Structural and thermodynamic aspects of water–carbonate exchange equilibrium for M^III/IV–EDTA–carbonate systems

Abstract

The results of a thermodynamic description of ternary M–EDTA–carbonate (where M = Er(III), Th(IV)) complex formation are presented. The crystal structures of the novel [C(NH₂)₃]₃[Er(EDTA)(CO₃)]·H₂O (I) and [C(NH₂)₃]₄[Th(EDTA)(CO₃)₂]·5H₂O (II) compounds were determined. The structural and UV-vis-NIR spectroscopic results of crystal I served as the model data to analyze the stoichiometry and stability of the Er(III)–EDTA–carbonate system in aqueous solutions. The formation of the [Er(EDTA)(CO₃)]^3– complex in solution under different conditions was examined by complementary techniques including temperature dependent UV-vis-NIR and NMR spectroscopy as well as potentiometry. It was established that the affinity of the carbonate for the Er(III)–EDTA chelate is strongly pH dependent. Thus reaction (A) [Er(EDTA)(H₂O)₂]⁻ + CO₃^2– ⇄ [Er(EDTA)(CO₃)]^3– + 2H₂O is more favoured at near neutral pH, while reaction (B) [Er(EDTA)(OH)(H₂O)₂]^2– + CO₃^2– ⇄ [Er(EDTA)(CO₃)]^3– + 2H₂O + OH⁻ occurs under more basic conditions. The log β values were found to be 3.66 ± 0.07 and 0.20 ± 0.12 for reactions (A) and (B), respectively. The temperature dependence of log β allowed the determination of the enthalpy and entropy changes of both reactions for the first time (ΔH_(A) = −2.8 ± 0.8 kJ mol⁻¹, ΔS_(A) = 62 ± 3 J mol⁻¹ K⁻¹ and ΔH_(B) = 28.1 ± 4.6 kJ mol⁻¹, ΔS_(B) = 92 ± 15 J mol⁻¹ K⁻¹). These data indicate that the carbonate anion more readily displaces H₂O than the OH⁻ ligand. The obtained results are important not only from the point of view of environmental lanthanide and actinide mobility, but also for designing MRI contrast agents.

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Introduction

Besides citrates, succinates and oxalates, EDTA is one of the main organic ligands, which is present in liquid radioactive waste due to its use in the separation process and decontamination operations in the nuclear industry.¹ For instance the Hanford mixed waste alone contains about 240 tons of radioactive waste containing the EDTA ligand, with initial concentrations of 0.1 M EDTA.^1,2 This waste has unique characteristics of being extremely heterogeneous and highly basic, and having high ionic strength.¹ The high solubility and thermodynamic stability of EDTA complexes with heavy metal ions may be a reason for the increased mobility of radionuclides to the environment, which may thus complicate the safe storage of radioactive waste. As an example, Tank241-T-106 at Hanford released 435 m³ of mixed radioactive waste containing Pu and EDTA into the subsurface during 1973.^3,4 Recent study results of PuO₂ solubility in EDTA solutions in the presence of Ca(II) cations and Fe(OH)₃ suggest that the environmental mobility of plutonium due to Pu(IV)–EDTA complex formation is significantly overestimated.⁴ However, in that study, only binary M–EDTA, and not ternary M–EDTA–L, complexes were taken into consideration.^3,4

Ln(III) and An(III)/An(IV) ions which are entrapped by six donor atoms of EDTA ligands, possess two, three or four additional binding sites usually filled by an appropriate number of water molecules.^5,6 These molecules, in turn, may be readily displaced by other bi- or tridendate ligands such as carbonates,⁷ phosphates, citrates etc.⁸ One of the most common inorganic O-donor ligands available in liquid nuclear waste⁹ and in the environment¹⁰ is a carbonate anion which strongly interacts with hard Pearson acids like trivalent lanthanides and actinides.^10–12 In the presence of this anion ternary [M(EDTA)(CO₃)_m]ⁿ⁻ complexes may be formed according to eqn (1):

The available experimental data for this reaction are rather limited and provide equilibrium constant values that differ by several orders of magnitude. For instance the log β_MLA values (where M = Ln(III), An(III/IV), L = EDTA, A = CO₃^2–) for reaction (1) derived from the electronic spectroscopy results were found to be: log β_NdLA = 0.83;¹³ log β_EuLA = 0.53,¹⁴ log β_HoLA = 0.60¹³ and log β_ErLA = 0.74,¹³ while those obtained from NMR data are by ca. two orders higher, log β_GdLA = 2.60 ± 0.02.¹⁵

The results of the potentiometric and spectroscopic study on An(III)–¹⁶ and An(IV)–EDTA–carbonate¹⁷ systems have shown that complexes of trivalent actinides are much weaker than those of tetravalent ones. For example the estimated log β_An(III)LA values (An = Am, Cm) were found to be between 3 and 4,¹⁶ whereas the log β_Pu(IV)LA value is equal to 9.07 ± 0.2.¹⁷

The majority of the thermodynamic data on lanthanide and actinide coordination compounds are obtained at room temperature.¹⁸ Almost no data are available for the effects of temperature on the stability of ternary complexes in aqueous solutions, although, the temperature of nuclear waste in storage tanks is significantly above the ambient temperature and can be up to 90 °C.¹⁹

Therefore the aim of this paper is to describe thermodynamically reaction (1) at different temperatures between 283 and 333 K, at high ionic strength and various pH values. The crystal structures of novel ternary coordination compounds of [C(NH₂)₃]₃[Er(EDTA)(CO₃)]·H₂O (I) and [C(NH₂)₃]₄[Th(EDTA)(CO₃)₂]·5H₂O (II) are presented. The UV-vis-NIR electronic spectroscopy results of crystal I and the Er(III)–EDTA–carbonate system in solution, extended by complementary potentiometric and ¹³C NMR results, enabled us to determine the thermodynamic functions ΔG, ΔH and ΔS for reaction (1) for the first time.

