Solvent Extraction and Complexation Studies of Pyridine-di-Phosphonates with Lanthanides(III) in Solutions

ABSTRACT In this work, we studied the complex formation (1H, 31P NMR-titration, UV–vis titration, luminescent titration) and solvent extraction of lanthanides with pyridine diphosphonates. The stoichiometry of the complexes was determined: ML and ML2 forms are present. This is confirmed by all of the above methods. It was found that the pyridine ring and P=O groups are involved in the coordination of the metal cation. The coordination environment of the Eu(III) cation was studied more thoroughly using the EXAFS method in solution. Coordination numbers and distances were determined for the complex in solution. The influence of the lanthanide radius on the value of the stability constant was shown. The change in extraction efficiency in the series of lanthanide is described. A new pattern, unusual for other phosphorus-containing ligands, was obtained. To explain the change in the parameters of complexation depending on the system, DFT calculations were carried out. The effect of various initial states of the extracted cations was shown. The initial state with a large amount of nitrates corresponds to a two-phase system during extraction, and with a smaller amount, to a single-phase system with acetonitrile. Additionally, the luminescent properties of the complexes were described in detail as one more applied aspect of the work. . GRAPHICAL ABSTRACT


Introduction
Lanthanide (Ln) complexes attract the attention of researchers due to their large number of areas of application. Important applied tasks are the study of the luminescent properties of the complexes [1][2][3] , the possibility of using the complexes in medical therapy and diagnostics, [4][5][6][7] development of magnetic materials [8][9][10] as well as in separation chemistry. [11][12][13][14] In particular, researchers are faced with the task of the separation of Ln. [15][16][17][18] The solution of all these practical issues involves the implementation of deep fundamental research related to 1) the search for new ligands, 2) the study of the patterns of the complexes formation, 3) properties of the complexes.
Phosphorus-containing organic ligands are a promising class of compounds for these investigations. Tributylphosphate (TBP) is the most studied phosphorus-containing ligand and has extensive experience in industrial use. [19,20] The search for new organophosphorus ligands with new properties attracts the attention of scientists in various fields of chemistry.
Previously, new phosphorus-containing ligands have been investigated: phenanthroline diphosphonates, [21][22][23] phenanthroline phosphine oxide, [24][25][26][27] and pyridine phosphine oxide. [28] Such fundamental properties as stoichiometry, coordination environment in a single crystal and stability of complexes come to the fore in studies of new ligands and complexes. At the same time, such important applied parameters as luminescent and extraction properties play a significant role in research.
When creating new classes of ligands, it is important to rely on the known properties of ligands, combining them. By combining the applied extraction properties of phenanthroline phosphine oxide and phenanthroline diphosphonates as well as the synthetic availability of pyridine ligands, we created a new class of pyridine-di-phosphonates. In the previous work, [29] extraction properties of pyridine-di-phosphonates were investigated. In addition, for this class of ligands, a regularity between the structure and properties of extractants was proposed.
In this work, we used several techniques (EXAFS, luminescence, NMR, and UV-vis titrations) to describe the coordination mode of these ligands with Ln(III) directly in organic solutions. Obtaining structural data for liquid samples, rather than for solid ones, is especially interesting from a fundamental point of view.
It was also shown [29] that the slope of logD(Me) versus logС(L) for pyridinedi-phosphonates was slightly more than 1, which indicated that the 1:1 and 2:1 (L:M) complexes were the extracted species in the organic phase. In this work, we tried to clarify the species composition in the organic phase and describe the complexation in more detail.
From the applied point of view, we studied the solvent extraction properties of the ligands toward Ln(III) series. Complementing the extraction data from the previous work and the new data in this work, we evaluated the possibility of using these extractants to separate components of the high level waste or Ln series. In addition, the evaluation of the luminescent properties of the complex suggests important fundamental and applied properties of the complexes.

Synthesis and structure
The synthesis of the studied extractants is described in detail in the work. [29] In this work, we were able to confirm the structure of the Py-PO-iPr ligand by SC-XRD ( Figure 1). The molecule occupies a general position in a crystal. The molecule adopts a twisted conformation with torsion angles N1-C1-P1-O3 = −149.1°, N1-C5-P2-O6 = −30.9°. For more details and XRD experiment, see SI.

