Stoichiometry of lanthanide(III) complexes with tripodal aminophosphonic ligands – a new solution to an old problem

Abstract

The Eu³⁺ and Gd³⁺ complexes with an N-(methylene-2-pyridine)-N,N-di(methylenephosphonate) ligand (H₄NP₂py), an analogue of nitrilotri(methylphosphonic) acid (H₆NTP), were synthesized and structurally characterized by X-ray single crystal diffraction. The determined crystal structures ([C(NH₂)₃]₅[Ln(NP₂py)₂]·12H₂O) are the first example of a monomeric Ln³⁺ complex encapsulated by two tripodal aminophosphonic ligands. Each of the NP₂py anions coordinates to Ln³⁺ through two oxygen atoms from each monodentate phosphonic group, amine nitrogen and pyridine nitrogen atoms, filling thus 8 coordination sites of Ln³⁺. The luminescence properties of [C(NH₂)₃]₅[Eu(NP₂py)₂]·12H₂O crystals were studied and compared with those of Eu–NP₂py complexes in solution. Speciation analysis of Ln–NP₂py complexes (Ln : NP₂py = 1 : 2), performed by luminescence and potentiometric methods, showed that both [Ln(NP₂py)]⁻ and [Ln(NP₂py)₂]⁵⁻ species may exist in solution. However, the formation of the latter one occurs in alkaline solutions at pH as high as 8. By implementing the Specific Ion Interaction Theory (SIT) it was possible to calculate the thermodynamic stability constants of the [Eu(NP₂py)]⁻ and [Eu(NP₂py)₂]⁵⁻ complexes. The corresponding log β⁰_Eul and values are 16.3 ± 0.11 and 19.5 ± 0.15, respectively.

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Introduction

The chemistry of metal-phosphonates has attracted increasing attention over the last few decades due to the variety of properties that can be introduced via a phosphonic moiety.¹ (Poly)aminopolyphosphonates are very strong complexing agents for alkaline earth, transition and rare earth metal ions.² Owing to the high basicity of the oxygen atoms,^3,4 phosphonates interact with cations more strongly than their carboxylic analogues and are able to create more stable complexes.^5,6 Phosphonate complexes with luminescent, paramagnetic lanthanide ions^7,8 play a significant role as promising phosphors for new technologies and potential contrast agents in magnetic resonance imaging (MRI)⁹ as well as paramagnetic shift reagents for biologically important cations (e.g. Na⁺).¹⁰ Owing to its good pharmacokinetics, biodistribution and bone-seeking properties the ¹⁵³Sm-EDTP complex,^1a,6e–h known as QUADRAMET®, was approved by the US FDA for use of painful skeletal metastases in humans.^1d,11

In general, polyaminopolyphosphonic acids are the analogues of the nitrilotris(methylenephosphonic) acid (hereinafter referred to as NTP). To date the NTP ligand has found many applications¹² driven in many cases by coordination properties of this ligand in Ln³⁺ complexes.¹³ Because the majority of its applications are related to the NTP properties in aqueous solution, it seems particularly important to study its properties in this medium. However, the formation of the Ln³⁺ complexes with ligands of the NTP type in solution remains still not fully understood. For example it is unclear whether bis(nitrilotris(methylenephosphonato))lanthanide complexes are formed in solution at all.^14–16 Moreover no crystal structures of monomeric Ln³⁺ complexes with tripodal aminophosphonic ligands have been reported so far. The high negative charge of the NTP ligand (−6) and the presence of rather bulky phosphonic groups are probably the main factors destabilizing the [Ln(NTP)₂]⁹⁻ complexes in solution.

The aim of this paper is to study the chemical properties of a modified NTP ligand – N-(methylene-2-pyridine)-N,N-di(methylenephosphonic) acid (hereinafter referred to as NP₂py – Scheme 1) to establish finally whether, [Ln(NP₂py)₂]⁵⁻ complexes may be indeed formed in solution.¹⁷

Scheme 1 Chemical structure of N-(methylene-2-pyridine)-N,N-di(methylenephosphonis acid) – H₄NP₂py.

We have focused our attention on the stoichiometry and stability of species in the solution of the Ln–NP₂py system by implementing various physical methods such as X-ray crystallography, luminescence spectroscopy, potentiometry as well as a theoretical approach based on Specific Ion Interaction Theory (SIT).¹⁸ Because coordination of aminopolyphosphonates to Ln³⁺ cations has not been completely clear, we believe that the presented data may be helpful in understanding the interaction of this important class of ligands with lanthanide ions in solution, in general.

Results and discussion

Crystal structures

The crystal structures of compounds of the following formula [C(NH₂)₃]₅[Ln(NP₂py)₂]·12H₂O (Ln = Eu or Gd) were determined. The crystals of both compounds are isostructural and belong to the P1̄ space group. The asymmetric unit comprises one [Ln(NP₂py)₂]⁵⁻ complex anion, five guanidinium cations out of which one is disordered and twelve water molecules out of which two are disordered. The monomeric [Ln(NP₂py)₂]⁵⁻ complex anions are completely deprotonated and their negative charge is compensated by [C(NH₂)₃]⁺ cations.

Two anionic [NP₂py]⁴⁻ ligands are bound to the Ln³⁺ cation. Each of them is linked with the Ln³⁺ by two oxygen atoms from both monodentate phosphonic groups, one tertiary nitrogen atom and one pyridine nitrogen atom, filling thus four coordination sites of the Ln³⁺ cation. The molecular structure of the [Eu(NP₂py)₂]⁵⁻ complex is presented in Fig. 1. The selected Ln–L bond lengths are presented in Table 1.

Fig. 1 Molecular structure of the [Eu(NP₂py)₂]⁵⁻ complex; the H atoms are omitted for clarity.

