Cm (III) Separation Mechanism with

Article Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX

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Theoretical Elucidation of Am(III)/Cm(III) Separation Mechanism with Diamide-type Ligands Using Relativistic Density Functional Theory Calculation Masashi Kaneko,* Hideya Suzuki, and Tatsuro Matsumura Nuclear Science and Engineering Center, Japan Atomic Energy Agency, 2-4, Shirakata, Tokai-mura, Ibaraki 319-1195, Japan

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S Supporting Information *

ABSTRACT: We elucidated the separation mechanism between Am(III) and Cm(III) ions by using two different types of diamide ligands, diglycolamide (DGA) and alkylated diamide amine (ADAAM), by means of the density functional theory technique and electron density analysis. The molecular geometries and formation reactions of the metal−ligand complexes were modeled by using [M(DGA)3]3+ and [M(ADAAM)(NO3)3(H2O)]. We successfully reproduced Cm(III) selectivity over Am(III) with DGA and Am(III) selectivity over Cm(III) with ADAAM. Furthermore, we analyzed the bonding properties between the metal ion and the diamide-type ligands by using model complexes, [M(DGA)3]3+ and [M(ADAAM)(NO3)3(H2O)], and revealed the differences in terms of the bond dissociation energy and the metal 5f orbital participation in the covalency between the Am(III) and the Cm(III) complexes. It was suggested that the differences were key factors to understand the Am(III)/Cm(III) selectivity.

1. INTRODUCTION The partitioning and transmutation (P&T) strategy is used for rational and safe disposal of high-level liquid waste (HLLW).1 For development of the P&T strategy, selective separation of minor actinides (MAs), which are Np(IV), Am(III), and Cm(III) ions, from HLLW is required owing to their extremely long half-lives and high radiotoxicity. Especially, mutual separation between trivalent MA ions and lanthanide (Ln) ions and between Am(III) and Cm(III) ions have been challenging tasks because the chemical properties of their metal ions in solution, for example, oxidation state, molecular geometry, chemical reactivity, and stability, are similar to each other, which makes selective separation difficult.2 Solvent extraction has been employed as one of the most useful techniques for MA separation by using various types of extraction reagents.3 Considerable research on reagent selection for MA separation by way of solvent extraction has enabled us to correlate the separation behavior with the bonding interaction between the metal ion and the reagents according to Pearson’s hard and soft acids and bases (HSAB) rule.4 The reagents indicate MA(III)/Ln(III) selectivity by recognizing the hardness or softness of the metal ions. In other words, harder bases such as oxygen-donor reagents favorably select Ln(III) ions over MA(III) ions; softer bases such as sulfur- and nitrogen-donor reagents favorably select MA(III) ions over Ln(III) ions. Suzuki and co-workers applied the difference in the metal ion recognition capabilities of the reagents to separate Am(III) from Cm(III) The combination of two different diamide-type © XXXX American Chemical Society

reagents, namely, alkyl diamide amine (ADAAM) and diglycolamide (DGA), shown in Figure 1, allowed for Am(III)

Figure 1. Chemical structures of diamide-type ligands for DGA (a) and ADAAM (b).

selectivity over Cm(III) with high separation factor of 41.5 Sasaki et al. achieved high selectivity for f-block metal ions compared to the other softer metal ions, indicating that DGA reagents work as hard-donor ligands.6 The previous study also implied that ADAAM reagent works as soft-donor ligand owing to its Am(III) selectivity over Eu(III) with a separation factor of 25.7 These studies meant that DGA and ADAAM reagents have high extraction ability for trivalent f-block metal ions and different selectivity of Am(III) ion over Cm(III) ion. It indicated that the selectivity of Am(III) ion over Cm(III) ion has the similar tendency of that of Am(III) ion over Eu(III) ion. The high Am(III) selectivity over Cm(III) might be ascribed to the synergistic effect of the softer property of hydrophobic ADAAM and harder property of hydrophilic Received: June 20, 2018

