“Straining” to Separate the Rare Earths: How the Lanthanide

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“Straining” to Separate the Rare Earths: How the Lanthanide Contraction Impacts Chelation by Diglycolamide Ligands Ross J. Ellis,*,† Derek M. Brigham,† Laetitia Delmau,† Alexander S. Ivanov,† Neil J. Williams,†,‡ Minh Nguyen Vo,†,§ Benjamin Reinhart,∥ Bruce A. Moyer,† and Vyacheslav S. Bryantsev*,† †

Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States Department of Chemistry, The University of Tennessee, Buehler Hall 1420 Circle Drive, Knoxville, Tennessee 37996-1600, United States § Department of Chemical & Petroleum Engineering, Swanson School of Engineering, University of Pittsburgh, 804 Benedum Hall, 3700 O’Hara Street, Pittsburgh, Pennsylvania 15261, United States ∥ Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, United States ‡

S Supporting Information *

ABSTRACT: The subtle energetic differences underpinning adjacent lanthanide discrimination are explored with diglycolamide ligands. Our approach converges liquid−liquid extraction experiments with solution-phase X-ray absorption spectroscopy (XAS) and density functional theory (DFT) simulations, spanning the lanthanide series. The homoleptic [(DGA)3Ln]3+ complex was confirmed in the organic extractive solution by XAS, and this was modeled using DFT. An interplay between steric strain and coordination energies apparently gives rise to a nonlinear trend in discriminatory lanthanide ion complexation across the series. Our results highlight the importance of optimizing chelate molecular geometry to account for both coordination interactions and strain energies when designing new ligands for efficient adjacent lanthanide separation for rare-earth refining.

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INTRODUCTION The rare-earth elements, consisting of primarily the 15 lanthanides (Ln), are essential for magnets, catalysts, lighting, and renewable-energy technologies. Separating the rare earths in an economically and environmentally sustainable manner is one of the most pressing technological problems of our time,1 stemming from the chemical similarity of the Ln(III) ions. Separation involves ligands that can exploit the incremental change in ionic radius brought about by the lanthanide contraction.2 Lipophilic ligands are called “extractants” and are used in liquid−liquid extraction processes to separate ions based on their different propensities to partition between coexisting water and extractant-oil phases.3 The major family of extractants used for rare-earth separation are the alkyl phosphorus acids, which have incrementally increasing affinity for lanthanide complexation from La(III) to Lu(III). This allows the light lanthanides to be separated from the heavies and for individual lanthanides to be separated from their neighbors. However, these extractants operate via a “pH-swing” mechanism (eq 1), consuming acid and base throughout the process and generating vast volumes of secondary wastes. Responsible waste management is expensive, making rare-earth refining uneconomical in countries that have stringent environmental legislation. This problem with materials balance associated with current rare-earth separation technology is the underlying cause of the rare-earth supply risk crisis that has © XXXX American Chemical Society

captured the attention of main-stream media and governmental organizations in recent years.4 3(LH)2(org) + Ln 3 + ⇌ Ln(LH ·L)3(org) + 3H+

(1)

New extractants are needed that can separate adjacent lanthanides without consuming large quantities of acid and base with the associated production of secondary wastes. To achieve this, a deeper fundamental understanding of the various factors influencing lanthanide ion complexation by organic ligands is needed. The selection of donor atoms is now wellunderstood, with concepts such as the hard and soft acid and base principle. However, the role of ligand architecture, especially for multidentate chelates, is much less wellunderstood beyond such ideas as size-match selectivity in macrocycles.5 Steric strain can have a pronounced effect on ion recognition by multidentate receptors6 but remains underexplored for lanthanide ion separation. One family of ligands that has emerged as promising candidates for adjacent lanthanide separation are the diglycolamides (DGA, Figure 1).7 These were originally developed for actinide separation in the nuclear fuel cycle,8 but it quickly became apparent that their operational chemistry Received: September 8, 2016

A

DOI: 10.1021/acs.inorgchem.6b02156 Inorg. Chem. XXXX, XXX, XXX−XXX

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conducting liquid−liquid extraction experiments across the lanthanide series under technologically relevant conditions. EXAFS was then used to characterize the solution structures of the extracted DGA-Ln(III) complexes that were modeled using DFT to understand the energetic changes associated with complexation across the lanthanide series. Finally, we relate the complexation energetics derived using DFT back to the extraction data to understand the fundamental origins of selectivity in lanthanide partitioning with DGA solvents. Our results highlight the importance of optimizing chelate molecular geometry to account for both coordination interactions and strain when designing new ligands for efficient adjacent lanthanide separation.

Figure 1. Structure of DGA ligand N,N,N′,N′-tetra(n-octyl)diglycolamide.

and extraction characteristics make them well-suited for rareearth separation.9,10 DGAs extract lanthanides based on an “anion-swing” basis (eq 2), so that extraction into the oil is favored by high concentration of anion (e.g., chloride) and reversed by low concentration. nL + Ln 3 + + 3Cl− ⇌ LnLnCl3