Table 1 Selected Ln–L bond lengths in Å

Bond lengths	Eu	Gd
Ln–O21	2.315(2)	2.308(5)
Ln–O13	2.337(2)	2.328(5)
Ln–O15	2.319(2)	2.316(5)
Ln–O24	2.353(2)	2.347(5)
Ln–O (aver.)	2.331(18)	2.325(17)
Ln–N12(am)	2.770(3)	2.764(7)
Ln–N21(am)	2.751(3)	2.744(7)
Ln–N (am aver.)	2.761(13)	2.754(14)
Ln–N11(py)	2.596(3)	2.592(7)
Ln–N22(py)	2.657(3)	2.634(6)
Ln–N (py aver.)	2.626(43)	2.613(29)

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As is seen the Eu–L and Gd–L bond lengths are similar within the error of bond length estimation. The Ln–L bond lengths increase in the order Ln–O < Ln–N_(py) < Ln–N_(am) which reflects the sequence of ligand donor properties.¹⁹

The coordination polyhedron of the Ln³⁺ cation may be described as a distorted prism (Fig. 2). The Ln³⁺ cation lies in the general position, but the approximate symmetry of the complex anion is C_i, as shown in Fig. 2.

Fig. 2 The coordination polyhedra of Eu³⁺ in the [Eu(NP₂py)₂]⁵⁻ complex anion.

The [Ln(NP₂py)₂]⁵⁻ complexes are held together by a network of hydrogen bonds and electrostatic interactions. Owing to the high negative charge of the anionic [Ln(NP₂py)₂]⁵⁻ complex the distance between the neighbouring anions is large and the anionic complexes are well separated from each other; the shortest Eu⋯··Eu’ and Gd⋯··Gd’ distances are 10.47(7) Å and 10.37(7), respectively.

Luminescence spectra of the [C(NH₂)₃]₅[Eu(NP₂py)₂]·12H₂O crystal

Out of Ln³⁺ the Eu³⁺ f–f transitions are characterized by a simple and informative spectral pattern that is why we have chosen this cation for detailed spectroscopic studies.

The luminescence spectra of the [C(NH₂)₃]₅[Eu(NP₂py)₂]·12H₂O crystal were observed when the Eu³⁺ was excited into f–f transitions as well as into ligand states. The luminescence excitation spectrum of the crystals under study is presented in Fig. 3.

Fig. 3 Luminescence excitation spectrum (λ_em = 592.35 nm) of the [C(NH₂)₃]₅[Eu(NP₂py)₂]·12H₂O crystals.

Narrow peaks attributed to the f–f transitions of the Eu³⁺ and broad band of the ligand (¹π → ¹π*, ¹n → ¹π*) are observed in the spectrum. The presence of the latter band indicates that the energy transfer from the ligand to the Eu³⁺ states occurs. The luminescence spectrum of the [C(NH₂)₃]₅[Gd(NP₂py)₂]·12H₂O complex indicates that the position of the triplet state of the ligand is centered at ∼437 nm, Fig. 1S.† ²⁰ The luminescence spectrum of the [C(NH₂)₃]₅[Eu(NP₂py)₂]·12H₂O crystal excited into the ligand band is shown in Fig. 4. The emission intensities of the ⁵D₀ → ⁷F_J transitions in relation to the ⁵D₀ → ⁷F₁ one are also included in this figure.

Fig. 4 Luminescence spectrum of the crystal under study (λ_ex = 276 nm).

Five bands attributed to the electronic transitions from the excited ⁵D₀ to the lower lying ⁷F_0,1,2,3,4 states are observed in the spectrum. All these transitions are induced electric dipole (ED) transitions, except for the ⁵D₀ → ⁷F₁, which is of magnetic dipole (MD) character. Thus the ⁵D₀ → ⁷F₁ transition may be used as a reference since its intensity does not depend on the chemical surrounding of Eu³⁺.²¹ The ⁵D₀ → ⁷F₀ and ⁵D₀ → ⁷F₃ transitions are forbidden due to the selection rules. For this reason, the intensities of these transitions are usually very low as compared with those of ⁵D₀ → ⁷F_1,2,4 transitions. Since the ground ⁷F₀ and the emitting ⁵D₀ states are nondegenerate, the ⁵D₀ ↔ ⁷F₀ transitions consist of a single unsplit line for the given Eu³⁺ surrounding. Therefore there is a one to one correspondence between the number of lines in the spectrum of this transition and the number of chemically distinct environments of the Eu³⁺ ion. The energy levels of the ⁷F_1,2,3,4 multiplets and their crystal field (e) as well as vibronic (v) components found in the RT spectra are presented in Table 2.

Table 2 The energy of the crystal field and vibronic lines of the selected multiplets for the 4f⁶ configuration at RT. Δ_CFS is the energy difference between the highest and lowest CF components of the ^2S+1L_J multiplet

^2S+1LJ	E/cm^−1		^2S+1LJ	E/cm^−1
^7F1	180	e	^7F3	1800	e
	452	e		1880	e
	512	e		1979	v
Δ CFS	332			2131	e
			Δ CFS	331
^7F2	889	e	^7F4	2577	e
	919	e		2717	v
	967	v		2901	e
	1050	v		2935	e
	1145	v		3007	v
	1259	v		3064	e
	1287	v		3144	e
	1440	e		3256	e
	1585	v		3269	e
Δ CFS	550		Δ CFS	692

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Because ⁵D₀ → ⁷F_0,2,3,4 transitions are strictly forbidden in centrosymmetric systems, the presence of these transitions in the luminescence spectrum indicates that the C_i symmetry of the [Eu(NP₂py)₂]⁵⁻ complex in the crystal is approximate. The determined luminescence lifetime of the ⁵D₀ state at RT is 1840 μs.

The next step of our studies was the analysis of the spectroscopic properties of the Eu–NP₂py complex in aqueous solution.

