Stability Trend Analysis of Light Lanthanide Complexes with a Fluorophenyl-dipicolinamide: A Quantum Chemical Study

Abstract


Introduction
Reprocessing spent nuclear fuel is crucial in improving sustainable energy systems, which has gradually become the key for many countries' nuclear energy strategies.The High-level waste (HLW) is generated after the reprocessing, posing huge environmental threats because of its long-lived radionuclides content including actinides [1].Other major components of HLW include light lanthanides (La, Ce, Pr, Nd, Pm, Sm, Eu) [2].Because of the high neutron − absorption cross sections, lanthanides can disturb the partitioning and transmutation (P&T) process [3], which is widely proposed to treat HLW [4,5].Besides, lanthanides have shown immense potential for various applications such as lighting, laser, catalysis and magnetism [6][7][8][9].The separation of lanthanides from actinides is an essential and eco-friendly option before the P&T process [10,11].
However, separating lanthanides and actinides has been a challenging topic so far.In the liquid-liquid extraction of spent nuclear fuel [12], trivalent actinides (An(III)) and trivalent light lanthanides (Ln(III)) exhibit similar geometric parameters and chemical properties.The latter is more attributed to their predominantly ionic bonding and the lack of redox activity [13].Other oxidation states of lanthanides, such as Ce 4+ , may be present, but they are not usually found in acidic spent nuclear fuel liquids under normal conditions [14].
Speci cally designed ligands are e cient and convenient choices to separate Ln(III) and An(III).Amide and diamide groups have been investigated extensively over the years as one of the possible solutions.Compared to the organophosphorus compounds such as octyl(phenyl)-N,N-diisobutyl carbamoyl methyl phosphine oxide (CMPO) and trialkyl phosphine oxide (TRPO) [15][16][17][18], they are incinerable, highly soluble, more cost-effective and have relatively benign radiolysis products [16][17][18][19][20][21], which can be treated more easily in wastewater.Substituents on nitrogen in the diamide series have been found to in uence extraction performance and solubility signi cantly [22], Comparing a number of diamide groups with different substituents, M. Yu.Alyapyshev and his coworkers concluded that the ones containing alkyl and aryl substituents possess the highest extraction rates [23].Furthermore, Alyapyshev studied nine different diamides with alkyl and aryl substituents and found that the diamide with ethyl substituent had the highest solubility [22].In addition, a pyridine diamide, N,N'-diethyl-N,N'-ditolyl-dipicolinamide derivative (EtTDPA), is known to have an extraction capacity similar to that of high-performance organophosphorus compounds [19].As a result, ligands of EtTDPA series have gained increasing attention.
Compared to EtTDPA, additional two uorine atoms decrease the extraction ability but increase its chemical stability.Thus, FDPA should be more stable towards hydrolysis and radiolysis than other derivatives.It has been demonstrated to separate Am from Eu with a separation factor (S.F.) up to 6 in the metanitrobenzotri uoride (F-3) [22].To alternate uorinated diluents, an ionic liquid [C n mim][NTf 2 ] (n = 4, 6, 8) based solvent system containing FDPA was investigated, which showed improved extractability for metal ions (Am(III), Eu(III) and Pu(IV)) even with low concentrations of FDPA, although it decreased the Am/Eu S.F. (< 3.3) [24].Since many ligands, including EtTDPA, prefer to bind An(III) before Ln(III) [25] (because An(III) has a greater covalent tendency at the M-L bond compared to Ln(III) [26]), lots of researches focused more on studying the chemical properties and coordination structure of both trivalent actinides and lanthanides, including Am(III) in particular, e.g.Am(III)/Eu(III).On the other hand, the extraction capacity for Ln(III) and other subsequent processes have not been fully explored yet [27].In industrial applications, extraction of Ln(III) will also occur if the extractant is in excess.Trivalent lanthanides have similar ionic radii because of the shrinkage of lanthanides, which leads to their similar chemical properties [28,29].It is appropriate to use theoretical calculations to simulate the extraction of Ln(III) in the acidic solvents before using radioactive complex single crystals to experimentally investigate.Density functional theory (DFT) plays a crucial role in simulating and predicting the coordination behavior of lanthanides in various chemical conditions.This work is aimed to simulate the tendency of FDPA to complex with seven Ln(III) (from La(III) to Eu(III)) in the acidic aqueous solution and to analyze their internal interactions.Furthermore, energy analysis is involved to con rm the feasibility of using FDPA to extract seven lanthanides from aqueous solvents.The theoretical calculation results and analyses provide valid reference data for future investigations into the complexation of similar ligands with Ln(III) ions.