NMR titration
For NMR titration experiments, the stock solutions of PO-Py-iPr (37 mM) and Lu(NO 3 ) 3 (15 mM) were all obtained by dissolving the weighed ligands and Lu(NO 3 ) 3 ·6 H 2 O in CD 3 CN, respectively. According to the certain molar ratios designed between the metal ions and ligands, certain volumes of lanthanides and ligand solutions were added to the NMR tubes to obtain a series of mixtures of Lu(III) and ligands, with molar ratios increasing from 0 to 1.7. After the complexation equilibrium was reached, the 1 H and 31 P NMR spectra were recorded on a Bruker AVANCE II model 600 MHz instrument.

EXAFS spectroscopy
Liquid samples were prepared by liquid−liquid extraction at 25 ± 1°C. The aqueous phase was the solution of 0.9 mol•L −1 of Eu(NO 3 ) 3 in 3 mol•L −1 of HNO 3 . The 0.1 mol•L −1 ligand solutions in 1-nitro-3-(trifluoromethyl)benzene (F-3) were used as the organic phase. The contact time was 30 min. After being thoroughly shaken, the samples were centrifuged, and 0.4 mL of the organic solution was taken for further analysis.
The EXAFS data were collected at the Structural Materials Science beamline [30] at the channel of the Kurchatov Center for Synchrotron Radiation of the National Research Center "Kurchatov Institute." A synchrotron source on the channel is a bending magnet with a 1.7 T field of the Sibir-2 storage ring. In synchrotron radiation generation, the electron beam energy is 2.5 GeV, an average current is 70 mA. The X-ray radiation was monochromatized with an Si(111) crystal. The Eu L 3 -edge EXAFS spectra were measured at room temperature; the energy scanning ranges were 6726−7709 eV. The spectra were recorded in the fluorescence mode.
The data were analyzed using the IFEFFIT [31] and Larch [32] software packages. Preprocessing of the XAS data in the Athena [33] program included standard procedures for background subtraction. The DFT model of the Py-PO-iPr•Eu (NO 3 ) 3 complex [29] was used as the initial model. The k range was chosen to minimize Fourier-transform distortions due to insufficient signal/noise statistics in the measured spectra (k = 3 − 11 Å −1 ). Structural parameters were obtained by nonlinear fitting of theoretical spectra. The theoretical data for photoelectron scattering amplitudes was chosen as s 0 2 = 1. [34] The experimental spectra were fitted to the theoretical model using the Larch software.

Luminescence titration of Py-PO-cHex and Py-PO-iPr
Luminescence spectra of samples in acetonitrile solutions were recorded on luminescence spectrometer Hitachi F-7000 in standard quartz cuvettes with a path length of 10 mm in 90°-geometry at 25°C. The temperature controller TC 125 was used to maintain a constant temperature in the cuvette compartment. Spectra were corrected for the effect of the internal filter according to the formula: where I 0 is the registered luminescence intensity, D ex and D em stand for absorbance at the excitation and emission wavelengths, respectively. Luminescence quantum yield was determined by the reference dye method with rhodamine 6 G as an etalon using the formula: The europium ion asymmetry coefficient was calculated as the ratio of the luminescence integral intensity bands corresponding to transitions to the 7 F 2 and 7 F 1 levels.
Luminescence kinetics was recorded upon excitation with a wavelength of 263 nm and registration at 619 nm. The luminescence lifetime was calculated as the time during which the luminescence intensity decreased by a factor of e.
A ligand solution was prepared for spectrophotometric titration (ca. 0.1-0.4 mmol•L −1 ). A titrant solution Ln(NO 3 ) 3 ·nH 2 O (Ln=La, Nd, Lu, n = 4-6) (ca. 1-6 mmol•L −1 ) was prepared by dissolution of a sample of nitrate hydrate salt. A ligand solution was titrated with the required aliquot of the Ln (NO 3 ) 3 ·nH 2 O solution. Spectrum analyses were evaluated using the HypSpec2014 program [35] to determine the stability constants of the complexes (lgβ 1 and lgβ 2 ). The results obtained were measured three times and were within confidence intervals relative to each other.