In this paper we attempt to find an answer to the question as to which of the structural and physicochemical factors determine the thermodynamic stability of ternary M(III/IV)–EDTA–carbonate complexes. This is particularly important for the study and prediction of the environmental An(III)/An(IV)–EDTA mobility process as well as for understanding the quenching of spin–lattice relaxation in some of the Gd(III)-based MRI contrast agents under physiological conditions.¹⁵ The presented study may elucidate what role the readily available carbonate coligand plays in both of these processes.

Results and discussion

X-ray crystal structure of [C(NH₂)₃]₃[Er(EDTA)(CO₃)]·H₂O

The crystal structure of [C(NH₂)₃]₃[Er(EDTA)(CO₃)]·H₂O (I) was determined while the structural details of [C(NH₂)₃]₂[Er(EDTA)(H₂O)₂]ClO₄·6H₂O (Ia) were taken from ref. 5 for comparison purposes. The details of the data collection and the structure refinement of I are given in Table S1 in the ESI.† In both compounds the Er(III) cation is eight coordinated and the EDTA ligand is bound to the Er(III) cation by four oxygen and two nitrogen atoms. The remaining coordination sites of Er(III) are filled by two oxygen atoms from the bidendate carbonate anion (in I) and two water molecules (in Ia). The views of both molecular anions are presented in Fig. 1.

Fig. 1 Molecular structure of [Er(EDTA)(CO₃)]^3– anion in I together with the atom labeling scheme and superimposed molecular structures of [Er(EDTA)(CO₃)]^3– (in red) and [Er(EDTA)(H₂O)₂]⁻ (in blue) complexes. Coordinates of the [Er(EDTA)(H₂O)₂]⁻ anion in Ia have been taken from ref. 5.

To find the closest coordinates of the ideal polyhedron, the continuous symmetry measure parameter²⁰ (hereinafter referred to as CSM) was calculated. Though the geometry of the first coordination sphere of Er(III) in I may be described as a biaugmented trigonal prism (BTPR-8, CSM = 11.9%) and that in Ia as a triangular dodecahedron (TDD-8, CSM = 1.604%) or a square antiprism (SAPR-8 CSM = 1.69%), the approximate symmetry of both complexes is C₂. The substitution of two water molecules by a carbonate anion brings about only minute changes of bond lengths in the ErEDTA moiety; thus the EDTA ligand adopts very similar conformations in both crystals as shown in Fig. 1. The selected Er–L bond lengths in I and Ia⁵ are presented in Table 1.

Table 1 Selected Er–L and Th–L bond lengths (Å) in I, Ia,⁵II and IIa⁶

Bond	[Er(EDTA)(CO3)]^3– (I)	[Er(EDTA)(H2O)2]^− (Ia)^5	Δ Er–L
Er–O(CO2^–)	2.257(3)–2.321(3)	2.2489(10)–2.2975(11)
Er–O(CO 2 ^– ) av	2.286(28)	2.275(26)	0.011
Er–N	2.570(4)–2.576(4)	2.5995(12)–2.5816(11)
Er–N av	2.573(4)	2.591(13)	−0.018
Er–L^a	2.328(3)–2.330(3)	2.3445(10)–2.3444(10)
Er–L av	2.329(2)	2.345(5)	−0.015
Er⋯Er	6.63	7.34

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	[Th(EDTA)(CO3)2]^4– (II)	[Th(EDTA)(H2O)4] (IIa)^6	Δ Th–L
a L = CO3^2– in I and II or L = H2O in Ia and IIa.
Th–O(CO2^–)	2.481(4)–2.503(4)	2.4014(15)–2.4576(15)
Th–O(CO 2 ^– ) av	2.491(10)	2.428(26)	0.063
Th–N	2.773(4)–2.801(5)	2.790(2)–2.819(2)
Th–N av	2.787(20)	2.805(21)	−0.018
Th–L^a	2.432(4)–2.484(4)	2.5693(16)–2.4911(16)
Th–L av	2.454(24)	2.532(33)	−0.078

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As is seen, the Er–O(CO₃^2–) and Er–OH₂ bond lengths are similar; however the former ones are a little bit shorter due to larger formal negative charges on carbonate oxygen atoms. The Er(III) cation is located in a saddle point formed by four Er–O(CO₂^–) bonds (Fig. 2).

Fig. 2 Saddle point formed by Er–O1, Er–O3, Er–O2 and Er–O4 bonds in I.

This point may be illustrated using the values of O1–Er–O3 (201.2°) and O2–Er–O4 (139.3°) angles, which are about 2° smaller in I than those in Ia. The binding of the CO₃^2– anion or two H₂O molecules with the [Er(EDTA)]⁻ moiety occurs in such a way that the inserted coligands fit to the saddle point (Fig. 2) to minimize the repulsion between carboxylate donor atoms (O1, O2, O3, and O4) and OC2, OC3 in I or OW10 and OW11 in Ia coligands. This is a reason why the rotation of CO₃^2–/H₂O coligands around C₂ axes is hindered. The encapsulation of the Er(III) ion seems to be slightly stronger in the [Er(EDTA)(CO₃)]^3– complex in comparison with that in the hydrated [Er(EDTA)(H₂O)₂]⁻ species. This is due to a stronger electrostatic Er(III)–carbonate anion interaction and better fitting of the planar carbonate anion to the coordination vacancy of the [Er(EDTA)]⁻ unit. To illustrate this problem it is worth comparing the distance between neighboring OC2⋯OC3 atoms from the CO₃^2– anion in I with that between neighboring coordinated water molecules OW10⋯OW11 in Ia, which have been found to be 2.204(3) Å and 2.772(1) Å, respectively.