Current research on the extraction of actinides by
EtTDPA is done in-depth, so lling some vacancies in research on lanthanide extraction may offer valuable insights into the design and development of more e cient extraction strategies in the future.

Computational Methods
All calculations were performed using the Gaussian 09 E.01 program suite.A popular density functional method, B3LYP, is adopted, whose reliability is also demonstrated in the calculations for lanthanide-containing molecules [30].The small-core relativistic effective core potential (SC-ECP) of Dolg et al. was used, which contains 28 core electrons.For the valence electrons, the a liated ECP28MWB-SEG basis sets were used.There are two positive charges and over a hundred electrons exist in the Ln-complexes we studied.Consequently, the standard Pople basis set of much accuracy 6-311g(d,p) was used for other light atoms(viz.C, H, O, N, F).The calculation was carried out in the nitrobenzene solution to simulate an acidic environment.
Small-core potential MWB28 was chosen to treat the inner 28 core electrons of each Ln cation.Furthermore, the a liated ECP28MWB-SEG basis set was used to treat valence electrons.To ensure these geometrical structures obtained are minimized on the potential energy surface, vibrational frequency calculations were performed at the same level of theory.To investigate the interaction of the Ln-O and Ln-N bonding, Bader's Quantum Theory of Atoms in Molecule (QTAIM) parameters at these key bonds' critical points (BCPs) were measured using Multiwfn 3.8 [31].The detailed QTAIM data are presented in Table 1.

Results and Discussion
The atomic structure of the FDPA in nitrobenzene solution N,N'-diethyl-N,N'-di(para) uorophenyl-2,6-dipicolinamid (FDPA), as shown in Fig. 2a, contains two uorophenyl-and two ethyl-.The optimized structure of FDPA is presented in Fig. 2b.It is a tridentate extractant with three coordination atoms: one nitrogen of pyridine and two oxygens of amides.Its overall structure is exible, which can better bring the advantages of extraction into play [32].Additionally, FDPA exhibits a higher solubility in polar diluents than many other derivatives [22].making it a promising ligand in acidic solutions.A. B. Patil and his colleagues tested the extraction capability of a synergistic mixture containing FDPA for several actinide ions, demonstrating its high extraction ability for metal ions, even at low concentrations [33].
The electrostatic potential (ESP) can help investigate the electrostatic interaction and indicate the possible reaction sites.As the interaction between ligand and f-block metal ion is typically ionic, ESP can show the most likely binding sites of FDPA.The ESP plots of FDPA (shown in Fig. 3) highlight the symmetrical structure, which results in paired extreme points with almost identical values.Precisely, the most negative (red area) ESP extreme points (-53.03kJ/mol and − 53.00 kJ/mol) are located among coordination atoms (one N in pyridine and two O in amides).This observation con rms that these three atoms are donor atoms.