A

DOI: 10.1021/acs.inorgchem.8b01624 Inorg. Chem. XXXX, XXX, XXX−XXX

Article

Inorganic Chemistry DGA, which works as a masking agent.5 This implied that Am(III) ion has the softer acid nature than Cm(III) ion. However, the hardness or softness of Am(III) and Cm(III) ions and the detailed selectivity are yet to be understood. Density functional theory (DFT) calculations have been employed as a powerful tool to discuss solvent extraction separation among f-block metal ions and bonding properties between metal ions and ligands in their complexes.8−11 In previous works, we successfully reproduced Am(III)/Eu(III) selectivity by using several extraction reagents, namely, Cyanex-301 (sulfur-donor), Cyanex-272 (oxygen-donor), tetrakis(2-pyridylmethyl)ethylenediamine (TPEN) (nitrogendonor), DGA (oxygen-donor), and nitrilotriacetamide (NTAamide) (nitrogen- and oxygen-donor), by applying DFT calculations to the complexation reaction in the solution phase.12−14 Furthermore, we suggested that the dependency of the Am(III)/Eu(III) selectivity on the chalcogen-donor atoms can be attributed to the difference in the degree of metal f orbital participation in the covalent interaction between the metal ion and the donor atoms, and it can be correlated to soft acid classification, which is based on the HSAB rule,4 by means of bond overlap population analysis.15 The present study aims to explain the difference in Am(III)/ Cm(III) selectivity between DGA and ADAAM reagents by using DFT calculation. We focus on the relative stability of the complex formation reaction in solution between Am(III) and Cm(III) complexes. For comparison of hardness or softness between Am(III) and Cm(III) ions, we perform bonding analysis between the metal ion and the ligand by using a simplified model complex. This study is expected to contribute to the understanding of fundamental properties, such as chemical bonding of actinide compounds, and accelerate the development of a process for mutual separation of MA(III) ions by theoretically explaining Am(III)/Cm(III) selectivity with practical extraction reagents.

three oxygen atoms of the amide group and one nitrogen atom of the amine group, for modeling the metal−ADAAM complex because MA(III) complexes in general have crystal structures and coordination spheres similar to those of Ln(III) complexes.25,26 Assuming that the metal−ADAAM complex maintains the coordination number of [Eu(NTAamide)(NO3)3] as 10, we modeled the complex as [M(ADAAM)(NO3)3(H2O)], in which the coordination of one amide group was substituted into the N-methyl group and one H2O donor, and all alkyl chains of two amide groups were replaced with methyl groups. Two stereoisomers, namely, cis-type and transtype, were considered for [M(ADAAM)(NO3)3(H2O)] depending on how to select the substitution of one amide into the water donor. To reduce computational costs, we ignored the conformational geometrical isomers, δδ- or δλtype, which appear owing to variations of then OC−CH2− N−CH2−CO conformation during chelation by the nitrogen atom of the amine group and the oxygen atom of the amide group to a metal ion. In the present study, the alkyl chain effect of amide and amine groups in DGA and ADAAM ligands is not discussed by replacing all alkyl chains with methyl groups, although it is important, because it has been indicated that the length of the alkyl chains hardly affects selectivity among trivalent f-block metal ions and the chemical component of the complexes, as reported in several publications, in which dialkyldithiophosphinic acids27 and malonamides,28 as well as DGA6,23,29 and ADAAM,7 were employed. Herein, we pursue the chemical stability and bonding property from the viewpoint of the interaction between the metal and the ligands in metal−DGA and metal−ADAAM complexes. 2.2. Modeling of Complex Formation Reaction. Complex formation reactions were modeled by referring to the stoichiometry suggested previously6,7 and by using the metal complexes, which were considered in the previous section. We estimated the relative stability of [M(TMDGA)3]3+ in the aqueous phase and [M(ADAAM)(NO3)3(H2O)] in the organic phase compared to two hydration species, [M(NO3)n(H2O)9−2n](3−n)+ (n = 0 and 1), as given by eqs 1 and 2 for the DGA and the ADAAM systems, respectively. In addition, we evaluated simply the masking effect of TMDGA onto the Cm(III) ion as eq 1 minus eq 2, as expressed by eq 3.