Solvent extraction
A series of samples containing a) aqueous solution of lanthanide ions (1 × 10 −3 mol•L −1 of the sum of lanthanides except for Pm in 3 mol•L −1 HNO 3 ) as an aqueous phase; b) 0.05 mol•L −1 solutions of the ligand in F-3 as organic phase were prepared. A reference sample without ligands was also prepared.
The phases were stirred for 30 minutes on a vortex shaker at 25 ± 1°C in an air thermostat. Then, samples were centrifuged (2 minutes, 10000 rpm) and aliquots of aqueous phase were taken for determination of lanthanide concentration. The aqueous phase was studied by the ICP-MS method (AnalytikJena PlasmaQuant MS Elite).
The distribution ratio (D) was calculated as the ratio of concentrations in organic phase and aqueous phase. The concentration of the cations in the organic phase was determined by subtracting the content of cations in the reference sample and the sample with the ligand. The D uncertainties varied from 2% for light cations to 10% for heavy cations.

DFT calculation
All structures were optimized at the DFT level in the gas phase (tolerance of gradient : 10 −7 au) without symmetry constraint. We used quantum chemical software PRIODA-19 developed by Laikov [36] to evaluate quantum chemical calculations. Full electron relativistic basis set L1 [37] of TZ quality including one polarization function was used to describe all atoms in the system to provide the most reliable result. At the PBE/L1 [37] theoretical level, we optimized geometries and calculated the corresponding frequencies, none of the stationary points on the potential energy surface (PES) had imaginary frequencies. At the PBE0/L1 theoretical level, we further optimized geometries to calculate energy of complex formation for La(III), Nd(III), Eu(III), Lu(III) trinitrate with Py-PO-iPr. For complexes of Nd(III) and Eu(III), the highest spin 4 and 7, respectively, were chosen according to the (2S + 1) rule.

NMR titration
NMR titration is an effective method to explore the complex species formed between organic ligands and diamagnetic metal ions. [38][39][40][41] Because of the paramagnetic nature of Eu(III), in this work, the diamagnetic Lu(III) was used to identify the complex speciation formed between trivalent lanthanide and ligand Py-PO-iPr in nitrate media by 1 H and 31 P NMR spectra in CD 3 CN.
To establish the involvement of different groups in binding to the Lu(III) cation, we observed the chemical shifts of phosphonate groups in the 31 P NMR spectra and protons of the aromatic region in the 1 H NMR spectra. The titration spectra are shown in Figures 2 and 3.
As shown in Figure 2, a well-defined peak located at δ = 8ppm that appeared in the initial 1 H NMR spectrum (M/L = 0). This peak corresponds to the three protons of the pyridine fragment contained in the free ligand.
With increasing concentration of Lu(NO 3 ) 3 from 0 to 0.73, this peak showed an obvious downfield shift, indicating the occurrence of a coordination reaction between the lanthanide ions and ligands. Moreover, the aromatic system is involved in the coordination of the metal cation. For M/ L ratio varying from 0 to 0.5, the degeneracy of the pyridine ring protons signal is not lifted, but one can observe a downfield shift of the peak. This unambiguously points to a rapid exchange of the ligand between the free ligand and the ML2 species. Above 0.5 equivalents, one first a shoulder appearesat low field (0.73 eq.) followed by the observation of a second peak. When the M/L ratio reaches 0.97 the second lowfield signal occurs. This peak can be assigned as a 4Py proton of ML complex as an integral intensity of the peaks at 8.4 and 8.24 ppm relates like 1 to 2 at the end point of titration. As the M/L ratios were varied from 0.97 to 1.7 with the presence of excess metal in the solution, the peak at 8.4 ppm was growing and sharpening. It can be assumed that under the titration conditions the first complex form is ML 2 and on excess of the metal the complex ML is formed.
To confirm the assumption that the Py-PO-iPr ligand can form both ML 2 and ML complexes, 31 P NMR titration was carried out. As presented in Figure 2, with increasing concentration of Lu(NO 3 ) 3 , the peak corresponding to the ligand (δ = 10.2 ppm) was greatly broadened. At a ratio greater than 0.16, a new group of peaks (sharp peak at δ = 18.4 ppm and broad once at δ = 17.2 ppm) appeared. The sharp lowfield peaks corresponds to ML complex species and broaden once -to ML 2 species. Before M/L ration reaches 0.5 the broad peak at 17.2 ppm mostly grow indicating the ML 2 complex concentration increase. When the M/L ratios were varied from 0.50 to 1.00 the second sharp peak at 18.4 ppm became more broadened and intense, suggesting that ML complex species concentration grows. The broadenings of the peaks indicate the rapid exchange between all species in solution. What is more, there was only one peak (δ = 18.5 ppm) when the M/L ratio was above 0.97, corresponding to ML complex species. This further confirms that this ligand forms both ML 2 and ML complexes. The result is consistent with the data obtained by slope analysis, [29] spectrophotometric titration (see 4.2) and fluorescent titration (see 4.3).
Previously, ML 2 complexes were registered for diamides of pyridinecarboxylic acids [42] and several phenanthroline-bisphosphonates. [23] NMR titration allows one to determine the fragments involved in the binding of the cation. The pyridine-ring signals of the formed complexes can be found at lower fields compared to the free ligand. This undoubtedly shows the incorporation of the pyridine-group into coordination with metals, as the same shifts were observed earlier for pyridine-ring signals of the lanthanum complex. [43] The downfield shift of signals in the 31 P-spectra support involving the P=O-group in coordination.