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EXPERIMENTAL SECTION

Solvent Extraction. N,N,N′,N′,-Tetraoctyl-diglycolamide (TODGA, Figure 1) was ordered from Marshallton Research Laboratories Inc. and used as received. Exxal 12 Alcohol and Isopar L Fluid were obtained from the ExxonMobil Chemical Company and used as received. Concentrated HCl was obtained from Alfa Aesar. Stock solutions of the lanthanides were prepared from the chloride salts obtained from Alfa Aesar. TODGA solutions (0.1 M) were prepared by massing out appropriate quantities of material followed by volumetric dissolution by 30%/vol Exxal 12 in Isopar L. Aqueous solutions were prepared from LnCl3 and HCl stock solutions at 1, 3, and 5 M HCl containing 0.1 mM of each lanthanide. Aliquots of 0.5 mL of aqueous solution were contacted with 0.5 mL of organic phase in a 2 mL conical vial. Samples were placed on a vertical rotating wheel for 1 h at 25 °C, after which the samples were centrifuged at 3000 rpm and 25 °C for 5 min to ensure phase disengagement. The phases were separated from one another, and the aqueous phase was saved for analysis. Metal concentrations in the aqueous phase were determined via inductively coupled plasma mass spectrometry before and after extraction, and metal content in the organic phase was determined by difference. All experiments were performed in triplicate. Extended X-ray Absorption Fine Structure. The collection and analysis of EXAFS data was performed using the same general method as reported previously in our publications.18 Briefly, the Pr, Nd, Eu, Yb, and Lu L3-edge spectra were collected in fluorescence mode at beamline 12-BM-B at the Advanced Photon Source (APS) at Argonne National Laboratory. A multielement Ge detector (Canberra) was used to collect the fluorescence signal at a sample-to-detector distance of ∼30 cm. The incident X-ray energy was calibrated against the inflection point energy of an Eu oxide foil. The solutions were injected into 1 mm Kapton capillaries for data acquisition, and three 1 h scans were averaged for each solution. Analyses of the k3χ(k) EXAFS was performed using EXAFSPAK, with curve-fitting using theoretical phase and amplitude functions that were calculated with FEFF8.01. The exact same model and fitting procedure was used as published previously.14 Density Functional Theory Calculations. All calculations were performed with the Gaussian 09,19 Revision D.01, software package using the B3LYP20,21 density functional. Standard 6-31+G* and 6311+G** basis sets were used for main-group elements and hydrogen for geometry optimization. Lanthanides were modeled using the largecore (LC) relativistic effective core potential (RECP) and the associated (7s6p5d)/[5s4p3d]22 basis sets. Additional 2f basis functions were added to the basis set when used in conjunction with 6-311+G** basis for light elements. Since LC RECP calculations include the 4f electrons in the core, they were performed on a pseudo singlet-state configuration. Frequency calculations at the B3LYP/LC/ 6-31+G* level were performed to ensure real vibrational modes for the minimum ground state structures and to provide zero-point energies (ZPE). ZPE and thermal corrections (T = 298.15 K) were added to the total energy to obtain the Gibbs free energy. Thermal contributions to the gas-phase Gibbs free energies were calculated using standard molecular thermodynamic approximations,23 except that vibrational frequencies lower than 60 cm−1 were raised to 60

(2)

Theoretically, this allows extraction to be controlled with decreased consumption of acid and base (relative to phosphorus acid extractants). However, the intralanthanide extraction properties of chelating ligands such as DGAs are often complex and difficult to predict, with nonlinear extractive behavior across the lanthanide series.11 To explore the origins of this behavior, we present a fundamental study of the solution structure and energetics of Ln(III)-DGA complexes in systems that are relevant to liquid−liquid extraction processes. Our findings provide a new fundamental perspective on lanthanide ion discrimination by chelating ligands, focusing on an interplay between coordination interactions and molecular strain energies. Solid-state crystallographic studies of DGA complexes show predominantly a nine-coordinate homoleptic [(DGA)3M]3+ species (M = f-block metal cation), with counterions displaced to the outer-coordination sphere and each DGA ligand forming a tridentate chelate between the two amido and central ether donors.12,13 Recently, the same inner-sphere Eu(III) coordination structure was characterized in a [Eu(DGA)3][(BiCl4)3]methanol solution using extended X-ray absorption fine structure (EXAFS) spectroscopy.14 Similar structural characteristics have also been observed in density functional theory (DFT) studies, where DGAs form tridentate chelates with lanthanides,15,16 with binding energies that apparently reflect the general extraction trend La < Eu < Lu.17 However, to date, the structural studies performed on DGA−lanthanide complexes are of limited relevance to adjacent lanthanide separation processes. Crystalline solids and dry methanol solutions containing bismuth tetrachloride do not reflect the waterimmiscible extractive solvents that contain coordinating anions and entrained water. DFT studies are usually focused on actinide−lanthanide separation with DGAs, having only been performed on up to three lanthanides across the series with stoichiometric species that do not reflect experiment (i.e., 1:1 and 2:1 DGA/Ln).15 Here we present a study that converges extractive experiments with solution-phase EXAFS and DFT simulations, spanning the lanthanide series under conditions that are relevant to adjacent lanthanide separation processes. This campaign was intended to pursue the subtle energetic differences underpinning adjacent lanthanide discrimination to better understand how the structure of chelating extractants like DGAs defines separation. Our approach involves first B