2. COMPUTATIONAL DETAILS 2.1. Modeling of Am(III) and Cm(III) Complexes. The hydration species was modeled as [M(H2O)9]3+ for both Am(III) and Cm(III) complexes because the coordination number of water to one metal ion has been reported as 9.00 and 8.98 for Am(III) and Cm(III), respectively.16 In addition, we considered the coordination of one nitrate ion to the metal ion, as recently reported by UV−vis absorption characterization17 and actinide L3-edge EXAFS studies18 as well as DFT calculation.19 Assuming that the coordination number was fixed at 9 and a nitrate ion works as a bidentate ligand, [M(NO3)(H2O)7]2+ was added to the hydration species.20,21 Both species were modeled by referring to single-crystal X-ray diffraction data of [Am(H2O)9](CF3SO3)320 and [Cm(H2O)9](CF3SO3)3.20,21 The metal−DGA complex was modeled as [M(DGA)3]3+, in which 3 equiv of DGA work as trident chelates, as characterized by solvent extraction of MA(III) ions.22 Here, we considered Δ- and Λ-type optical isomers of [M(TMDGA)3]3+ by using tetramethyl DGA (TMDGA) and referring to single-crystal data of [Am(TMDGA)3](ClO4)3.23 In the case of the metal−ADAAM complex, the solvent extraction study indicated that the metal/ligand ratio was 1:1 for the Am(III) and the Cm(III) systems,5 as well as for the Eu(III) system.7 We employed the single-crystal data of 10fold coordination complex [Eu(NTAamide)(NO3)3],24 in which NTAamide works a tetradentate chelate by using

[M(NO3)n (H 2O)9 − 2n ](3 − n) +aq + 3TMDGA aq → [M(TMDGA)3 ]3 +aq + n NO3−aq + (9 − 2n)H 2Oaq

(1)

[M(NO3)n (H 2O)9 − 2n ](3 − n) +aq + ADAAMorg + (3 − n)NO3−aq → [M(ADAAM)(NO3)3 (H 2O)]org + (8 − 2n)H 2Oaq

(2)

[M(TMDGA)3 ]3 +aq + ADAAMorg + 3NO3− + H 2O → [M(ADAAM)(NO3)3 (H 2O)]org + 3TMDGA aq

(3)

Stabilization energies due to complexation were calculated as the difference in standard Gibbs energies, ΔG°, under the condition of 298.15 K and 1.0 atom. ΔG° values were estimated as the difference between final state, G°fin, and initial state, G°ini, as shown in eq 4. The Gibbs energy of each compound is described by inner energy, U, Boltzmann constant, kB, temperature, T, and entropy, S, as expressed by eq 5. U is calculated as the sum of total energy from the B


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Inorganic Chemistry electronic structure calculation by using DFT, Etotal, and the thermal correction energies, including contributions to vibration, rotation. and translation, denoted as Evibration, Erotation, and Etranslation, respectively, as expressed by eq 6. S is calculated as the sum of contributions to spin multiplet, vibration, rotation and translation, denoted as Sspin, Svibration, Srotation, and Stranslation, respectively, as expressed by eq 7. Etotal consists of the interaction energies of nucleus−nucleus, nucleus−electron, and electron−electron and kinetic energy of electrons, in which the relativistic effect between the nucleus and the electron at the scalar-relativistic level,30−32 and the solvation effect by bulk solvent are included implicitly.33 Vibrational contribution to the inner energy and entropy was estimated by means of quasi-harmonic approximation, and to this estimate, correction for the well-known breakdown of the harmonic oscillator model for free energies of low-frequency vibrational modes was introduced by raising the vibrational frequencies less than 60 to 60 cm−1.34,35 Rotational contribution to energy and entropy was calculated by assuming a rigid rotator, in which the symmetric number was set to 3 for [M(H2O)9]3+, 1 for [M(NO3)(H2O)7]2+, 3 for [M(TMDGA)3]3+, and 1 for [M(ADAAM)(NO3)3(H2O)]. ΔG° = G°fin − G°ini

(4)

G = U + kBT − TS

(5)

U = Etotal + Evibration + Erotation + Etranslation

(6)