Luminescence spectra of the Eu–NP₂py and Tb–NP₂py systems in solution

Ln–NP₂py complexes with the metal to ligand ratio 1 : 1. Taking into account Eu–L bond lengths it may be reasonably assumed that the encapsulation of the Ln³⁺ cation by the NP₂py ligand is achieved by the coordination of phosphonic and pyridine groups. The binding of the N(imino) atom to the Ln³⁺ is forced by the former ones. In this context, it seems to be important to indicate how the coordination of phosphonate and pyridine groups depends on the pH of a solution. In order to find the binding mode of the NP₂py ligand and the stoichiometry of the formed Ln–NP₂py species, the luminescence spectra of Eu–NP₂py and Tb–NP₂py complexes in aqueous solution were recorded. The selected luminescence spectra of the Eu–NP₂py complex at different pH are presented in Fig. 5.

Fig. 5 Luminescence spectra of the Eu–NP₂py complex (λ_ex = 393 nm, Eu : NP₂py = 1 : 1) in aqueous solution at different pH.

At pH 2.26 the intensity of the hypersensitive ⁵D₀ → ⁷F₂ transition (1.08) is similar to that of the magnetic dipole ⁵D₀ → ⁷F₁ transition and higher than the relative intensity for the aqua ion (0.68). The increase of pH brings about an increase of the relative intensity of the ⁵D₀ → ⁷F₂ transition from 1.08 (pH = 2.26) to 2.74 (pH = 10.5). It means that the NP₂py ligand starts to coordinate at pH ∼2.26. Under these conditions competing reactions undergo between the protonation and coordination of phosphonate groups to the Eu³⁺.

The protonation of the N_py atom at low pH prevents the Eu–N_py interaction and consequently may hinder the L–Eu energy transfer. Therefore the question arises whether the efficiency of an antenna effect as a function of pH may serve as a coordination probe for establishing the binding of pyridine to the Eu³⁺. In general the Tb³⁺ compounds are more convenient to study the energy transfer process in comparison with those of Eu³⁺ for which the ligand band may be imposed on the L–M charge transfer spectra of Eu³⁺.²² Accordingly, to find the pH range in which the coordination of the pyridyl group to the Ln³⁺ occurs, the luminescence spectra of the Tb–NP₂py complex at various pH with an excitation wavelength of 266 nm were recorded (Fig. 6). The oscillator strengths of the ¹π → ¹π*, ¹n → ¹π* transition calculated from absorption spectra versus pH are also presented in the insert of this figure.

Fig. 6 Luminescence spectra of the Tb–NP₂py 1 : 1 complex at different pH. The plot of the oscillator strengths of the ¹π → ¹π*, ¹n → ¹π* transition versus pH is shown in the insert.

As can be seen the largest increase of the luminescence intensity of all f–f transitions is observed between pH 3 and 5.5. Simultaneously the oscillator strength of the ligand band monotonically decreases. These results indicate that the changes of the efficiency of the antenna effect may be used to study the coordination modes of chromophore groups to the Tb³⁺. The determined values of luminescence quantum yields Φ_Tb3+ of the Tb : NP₂py 1 : 1 and 1 : 2 systems (Fig. 2S†) may confirm this conclusion.

It is also worth considering the changes of the energy of the ligand centered transitions, caused by coordination of the NP₂py ligand to the Tb³⁺ (Fig. 3S†). Because the ¹π → ¹π*, ¹n → ¹π* transitions are particularly sensitive to the interaction of the N pyridine atom with the metal cation, a remarkable bathochromic shift of the ligand band (∼550 cm⁻¹) is observed in the spectra of the Tb–NP₂py complex at pH above 6 as compared with the spectra of the free ligand (see Fig. 3S). The observed changes of the f–f and ligand bands above pH ∼ 3 support the conclusion that the coordination of the pyridyl group to the Tb³⁺ occurs at pH between 3.0 and 5.5. The coordination of the NP₂py ligand is completed above pH = 6.

Ln–NP₂py complexes with the metal to ligand ratio 1 : 2. The luminescence spectra of the Eu–NP₂py system with the Eu : L = 1 : 2 in solutions at different pH are presented in Fig. 7.

Fig. 7 Luminescence spectra of the crystal and solutions of Eu³⁺ : NP₂py = 1 : 2 and 1 : 1. The bands attributed to the [Eu(NP₂py)]⁻ species are marked with asterisks.

As can be seen in Fig. 7 the spectral pattern of f–f bands strongly depends on pH. A qualitative comparison between the spectra of the crystal and solutions of the Eu : NP₂py = 1 : 2 complex demonstrates that at pH = 10.5 [Eu(NP₂py)₂]⁵⁻ is a predominant species. As the pH decreases, the CF components of individual multiplets of the [Eu(NP₂py)₂]⁵⁻ complex vanish and below pH 8 they completely disappear. It may suggest that the formation of the [Eu(NP₂py)₂]⁵⁻ complex starts at pH ∼ 8. The presence of additional bands (marked with an asterisk in the spectra in Fig. 7) may indicate that the other species, different to that found in the crystal, also exist in solution.

Owing to the simplicity of the ⁵D₀ → ⁷F₀ spectrum it was used to monitor the changes in the nearest coordination sphere of the Eu³⁺ cation. The luminescence spectra of the ⁵D₀ → ⁷F₀ transition of solutions and the crystal are presented in Fig. 8.

Fig. 8 Luminescence spectra of the ⁵D₀ → ⁷F₀ transition of the Eu–NP₂py complexes in the crystal and in solutions at pH = 10.5.