The structures of the complexes in nitrobenzene solution
Based on the above analysis, each Ln(III) cation is assumed to be located in the center of symmetry, surrounded by two symmetrically placed FDPA ligands.
Because the Am/Eu S.F. of EtTDPA increases when the aqueous phase acidity decreases [25], only one additional is attached to the cation.The corresponding Ln hydrate is.The FDPA ligands are dissolved in the nitrobenzene solution.Based on our simulation, each FDPA ligand provides two O atoms and one N atom as donors (Fig. 4).The calculated Ln-O and Ln-N bond lengths (averaged for the same bonds) are presented in Fig. 5. Due to the ligand structure, Ln-N bonds must be longer than Ln-O bonds.Speci cally, the average lengths of Ce-O and Ce-N bond are 2.493 Å and 2.757 Å, respectively.As shown in Fig. 5, the Ln-N bond lengths gradually shorten from left to right, while the trend of Ln-O bond lengths is a little disordered and decreases abruptly at Ce.These two trends may be mainly attributed to the shortening of the radius.Since Ln-O bonds are shorter than Ln-N bonds, O atoms are expected to be the leading donors rather than N atoms.It is generally accepted that Ln(III)s are 'hard' acids that prefer binding with 'harder' atoms, viz.O atoms, which in turn causes four O atoms to push two N atoms further apart.As shown by the Ln-O polyline, the Ln-O bond of Ce and Nd is shorter than their both sides, especially Ce, whose Ln-O bond length has an abrupt decrease.It may suggest that FDPA has an additional a nity for the two cations.
Despite the observed variations in bond lengths among the complexes, these differences may not indicate a relationship with the stability of complexes.Even if the data of Ce is special, further correlated analysis is required.Further analysis is done of the binding properties of series from more perspectives.In order to learn the nature of chemical bonding between light Ln(III) and O, N donor atoms, a topological analysis of seven Ln-FDPA complexes was performed using Quantum Theory of Atoms in Molecules (QTAIM) [34].Following parameters () at critical points (CPs) of Ln-O and Ln-N bonds (also averaged) are presented in Table 1.Generally, the type of interaction between Ln(III) and the O, N donor atoms can be classi ed by electron density and Laplacian.The parameters with > 0.20 a.u. and < 0 indicate a covalent interaction, while < 0.10 a.u. and > 0 mean a closed-shell interaction (van der Waals, Hydrogen bonds, ionic, etc.).Just as presented in Fig. 6, it is clear that all the Ln-O and Ln-N bonds can be classi ed as the closed-shell interaction, namely electrostatic interaction, as all the > 0. Since the trend is not precisely upward, perhaps FDPA does have a speci c extraction a nity for certain lanthanides.At the very least, Ce deserves continuous observation.

Bonding characteristic analyses of complexes
The electronic energy density (H) and |V|/G values have also been calculated.These two parameters can help indicate the "covalence" of the interaction to some extent.A previous study [35] has gured out that at CPs: As shown in Fig. 7, all the H of Ln-N and Ln-O bonds positive, suggesting all these bonds possess closed-shell interactions.As predicted by the previous parameters, the H value of Ce(III) shows a sharp peak, and its Ln-N value is the only one higher than its Ln-O value.It implies that FDPA may bind Ce much stronger.In addition, the H data for Eu-N bond is close to zero, which indicates that the Eu-N bond is almost weak enough to become the dative bond.It may be attributed to the structure of FDPA and the minimum radius possessed by Eu(III); after all, the H value of Eu-O does not decrease substantially.
As also presented in Fig. 7, the calculated |V|/G values are all less than 1, indicating that they all possess closed-shell interactions.Not surprisingly, the valleys of Ce-N, Ce-O and the Eu-N match well with their H data, which could provide another evidence for the FDPA's preference for Ce and the relative weakening of Eu-N bonds.The mirror relationship between H and |V|/G data corresponds to the same bond properties.
Bond Strength Analysis In order to evaluate the bond strength in the studied complexes further, the Mayor Bond Order (MBO) of Ln-O and Ln-N bonds was calculated.MBO is commonly known to be positively correlated with bond strength.As presented in Fig. 8, it was observed that the FDPA ligands bind much more strongly to Ce(III) and Nd(III) than to the other elements, which agrees with the results of the above analysis.It should be noted that apart from Ce(III) and Nd(III), other elements displayed similar values with a slight increasing trend in the intervals of (0.158,0.186) and (0.286,0.323), respectively.Compared to Ce and Nd, this trend could be attributed to their physical properties.Considering the special values of Ce and Nd as always, especially Ce, the FDPA ligand may have a stronger a nity for Ce(III) and Nd(III) cation than for others, which would be con rmed in the energy analysis of this extraction process.Except for Ce and Nd, all other elements correspond to negative values, thus the FDPA ligands are better than water for light Ln(III).Many works have concluded that the hydration energies of light Ln cations have a descending trend, and the energy trend shown in Table 3 agrees with this conclusion.Therefore, the energy trend of forming Ln-donor atom bonds in Ln-FDPA can compensate the change of hydration energy (except Ce(III) and Nd(III)).More speci cally, the difference among these ve values tends to zero, which means the energy trend of ligand bond formation is consistent with the decreasing trend of hydration Gibbs free energy.Consequently, the differences detected by FDPA among these ve elements are just variations in physical size, which is the same as the case of water molecules.As hydration energies change synchronously, FDPA may not be selective for these elements.In general, FDPA can extract La(III), Pr(III), Pm(III), Sm(III), Eu(III) from acidic aqueous solution, leaving Ce(III) and Nd(III) behind.Some previous works have discovered the exclusion of Nd by the ligand [37,38] This phenomenon calls for a further investigation into the mechanism behind the selective extraction process of FDPA and its ability to exclude certain Ln(III).Our team is currently conducting additional studies.