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Inorganic Chemistry cm−1. This procedure is based on the so-called quasiharmonic approximation, which was first introduced by Truhlar et al.24 and serves as a way to correct for the well-known breakdown of the harmonic oscillator model for the free energies of low-frequency vibrational modes. Free energies of solvation were calculated at the B3LYP/LC/6-31+G* level using the IEF-PCM (IEF)25 implicit solvation model with default settings. Natural Bond Orbital Analysis. Chemical bonding analysis of the [Ln(TMDGA)3]3+, Ln = La(III), Eu(III), Lu(III) complexes was performed with the natural bond orbital (NBO) method26,27 at the B3LYP/LC/6-311+G** level using NBO 6.0 program. NBO analysis provides a good quantitative description of interatomic and intermolecular interactions in accordance with the basic Pauling− Slater−Coulson representations of bond polarization and hybridization.26,27 The donor−acceptor interaction energy in the NBOs was estimated via second-order perturbation theory analysis of the Fock matrix.26,27 For each donor orbital (i) and acceptor orbital (j), the stabilization energy E(2) associated with i→j delocalization is given by Ei(2) , j = − Oi

the light members of the series (with an average separation factor of ∼2.6) than for the heavy members of the series (average separation factor of ∼1.2). This pan-lanthanide extraction trend is markedly different than the linear functions obtained when extracting with phosphorous acid extractants that have consistent adjacent lanthanide separation factors of ∼1.6 under optimal conditions.29 The transition in adjacent lanthanide separation factors is also evident in Figure 2b, which shows the extraction of lanthanides by TODGA from 3 M HCl as a function of Ln(III) 1/r (r = ionic radii at coordination number of nine; see below for justification). This suggests that the nonlinear trend is not an artifact of the nonlinear decrease in lanthanide(III) ionic radii but originates from elsewhere in the coordination structure. Toward addressing the fundamental origins of the nonlinear extractive behaviors shown in Figure 2, the first step was to characterize the solution-phase structures of the DGA-Ln(III) coordination complexes in the liquid−liquid extraction system. EXAFS measurements were taken from 0.25 M TODGA organic phases after extraction of 0.05 M lanthanide. Organic phases containing Pr, Nd, Eu, Yb, and Lu were studied to understand how the solution structure of the coordination complex changes for adjacent lanthanide pairs as well as across the series. In all cases, the L3-edge EXAFS data (presented in Supporting Information) show sinusoidal-like behavior in the region (2 ≤ k ≤ 9 Å−1). Real-space functions were generated using a Fourier transform (FT), providing a physical portrayal of the atomic ordering around the lanthanide ions. The FTEXAFS for the Eu-DGA organic phase is shown in Figure 3,

⟨i|F(̂ i , j)|j⟩2 εj − εi

where oi is the donor orbital occupancy, F̂(i,j) is the Fock operator, and εi and εj are the orbital energies.

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RESULTS AND DISCUSSION Extraction experiments were performed under conditions that are relevant to rare-earth refining processes. The aqueous phase involved lanthanide chloride salts dissolved in hydrochloric acid, which is a popular acid in the metallurgy industry.28 The DGA extractant TODGA (Figure 1) was dissolved in a typical hydrocarbon solvent used in liquid−liquid extraction processes, consisting of a mixture of paraffinic oils and branched alcohols. Figure 2a,b shows how the extraction of lanthanides by

Figure 3. FT-EXAFS data for the Eu-DGA solution in the extraction experiments (red) compared to the previously characterized [Eu(TODGA)3]3+ data (black).14 The peaks are assigned backscattering atoms based on the [Eu(TODGA)3]3+ structure (right). The model was based on that used in the previous publication.14 Figure 2. (a) The distribution coefficient (D) of lanthanides across the series by atomic number. D is the concentration ratio of lanthanide in the organic phase over the aqueous phase. The markers correspond to a 0.1 M TODGA organic phase at various aqueous phase HCl concentrations. (b) The extraction of lanthanides by 0.1 M TODGA organic phase from 3 M HCl as a function of ionic radii assuming coordination numbers of nine (taken from Shannon).30 The average adjacent lanthanide separation factors (SF = DLn1/DLn2) for the first and last four adjacent lanthanides are shown.

and the FT-EXAFS data for the rest of the lanthanides can be found in the Supporting Information. For all the lanthanides, the FT-EXAFS shows an intense peak at 1.92 Å (r + Δ) for Pr to 1.89 Å (r + Δ) for Lu that can be attributed to the innersphere donor atoms. Following the intense peak, there are two more oscillations (at 2.9 and 3.1 Å (r + Δ) for the Eu data in Figure 3), followed by broad features at higher r. The positions and intensities of these features vary slightly between the lanthanides, as is expected from the different harmonics generated from the varying bond distances caused by the lanthanide contraction. In Figure 3, The FT-EXAFS data from the Eu-DGA solution formed in the extraction experiment (red) is compared with the EXAFS data from the previously characterized and published homoleptic [Eu(TODGA)3]3+ complex (black).14 The positions and relative intensities of all significant peaks are strikingly similar between the two data sets, strongly suggesting that the

TODGA varies across the series. In Figure 2a, extraction from aqueous solutions of 1, 3, and 5 M HCl by TODGA is shown as a function of lanthanide atomic number. Generally, extraction is favored at high hydrochloric acid concentration, and a nonlinear trend is observed across the lanthanide series; a steep increase in extraction from La to Tb is followed by a leveling off from Tb to Lu. The outcome of this trend is that better separation between adjacent lanthanides is achieved for C

DOI: 10.1021/acs.inorgchem.6b02156 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry same inner-sphere [Eu(TODGA)3]3+ species prevails in both solutions. A three-shell oxygen−carbon-carbon (O, C, C) model, used in the aforementioned EXAFS study to account for the first three peaks in the FT-EXAFS,14 was therefore used to fit the EXAFS data in this study. The first O shell corresponds to the inner-sphere ether and amido O donors, presumably causing the first and major FT-EXAFS peak. The two C shells at longer distances account for the α and β diglycolamide carbons (structure shown in Figure 3) that presumably cause the two minor oscillations after the major peak. The final broad feature at ∼3.8 Å (r + Δ) may correspond to the amido N, but this was not incorporated in the model to control the number of variables in the fitting. Good fits to the EXAFS data were obtained using this model for all five Ln-DGA solution (see Supporting Information for fitted data), providing physically reasonable parameters that are shown in Table 1. As expected