EXAFS spectroscopy
In section 4.1, it was shown that the pyridine fragment and the P=O groups are involved in the coordination of the metal cation. For a more detailed study of the coordination of the cation with the ligands, we used EXAFS spectroscopy. This method allows obtaining structural data in the solution rather than in a solid. In particular, it is possible to determine the coordination numbers and distances to atoms.
To process the EXAFS spectra, we used the DFT model of the Py-PO-iPr•Eu (NO 3 ) 3 complex. [29] Since there was an excess of europium salt in the solution during the preparation of the samples, we used the ML model for the fit. In addition, the fit for the ML 2 complex had a high r-factor, so this model was discarded. The experimental spectrum and the theoretical model are shown in Figure 4. The theoretical model used to fit the spectra describes the experimental data well. The R-factor is equal to 0.03. It is important to note that the contribution of multi-scattering has significantly improved the fit and has a large relative contribution to the construction of the theoretical model. The structural parameters and the fit parameters are presented in Figure 4 and Table 1.
It is difficult for EXAFS methods to distinguish light atoms (oxygen and nitrogen, for example). Therefore, it is hard to unambiguously state which small molecules (H 2 O or HNO 3 ) are included in the coordination  environment. We tried to draw conclusions from the fit and offer one of the possible, but certainly not the only possible model of the coordination environment. Nevertheless, some conclusions are reliable and useful for understanding the coordination of Eu(III). The first scattering path corresponds to the oxygen atoms of the nitrateanions and the oxygen atoms of the P=O groups. The next four atoms correspond to the nitrogen atoms of the nitrates and the pyridine nitrogen atom. The participation of the pyridine atom in the binding of the metal cation is consistent with the results of NMR titration (see 4.1). The presence of atoms at a distance 2.75-2.84 Å, in addition to pyridine nitrogen, allows us to state that the coordination environment includes nitrate anions. Also, a significant contribution of multi-scattering indicates the presence of nitrogen groups in the nearest coordination environment.
The third scattering path includes atoms of phosphorus groups. This result also confirms the results of NMR titrations, according to which these groups are involved in the binding. In addition, the presence of two phosphorus atoms confirms the formation of the ML complex.
Thus, it is shown that the coordination of the cation in solution can be described using the computational model proposed by us earlier. [29] In this work, this conclusion is confirmed experimentally and is consistent with other methods. The distances to atoms were also refined.

Luminescence titration of Py-PO-cHex and Py-PO-iPr
Luminescent titration is another method for determining the stoichiometry of complexes, which confirms that the system contains complexes ML and ML 2 . Here we have given brief information about luminescent titration, in more detail the experiment and the results are described in SI.
We studied the ligands Py-PO-cHex and Py-PO-iPr with Eu(NO 3 ) 3 complexation in acetonitrile using luminescence titration. We observed changes in Eu(III) emission luminescence spectra under excitation by the light with a wavelength of 263 nm upon adding of Eu(NO 3 ) 3 ·6 H 2 O. The europium luminescence intensity increases when europium nitrate is added, which indicates the formation of europium complexes with the studied ligands.
The integral europium luminescence intensity (the sum of all luminescence intensities in the range of 570-720 nm) increases with increasing content of the europium ion and reaches maximum when the ligand/europium ratio becomes ~2:1 (Figure 5a). The europium luminescence intensity decreases with a further increase in the europium concentration, that is, the luminescence of the europium complex is quenched by unbound europium nitrate. This result makes it possible to judge the presence of two forms of the complex in the solution.
Similarly, when the ligand/europium ratio becomes ~2:1 both asymmetry ratios and absolute luminescence quantum yield change (Figure 5b,c), which also confirms that the system contains complexes ML and ML 2 .