X-ray crystal structure of [C(NH₂)₃]₄[Th(EDTA)(CO₃)₂]·5H₂O

Thorium, which is characterised by a very stable +4 oxidation state, is thought to be a natural analog of tetravalent actinides. It seems to be important to elucidate how the increase of the oxidation state of the central metal cation disturbs the stoichiometry and in general the structure of the formed complexes. Crystals of the formula [C(NH₂)₃]₄[Th(EDTA)(CO₃)₂]·5H₂O (II) were obtained and the molecular structure of the [Th(EDTA)(CO₃)₂]^4– anion is presented in Fig. 3. The details of the data collection and the structure refinement of II are provided in Table S1 in the ESI.†

Fig. 3 The molecular structure of the [Th(EDTA)(CO₃)₂]^4– anion in II together with the atom labeling scheme and superimposed molecular structures of [Th(EDTA)(CO₃)₂]^4– (in red) and [Th(EDTA)(H₂O)₄] (in blue) complexes. Coordinates of [Th(EDTA)(H₂O)₄] (IIa) have been taken from ref. 6.

The EDTA ligand in the [Th(EDTA)(CO₃)₂]^4– anion is coordinated to Th(IV) in the same fashion as in I and Ia; however the conformation of the EDTA ligand in II is different. Four remaining coordination sites of Th(IV) are occupied by two bidendate carbonate anions thus giving a coordination number of 10. This is the most common coordination number of Th(IV) which was also found in the hydrated [Th(EDTA)(H₂O)₄] complex.⁶ The superimposed molecular structures of [Th(EDTA)(CO₃)₂]^4– and [Th(EDTA)(H₂O)₄] complexes are shown in Fig. 3. The increase of the coordination number from 8 in I and Ia up to 10 in II and IIa is caused by the increase of the charge density of Th(IV) (17.0 esu Å⁻¹) in comparison with Er(III) (14.3 esu Å⁻¹). The selected Th–L bond lengths in II and IIa are presented in Table 1. The Th–O(CO₂^–) bond lengths are slightly longer in II than in IIa, while the corresponding Th–N bond lengths for both crystals are similar within the error of experimental limits. The largest variation of bond lengths has been found for the case of Th–coligand interactions. The average Th–O(CO₂^–) bond lengths in II are about 0.078 Å shorter than the Th–O(H₂O) ones in IIa. Interestingly the corresponding Er–coligand bond lengths in I and Ia differ only slightly. The binding of negatively charged coligands with Th(IV) (i.e. carbonate) brings about certain elongation of Th–O(CO₂^–) bonds while coordination of neutral coligands (i.e. H₂O) causes their shortening. This is likely due to increased repulsion between negatively charged oxygen atoms from carboxylate and carbonate groups. The geometry of the first coordination sphere of Th(IV) in both complexes may be described as sphenocorona (JSPC-10) with CSM factors equal to 3.47% and 2.96% for II and IIa, respectively. The symmetry of the Th(IV) complexes under study may be approximated as C₂.

UV-vis spectra of crystals I and Ia

Because the 4f electrons are essentially core orbitals, screened by the closed 5s and 5p subshells, they cannot participate significantly in covalent bonding. For instance the calculated values of ligand field stabilization for the Nd(Cp′′)₃ complex (where Cp′′ is 1,3-bis-(trimethylsilyl)cyclopentadienyl) is about 58.6 kJ mol⁻¹ (ref. 21) while for the substantially ionic compound [Nd(H₂O)₉](BrO₃)₃ this energy is only about 6.3 kJ mol⁻¹.²² Therefore the geometry of ligands around Ln(III) ions is controlled mainly by steric factors. Thus only the nearest donor atoms of ligands bonded directly with Ln(III) may affect to some extent the 4f electrons. The influence of the outer coordination sphere is rather less important. Thus the spectral pattern of the f–f transitions, especially the hypersensitive ones, may be a “fingerprint” for a given system.

The UV-vis-NIR spectra of I measured at room and liquid helium temperatures in the spectral range 250–900 nm are presented in Fig. S1 in the ESI.† The crystal field (CF) levels of the selected multiplets determined from the spectra of I and Ia, recorded at 4.2 K are presented in Table S2.† The number of CF components observed in the spectra of I indicates that there is one symmetry independent site of Er(III) which is consistent with the X-ray structural data; however some of the CF components of the ⁴S_3/2 multiplets are additionally slightly split. The crystal field splitting (Δ_CFS Table S2†) of the particular ^2S+1L_J multiplets, except those of ⁴S_3/2 and ⁴I_11/2, are smaller in I than in Ia.⁵ The observed bathochromic shift of the highest energy CF component and the gravity center of all multiplets in the spectra of I in comparison with those in Ia may suggest some increase of the covalent contribution to Er–L bonding in I. It should be noted that the comparison of such spectroscopic properties is justified for systems with the same symmetry and is usually made for simple inorganic compounds which possess high point symmetry.²³ Although the molecular systems under study have low symmetry (∼C₂), the geometry of anionic complexes is substantially very similar. Therefore a comparison of crystal field splitting (Δ_CFS) for the given multiplets in I and Ia can be done. The observed variation in the absorption spectra of f–f transitions may be attributed to different donor properties of binding coligands. The changes in the Δ_CFS values and the energy of the gravicenter of the ^2S+1L_J multiplets correspond to the positions of CO₃^2– and H₂O ligands in the spectrochemical and nephelauxetic series.²⁴

A comparison of the spectral features of the hypersensitive transitions recorded for single crystals, containing a well-defined molecular lanthanide complex, with those of solutions, may provide crucial information about the stoichiometry, structure and concentration of the complex species in solution.^12,25 The spectra of the ⁴I_15/2 → ²H_11/2 and ⁴I_15/2 → ⁴S_3/2 transitions of the Er(III) compounds are particularly informative in this regard. The absorption spectra of crystals I and Ia and solutions of the Er(III)–EDTA–carbonate complexes at pH ∼ 7.5 and ∼12 (μ_KCl = 3.5 M) were recorded and are shown in Fig. 4.

Fig. 4 Absorption spectra of crystals I and Ia and solutions of the Er(III)–EDTA–carbonate systems (c_ErEDTA = 29.5 mM) at different concentrations of the carbonate, at pH ∼ 7.5 and 12.