The EXAFS modeling parameters, as well as the close qualitative correlation between the EXAFS from the Eu extraction phase and the published [Eu(TODGA)3]3+ species, suggests that the homoleptic [Ln(TODGA)3]3+ complex prevails in the liquid−liquid extraction system across the lanthanide series. However, as with all experimental techniques used to probe solution-phase structure, data interpretation is only as good as the model used. It is possible that other plausible models could be used to give equally good fits, although we could not conceive of any for our data sets. Despite the inherent ambiguities that comes with solution structural studies, the combination of EXAFS and previous crystallographic studies supports the use of the [Ln(TODGA)3]3+ species in our DFT modeling studies. It is our hypothesis that the nonlinear extraction behavior shown in Figure 2 arises from the effect of the lanthanide contraction on the coordination energetics of the [Ln(TODGA)3]3+ species. To investigate these effects, we conducted DFT calculations on the corresponding complexes with a model ligand, N,N,N′,N′-tetramethyldiglycolamide (TMDGA), in which the hydrophobic n-octyl substituents present in the experimental extractants were replaced by the methyl groups. On the basis of structural information from the EXAFS herein and the previously published X-ray diffraction (XRD) experiments12,32 for longer aliphatic chain analogues, we studied the homoleptic 3:1 ligand−metal [Ln(TMDGA)3]3+ complexes across the lanthanide series. A plot of the Ln−O interatomic distances between the donor oxygen atoms of TMDGA against the Shannon33 effective ionic radii (coordination number nine) of Ln3+ cations is shown in Figure 4. As all

Table 1. Metrics from the EXAFS Data Fitting Using the Three-Shell O,C,C Model CN (O,C,C) Pr

9,6,6

Nd

9,6,6

Eu

9,6,6

Yb

9,6,6

Lu

9,6,6

r, Å (O,C,C) 2.460(7), 3.27(2), 3.53(2) 2.446(6), 3.35(2), 3.59(3) 2.423(5), 3.44(2), 3.69(1) 2.324(4), 3.26(2), 3.48(2) 2.317(4), 3.21(1), 3.51(2)

σ2, Å2 (O,C,C) 0.0093(6), 0.003(2), 0.003(3) 0.0105(5), 0.007(3), 0.009(4) 0.015(5), 0.007(2), 0.010(2) 0.0120(4), 0.007(2), 0.007(3) 0.0118(3), 0.010(1), 0.008(2)

ΔE(0), eV 4.7(10) 3.4(7) 5.2(7) 1.5(4) 1.3(4)

from the lanthanide contraction, the inner-sphere Ln−O bond length decreases from Pr to Lu. The positions of the α and β C shells for all the lanthanides in Table 1 fall between 0.9 and 1 Å and 1.1−1.2 Å behind the inner-sphere O shell, just like in the previously characterized homoleptic [Ln(TODGA)3]3+ species.14 The reason why only one O shell was used to approximate the combined ether and amido donor contributions to the EXAFS, but two C shells were used for the separate Ca and Cb contributions, is because of the expected interatomic distance resolution (Δr) of EXAFS data given by Δr ≥ π/(2Δk).31 With a data range of (Δk = 9−9.5 Å−1), the interatomic distance resolution is calculated to be greater than or equal to 0.17 Å. Crystallography tells us that the average distance difference between the amidic and etheric O atoms is ∼0.1−0.15 Å, whereas the DFT simulations slightly overestimate this difference at 0.15−0.2 Å. Therefore, unfortunately, the interatomic distance between the ether and amide O shells is insufficient to be resolved using EXAFS in this k-range. This may be why the intense near-neighbor peak in the FT-EXAFS is broad and symmetric, giving no compelling reason to fit it with two shells. As the data do not have the resolution to fit the two O shells, the data were modeled in a conservative manner with a single shell of O atoms with a single (large) Debye− Waller factor, like in the previous publication from Antonio et al.14 In contrast, the M−C(carbonyl) and M−C(ether) distances are resolvable, with the distance difference being just longer than the resolution of the EXAFS data (0.22−0.3 Å). This, again, is reflected in the FT-EXAFS that show two minor longer-distance oscillations that are attributable to the positions of these carbons. Thus, we used two carbon shells to fit the data, one for Eu−C(sp2) and one for Eu−C(sp3).

Figure 4. Comparison of the DFT calculated vs experimental12 Ln− Oether and Ln−Oamide bond lengths in Ln3+−TODGA complexes.

complexes exhibit high (D3) point-group symmetry in the gas phase, only two types of Ln−O bonds are given: the Ln−Oa bond with the amide oxygen atom and the Ln−Oe bond with ether oxygen atom. Also shown in Figure 4 are the corresponding Ln−Oa and Ln−Oe bond lengths observed in two series of isomorphic crystals,12 [Ln(TEDGA)3]3+, where TEDGA is N,N,N′,N′-tetraethyldiglycolamide. As expected from the reported performance of the B3LYP functional to reproduce the structure of coordination complexes with lanthanides,16,34 the predicted Ln−O distances are somewhat overestimated compared to the crystallographic data: on average by 0.04 Å for Ln−Oa and 0.13 Å for Ln−Oe. The amide−Ln bond distances for the crystal structures of the short alkyl chain [Ln(TEDGA)3]3+ are, however, very close to the D