S = Sspin + Svibration + Srotation + Stranslation

(7)

which cavity sizes of 1.99 and 1.95 Å were used for Am and Cm atoms, respectively.45 The cavity size effect to the complexation reaction energies has been indicated to be sufficiently small (below 0.06 kcal mol−1) by comparing the relative complexation energies with different cavity size, for examples, 2.24 and 1.72 Å, which corresponding to the sizes of Ac(III) and Lr(III) ions, respectively.45 The resolution of identity approximation46,47 was employed for all self-consistent field (SCF) calculations to reduce the computational cost of two-electron integrals. The SCF condition for convergence was set to the same criteria as in our previous methods,12−15 in which a threshold value of 10−8 hartree to total energy difference during iteration and angular grid points of Lebedev194 for optimization without final grid calculation and Lebedev302 with Levedev434 as final grid for single-point calculation, where the special grid was additionally constructed for Am and Cm atoms with an integral accuracy of 14.0, were imposed. The ground state of the metal complexes was obtained as the septet state for Am(III) complexes and the octet state for Cm(III) complexes by using the spinunrestricted Kohn−Sham procedure. Spin contamination of their spin multiplets was negligibly small by checking the value, {⟨s2⟩ − s(s + 1)}/⟨s2⟩, where s and ⟨s2⟩ denote spin quantum number and the expectation value, respectively, which was only ca. 0.07% for Am systems and ca. 0.06% for Cm systems. Electron population analysis was performed for the singlepoint calculation results by using natural population analyses48,49 by using NBO program50 and Mulliken’s method.51,52 The optimized structures and the MO surfaces were visualized three-dimensionally by using VESTA ver. 3.0.53

2.3. DFT Calculations. All DFT calculations were performed using ORCA program package ver. 3.0.36 The allelectron relativistic effect was considered in scalar-relativistic zeroth-order regular approximation (ZORA) Hamiltonian,30,31 to which the spin−orbit coupling effect determined using the Breit−Pauli perturbative method was added.32 In the trial calculations, we have confirmed that the perturbative spin− orbit coupling effect has only minor contribution (below 0.005 kcal mol−1) to the Gibbs energy calculation for complex formation reactions, although it is important to reproduce the correct trend of the reduction potentials for actinide ions.9 The relativistic all-electron basis set was assigned to actinide atoms37 and the other atoms.38 Geometry optimization and normal vibration frequency calculations were performed using the BP86 functional39,40 without any constraints of geometry and symmetry. Single-point energy calculations were performed using the B2PLYP functional.41 The validity of the functionals was confirmed by comparing the corresponding experimental results, such as single-crystal X-ray structures and Mössbauer isomer shifts.42−44 Especially, it was indicated that the reproducibility of Mössbauer isomer shifts of 151Eu and 237 Np nuclides in the complexes depends on a degree of exact Hartree−Fock exchange admixture in the density functional and the admixture of 53% of B2PLYP functional was more suitable than BP86 and B3LYP functionals, which it might be due to overestimation of covalency by using the functional with smaller amount of the admixture.42 In the single-point calculation relating to the Etotal term in eq 6, the bulk solvent effect was included as the continuum dielectric model for the water phase (relative permittivity = 80.4, refractive index = 1.33) and n-dodecane phase (relative permittivity = 2.0, refractive index = 1.42) by using the conductor-like screening model (COSMO) method,33 in

3. RESULTS AND DISCUSSION 3.1. Equilibrium Structures of [M(NO3)n(H2O)9−2n](3−n)+, [M(ADAAM)(NO3)3(H2O)], and [M(TMDGA)3]3+. The calculated equilibrium structures are shown as ball-and-stick descriptions in Figure 2. Normal vibrational frequency analysis confirmed that all optimized geometries were located at the local minimum structures. All Am(III) complexes were observed to have the same symmetry as the Cm(III) complexes in their coordination spheres. Their Cartesian coordinates in Angstrom units are available in the Supporting Information (given as xyz format files). When focusing on the coordination geometry of [M(NO3)n(H2O)9−2n](3−n)+ (n = 0, 1), which is shown in Figure 2a, the coordination geometry of [M(H2O)9]3+ was obtained as a tricapped trigonal structure with the D3d point group. In the case of [M(NO3)(H2O)7]2+, the coordination sphere was obtained as a bicapped trigonal structure, which included one nitrogen atom of nitrate and five oxygen atoms of water as the vertexes of a trigonal prism, and it had mirror symmetry, in which the mirror plane passed through the nitrogen atom of nitrate, segmenting the trigonal prism perpendicularly. The coordination sphere of [M(TMDGA)3]3+ was indicated to have tricapped trigonal geometry, in which six oxygen atoms of amides and three oxygen atoms of ethers are arranged as the vertexes of a trigonal prism and a tricapped structure, respectively, with C3 rotational axis for both the Δ and the Λ isomers. The coordination spheres of [M(ADAAM)(NO3)3(H2O)] were obtained as low-symmetry polygons with the C1 point group for both cis- and trans-type isomers, as indicated by the single-crystal structure of [Eu(NTAamide)(NO3)3].24 In the case of the trans-type isomer, pseudomirror symmetric geometry was observed, in which the mirror plane C