Two well separated ⁵D₀ → ⁷F₀ peaks in the spectrum of the solution of the Eu : NP₂py = 1 : 2 system at pH 10.5 are observed. The comparison of the energy of these peaks with those in the crystal and the solution of Eu : NP₂py = 1 : 1 at pH = 10.5 enabled us to attribute the higher energy peak at 17 330 cm⁻¹ to the [Eu(NP₂py)₂]⁵⁻ species, while the lower energy peak centered at 17 286 cm⁻¹ to the [Eu(NP₂py)]⁻ species. Both ⁵D₀ → ⁷F₀ peaks are separated by 56 cm⁻¹. This difference is probably caused by the change of the number of donor atoms and/or number of water molecules coordinated to the Eu³⁺ (see section “Number of coordinated H₂O molecules to the Eu³⁺ cation” in the ESI†).

Quantitative analysis of the EuL + L ⇆ EuL₂ reaction. In the next step we focused our attention on a quantitative description of the reaction (1) expressed by the equilibrium constant K₁₂

[Eu(NP₂py)]⁻ + NP₂py⁴⁻ ⇆ [Eu(NP₂py)₂]⁵⁻ (1)

To determine the K₁₂ constant we used the method based on the fitting of the spectra of the crystals to those of solutions.²³ The spectrum of the crystal under study served us as a model of 1 : 2 species while the spectrum of Eu–NP₂py 1 : 1 at pH = 10.5 was used as the spectrum of a pure 1 : 1 complex. However owing to the dynamic effects,^23,24 the spectra of f–f transitions in the solution are broadened in comparison to the spectra of the crystal. For this reason the simulated spectra of the [Eu(NP₂py)₂]⁵⁻ species derived from the spectra of the crystal were artificially broadened. The equation that was used to calculate the simulated spectrum of the [Eu(NP₂py)₂]⁵⁻ species in solution is as follows:

where:

J _calc – intensity at a given value of λ;

z – the number of peaks for the given ⁵D₀ → ⁷F_J transition;

J _max – the maximum intensity of the peak;

λ _max – the wavelength of the peak maximum;

Δλ – the half-width of a peak;

A ₁₂ and B₁₂ are adjustable parameters connected with artificial broadening of bands.

The final set of parameters used to calculate the simulated spectrum of the [Eu(NP₂py)₂]⁵⁻ species is presented in Table 1S (ESI†). The simulated and experimental spectra of compounds under study are shown in Fig. 9.

Fig. 9 Simulated spectra of the [Eu(NP₂py)₂]⁵⁻ (red) and [Eu(NP₂py)]⁻ (blue) species. The fitted and experimental spectra of the Eu : NP₂py 1 : 2 system at pH 10.5.

Next, the simulated spectra of the ⁵D₀ → ⁷F_1,2,4 transitions were used to calculate the molar fractions χ of [Eu(NP₂py)]⁻ and [Eu(NP₂py)₂]⁵⁻ species (Table 3).

Table 3 Molar fractions χ of [Eu(NP₂py)]⁻ and [Eu(NP₂py)₂]⁵⁻ species in aqueous solution at pH = 10.5 determined from various ⁵D₀ → ⁷F_1,2,4 transitions

Transition	χ [Eu(NP2py)]−	χ [Eu(NP2py)2]^5−	log K12
^5D0 → ^7F1	25% ± 10%	75% ± 10%	4.2 ± 0.5
^5D0 → ^7F2	18% ± 10%	82% ± 10%	4.5 ± 0.5
^5D0 → ^7F4	15% ± 10%	85% ± 10%	4.6 ± 0.5
Average	19(5)	81(5)	4.4 ± 0.5

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The average molar fractions of [Eu(NP₂py)₂]⁵⁻and [Eu(NP₂py)]⁻ species are ∼81% and ∼19%, respectively. These results are consistent, within the error of experimental limits (±10%), regardless of the transition taken for the calculation. The estimated averaged value of log K_1–2 for the reaction (1) is about 4.4 ± 0.5.

It should be noted that the presented speciation analysis for the case of f-elements is not always feasible, because the complexes existing in equilibrium are usually characterized by similar spectral patterns as it was shown previously by Horrocks et al. for the case of lanthanide complexes with NTP.¹⁵

To support the presented results the analysis was extended by potentiometric measurements.

Potentiometric study

Protonation of the ligand. We performed potentiometric titrations of a free ligand in order to determine its acid–base properties. The fully protonated form of the H₄NP₂py possesses six dissociable protons [H₆L]²⁺ (see Fig. 6S†) two at each phosphonic group, one at the pyridine moiety and one on the central tertiary N amine atom. However, it was possible to determine only four protonation constants (K₁–K₄) because the K₅ and K₆ values corresponding to the dissociation of one proton from each of the PO₃H₂ groups can be determined only for solutions at pH below 2. This is beyond the available range for standard potentiometric titrations, and the log K₅ and log K₆ values were determined previously by the NMR method.¹⁷ Measurements in different ionic strengths (KCl): 0.075 M, 0.1 M, 0.2 M, 0.5 M, 1 M and 2 M were also performed. The calculated log K_n values are listed in Table 4.

Table 4 The protonation constants of H₄NP₂py in 25 °C in different ionic strengths and background electrolytes

	I [M]	log K1 (HL)	log K2 (H2L)	log K3 (H3L)	log K4 (H4L)
0.1	NaClO4	10.63(2)	6.74(6)	5.61(8)	2.23(9)
0.075	KCl	10.87(1)	6.55(2)	5.47(2)	2.17(2)
0.1	KCl	10.83(1)	6.61(2)	5.29(2)	1.60(6)
0.2	KCl	10.78(1)	6.41(2)	5.37(2)	2.00(3)
0.5	KCl	10.59(1)	6.27(2)	5.25(2)	1.60(6)
1	KCl	10.50(1)	6.17(2)	5.26(2)	2.01(4)
2	KCl	10.51(1)	6.19(2)	5.27(2)	1.60(8)