The different donor properties of both coligands are also reflected in the intensity of the f–f transitions, particularly of the hypersensitive ones. The oscillator strengths of the hypersensitive ⁴I_15/2 → ²H_11/2 transitions for the systems under study are presented in Table 2. The Judd–Ofelt^26,27 analysis of the f–f transitions of I and Ia are discussed in the ESI (Table S3†).

Table 2 The oscillator strengths (P) of the hypersensitive ⁴I_15/2 → ²H_11/2 transition for the systems under study

System	P × 10^8
Solid
I	853
Ia	308
Solution
Er : EDTA 1 : 1; pH ∼ 7.5	505
Er : EDTA : carbonate 1 : 1 : 15; pH ∼ 7.5	1072
Er : EDTA 1 : 1; pH ∼ 12	705
Er : EDTA : carbonate 1 : 1 : 4; pH ∼ 12	1128

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The replacement of water molecules in Ia by more polarizable, bidendate CO₃^2– anion in I brings about a significant increase in the intensities of the hypersensitive ⁴I_15/2 → ⁴G_11/2 and ⁴I_15/2 → ²H_11/2 transitions, as the polarizability of CO₃^2– anions (α_CO3 = 3.85 ų) is about 2.7 times higher than that of water (α_H2O = 1.442 ų).²⁸

Solution structure and stability of the ternary Er–EDTA–carbonate complex

The spectra of Er(III)–EDTA solutions at pH ∼ 7.5 in the absence of carbonate anions are similar to those in Ia. It has been shown previously that under these conditions [Er(EDTA)(H₂O)₂]⁻ is the predominant species (∼95%).⁵ With the increase of the concentration of the carbonate anion the spectra of the Er(III)–EDTA–carbonate solution become more similar to that in I. Thus the following reaction (2) occurs in a solution of the Er(III)–EDTA–carbonate system at pH ∼ 7.5, for which the formation constant is described by eqn (3).

To examine reaction (2), the spectrophotometric titration of the Er(III)–EDTA 1 : 1 complex with the carbonate at pH ∼ 7.5 was performed (Fig. 4). Factor analysis²⁹ of the set of these spectra was used to determine the molar fractions of Er(III) complexes existing in solutions and consequently to calculate the conditional stability constants β_(A) (eqn (3)). The appropriate dependence needed for β_(A) calculation is derived in Table S4 in the ESI† and the retrieved spectra of both [Er(EDTA)(H₂O)₂]⁻ and [Er(EDTA)(CO₃)]^3– species are shown in Fig. S2 in the ESI.† The determined value of log β_(A) is 3.66 ± 0.07.

To study the influence of the solution pH on the binding of the carbonate anion with the Er(III)–EDTA complex the titration of the Er(III)–EDTA 1 : 1 complex with the carbonate under basic conditions (pH ∼ 12) was also performed. It should be noted that the spectra of the Er(III)–EDTA system under neutral and basic conditions in carbonate free solutions differ remarkably. It may be caused by the hydrolysis of the [Er(EDTA)(H₂O)₂]⁻ complex above pH > 9.³⁰ Therefore an additional spectrophotometric titration of the [Er(EDTA)(H₂O)₂]⁻ complex with KOH was performed (Fig. 5).

Fig. 5 Absorption spectra of the solutions of the Er(III)–EDTA 1 : 1 system at different pH (c_ErEDTA = 29.5 mM) (A); the [Er(EDTA)(H₂O)₃]⁻ complex in a Na[Er(EDTA)(H₂O)₃]·5H₂O crystal – Ib (B).

The band shape and intensity of ⁴I_15/2 → ²H_11/2 and ⁴I_15/2 → ⁴S_3/2 transitions are almost the same in solutions at pH between 4 and 8. The predominant solution species under these conditions is [Er(EDTA)(H₂O)₂]⁻.⁵ Above pH > 8 considerable changes of the spectral patterns of ⁴I_15/2 → ²H_11/2 and ⁴I_15/2 → ⁴S_3/2 transitions are observed. Interestingly the final spectra of strongly basic solutions become more similar to those of the nine-coordinate [Er(EDTA)(H₂O)₃]⁻ complex in a Na[Er(EDTA)(H₂O)₃]·5H₂O crystal⁵ (hereinafter referred to as Ib) for which the UV-vis spectrum is also presented in Fig. 5, for comparison purposes. The resemblance of the spectra for both systems may suggest certain structural similarities of both complexes. It is particularly well observed in the spectra of the ⁴I_15/2 → ⁴S_3/2 transition which is very sensitive to the changes of the coordination number, as shown previously.⁵ As the pH value of the solution increases the additional peaks appear with the positions similar to those observed in the spectra of the nine-coordinate [Er(EDTA)(H₂O)₃]⁻ complex in crystal Ib. The observed hypsochromic shift of the highest-energy CF components of the ⁴I_15/2 → ⁴S_3/2 transition in the spectra of Er(III)–EDTA solutions under basic conditions in comparison with those at neutral pH, may suggest the changes of the coordination sphere of the Er(III) ion due to the formation of the hydrolyzed complex according to the simplified equation

However, it should be noted that there is no convincing evidence for CN changes, except that obtained from the kinetic study results of the hydrolysis of a Yb–EDTA system.^30c