Determination of stability constant
After a detailed description of the coordination of the central atom by the ligand, we described the properties of the Ln(III)-complexesin particular, their stability. In addition, the effect of the lanthanide radius on the properties of the complex was shown. Variation of both the substituents and the cation makes it possible to study more fully the factors influencing the nature of the stability of the complex.
Determining the stability constants is an important approach that allows to trace the complex formation trends in the Ln series. Quantitative characteristics of complexation make it possible to compare ligands and their complexes more clearly.
The titration curves for La(III) are shown in Figures 6 and 7. The change of trend at an equivalence of 0.5 indicates the presence of 2 different species (the ML and ML 2 ) for all investigated metals.
The stability constants of the lanthanide complexes β 1:1 and β 2:1 were calculated by nonlinear least-squares regression analysis using the HypSpec2014 program ( Table 2). The fitting of molar absorptivities along with the experimental ones are presented in Figure S5.
In Figure 8 the dependence of the values of stability constant β 1:1 of the complexes with Py-PO-iPr on the size of the ionic radius is shown. As the ionic radius increases from Lu(III) to Nd(III)), the stability constants of the complex also increase. With a further increase in the ionic radius from Nd(III) to La(III), the value of the stability constant decreases. The value of the stability constant for Nd(III) is the biggest among the four studied cations. Also, among the four studied cations the highest value of the stability constant for Nd(III) is observed for the Py-PO-cHex ligand.
A similar effect for Nd(III), apparently associated with steric effects, was shown earlier for other N-, O-donor ligands. [45] This behavior was explained also in work [46] in terms of the steric requirement upon sidearm ligation. Only the most size-fitted ion accommodated in the cavity of the ligand binds most efficiently. For the previously described phenanthroline diphosphonates (see Table 2), such steric specificity in the lanthanide series was not shown.
Moreover, the higher value of the stability constant of the complex with Nd(III) as a structural analog of Am(III) [47] is confirmed by the higher   Phen-PO-iPr [23] Phen-PO-cHex [23] Phen-PO-C4 [22] Phen-PO-C2 [44] log β 11.0 ± 0.9 Eu(III) [29] 5.09 ± 0.04 extraction of Am(III) than Eu(III). In addition, the ratio β 1:1 (Nd)/β 1:1 (Eu) for the Py-PO-iPr ligand is 2.24, and in the case of the Py-PO-cHex ligand this ratio is 7.76. This confirms that the cyclohexyl extractant has a higher selectivity in the Am(III)/Eu(III) pair compared to the isopropyl extractant. [29] Solvent extraction Next, we studied the extraction properties of the studied ligands with cations of the Ln series. It was important to determine how the efficiency of complex formation changes upon transition to two-phase systems. For a more detailed study of the effect of the substituent on the properties of the ligand, the additional Py-PO-C5 and Py-PO-2EtHex (see Table 3) were investigated. The extraction of the rare earth elements from the 3 mol•L −1 solution of nitric acid was studied. The solutions of each ligand in F-3 were used as the organic phase. Solvent F-3 was chosen because of high solvation ability towards heterocyclic ligands and their complexes with f-elements and low fire hazard. [48] The resulting distribution ratios are presented in Figures 9  and 10.
PyPOcHex extractant is the most effective among the studied ligands. This is explained, on the one hand, by the donor effect of the secondary carbon  atom in the substituent and by the low preorganization energy due to the cyclic rigid substituent, as shown in the previous article. [29] It is shown that for all the studied ligands the extraction efficiency decreases when moving from light Ln(III) to heavy Ln(III). This pattern is preserved for all ligands, regardless of the type of the substituent.
The extraction of Nd(III) as the structural analog of Am(III) [47] is higher than that of Eu(III). In addition, it was shown that the highest selectivity in the Nd(III)/Eu(III) pair is achieved in the system with the Py-PO-cHex ligand. This data agrees with the extraction data for the Am(III)/Eu(III) pair. [29] For another organophosphorous ligands inverse dependences of the extraction ability of the ligand depending on the cation radius was obtained. [49][50][51][52][53] The distribution ratios for Lu(III) in these works was higher than those for Eu(III) and La(III). Thus, in the present work, the new inversed dependence of the extraction efficiency on the cation radius was obtained, which is atypical for other P=O donor extractants.
An increase in the extraction ability with an increase of the atomic number of the lanthanide is observed for other classes of N-, O-donor extractants based on the pyridine: 2,6-dicarboxypyridine diamides) [54] and bistriazinpyridine. [55] The dependence of the distribution ratio of the lanthanide cations on the ionic radius is shown in Figure 9. With the decrease of the nuclear charge along with the increase of the ionic radius from Lu(III) to La(III) the size effect prevails over ionic interactions. [56] In this case, we can confirm that the presence of regularity has a size selective origin (see 4.3). It can be assumed that in this case the tridentate ligand acts as a pseudocavity.
The dependence of the distribution ratios on the radius of the lanthanide differs from the dependence of the stability constants on the radius (Figure 8) therefore it is important to discuss the differences between these systems. Firstly, the nature of single-phase and two-phase systems differs, because not only the processes occurring in the volume are important, but also at the interface. Different properties of the F-3 and acetonitrile as solvent, different acidity of the medium, and the presence of an excess of nitrate ions also affect the formation of complexes. The effect of the initial state of the cation on the process of complexation is shown by DFT calculations (see 3.4).
At the next stage, the dependence of the extraction efficiency of Ln cations on the concentration of nitric acid in the aqueous phase was obtained. For this, the PO-Py-cHex ligand was chosen, since it has the highest extraction efficiency with respect to lanthanides.
It is shown ( Figure 11) that with an increase in the concentration of nitric acid, the distribution ratio for Ln cations increases. This result agrees with the extraction data obtained earlier for the Eu(III) cation and can be explained by the effect of salting out in the system. [29] In turn, it should be noted that the trend towards a decrease in the extraction efficiency when moving from light Ln(III) to heavy Ln(III) persists at all studied concentrations of nitric acid.
The handling of a multicomponent high-level waste mixture implies not only the separation of the Am/Eu pair, but the Am/Ln group separation. In order to assess the possibility of such separation, it is necessary to interpret the data on the extraction of the entire series of Ln. The extraction data obtained for a number of Ln demonstrate that the ligands have a greater affinity to the lanthanide cations of the beginning of the series than to the cations of the end of the series. As mentioned above, Nd(III) is a structural analogue of Am(III), which suggests that the extraction of the beginning of Ln(III) the series would compete with that of Am(III). The data for the value of the distribution ratio of Am(III) in 3 mol•L −1 nitric acid are plotted in the Figure 11 and illustrate this. Based on these data we can assume that these ligands can be used for group extraction of Am(III) and light Ln(III) and isolation of Am(III) requires selective back-extraction by aqueous ligands.
Also, we can assume that pyridine-di-phosphonates are probably can be used for the separation of rare earth elements with the additional use of watersoluble aminopolycarboxylate ligands with a direct relationship between binding constant and REE order number. [49] The possibility of selective backextraction for such type extractants has been described. [57][58][59]