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The most basic constant log K₁ = 10.63(2) (Table 4) corresponds to the protonation of the nitrogen of the tertiary amino group and is two logarithmic units higher than that of H₆NTP acid.^14,25–27 The values of this constant for NTP, determined by potentiometric methods in 0.1 M ionic strengths in different electrolytes at 25 °C were found to be: 12.7(1),¹⁴ 12.8(2),²⁵ 12.20(6),²⁶ 12.5.²⁷ Such a decrease of the highest protonation constant of H₄NP₂py is clearly caused by substitution of one of the phosphonic groups by the pyridine moiety. The same phenomenon has been noticed by Kurzak et al.²⁸ in N-3-picolyliminodi(methylenephosphonic) acid (NP₃py); the log K value of the tertiary amine was found to be 10.40(1) in 0.2 M KCl. The following deprotonation steps of H₄NP₂py release the protons from both phosphonic groups; log K₂ = 6.74(4), log K₄ = 2.23(5) and the pyridine moiety; log K₃ = 5.61(4) (Table 4). Such deprotonation of H₄NP₂py is consistent with ³¹P NMR results¹⁷ and based on those data it was concluded that the third and fourth dissociation steps occur at pH between 2 and 3 (log K₄) and 4–7 (log K₃, log K₂) and deprotonation of phosphonic groups is completed at pH above 8.2. The observed changes for the chemical shifts of pyridyl protons suggested that deprotonation of pyridine nitrogen occurs between pH 5 and 6, thus the pK₃ value was assigned to pyridine nitrogen. This conclusion is confirmed by the observed changes in the UV-vis spectra of the NP₂py ligand. The spectrophotometric titration curve is shown in Fig. 10.

Fig. 10 Spectrophotometric titration curve of the NP₂py ligand.

As was mentioned above, the ¹π → ¹π* and ¹n → ¹π* band observed in the UV spectrum of the NP₂py ligand is particularly sensitive to the protonation of pyridine N (Fig. 3S†). A remarkable decrease of the ε value is observed between pH 5 and 7. This unequivocally confirms the attribution of log K₃ to the protonation of the pyridine moiety.

The minimalization of the sum equal to by using eqn (4) enabled us to determine the β_n values which are converted into K_n values (Table 5).

where:

ε _exp, ε_calc – experimental and calculated absorption molar coefficients (M⁻¹ cm⁻¹) at λ = 259.6 nm;

ε _L–ε_HnL – absorption molar coefficients of individual species;

β _n – cumulative protonation constant.

Table 5 The comparison of the protonation constants of the NP₂py ligand using different methods

	^31P NMR^17	UV-vis	Potentiometry
log K (HL)	10.9(9)	11.0(9)	10.63(2)
log K2 (H2L)	6.7(9)	6.6(9)	6.74(6)
log K3 (H3L)	5.5(9)	5.6(9)	5.61(8)
log K4 (H4L)	2.3(9)	2.7(9)	2.23(9)
log K5 (H5L)	0.98(5)	—	—
log K6 (H6L)	0.70(5)	—	—

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As is seen from Table 5 the values of the respective log K_n determined from different methods are the same, within the experimental error. Finally the calculated values of log K_n were used to determine the speciation distribution curve, which is presented in Fig. 6S.†

Formation constants. Potentiometric titrations of the Ln–NP₂py system (where Ln = Sm³⁺, Eu³⁺, Gd³⁺ and Tb³⁺) were performed in order to determine the stoichiometry and stability constants of the formed complexes. The potentiometric measurements were performed for two Ln : NP₂py molar ratios 1 : 1 and 1 : 2. The calculated stability constants of LnL = [Ln(NP₂py)]⁻ and LnL₂ = [Ln(NP₂py)₂]⁵⁻ complexes (at 25 °C, I_NaClO4 = 0.1 M) are collected in Table 3S† and selected values are shown in Table 6.

Table 6 The stability constants of Ln³⁺ complexes with the NP₂py ligand for Ln : NP₂py molar ratios of 1 : 1 and 1 : 2, at 25 °C, I = 0.1 mol dm⁻¹ (NaClO₄)

Ln : NP2py	1 : 1	1 : 2
	log βLnL	log βLnL	log βLnL2
Sm^3+	11.87(6)	11.83(5)	16.99(8)
Eu^3+	12.85(8)	12.85(6)	18.44(9)
Gd^3+	12.32(10)	12.45(6)	17.88(7)
Tb^3+	13.36(7)	13.47(10)	17.86(9)

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The species distribution curves are depicted in Fig. 7S.† The potentiometric measurements of Eu : NP₂py = 1 : 1 and 1 : 2 systems at different ionic strengths (KCl) were also performed and the determined stability constants are given in Table 4S.†

Based on potentiometric data it was possible to calculate log K₁₂ for reaction 2, which is equal to 5.27 and similar within the limit of experimental error to that estimated from the spectroscopic data (4.4 ± 0.5).

The determined stability constants for Eu–NP₂py systems were used to calculate the average ligand number (n̄) as a function of pH (Fig. 11). The data for the Eu–NTA (1 : 2) complex (where NTA is nitrilotriacetic acid) are also included in this figure for comparison purposes.^29a

Fig. 11 The average ligand number n̄ as a function of pH for Eu–NTA (1 : 2 ratio) as well as for Eu–NP₂py complexes (1 : 2 and 1 : 1 ratios).