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binding of Ln(III) ions, we included weakly coordinated counterions in the aqua Ln3+ ions. The current theoretical model does not consider the effects of outer-sphere counterions on the binding properties of ligands, since no counterions were included in complexes with TMDGA. Nitrate anions with close to zero aqueous binding affinities to Ln(III) (e.g., log K1 = −0.1, 0.0, and 0.2 for La3+, Gd3+, and Lu3+, respectively)37 were added only to unligated metal ions to correct the imbalance of solvation effects that would have been present if we had considered only nona-aqua metal ions.33 Other weakly coordinated anions can equally be used to describe the differential effect of solvation in the competitive binding of Ln(III) ions. The results of free energy calculations for reaction 3 presented in Figure 5a confirm a steady but nonlinear increase

average Ln−Oa bond distance for the long-chain Ln-TODGA complexes in solution. This, again, supports the conclusion that the homoleptic [Ln(TODGA)3]3+ species prevails in the extraction solutions and suggests that the shortened alkyl chain length used in the simulations has a minimal impact on the coordination geometry. We tested the inclusion of the dispersion correction using the D3 method,35 which resulted in slight shortening of the Eu−Oa and Eu−Oe bonds by 0.015 and 0.030 Å, respectively. Additionally, while the gas-phase optimization of several Ln-TMDGA complexes at the M06/ LC/6-311+G** level of theory36 leads to a better agreement with the corresponding experimental crystal structures, showing only slight overestimation of Ln−Oa and Ln−Oe distances by 0.02 and 0.08 Å, respectively, both the B3LYP and M06 density functionals yield similar trends in the calculated aqueous selectivities for trivalent lanthanides (Table S1 of the Supporting Information). Although the absolute Ln−O bond lengths calculated by DFT somewhat deviate from the experimentally measured bond lengths (a full comparison of the calculated and experimental Ln−O bond lengths is given in Table S2 of the Supporting Information), the variations in bond distances with the contraction of ionic radii correspond well to those obtained by X-ray diffraction12 and EXAFS. For example, the difference in Ln−O bond length between the Pr and Nd complexes was calculated to be 0.014 Å using EXAFS and 0.016 Å in the simulations (the average distances including both the ether and amide O). This is substantially longer than the difference in the Ln−O distance for the heavy adjacent lanthanide pairs, Yb and Lu, which were 0.007 Å for EXAFS and 0.008 Å for simulation. Such resolution is admittedly at the error limits of the EXAFS data fitting (Table 1) but is an encouraging convergence between our EXAFS experiment and simulation. Consistent with the previously published XRD measurements,12 there is practically a linear variation of the Ln−Oa bond length with r, which is indicative of the ability of ligand cavity to adapt to a range of metal ions with different radii. However, the dependence of the Ln−Oe bond length on ionic radius is better described as parabolic. A small, but notable, deviation of the Ln−Oe bond length from linearity by leveling off at smaller ionic radii is a reflection of a slightly less optimal arrangement of ether donor atoms in DGA around heavy lanthanide ions. As the analysis of bond distances alone is not sufficient for understanding and predicting ligand selectivity, we now proceed to the thermodynamic analysis of competitive metal ion complexation. Recently, we developed an approach34 for predicting stability trends along the Ln(III) series that was capable of reproducing aqueous selectivities arising from the variation in the size of the trivalent f-block metal ions. According to this approach, a competitive complexation of La(III) over Ln(III) with TMDGA can be written as:

Figure 5. Plots of (a) predicted aqueous-phase selectivities, ΔΔGaq (La/Ln), [kcal/mol] and (b) TMDGA ligand strain energy (shown per ligand), ΔΔEstrain (La/Ln), [kcal/mol] vs 1/r [1/Å], where r is ionic radius30 of lanthanide ions.

in selectivity with decreasing size of the metal ion, with a much larger slope for the early Ln(III). In general, these computational results are consistent with liquid−liquid extraction studies (Figure 2), demonstrating the correct trend of much higher separation ability of TODGA for the adjacent lighter Ln(III) and higher extraction strength for the heavier Ln(III). However, the magnitude of predicted selectivity pertaining to aqueous-phase systems is consistently larger than in the extraction studies. It is generally expected that the selectivity for the biphasic extraction of heavier Ln(III) would be lower

[Ln(TMDGA)3 ]3 +(aq) + [La(NO3)3 (H 2O)3 ](aq) ⇌ [Ln(NO3)3 (H 2O)3 ](aq) + [La(TMDGA)3 ]3 +(aq) , ΔΔGaq (La(III)/Ln(III))

(3)

To assist in dispersing the high cationic charge of strongly solvated Ln3+ ions into the medium and more accurately describing the differential effect of solvation in the competitive E

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lanthanide (LPOamide→n*Ln) and ether oxygen→lanthanide (LPOether→n*Ln) interactions depicted in Figure 6 are representative of the so-called “σ donation”, reflecting the charge transfer from the TMDGA ligands to Ln(III) ion. The leading LPOamide→n* Ln and LPOether→n*Ln donor−acceptor NBO interactions associated with the donation of electron density from the oxygen donor atoms of the TMDGA ligand to Ln = La(III), Eu(III), Lu(III) are summarized in Table 2. The