DFT calculations
The trend towards a decrease in the extraction ability in the series of lanthanides differs from the series of obtained stability constants with a maximum in the neodymium cation. First of all, this may be due to the transition from a single-phase system to a more complex two-phase system during extraction. However, in this work, it was necessary to further investigate the process of complex formation under various conditions in order to explain the various trends in complex formation. To do this, we carried out DFT calculations to optimize the structures under study and calculate the preorganization energies and complex formation energy. All calculations are performed in the gas phase. This approach leads to incorrect absolute values; however, it reproduces experimental trends well as previously demonstrated in. [60,61] At the first stage, we optimized the structure of Py-PO-iPr, two projections (a) and (b) are presented in Figure 12.
Further, we chose structure [LnPy-PO-iPr](NO 3 ) 3 according to the solvation number in solution. [29] To evaluate the effectiveness of binding of ligands to lanthanides, we used several model reactions (1-3) based on different initial states. To better represent the real system, we included water molecules in the lanthanide complexes. Mononitrate, dinitrate, and trinitrate lanthanides aqua complexes were chosen as initial state. Nitrates in outer coordination sphere bind with lanthanide complex via hydrogen bond with water molecules in the inner coordination sphere.
After choosing the initial state, the optimization of the structures of the complex was carried out for each model. The optimized structure of [LnPy-PO-iPr](NO 3 ) 3 as an example of a lanthanide complex is presented in Figure 13 in two projections (a) and (b).
The preorganization energy (i.e. difference between the energies of bonded and free forms of the ligand [62] is an important parameter to describe the binding efficiency of a ligand. Preorganization energy for corresponding complexes and the energy of complex formation were also calculated and presented in Table 4 and Figure 14. It is important to note that the absolute values are of secondary importance compared to the trend of dependence of the energy of complex formation. Lower values of the energy of complex formation correspond to a more stable complex. All the negative ΔE values indicate that the reactions are exothermic and occur spontaneously. Different initial states are suitable for describing a corresponding system. Model II and model III are in consistent with experimental values of stability constant determined in acetonitrile, that reveal the Nd complex as the most stable thermodynamically. Model I (trinitrate) provides values correlated better with distribution ratio of solvent extraction from nitric acid solution, the stability of complexes decreases with decreasing ionic radius of lanthanides. So, depending on the experimental results, various models should be used.
For La, Nd, and Eu, the preorganization energy is approximately the same, the highest value is for the smallest metal Lu, which can explain the experimentally low stability of the Lu complex. This also proves that the idea of size effect influenced complexation. Table 5 shows theoretical bond lengths of M-O and M-N. It can be assumed that equal angles in the case of the Nd cation correspond to a more symmetrical structure. This may be due to the more appropriate cation size. However, this assumption requires further study.
In the gas phase at the PBE0/L1 theoretical level distance M-O and M-N decreases monotonously with decreasing ionic radius of the metal.