As is seen in Fig. 11 the coordination of the NP₂py ligand to the Eu³⁺ starts at about pH 3 for 1 : 1 and 1 : 2 complexes. In the case of the Eu : NP₂py 1 : 2 system the formation of the [Ln(NP₂py)₂]⁵⁻ complex starts at about pH 8 and it is consistent with the spectroscopic data described above. The difference between Eu–NTA and Eu–NP₂py complexes with the molar ratio 1 : 2 is clearly seen. The coordination of two NTA ligands occurs at low pH ∼ 2²⁹ and is completed at pH ∼ 6. As far as Eu–NP₂py of the 1 : 2 system is concerned, the [Eu(NP₂py)]⁻ complex is a predominating species within the pH range 3–9 and the formation of the [Eu(NP₂py)₂]⁵⁻ complex takes place at pH above 8. This may be explained qualitatively by considering the formal charge of reacting species. In the case of the Ln–NTA system the neutral LnNTA complex reacts with the H_nNTA ligand to form finally [Ln(NTA)₂]³⁻ species with the formal charge −3. The formal charge of the Ln(NP₂py)₂ complex is −5 and the formed complex is not as stable as [Ln(NTA)₂]³⁻. Out of the considered complexes, the [Ln(NTP)₂]⁹⁻ one is the most negatively charged, therefore this may suggest that the stability of the complexes should change in the following order: Ln(NTA)₂ > Ln(NP₂py)₂ > Ln(NTP)₂. Such an assumption is consistent with potentiometric results derived from Sawada et al.¹⁴ These authors have shown that only the [Ln(NTP)]³⁻ complex is formed in solution, on the other hand Kozlovski et al.¹⁶ assumed the existence of both – [Ln(NTP)]³⁻ and [Ln(NTP)₂]⁹⁻ species.

Extrapolation of [Eu(NP₂py)]⁻ and [Eu(NP₂py)₂]⁵⁻ stability constants to zero ionic strength

The SIT approach (Specific Ion Interaction Theory)¹⁸ was used for the extrapolation and correction of equilibrium data to the infinite dilution standard state. This simple method provides good estimations of activity coefficients and is recommended for use by the OECD Nuclear Energy Agency.³⁰ The extrapolation of the formation constants to ionic strength equal to zero requires the estimation of activity coefficients of all species that participated in chemical reactions. This may be performed by the SIT model. For the reactions:

L⁴⁻ + nH⁺ ⇄ H_nL⁻⁴⁺ⁿ (5)

Eu³⁺ + mL⁵⁻ ⇄ [EuL_m]^−4m+3. (6)

According to the SIT procedure, the logarithms of stability constants at a fixed ionic strength log β_n(I) are related to the corresponding logarithms of thermodynamic constants β⁰_n by the following equations:where γ are activity coefficients of individual species.

The log γ_j of the j-species may be calculated by using the following formula:

where:

z – charge of the j-species;

I _m – ionic strength of solution expressed in mol kg⁻¹;

ε _j – the interaction coefficient of ion pairs.

Combining eqn (8) or (9) with (10), the following equations are derived:

where:

Δz² = ∑z²_products − ∑z²_substrates;

Δε² = ∑ε²_products − ∑ε²_substrates.

Linear regressions of eqn (10) and (11), using the experimental values of log β(I_m) and I_m give the thermodynamic values of and (Table 7).

Table 7 Formation constants log β⁰_AB of compounds under study at the zero ionic strength at 25 °C

AB	log β^0AB	Δε	R ^2
HL	11.8 ± 0.05	−0.31 ± 0.05	0.92
H2L	19.0 ± 0.05	−0.48 ± 0.04	0.98
H3L	24.6 ± 0.11	−0.88 ± 0.10	0.96
H4L	26.9 ± 0.26	−0.76 ± 0.25	0.76
EuL	16.3 ± 0.11	−0.82 ± 0.11	0.95
EuL2	19.5 ± 0.15	−0.46 ± 0.15	0.77

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In general, these data may be useful in finding a reliable, thermodynamic model of the complexation reaction of aminophosphonic ligands with lanthanides particularly that, to the best of our knowledge, there are no stability constants of lanthanide/actinide phosphonates extrapolated to the zero ionic strength. This is the reason for which we are unable to refer our data to other ones.

Summary and conclusions

The compounds of the formula [C(NH₂)₃]₅[Ln(NP₂py)₂]·12H₂O (where Ln = Eu, Gd) with new tripodal NP₂py ligands were synthesized and their crystal structure was determined. The crystal comprises monomeric [Eu(NP₂py)₂]⁵⁻ anions. Both ligands are bonded with the Eu³⁺ cation by two oxygen atoms from monodentate phosphonic groups, one tertiary nitrogen atom and one pyridine nitrogen atom, filling thus the eight coordination sites of the Eu³⁺ cation. The approximate C_i symmetry of the [Eu(NP₂py)₂]⁵⁻ complex is reflected in the luminescence spectra, in which the intensity of the magnetic dipole ⁵D₀ → ⁷F₁ transition dominates over the intensities of the remaining ⁵D₀ → ⁷F_0,2,3,4 transitions.

The luminescence spectra of Eu–NP₂py and Tb–NP₂py complexes in aqueous solutions at different pH with various Ln : L ratios were studied in order to find the coordination mode of the NP₂py ligand and the stoichiometry of complexes. The NP₂py ligand starts to coordinate through phosphonic oxygen atoms with Ln³⁺ at pH ∼ 2. The coordination of the pyridyl group to the Tb³⁺ occurs at pH between 3.0 and 5.5. The binding of the NP₂py ligand is completed above pH = 6.

This study has demonstrated that both [Ln(NP₂py)]⁻ and [Ln(NP₂py)₂]⁵⁻ complexes exist in solution, however, the [Ln(NP₂py)₂]⁵⁻ starts to form at pH as high as 8. The comparison of the luminescence spectra of the [C(NH₂)₃]₅[Eu(NP₂py)₂]·12H₂O crystals with those of Eu : NP₂py (1 : 2) solutions enabled us to estimate the molar fraction of [Eu(NP₂py)]⁻ (∼19%) and [Eu(NP₂py)₂]⁵⁻ (∼81%) complexes at pH = 10.5, and finally, to calculate the conditional formation constant of reaction [Eu(NP₂py)]⁻+NP₂py⁴⁻ ⇄ [Eu(NP₂py)₂]⁵⁻ (log K₁₂ = 4.4 ± 0.5).