than the selectivity in the homogeneous aqueous phase with the same type of ligand, because the difference in the solvation free energy between two Ln(III) complexes in the nonpolar organic phase would be less than in the aqueous phase. This is in line with the difference in selectivities between the theoretically predicted values in the aqueous phase and the values determined by solvent extraction. The nonlinear trend in selectivity is related to a nonlinear change in the ligand strain energy across the lanthanide series (Figure 5b), as will be discussed in further detail below. Overall, good consistency between theory and experiment demonstrates that the computational approach based on the thermodynamic analysis of complexation provides the essential foundation for understanding ligand selectivity across the Ln(III) series. To gain additional insight into the structure and chemical bonding of [Ln(TMDGA)3]3+, we performed NBO analysis of the representative [Ln(TMDGA)3]3+ complexes, where Ln = La, Eu, and Lu. Analysis of the experimental crystal structures and DFT-optimized geometries of [Ln(TMDGA)3]3+ shows that the Ln−Oe bond distances are typically ∼0.10−0.20 Å longer than the Ln−Oa distances. This suggests that the amide oxygen donor atoms possess stronger electron-donating ability toward Ln(III) compared to the ether oxygen atom of TMDGA. Accordingly, the Wiberg bond indices (WBIs), which can be viewed as a measure of bond order, are much higher for the Ln−Oa bond (0.175−0.195) than they are for the Ln−Oe bond (0.109−0.117). The low magnitude of WBIs indicates that the bonding of TMDGA ligands to lanthanide ions is essentially ionic, which is in agreement with the results of previous chemical bonding studies on the Ln(III)−TODGA systems.16,34 To quantitatively assess the interactions between Ln(III) and the TMDGA ligands, a more detailed analysis of chemical bonding was performed within the framework of the second-order perturbation theory (SOPT), implemented in the NBO program. SOPT describes the [Ln(TMDGA) 3 ] 3+ complex as Lewis acid (Ln) bonded to Lewis base (TMDGA). This description means that the strength of donor (occupied electron lone pairs of the amide, LPOamide, and ether, LPOether, oxygens)−acceptor (vacant valence orbitals of Ln(III), n*Ln) interactions in [Ln(TMDGA)3]3+ would be defined by the Lewis basicity/acidity of the components. Figure 6 shows the form of the interacting lanthanide and ligand NBOs and the complementary overlap of the donor and acceptor NBO hybrids. The coordinative amide oxygen→

Table 2. Leading Donor−Acceptor Natural Bond Orbital Interactions and Their Second-Order Stabilization Energies E(2) donor NBO→acceptor NBOa in [Ln(TMDGA)3]3+, Ln = La(III), Eu(III), Lu(III)

complex

LPOamide→n*M (two amide oxygens)

LPOether→ n*M (ether oxygen)

total (one TMDGA ligand)

charge on Ln(III)

[La(TMDGA)3]3+ [Eu(TMDGA)3]3+ [Lu(TMDGA)3]3+

120.0 133.7 149.7

28.4 31.1 33.7

148.4 164.8 183.4

+2.19 +2.13 +2.07

a

The unstarred and starred labels correspond to Lewis (donor) and non-Lewis (acceptor) NBOs, respectively. Functional groups of TMDGA contributing to the particular interaction are shown in parentheses. LP denotes an occupied lone pair; n* denotes vacant Ln(III) orbitals. Energies given in kilocalories per mole.

second-order perturbation theory suggests that [La(TMDGA)3]3+, [Eu(TMDGA)3]3+, and [Lu(TMDGA)3]3+ complexes are stabilized by 148.4, 164.8, and 183.4 kcal/mol, respectively. Consistent with this trend, NBO charges on Ln(III) in the corresponding complexes (Table 2) decrease in the order La(III) > Eu(III) > Lu(III). As expected, the strength of the donor−acceptor interaction involving amide oxygen (LPOamide→n*Ln) is significantly higher than that involving ether oxygen (LPOether→n*Ln), with the difference in E(2) (kcal/ mol) to be 31.6 for La, 35.8 for Eu, and 41.2 for Lu. Such a difference in binding strengths can be readily understood by considering how empty s and d lanthanide orbitals are spatially distributed, relative to the ligand’s amide and ether oxygen lone pairs(LPs). It appears that the amide oxygen provides two directional sp hybridized (s7.2%; p92.8% and s52.5%; p47.5%) LPs that overlap favorably with the acceptor lanthanide orbitals. In contrast, the ether oxygen has only one directional sp (s41.0%; p59.0%) LP, while the other one is a pure p-type (p100%) LP with its lobes oriented perpendicular to the Ln− Oether axis, which significantly diminishes the overlap with the lanthanide orbitals. Another factor contributing to the observed stronger binding of the amide oxygen donors is a resonance stabilization of the amide functional group that leads to more spatially extended sp LPs and thus greater overlap with metal orbitals. Overall, the chemical bonding analysis of [Ln(TMDGA)3]3+ complexes suggests that upon traversing the series from La(III) to Lu(III) the binding strength between TMDGA and Ln(III) increases. This trend can be seen as a consequence of the stronger TMDGA−heavier Ln ionic attractions caused by the lanthanide contraction, which forces the lanthanide and ligand into close proximity, enabling greater overlap of donor−acceptor orbitals and thus strengthening TMDGA−Ln coordination. While the thermodynamic calculations can predict the correct order of selectivities from liquid−liquid extraction and aqueous-phase complexation studies, they do not necessarily

Figure 6. Donor−acceptor interactions with leading contributions to second-order stabilization energies in [Ln(TMDGA)3]3+, Ln = La(III), Eu(III), Lu(III) complexes. Color legend: O, red; N, blue; C, gray; H, white; Ln, turquoise. F