To describe reaction (2) qualitatively, the factor analysis of the ⁴I_15/2 → ²H_11/2 and ⁴I_15/2 → ⁴S_3/2 spectra was performed assuming two principal equilibrium species: [Er(EDTA)(H₂O)₂]⁻ and [Er(EDTA)(OH)(H₂O)₂]^2–. The retrieved spectra of both species are shown in Fig. S3 in the ESI.† Because of the high thermodynamic stability of the Er–EDTA complex (log β_ErEDTA = 18.85 at μ_KNO3 = 0.1 M,³¹ log β_ErEDTA = 17.45 ± 0.06 at μ_NaClO4 = 0.5 M)³² the concentrations of uncomplexed Er(III) and EDTA ions were neglected. The solutions under conditions under study were homogenous (no precipitate was formed). A speciation diagram, i.e. the molar fraction of the Er(III) species as a function of pH, is shown in an inset in Fig. 5. As is seen from this diagram, in solutions at the pH range between 6 and 9 the [Er(EDTA)(H₂O)₂]⁻ complex is the predominant species. Above pH > 9 this complex starts to hydrolyse forming the [Er(EDTA)(OH)(H₂O)₂]^2– species. At pH ∼ 10.6 the concentrations of both [Er(EDTA)(H₂O)₂]⁻ and [Er(EDTA)(OH)(H₂O)₂]^2– complexes are equal, and above this pH the hydrolysed complex begins to dominate. The obtained species concentrations were used to determine the hydrolysis constant β_OH from eqn (5) of reaction (4):

The final values of log β_OH determined on the basis of spectroscopic and potentiometric titrations are 3.40 ± 0.16 and 3.56 ± 0.21, respectively. These values are slightly higher in comparison with those obtained for the other Ln(III)–EDTA systems using other physical methods.³⁰ The differences seem to be caused by the ionic medium effect as the presented results were obtained at a relatively high ionic strength (μ_KCl = 3.5 M).³³ Because log β_(A) = 3.66 ± 0.07 and log β_OH = 3.40 ± 0.16 are very similar, the competition between carbonate anion and OH⁻ binding by the [Er(EDTA)(H₂O)₂]⁻ complex is likely to arise. Thus under basic conditions (pH > 10.6) in the presence of carbonate anions the following reaction (6) should be expected. Reaction (6) is described using the formation constants β_(B) (eqn. (7)).

Because the molar fractions of the [Er(EDTA)(CO₃)]^3– and [Er(EDTA)(OH)(H₂O)₂]^2– species are controlled by the concentrations of CO₃^2– and OH⁻ anions, the spectrophotometric and pH measurements were performed simultaneously. The determined value of log β_(B) was 0.20 ± 0.12. It is worth noting that the calculated value of log β_(B) = log β_(A) − log β_OH is equal to 0.26, and both log β_(B) values, although obtained from the independent set of data, are in very good agreement. As is seen, the β_(A) value is about three orders of magnitude larger than the β_(B) one. It means that the carbonate anion substitutes water molecules more efficiently than the hydroxy anion. The latter is more strongly attracted by the Ln(III) cation than neutral H₂O molecules. The determined log β_(A) value is comparable to that estimated for the Am(III)–EDTA–carbonate system for which the latter value was between 3 and 4.¹⁶ On the other hand it is significantly larger than 0.74 reported for the [Er(EDTA)(CO₃)]^3– complex in ref. 13. This underestimation of log β_(A) = 0.74 is likely due to the simplified model used for the description of reaction (1).

Because the geometries of the [Er(EDTA)]⁻ moiety in crystals I and Ia are very similar, the substitution of H₂O molecules by the CO₃^2– anion (reaction (2)) is due to the changes of the Er–coligand interactions only. Thus the bond energies of Er–OH₂ and Er–O(carbonate) (hereinafter referred to as E_Er–L) may be estimated from eqn (8) and (9), respectively.

where N_a is the Avogadro constant; |z_±| denotes the charge numbers with z₊ = +3 and z₋ = –⅔; e is the charge of the electron; μ is the dipole moment of water; ε and ε₀ are the dielectric permittivities of water and vacuum; and r is the Er–L bond length.

All the used quantities are presented in Table S5.† The bond energy change calculated in this way is defined as ΔE_Er–L = E_{Er–O(carbonate)} − E_Er–OH2 and is equal to −22.1 kJ mol⁻¹. The changes of the Th–L bond energy (ΔE_Th–L) values for the hypothetical reactions (10) and (11) calculated in the same way are equal to −29 kJ mol⁻¹ and −58 kJ mol⁻¹, respectively.

Although the presented model of the estimation of the M–L bond energy is simplified, as it does not take into account the covalent contribution to the M–L bonds,³⁴ the obtained values may indicate that the Ln(III)–L bond energy is lower than the An(IV) one; moreover they may suggest that the dicarbonato [Th(EDTA)(CO₃)₂]^4– complex should be more stable than the monocarbonate [Th(EDTA)(CO₃)(H₂O)₂]^2– species.

The speciation curves for the Er–EDTA–carbonate 1 : 1 : 1 system are presented in Fig. 6. The formation of [Er(EDTA)(CO₃)]^3– starts under slightly acidic conditions and it is the most stable species at pH 10. Above pH > 10 the binding of the carbonate anion competes with OH⁻ anion coordination.

Fig. 6 Speciation diagram of the Er–EDTA–carbonate 1 : 1 : 1 system. c_Er = 50 mM.

To obtain a more comprehensive picture of the substitution of H₂O/OH⁻ ligands by carbonate anions, a study of the temperature effects on the stability of ternary complexes is required. Therefore reactions (2) and (6) were studied at elevated temperatures.

Thermodynamic description of [Er(EDTA)(CO₃)]^3– complex formation

Due to the low thermal stability of the carbonate/bicarbonate solutions, the reactions of (2) and (6) were studied in the temperature range between 283 and 333 K only.³⁵ Because reactions (2) and (6) are pH dependent, the spectrophotometric and potentiometric measurements were performed simultaneously at a given temperature.

The spectra of Er–EDTA–carbonate 1 : 1 : 1 systems at pH ∼ 7.4 and ∼12.6 were measured at different temperatures between 283 and 333 K and are presented in Fig. S3 in the ESI.† It should be noted that the absorption spectra of the ⁴I_15/2 → ²H_11/2 and ⁴I_15/2 → ⁴S_3/2 transitions of solutions at pH around 12 are more temperature-sensitive than those at pH 7.4. It is likely connected with the change of the CN of the Er(III) ion in complexes under study under more basic solutions. The factor analysis of these spectra enabled us to determine the molar fractions of the Er(III) species in solutions under study at elevated temperatures. The combined glass electrode with a built-in temperature sensor was used to measure the pH of solutions at different temperatures.