The potentiometric measurements were applied to determine the stability constants of complexes under study. The stability constants are between 11.83(5) for [Sm(NP₂py)]⁻ and 13.47(7) for [Tb(NP₂py)]⁻ and are slightly lower than those obtained for Ln–NTP complexes.¹⁶ Thus, the substitution of one phosphonic group by a pyridyl moiety slightly affects the stability of the [Ln(NP₂py)]⁻ complex in comparison with the [Ln(NTP)]³⁻ one.¹⁶ On the other hand the of the [Ln(NP₂py)₂]⁵⁻ complexes are about 5–6 orders smaller in comparison with those reported for [Ln(NTP)₂]⁹⁻.¹⁶ It should be noted, however, that the existence of [Ln(NTP)₂] complexes in solution has not been proved unequivocally.^14–16

Potentiometric titrations at various ionic strengths were also performed in order to find the thermodynamic stability constants of [Eu(NP₂py)]⁻ and [Eu(NP₂py)₂]⁵⁻ complexes. Such data are, in principle, preferable as a basis for discussion on the factors governing the stabilities of the complexes. The extrapolation of the formation constants to zero ionic strength under standard conditions was performed by the SIT procedure. The estimated log β⁰_EuL and values are 16.3 ± 0.11 and 19.5 ± 0.15, respectively. For lanthanide aminophosphonate complexes there are no thermodynamic quantities in the literature therefore we refer the obtained data to the well-known [Eu(NTA)] and [Eu(NTA)₂]³⁻ complexes, only.²⁹ The latter are characterized by the thermodynamic stability constants: log β⁰_EuNTA = 13.34 and = 22.66.

Taking into account all these data one may conclude that the high negative charge of a ligand may stabilize the LnL complex, but simultaneously destabilizes the LnL₂ one.

Experimental

Materials

All chemicals used were of analytical grade. The stock solutions of anhydrous Ln³⁺ chlorides (Aldrich) were standardized against EDTA using xylenol orange as an indicator. N-(methylene-2-pyridine)-N,N-di(methylenephosphonate) as a diammonium dihydrogen compound was synthesized as described previously.¹⁷

Crystal preparation

The crystals of the formula [C(NH₂)₃]₅[Ln(NP₂py)₂]·12H₂O (Ln = Eu or Gd) were obtained in the following way:

The suspension of 0.5 mmol Ln₂O₃ (Eu₂O₃ Stanford Materials 99.995%, Gd₂O₃ Stanford Materials 99.99%) and of 2.2 mmol (NH₄)₂H₂NP₂py salt in H₂O were heated at 90 °C ± 5 °C. After dissolution of the reagents, the solution was alkalized by using [C(NH₂)₃]₂CO₃ to the final pH ∼ 10.5 and left for crystallization. The colourless crystals were formed after three months.

The luminescence quantum yields for solutions of the Tb³⁺-NP₂py complexes were determined in relation to fluorescein in 0.1 M NaOH (Φ = 93%), by using eqn (13):

where Q stands for the quantum yield, n is the refraction index (n_X = 1.38, n_S = 1.33), the integrals were taken for the emission spectra corrected for the instrument response, ε is the molar absorption coefficient, c – concentration, and d – thickness of the cuvette (1 cm). The subscripts X and S stand for the sample and the standard, respectively. The pairs of the sample and the standard spectra used in the above equation were taken at the same instrument setting (slit widths, photomultiplier voltage etc.). The slits were 1 nm for the excitation and 1 nm for the emission recording.

Elemental analysis. C₂₁H₇₄EuN₁₉O₂₄P₄: N%_calc – 21.24%, N%_exp – 20.85%, C%_calc – 20.13%, C%_exp – 20.56%, H%_calc – 5.95%, H%_exp – 5.28%; C₂₁H₇₄GdN₁₉O₂₄P₄: N%_calc – 21.15%, N%_exp – 22.48%, C%_calc – 20.05%, C%_exp – 21.56%, H%_calc – 5.93%, H%_exp – 5.30%.

X-Ray crystal analysis

The crystallographic measurements were performed on an Xcalibur, Sapphire2 four-circle diffractometer with graphite-monochromatized MoKα radiation. The data for the crystal were collected at 100(2) K using the Oxford Cryosystems cooler and were analytically corrected for absorption with the use of the CrysAlis RED program of the Xcalibur software. The structures were solved routinely by using Patterson synthesis. The C- and N-bonded hydrogen atoms were placed in positions calculated from the geometry. The final refinement was anisotropic for all non-H atoms. The computations were performed with the SHELXS97³¹ and SHELXL97 programs,³² and the molecular graphics was prepared with XP–Interactive Molecular Graphics.³³ High residual peaks suggest that the C50 guanidine cation is partially distorted, however it was not possible to resolve this distortion. A summary of the conditions for the data collection and the structure refinement parameters is given in Table 8.

Table 8 Crystal data

CCDC no.	CCDC 1541895	CCDC 1541894
Chemical formula	C21H74EuN19O24P4	C21H74GdN19O24P4
M r	1252.83	1258.12
Crystal system, space group	Triclinic, P1̄	Triclinic, P1̄
Temperature (K)	100(2)	100(2)
a, b, c (Å)	11.9255 (11), 14.1373 (12), 16.1417 (15)	11.9496 (6), 14.1528 (7), 16.1651 (9)
α, β, γ (°)	105.889 (8), 94.515 (7), 90.629 (7)	105.710 (5), 94.360 (4), 90.901 (4)
V (Å^3)	2607.8 (4)	2622.2 (2)
Z	2	2
μ (mm^−1)	1.39	1.48
Crystal size (mm)	0.45 × 0.07 × 0.04	0.27 × 0.05 × 0.02
T min, Tmax	0.709, 0.958	0.816, 0.979
No. of measured, independent and observed [I > 2σ(I)] reflections	51 538, 25 885, 19 822	23 976, 15 463, 8529
R int	0.053	0.093
(sin θ/λ)max (Å^−1)	0.851	0.737
R[F^2 > 2σ(F^2)], wR(F^2), S	0.061, 0.147, 1.15	0.101, 0.184, 1.05
No. of reflections	25 885	15 463
No. of parameters	601	601
No. of restraints	6	6
Δρmax,Δρmin(e Å^−3)	4.71, −2.10	1.26, −1.25

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Spectroscopic measurements

Luminescence spectra and luminescence lifetimes were recorded on an Edinburgh Instruments FLS 920 spectrometer at RT. UV-vis absorption spectra were recorded on a Cary 500 UV/Vis/NIR spectrophotometer.