DOI: 10.1021/acs.inorgchem.6b02156 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry explain why certain ligands exhibit high metal ion selectivity and what ligand design strategies could be explored to enhance metal ion selectivity. To understand the underlying factors determining the selectivity across the Ln(III) series, it is instructive to analyze on the comparative basis two binding characteristics: ligand strain induced by metal complexation and complementarity.38 The ligand strain is associated with the energy cost of structural reorganization upon metal ion complexation. Complementarity is a concept of achieving an optimal orientation of each binding group in a chelate with respect to the metal center. The optimal metal binding geometry with each functional group can be determined from either quantum chemical calculations for separate fragments or crystallographic evidence. The maximum binding affinity with the amide O can be attained when the metal ion lies within the plane of the amide group, with an M−OC bond angle close to 143°.39 With the ether and pyridine donors, the strongest interaction with the metal ion occurs in the plane of the molecule along the dipole moment of each group.40,41 Attaching vectors to each donor atom with a length close to the average M−donor atom bond distance42,43 and directionality at the ideal metal ion position provides a useful way to visualize the degree of complementarity between the functional groups in a ligand and a metal center. The equilibrium distance between donor atoms in a free ligand due to electrostatic repulsion between electron lone pairs on the ligand is typically larger than the optimal distance for chelating with the largest lanthanide, La3+. Hence, ligand strain would almost always increase with decreasing the size of the Ln3+ ion. The incurred higher strain as Ln3+ goes from La3+ to Lu3+ can be compensated by stronger metal−ligand bond energy, typically obtained with unconstrained monodentate ligands.44 Very high selectivity for smaller over larger Ln can be obtained if two conditions are met. First, the ligands should have sufficient flexibility to accommodate metal ions with smaller ionic radius. Second, the building blocks used to construct a multidentate host must be able to adopt a conformation in which all binding sites are positioned to achieve a high degree of complementarity with the metal ion and attain maximum binding affinity. Conversely, for a ligand to be more selective for larger Ln3+, it should be rigid to yield high reorganization energy for smaller Ln and/or poorly organized for complexation with smaller metal ions. To illustrate the utility of our analysis to rationalize the stability trends in Ln(III) complexes, we compared binding characteristics of three neutral ligands, namely, TMDGA, N,N,N′,N′-treraalkyl-3,6-dioxaoctanediamide (DOODA), and 1,10-phenanthroline-2,9-dicarboxamide (PDAM). Compared to TODGA, DOODA exhibits opposite selectivity in extractant-phase complexation studies,45 while PDAM shows no selectivity in the aqueous phase for Lu3+ over La3+.46 The structures of the La3+, Gd 3+, and Lu3+ complexes (only one ligand is shown for clarity) along with the vectors representing the direction of the ideal metal position with respect to each donor are depicted in Figure 7. For each building block in TMDGA and PDAM these vectors are reasonably converged at both La3+ and Lu3+, with slightly larger deviation for the latter ion. However, as evident from the side view of the complexes, the ether binding sites in the metal-bound conformation of DOODA do not converge at the Ln(III), indicating that this architecture fails to provide a complementary orientation for Ln(III). As a result of this structural organization, DOODA is a weaker extractant than TODGA, despite having an additional

Figure 7. DFT-optimized geometries of [Ln(TMDGA)3]3+, [Ln(DOODA)2]3+, and [Ln(PDAM)2]3+ (Ln = La(III), Gd(III), Lu(III)), with vectors illustrating the optimal placement of La(III), Gd(III), and Lu(III) ions relative to each donor group. Only one ligand in the considered complexes is visualized for clarity. ΔΔEstrain (kcal/mol) denotes strain energy per ligand upon complexation with Gd(III)/ Lu(III) relative to complexation with La(III).

ether group.45 The results also establish that DGA exhibits the smallest reorganization energy (the magnitude of ΔΔEstrain for each ligand is shown in Figure 7) upon complexation with Lu3+ relative to complexation with La3+, and thus, DGA is the most adaptive to the change in the metal ion radius. Furthermore, a closer inspection of ΔΔEstrain for DGA across the Ln(III) series (Figure 5b) reveals a quadratic dependence on the ionic radius. A steeper increase in ΔΔEstrain for smaller Ln(III) is consistent with the predicted nonlinear increase in the Ln(III) binding affinity with decreasing the size of the metal ion (Figure 5a) and diminished ability of DGA to separate this group of Ln(III). It is, however, important to remember that the difference in the steric strain is only one component of the overall difference in the complexation strength that can give rise to a nonlinear trend in discriminatory lanthanide ion complexation across the series. On the basis of the foregoing analysis, DOODA is a flexible ligand with quite small difference in the strain energy between La3+ and Lu3+ (ΔΔEstrain in Figure 7), but its ethylene-linked ether building block exhibits poor complementarity for metal complexation. On the contrary, PDAM achieves a high degree of structural organization, but it is too rigid to provide optimal cavity size without too much strain for small metal ions. Only in the case of DGA, when two criteria of high complementarity and low strain are achieved, a significant thermodynamic preference for smaller metal ions is observed. Thus, rigidifying the DGA framework is not expected to be a viable approach for further increasing the binding affinity for heavy Ln(III) compared to light Ln(III). However, incorporating DOODA and PDAM into a more rigid framework could be a successful strategy in achieving high selectivity for light Ln(III). G