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Inorganic Chemistry

consisted of the metal atom and the two nitrogen atoms of one nitrate group and one amine group in the ADAAM ligand. When comparing the Gibbs energies of the pairs of isomers, Λtype isomer for [M(TMDGA)3]3+ and cis-type isomer for [M(ADAAM)(NO3)3(H2O)] were indicated to be more stable slightly than another isomer. Table 1 lists the calculated and experimental bond lengths between the metal ion and the donor atoms. The value in parentheses shows the standard deviation from the average bond lengths with more than three bonds between the metal and the donor atoms. When comparing the calculated bond lengths with the experimental ones, the bond lengths of the metal ion toward the water and the nitrate ligands are consistent within ca. 0.1 Å, but those of the metal ion toward the ADAAM ligand tend to be overestimated. We have also considered optionally the nine-coordinated species of the metal−ADAAM complex as [M(ADAAM)(NO3)3]. This was modeled by geometry optimization of the model, in which one H2O donor molecule was removed from [M(ADAAM)(NO3)(H2O)] for cis- and trans-type conformers. Their metal− N(amine) bond lengths for Am/Cm were 2.809/2.766 Å for cis-type conformers and 2.832/2.809 Å for trans-type conformers, indicating the overestimation compared to [Eu(NTAamide)(NO3)3] single crystal by ca. 0.06−0.12 Å. We believe that the overestimation observed in [M(ADAAM)(NO3)(H2O)] and [M(ADAAM)(NO3)3] is acceptable considering that Shannon’s effective ionic radius of the Eu(III) ion is smaller than that of the Am(III) ion or the Cm(III) ion by 0.02−0.03 Å,54 and the Eu−N(amine) bond lengths of Eu− NTAamide complexes vary from 2.71 to 2.77 Å in the crystal structures,24,55 thus minimizing the largest deviation by 0.15 Å. It should be noted that this overestimation indicates no substantial covalent interaction between the metal ion and N(amine) donor atom and can be compensated by improving the long-range correction part of the two-electron exchangecorrelation term in the BP86 functional during optimization by using a long-range corrected functional, such as CAMB3LYP56 or the LC-BOP57 method. We, however, think it important to discuss the weak covalent interaction, as shown in 3.3, although the long-range correction is to be considered in our future task. A comparison of the calculated bond lengths of

Figure 2. Ball−stick description of coordination geometries of [M(NO3)n(H2O)9−2n](3−n)+ (a), [M(TMDGA)3]3+ (b), and [M(ADAAM)(NO3)3(H2O)] (c). Black, red, blue, and brown spheres denote metal, oxygen, nitrogen, and carbon atoms, respectively; hydrogen atoms are omitted for clarity. The values below of Δ/Λ and cis/trans isomers for [M(TMDGA) 3 ] 3+ and [M(ADAAM)(NO3)3(H2O)], respectively, denote the relative Gibbs energy between the pairs of isomers for Am/Cm complexes in kcal mol−1.

Table 1. Comparison of Calculated and Experimental Metal−Ligand Bond Lengthsa complexes [M(H2O)9]3+ [M(NO3)(H2O)7]2+ [M(TMDGA)3]3+ (Δ) [M(TMDGA)3]3+ (Λ)

[M(ADAAM)(NO3)3(H2O)] (cis)

[M(ADAAM)(NO3)3(H2O)] (trans)

M−L bond M−Oave(trigonal) M−Oave(tricapped) M−Oave(nitrate) M−Oave(water) M−Oave(amide) M−Oave(ether) M−Oave(amide) M−Oave(ether) M−N(amine) M−Oave(amide) M−Oave(nitrate) M−O(water) M−N(amine) M−Oave(amide) M−Oave(nitrate) M−O(water)

calculated bond lengths (Å) M = Am/M = Cm M = Am/M = Cm M = Am/M = Cm M = Am/M = Cm M = Am/M = Cm

