold) excess of Cu (1.0 × 10 M) was used in reaction mixtures. The ionic
strength was adjusted to 0.10 M with LiClO . Pseudo-first order rate constants (kobs) were
4
calculated using the integral rate method by fitting the absorbance versus time data to the
−
kobs·t
equation: A = A + A (1−e
). Sigma Plot software was used for curve fitting. Rate
t
0
∞
constants quoted represent the average values of two to three kinetic runs and were repro-
ducible with 10%.

Kinetics of trivalent lanthanides
2215
Funding
The authors wish to thank the National Science Council and the Atomic Energy Council of the Republic of China
Taiwan) for financial support [grant number NSC-98-2113-M-010-001-MY3], [grant number NSC 96-NU-7-009-
03], and [grant number NSC-100-2811-M-010-003] of this work.
(
0
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