To calculate the ΔG values of reactions (2) and (6), the values of the ionic product of water (K_w) and the dissociation constants of carbonic acid K₁ and K₂ at various temperatures are also needed. The pK_w values³³ and the corresponding values of pK₁, pK₂ at μ_KCl = 3.5 M at a given temperature, which were calculated from the empirical model given in ref. 36 are presented in Table S6 in the ESI.† The obtained data sets of the molar fractions of the Er(III) and carbonate species with the calculated ΔG values at a given temperature and pH of the solution are compiled in Table S7.†

To enhance the obtained thermodynamic results, the temperature dependent ¹³C NMR spectra of Er(III)–EDTA–carbonate 1 : 1 : 1 solutions containing ¹³C enriched carbonate anions were measured at elevated temperature. It is known that the comparison of the intensities of carbon signals in the spectra of organic compounds is not recommended because of the low concentration of the ¹³C isotope in natural samples and different ordering of carbon atoms. Due to the same order of carbon atoms in bound and unbound carbonate species and the high concentration of the ¹³C isotope in the systems under study, the comparison of the intensities of the ¹³C NMR signals is justified.

Because of the low stability of the carbonate/bicarbonate solutions at pH ∼ 7 at elevated temperatures, only the ¹³C NMR spectra of the solutions at pH ∼ 12.4 could be recorded. Two ¹³C signals attributed to the bound (∼50 ppm) and unbound (∼160 ppm) CO₃^2– anions were observed in the ¹³C NMR spectra, in which the intensity and position change with the temperature. The main conclusion that could be drawn from the ¹³C NMR spectroscopy data is that the formation of the ternary [Er(EDTA)(CO₃)]^3– complex is more favorable at higher temperatures. Unfortunately due to experimental difficulties it was not possible to measure the pD of solutions under study at different temperatures. Thus, only the molar fractions of bound and unbound carbonate species could be determined. The ratios of the molar fractions of the Er(III) species derived from the ¹³C NMR and UV-vis spectroscopy results calculated in this way are compiled in Fig. 7.

Fig. 7 The ratio of the molar fractions of the Er(III) species, derived from the ¹³C NMR and UV-vis spectroscopy results.

As seen in this figure the results obtained from both independent and compatible techniques are in very good accordance. The ¹³C NMR spectroscopy results are described and discussed in more detail in the Appendix.

By plotting ΔG versus temperature (Fig. 8) it was possible to determine the ΔH and ΔS of reactions (2) and (6). The determined values of the thermodynamic functions are provided in Table 3.

Fig. 8 ΔG of reactions (2) – top and (6) – bottom, plotted as a function of temperature. The red lines are linear regression lines through the experimental data (black squares).

Table 3 Thermodynamic parameters determined for reactions (2) and (6)

Reaction	ΔH/kJ mol^−1	ΔS/J mol^−1 K^−1
(2)	−2.8 ± 0.8	62 ± 3
(6)	28.1 ± 4.6	92 ± 15

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As is seen, reaction (2) is slightly exothermic while reaction (6) is endothermic.

The replacement of H₂O molecules by the carbonate anion is mainly entropy driven, although the formation of the [Er(EDTA)(CO₃)]^3– complex may be additionally enthalpy stabilized due to stronger electrostatic interactions of highly negatively charged oxygen carbonate atoms than neutral water molecules with Er(III) cations.

Because there is a lack of knowledge regarding thermodynamic data of carbonate binding by Ln(III) in general, we have referred the obtained data to those for the [Eu(CO₃)]⁺ and [Eu(CO₃)₂]⁻ systems, only. The enthalpy of formation of the [Eu(CO₃)]⁺ and [Eu(CO₃)₂]⁻ complexes are slightly positive and equal to 6.8 ± 2 kJ mol⁻¹ and 7.5 ± 3 kJ mol⁻¹, respectively.³⁷ The enthalpy of reaction (6) is large and positive, as much more energy is needed to substitute the OH⁻ anion than the H₂O molecule, by the CO₃^2– anion. Moreover this reaction is probably accompanied by a decrease of the coordination number from nine to eight. Such a decrease of the CN connected with the dissociation of water molecule(s) is usually endothermic for the other lanthanide systems.^11,38 Both reactions are strongly entropy driven, resulting in the release of H₂O/OH⁻ ligands from the first coordination sphere of Er(III) and dehydration of carbonate anions. It is likely that the enthalpy changes reflect mainly the Er–L bond formation, while entropy changes are caused by disordering of the bulk solution “structure”. The other factor stabilising ternary eight coordinate [Er(EDTA)(CO₃)]^3– complexes is the spatial fitting of the planar bidentate CO₃^2– anion to the coordination vacancies arising from the dissociation of H₂O/OH⁻ ligands.

Conclusions

The presented results are the first example of the thermodynamic description of carbonate ternary complex formation that was additionally structurally supported.

The novel [C(NH₂)₃]₃[Er(EDTA)(CO₃)]·H₂O I and [C(NH₂)₃]₄[Th(EDTA)(CO₃)₂]·5H₂O (II) compounds containing ternary [M(EDTA)(CO₃)_n]^m− complexes were structurally characterized for the first time. In the eight coordinate [Er(EDTA)(CO₃)]^3– complex Er(III) is surrounded by six donor atoms (O₄N₂) from the EDTA ligand and two oxygen atoms from the bidendate carbonate anion. In the ten coordinate [Th(EDTA)(CO₃)₂]^4– complex the EDTA ligand is bonded with Th(IV) in the same fashion as in [Er(EDTA)] systems, and the remaining four coordination sites are occupied by two bidendate carbonate anions. The increase of the oxidation state of the central metal cation from +3 to +4 is probably the main reason for the increase of the coordination number from 8 to 10, respectively.