Conclusion
Through a multifaceted comparison of computational results, we theoretically analyzed the stability trend of seven light Lanthanides (from La(III) to Eu(III)) combined with FDPA.Based on MBO and QTAIM analyses, all the Ln-O and Ln-N bonds can be classi ed as closed shell interactions, and FDPA has a strong a nity for Ce/Nd cations.However, our energy analysis reveals a great repulsion between them, indicating that Ce(III) and Nd(III) are unsuitable extraction targets.
For La, Pr and from Pm to Eu, we conclude that the trends of bond lengths, Mayer bond order and QTAIM parameters of complexation bond formation are in uenced mainly by normal physical changes, such as changes in radius.The extraction mechanism of FDPA is similar to that of water molecules.Hence it complexes with the ve elements with the same energy change trend as the hydration Gibbs free energy change (binding to water), resulting in a similar free energy change () value for each element, which is negative.
Overall, FDPA is a extractant than water which can extract light lanthanide ions until only Ce(III) and Nd(III) remain in the water.As the isolation and puri cation of certain Ln cations in spent nuclear fuel are greatly di cult, our calculations about the stability trend of light lanthanide complexes, as presented in this work, may help better to reveal the mechanism of the stability trend of these complexes and provide guidance for designing ligands that are more capable of differentiating Ln(III) directly and effectively in nuclear waste reprocessing.

Declarations Figures
The The attening structure of .The real-simulated structure is stereo symmetrical.

Figure 3 (
Figure 3 (a) The top view and (b) the side view of the ESP plots for the optimized FDPA at 6-311g(d,p) level of theory.

Figure 5 Variation
Figure 5 Variation of the calculated average bond lengths of Ln-O and Ln-N in Ln-FDPA complexes.

Figure 6
Figure 6 Variation of the calculated average QTAIM parameters and at Ln-O and Ln-N bonds' BCPs.

Figure 7 Variation
Figure 7 Variation of the calculated QTAIM parameters H and |V|/G values at Ln-O and Ln-N bonds' CPs.

Table 1
Calculated four QTAIM parameters of Ln-N and Ln-O in average.

Table 2
The Mayor Bond Order of Ln-N and Ln-O bonds.Energy Analysis In order to get an overall picture of the results produced by the stability trend of FDPA binding to light lanthanide ions, especially Ce(III) and Nd(III), the Gibbs free energy changes () for the Ln(III) extraction process were calculated.The data were obtained by calculating the change in Gibbs free energy before and after extraction in nitrobenzene solution.To model the extraction from the aqueous acidic condition, each Ln(III) ion is attached by seven H 2 O and one, viz..So the hypothetical extraction is:Undeniably, there can be discrepancies in the magnitude of between the calculated and experimental results[26, 36].However, the calculated stability trend can still conform to the experimental results, which helps to illustrate the relative a nity of FDPA for seven light Lanthanides.As shown in Fig.9, the calculated of Ce(III) is 1.534 kJ/mol.Hence are much less stable than others.It is a surprising result, as the calculations above repeatedly indicate that the binding between FDPA and Ce(III) may be much stronger than the others.Similarly, the calculated corresponding to Nd(III) is 0.781 kJ/mol, which is also positive and much bigger than other Ln cations.The two values indicate that the FDPA has the lowest possibility to absorb Ce(III)and Nd(III), even if their complexes are stronger.In other words, Ce(III) and Nd(III) are not 'good cations' that FDPA can trap.