DOI: 10.1021/acs.inorgchem.6b02156 Inorg. Chem. XXXX, XXX, XXX−XXX

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Inorganic Chemistry

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(6) Hancock, R. D.; Martell, A. E. Ligand design for selective complexation of metal ions in aqueous solution. Chem. Rev. 1989, 89 (8), 1875−914. (7) Ansari, S. A.; Pathak, P.; Mohapatra, P. K.; Manchanda, V. K. Chemistry of Diglycolamides: Promising Extractants for Actinide Partitioning. Chem. Rev. 2012, 112, 1751−1772. (8) Sasaki, Y.; Sugo, Y.; Suzuki, S.; Tachimori, S. The novel extractants, diglycolamides, for the extraction of lanthanides and actinides in nitric acid n-dodecane system. Solvent Extr. Ion Exch. 2001, 19, 91−103. (9) Naganawa, H.; Sugo, Y.; Shimojo, K.; Mitamura, H. Diglycolamide-type agent and method for extraction of rare earth metals. JP2007327085A, 2007. (10) Narita, H.; Tanaka, M. Separation of rare earth elements from base metals in concentrated nitric acid, sulfuric acid and hydrochloric acid solutions with diglycolamide. Solvent Extr. Res. Dev., Jpn. 2013, 20, 115−121. (11) Sasaki, Y.; Sugo, Y.; Morita, K.; Nash, K. L. The Effect of Alkyl Substituents on Actinide and Lanthanide Extraction by Diglycolamide Compounds. Solvent Extr. Ion Exch. 2015, 33 (7), 625−641. (12) Okumura, S.; Kawasaki, T.; Sasaki, Y.; Ikeda, Y. Crystal structures of lanthanoid (Ln, Ln = Tb, Dy, Ho, Er, Tm, Yb, and Lu) nitrate complexes with N,N,N′,N′-tetraethyldiglycolamide. Bull. Chem. Soc. Jpn. 2014, 87 (10), 1133−1139. (13) Reilly, S. D.; Gaunt, A. J.; Scott, B. L.; Modolo, G.; Iqbal, M.; Verboom, W.; Sarsfield, M. J. Plutonium complexation by diglycolamide ligands-coordination chemistry insight into TODGAbased actinide separations. Chem. Commun. 2012, 48 (78), 9732− 9734. (14) Antonio, M. R.; McAlister, D. R.; Horwitz, E. P. An europium diglycolamide complex: insights into the coordination chemistry of lanthanides in solvent extraction. Dalton Trans. 2015, 44, 515−521. (15) Wang, C.-Z.; Lan, J.-H.; Wu, Q.-Y.; Zhao, Y.-L.; Wang, X.-K.; Chai, Z.-F.; Shi, W.-Q. Density functional theory investigations of the trivalent lanthanide and actinide extraction complexes with diglycolamides. Dalton Trans. 2014, 43 (23), 8713−8720. (16) Narbutt, J.; Wodynski, A.; Pecul, M. The selectivity of diglycolamide and bis-triazine-bipyridine ligands in actinide/lanthanide complexation and solvent extraction separation - a theoretical approach. Dalton Trans. 2015, 44 (6), 2657−2666. (17) Ali, S. M.; Pahan, S.; Bhattacharyya, A.; Mohapatra, P. K. Complexation thermodynamics of diglycolamide with f-elements: solvent extraction and density functional theory analysis. Phys. Chem. Chem. Phys. 2016, 18 (14), 9816−9828. (18) Ellis, R. J.; Meridiano, Y.; Chiarizia, R.; Berthon, L.; Muller, J.; Couston, L.; Antonio, M. R. Periodic behavior of lanthanide coordination within reverse micelles. Chem. - Eur. J. 2013, 19, 2663−75. (19) Frisch, M. J. et al. Gaussian 09, revision D.01; Gaussian, Inc: Wallingford, CT, 2009. (20) Becke, A. D. Density-functional thermochemistry: The role of exact exchange. J. Chem. Phys. 1993, 98 (7), 5648−52. (21) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37 (2), 785−9. (22) Dolg, M.; Stoll, H.; Savin, A.; Preuss, H. Energy-adjusted pseudopotentials for the rare earth elements. Theor. Chim. Acta 1989, 75 (3), 173−94. (23) McQuarrie, D. A.; Simon, J. D. Molecular Thermodynamics; University Science Books: United States, 1999. (24) Ribeiro, R. F.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Use of Solution-Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation. J. Phys. Chem. B 2011, 115 (49), 14556−14562. (25) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105 (8), 2999−3093. (26) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint. Chem. Rev. 1988, 88 (6), 899−926.

CONCLUSIONS Our approach converged liquid−liquid extraction experiments with solution-phase EXAFS and DFT simulations to investigate the subtle energetic differences underpinning adjacent lanthanide discrimination with diglycolamide ligands. EXAFS measurements suggest that the homoleptic [(DGA)3Ln]3+ complex persists in the organic extractive solution across the lanthanide series, and this was used as a model in our DFT calculations. The simulations point to an interplay between steric strain and coordination energies that gives rise to the nonlinear trend in lanthanide ion complexation across the series. Our investigations demonstrated the importance of strain energies in designing chelating ligands for adjacent lanthanide separations.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.6b02156. EXAFS data for Pr, Nd, Eu, Yb, and Lu, along with model fits; calculated Gibbs free energies for the reaction given by eq 3 at the M06/LC/6-311+G** level of theory, and a full comparison between the calculated and experimental Ln−O bond lengths (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. (R.J.E.) *E-mail: [email protected]. (V.B.) ORCID

Ross J. Ellis: 0000-0001-7691-5205 Vyacheslav S. Bryantsev: 0000-0002-6501-6594 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Critical Materials Institute, an Energy Innovation Hub funded by the U.S. Department of Energy, Office of Energy Efficiency and Renewable Energy, Advanced Manufacturing Office. M.N.V was supported through ASTRO2016 internship program at ORNL. This research used resources of the National Energy Research Scientific Computing Center supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC0205CH11231.

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REFERENCES

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DOI: 10.1021/acs.inorgchem.6b02156 Inorg. Chem. XXXX, XXX, XXX−XXX