The structural and UV-vis-NIR results of [C(NH₂)₃]₃[Er(EDTA)(CO₃)]·H₂O (I), [C(NH₂)₃]₂[Er(EDTA)(H₂O)₂]ClO₄·6H₂O (Ia) and Na[Er(EDTA)(H₂O)₃]·5H₂O (Ib) were used as the model data to study carbonate binding with the Er(III)–EDTA complex and the hydrolysis reaction of the latter one in aqueous solutions.

Formation of the ternary [Er(EDTA)(CO₃)]^3– complex under different conditions (pH and temperature) was examined by UV-vis and NMR spectroscopy as well as by potentiometry. The equilibrium constant for reaction (A): [Er(EDTA)(H₂O)₂]⁻ + CO₃^2– ⇄ [Er(EDTA)(CO₃)]^3– + 2H₂O was determined to be log β_(A) = 3.66 ± 0.07. For the reaction that occurs in more basic solutions (B): [Er(EDTA)(OH)(H₂O)₂]^2– + CO₃^2– ⇄ [Er(EDTA)(CO₃)]^3– + 2H₂O + OH⁻, the corresponding log β_(B) value was found to be 0.20 ± 0.12. It was also observed that the hydrolysis reaction [Er(EDTA)(H₂O)₂]⁻ + OH⁻ ⇄ [Er(EDTA)(OH)(H₂O)₂]^2– is likely to accompany with the increase of the coordination number of Er(III) from eight to nine. The determined value of log β_OH is equal to 3.40 ± 0.16.

The temperature dependence of log β_(A) and log β_(B) allowed us to determine the enthalpy and entropy of both (A) and (B) reactions, which were found to be ΔH_(A) = −2.8 ± 0.8 kJ mol⁻¹, ΔS_(A) = 62 ± 3 J mol⁻¹ K⁻¹ and ΔH_(B) = 28.1 ± 4.6 kJ mol⁻¹, ΔS_(B) = 92 ± 15 J mol⁻¹ K⁻¹. The obtained data indicate that the carbonate anion readily displaces H₂O than the OH⁻ ligand.

The formation of stable Ln(III)–EDTA–carbonate complexes at physiological pH is probably one of the reasons why Gd(III)–EDTA complexes could not be used as MRI contrast agents, as the high relaxivity of this complex is substantially reduced in the presence of carbonate anions.¹⁵ It may be expected that the other chelate complexes with two inner-sphere water molecules should also strongly interact with carbonate anions, due to spatial fitting of the carbonate ligand to the coordination vacancy that is formed as a result of water molecule dissociation.

The presented results are particularly important for the study and prediction of the environmental An(III)/An(IV)–EDTA mobility process. The binding of carbonate ligands with the An–EDTA moiety due to the formation of stable ternary [An(EDTA)(CO₃)]^3– and [An(EDTA)(CO₃)₂]^4– complexes may certainly inhibit the hydrolysis of the An(III)/An(IV)–EDTA species to sparingly soluble hydroxo/oxo compounds. This, in turn, may enhance the mobility of trivalent and tetravalent actinides in the environment.

Experimental

Materials and sample preparation

Stock solutions of erbium chloride and erbium perchlorate were prepared by dissolving Er₂O₃ (99.9%, MERCK) in 2 M hydrochloric or chloric(VII) acids, respectively. The metal concentration was determined complexometrically by using xylenol orange as an indicator.

Equimolar amounts of ErCl₃ solution (6 mmol) and solid H₄EDTA (98%, MERCK; 6 mmol) were mixed together and heated at 90 °C (±5 °C) until the precipitate was dissolved. Next, the solid [C(NH₂)₃]₂CO₃ (Aldrich) (30 mmol) was added to the solution to adjust the pH to ∼11. Large pink crystals of [C(NH₂)₃]₃[Er(EDTA)(CO₃)]·H₂O (I) were formed after one weak.

In a similar way the crystals of the [C(NH₂)₃]₄[Th(EDTA)(CO₃)₂]·5H₂O (II) compound were obtained, but as a starting compound Th(NO₃)₄·5H₂O (Serva Heidelberg) was used. The crystals of [C(NH₂)₃]₂[Er(EDTA)(H₂O)₂]ClO₄·6H₂O (Ia) and Na[Er(EDTA)(H₂O)₃]·5H₂O (Ib) were prepared according to the procedure described in ref. 5.

The solutions of Er(III)–EDTA systems used for spectroscopic measurements were prepared in deionised water with a specific conductivity of 0.05 μS cm⁻¹. The concentration of Er(III) was 0.025–0.055 M. The ionic strength of the solution was adjusted with KCl to μ = 3.5 M.

For NMR spectroscopic measurements solutions of the Er(III)–EDTA–carbonate 1 : 1 : 1.4 systems were prepared at concentrations of [ErEDTA] and [CO₃^2–] equal to 0.049 M and 0.067 M, in D₂O solution (μ_KCl = 3.5 M). For this experiment an isotopically enriched ¹³C (99%) NaH¹³CO₃ sample (Cambridge Isotope Laboratories) was used. The final pD = 12.4 of the solution was adjusted with KOD. NMR spectra were recorded with an AMX Bruker 300 MHz NMR spectrometer.

Temperature dependent measurements

For all samples the temperature was increased from 283 K to 333 K in steps of 10 K. At each temperature the sample was equilibrated for 15 min before an absorption UV-vis-NIR spectrum was recorded. No change of the spectra was observed after this time, proving that the thermodynamic equilibrium was reached.

The pH of solutions at elevated temperatures was measured using a micro-combination pH electrode InLab Micro Pro-ISM (Mettler Toledo) with an integrated temperature sensor.

The standard solutions used for electrode calibration were prepared according to UPAC and NIST recommendations.^39,40 The pure materials with indicated weights were dissolved in water with a specific conductivity 0.05 μS cm⁻¹ at 25 °C.