Potentiometric titrations

The solution studies were carried out in double-distilled water. The titrations were performed using a MOLSPIN pH-meter system equipped with a Mettler Toledo InLab® Micro electrode filled with 3 M KCl and the automatic burette. The electrode was calibrated daily against hydrogen concentrations using HClO₄ (Merck) or HCl (POCh) according to the procedure of Irving et al.³⁴ The purity and exact concentration of the ligand were determined by the method of Gran.³⁵ Alkali, carbonate-free, was standardized by titration with potassium hydrogen phthalate (Merck).

Measurements in 0.1 M ionic strength:

The ionic strength was fixed at I = 0.1 M with NaClO₄ (VWr). The ionic product of water under the used conditions was 10^–13,77 mol² dm⁻⁶. Alkali: 0.1 M sodium hydroxide solution (Aldrich).

Measurements in various ionic strengths:

The ionic strength was fixed at I = 0.075 M, 0.1 M, 0.2 M, 0.5 M, 1 M and 2 M with KCl (POCh). The ionic product of water under the used conditions was 10^–13,78, 10^–13,77, 10^–13,72, and 10^–13,75 mol² dm⁻⁶, respectively.³⁶ Alkali: 0.1 M potassium hydroxide solution (Aldrich).

All the titrations were carried out on 2.0–3.0 ml samples at 25 ± 0.2 °C under an atmosphere of Ar. SUPERQUAD³⁷ and HYPERQUAD2008³⁸ computer programs that use non-linear least-squares methods³⁹ were applied to calculate the stability constants. The results were obtained in the form of concentration overall stability constants β_pqr = [M_pH_qL_r]/[M]^p[H]^q[L]^r, where M stands for metal, H is proton and L the deprotonated form of the ligand. They are, however, a good indication of the importance of a particular species in the equilibrium. Triplicate titrations of the free ligand (number of recorded points: 150–180) and the complexes were carried out at metal to ligand ratios 1 : 1 and 1 : 2 (number of recorded points: 180–210). Each time about 120–150 and 150–190 titration points have been used for the calculations, respectively. The ligand concentration was 0.7–1 × 10^–3 mol dm⁻³ in all titrations. No precipitation was noticed in any titration. The distribution curve of the protonated species of L as a function of pH was calculated using the HySS2009 program.⁴⁰

The ligand used for potentiometric measurements was in the form of a diammonium salt ((NH₄)₂H₂NP₂py); NP₂py = [H₆L]²⁺ in order to improve its solubility in water. Therefore two ammonium cations were also considered in the overall acid–base equilibrium calculations of the compound. The determined values of the protonation constants which belong to the ammonia log K_NH4 vary within the range 8.98(1)–9.73(1) for different studied ionic strengths and are very close to those previously reported in the literature: log K = 9.38(1),⁴¹ log K = 9.50,⁴² log K = 9.10(3),⁴³ (I = 0.1 M).

CAUTION! Although no problems were encountered in this work, transition metal perchlorate complexes are potentially explosive and should be handled with appropriate precautions.

Acknowledgements

This work was supported by MNiSW grant no 2273/M/WCH/12.

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Footnote

† Electronic supplementary information (ESI) available: Table 1S. The fitting parameters for eqn (3), determined from the spectra of the ⁵D₀ → ⁷F_1,2,4 transitions of the [Eu(NP₂py)₂]⁵⁻ complex in aqueous solution; Table 2S. Selected luminescent data of Eu–NP₂py and Tb–NP₂py systems; Table 3.The complex formation constants of NP₂Py with Sm³⁺, Eu³⁺, Gd³⁺ and Tb³⁺ at 25 °C, I = 0.1 mol dm⁻³ (NaClO₄), in 1 : 1 and 1 : 2 molar ratios Ln : L; Table 4S. Stability constants of NP₂Py with Eu³⁺ at 25 °C in different ionic strengths (KCl); Fig. 1S. Phosphorescence spectrum of [C(NH₂)₃]₅[Gd(NP₂py)₂]·12H₂O crystals at 77 K; Fig. 2S. The plot of luminescence quantum yields of Tb : NP₂py 1 : 1 and 1 : 2 systems versus pH; Fig. 3S. UV spectra of the NP₂py ligand and Tb : NP₂py complex at various pH; Fig. 4S. Plot of q_H2Oversus pH of solution for the Eu–NP₂py complex with Eu : NP₂py ratios of 1 : 1 and 1 : 2. The Δq_H2O is the difference between q_H2O for 1 : 1 and 1 : 2 solutions at the same pH; Fig. 5S. Plot of q_H2Oversus pH of solution for the Tb–NP₂py complex with Tb : NP₂py ratios of 1 : 1 and 1 : 2; Fig. 6S. Species distribution curves of H₆NP₂py acid (L). Charges omitted for brevity; Fig. 7S. Species distribution curves for the Ln³⁺–N₂Py complexes as a function of pH for a 1 : 1 Ln : L molar ratio (A) and 1 : 2 Ln : L (B). Equimolar complexes are marked in blue, biscomplexes in red color, I = 0.1 M NaClO₄, 25 °C. CCDC 1541894 and 1541895. For ESI and crystallographic data in CIF or other electronic format see DOI: 10.1039/c7qi00191f

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