Conclusion
In this work, a complete, consistent, and in-depth study of the complexes of lanthanide cations with pyridine diphosphonates was carried out. We consistently established and confirmed the stoichiometry of the complexes by the NMR, UV-vis, and luminescence titration, proving that both ML and ML 2 complexes are present in the system. EXAFS analysis of complexes in solution was used for description of the coordination of europium cation. Distances, and coordination numbers for the central atom were obtained. It is shown that the distances between europium and the nearest oxygen atoms (attributed to either -P=O group or nitrates, Eu-O P=O, NO3 ) for Py-PO-iPr•Eu(NO 3 ) 3 complexes are equal to 2.43-2.44 Å. The distances between europium and the nearest nitrogen atoms (attributed to either pyridine core or nitrates, Eu-N Py, NO3 ) are different and equal to 2.62 Å and 2.55 Å, respectively.
The values of the stability constants were obtained for the single-phase systems in acetonitrile. A nonlinear dependence of the stability constants on the lanthanide radii with the maximum for Nd(III) was obtained. This may indicate that the pyridine-di-phosphonates polydentate ligands act as a pseudo-cavity, and, in this case, the size of the cation plays a decisive role for efficient binding.
In two-phase systems, a gradual decrease in the extraction efficiency with an increase in the atomic number of the cation was shown. Thus, a new inversed trend, unusual for other phosphorus-containing ligands, was obtained. The type of substituent in the ligand structure and the change in the acidity of the medium in the range of 1-5 mol•L −1 does not affect this trend. This extraction pattern can be used further to develop «push-pull» systems for separating f-elements. [63] To explain the differences in the single-and two-phase systems, a DFT calculation was carried out. The number of nitrates in the first coordination sphere of the cation was varied for the initial states of the system. The absolute values of complex formation energies have the highest value for Nd(III) in the case of systems with a small number of nitrate anions. The same trend was observed for the stability constants obtained by UV-vis titration in a single-phase system in acetonitrile where no nitric acid was added. It can be assumed that a small amount of nitrate anions does not prevent the entry of Ln cation into the pseudo-cavity of the ligand. Accordingly, for the systems with a large number of nitrate anions, the value of the complexation energy changes gradually, which is similar to the results of liquid-liquid extraction from 3 mol•L −1 HNO 3 . Thus, the local environment of the Ln cation in the aqueous solution may hinder the selectivity of the ligand.