Recommended pH (at 298 K)	7.41	10.12	12.45
Composition	0.025 M KH2PO4 0.025 M Na2HPO4	0.025 M NaHCO3 0.025 M Na2CO3	Ca(OH)2 (saturated at 298 K)

Electronic absorption spectra were recorded with a Cary 5000 UV/Vis/NIR spectrophotometer. The spectra of crystals were measured at different temperatures (298 K and 4.2 K) in a continuous flow helium cryostat (Optistat, Oxford). The spectra of solutions were measured in a home-made thermostated appliance. The experimental oscillator strengths (P_exp) were determined by using eqn (12):

where c is the concentration of the Er(III) ion in M, d is the length of the optical path in cm and A(v̄) is the absorbance as a function of the wavenumber in cm⁻¹. The experimental P values were used for the calculation of phenomenological Ω_λ intensity parameters according to the Judd–Ofelt^26,27 relationship:where P_ED is the oscillator strength of the electric dipole transition, χ = (n² + 2)²/9n; n is the refractive index (n = 1.5 for crystals and n = 1.33 for solutions), m is the electron mass, c is the speed of light, v̄ is the wavenumber of the band maximum in cm⁻¹, h is the Planck's constant, J is the ground state quantum number, and |〈ψ′J′||U^(λ)||ψJ〉| are the reduced matrix elements of the respective unit tensor operator U^(λ). The 〈ψ′J′||U^(λ)||ψJ〉² = U(λ) values were taken from the paper of Carnall et al.⁴¹

The accuracy of the intensity parameter fitting was determined by the root mean square deviation (rms) using the following equation:

where P_calc is the oscillator strength calculated from eqn (13), n is the number of absorption bands and 3 indicates the number of fitting parameters (Ω₂, Ω₄, and Ω₆).

Factor analysis was performed according to the procedure described in ref. 29.

Crystal structure determination

Suitable crystals were cut from larger ones, mounted on a Kuma KM4 diffractometer equipped with a CCD counter and measured at 100 K. The structures were solved routinely by using Patterson synthesis. The C- and N-bonded hydrogen atoms were placed in positions calculated from the geometry, and those bonded to O atoms were found from the difference Fourier maps, but not all were found. The final refinement was anisotropic for all non-H atoms. The computations were performed with the SHELXS97⁴² and SHELXL⁴³ programs, and the molecular graphic was prepared with DIAMOND.⁴⁴

C ₁₄ H ₃₂ ErN ₁₁ O ₁₂ (I), M = 713.76, monoclinic, space group P2₁/n, Z = 4, a = 14.749(3), b = 10.683(2), c = 15.594(3) Å, β = 92.30(2)°, V = 2455.2(1) ų, μ = 3.50 mm⁻¹, D_c = 1.931 g cm⁻³, F(000) = 1428, crystal size = 0.31 × 0.20 × 0.07 mm, θ = 3–28°, index ranges: −19 ≤ h ≤ 13, −13 ≤ k ≤ 14, −20 ≤ l ≤ 20. Final R indices R_int = 0.038, R[F² > 2σ(F²)] = 0.039, wR(F²) = 0.105, S = 1.04. Largest diff. peak and hole: 2.15 and −1.21 e Å⁻³.

C ₁₆ H ₄₆ N ₁₄ O ₁₉ Th (II), M = 970.71, monoclinic, space group P2₁/c, Z = 4, a = 18.825(4), b = 8.827(1), c = 21.845(4) Å, β = 104.50(2)°, V = 3401.3(1) ų, μ = 4.48 mm⁻¹, D_c = 1.869 g cm⁻³, F(000) = 1928, crystal size = 0.41 × 0.35 × 0.03 mm, θ = 3–28°, index ranges: −18 ≤ h ≤ 23, −11 ≤ k ≤ 11, −26 ≤ l ≤ 28. Final R indices R_int = 0.043, R[F² > 2σ(F²)] = 0.041, wR(F²) = 0.101, S = 0.99. Largest diff. peak and hole: 3.26 and −1.90 e Å⁻³.

CCDC 1870488 and 1870487 for I and II contain the supplementary crystallographic data for this paper.

Conflicts of interest

There are no conflicts to declare.

Appendix

In order to examine the influence of the temperature on the formation of the [Er(EDTA)(CO₃)]^3– complex the ¹³C NMR spectra were measured at elevated temperatures. The solutions under study contained isotopically enriched ¹³C carbonate anions. The ¹³C labelling allowed shorter acquisition times which is remarkable in comparison with samples containing natural carbonates. Because the EDTA was not ¹³C enriched the ¹³C NMR signals attributed to this ligand were not observed in the experiment. Consequently only two signals of carbonate species attributed to the bound (∼50 ppm) and unbound (∼160 ppm) CO₃^2– anions were observed in the spectrum of Er–EDTA–carbonate 1 : 1 : 1 systems at different temperatures (Fig. 9).

Fig. 9 ¹³C NMR spectra of the Er–EDTA–carbonate system at different temperatures. [ErEDTA] = 49.1 mM, [CO₃^2–] = 67.6 mM, pD = 12.4.

The observed temperature line broadening is caused by the increase of dynamic effects of carbonate exchange. A similar effect was observed for the other AnO₂²⁺–carbonate systems (where An = U, Pu, and Np).⁴⁵ With the increase of the temperature, the signal at ∼50 ppm is gradually shifted to lower fields and its total intensity increases in comparison with the signal at 168 ppm. This indicates that the formation of the ternary [Er(EDTA)(CO₃)]^3– complex is more favorable at higher temperatures. Unfortunately due to experimental difficulties it was not possible to measure the pD of solutions under study at different temperatures. Thus, only the molar fractions of bound and unbound carbonate species could be determined from the intensity ratios of the ¹³C NMR peaks.

Acknowledgements

This work has been supported by the Program Operacyjny Kapitał Ludzki, Uniwersytet Wrocławski, POKL.04.01.01-00-054/10-00.

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Footnote

† Electronic supplementary information (ESI) available: Selected crystal data and structure refinement for I and II as well as spectroscopic and thermodynamic data. CCDC 1870487 and 1870488. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c8qi01062e

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