M = Am/M = Cm

2.542(24)/2.549(1) 2.531(13)/2.521(2) 2.405/2.405 2.564(37)/2.541(30) 2.445(18)/2.438(5) 2.644(1)/2.626(3) 2.443(18)/2.437(3) 2.626(3)/2.624(1) 2.873/2.937 2.543/2.519 2.507(41)/2.507(43) 2.646/2.614 2.938/2.944 2.551/2.542 2.507(31)/2.512(47) 2.644/2.587

experimental bond lengths (Å) M = Am/M = Cm

M = Am M = Am

2.465b/2.453c 2.578b/2.564c

2.428(21)d 2.519(8)d 2.428(21)d 2.519(8)d

a

The numbers in the parentheses show the standard deviation values with respect to average bond lengths. bRef 20. cRef 21. dRef 22. D


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Inorganic Chemistry

Table 2. Comparison of Calculated Gibbs Energy Differences, ΔG°, and Total Energy Differences, ΔEtotal, across Several Complexation Reactions and Separation Factor of Am(III) Ion from Cm(III) Ion (SFAm/Cm) ΔG° (M) (kcal mol−1) reaction eq 1 eq 2 eq 3

n n n n

= = = =

0 1 0 1

ΔEtotal(M) (kcal mol−1)

ΔEtotal,gas(M) (kcal mol−1)a

SFAm/Cmb

M = Am/M = Cm

ΔΔG° (kcal mol−1)

M = Am/M = Cm

ΔΔEtotal (kcal mol−1)

M = Am/M = Cm

ΔΔEtotal,gas (kcal mol−1)a

calcd

−89.07/−87.81 −74.18/−75.03 −53.17/−49.98 −38.29/−37.21 35.89/37.83

−1.26 0.85 −3.19 −1.08 −1.93

−40.73/−39.29 −36.31/−37.01 −19.08/−15.57 −14.66/−13.29 21.65/23.72

−1.45 0.70 −3.52 −1.37 −2.07

−152.67/−151.60 84.01/82.64 −514.75/−511.96 −278.08/−277.72 −362.08/−360.36

−1.07 1.37 −2.79 −0.36 −1.72

8.3 0.24 220 6.2 26

a

exp 0.38c 5.5d 5.7−41d

b

The total energies obtained under gas phase condition were used. The values were estimated using the relationship SFAm/Cm = DAm/DCm = exp(−ΔΔG°/RT). cThis value was obtained from ref 20 under the extraction condition of 1 M HNO3 with 0.1 M TODGA/n-dodecane. dTheis value was obtained from ref 5 under the extraction condition of 1.5 M HNO3 with 0.75 M ADAAM(EH)/n-dodecane.

eqs 1 and 2 shows that the systematic tendency in the values did not change, but the degree of variation between n = 1 and 2 or that between the eqs 1 and 2 was different, and the degree of variation of ΔG° was larger than that of ΔEtotal. The ΔG°(Am) and ΔEtotal(Am) values, for example, increased from n = 0 to n = 1 by 14.9 and 4.7 kcal mol−1, respectively, and they increased from eq 1 to eq 2 by 35.9 and 21.7 kcal mol−1, respectively. This difference between the ΔG°(Am) and ΔEtotal(Am) values might be caused by the fact that the thermal correction term of Gibbs energy tends to overstabilize the state, leading to the inclusion of the greater number of molecules between the initial and the final states. In this case, the numbers of molecules from the initial and the final states increase by 6 and 5 for n = 0 and 1 in eq 1, respectively, and by 4 and 3 for n = 0 and 1 in eq 2, respectively. Relative lowering of the increase in the number of molecules through the reaction from n = 0 to n = 1 or from eq 1 to eq 2 can possibly be attributed to a relative destabilization of the corresponding final state, resulting in overestimation of the variation of ΔG°(M) compared to that of ΔEtotal(M). The change in the number of molecules also explains the larger ΔG°(M) values compared to the ΔEtotal(M) values by ca. 14 kcal mol−1 in eq 3, where the number of molecules decreases through the reaction. In addition, we compared ΔEtotal(M) to ΔEtotal,gas(M), which is the total energy difference under the gas phase condition, as listed in Table 2. The ΔEtotal,gas(M) values overestimate the absolute values and have positive signs in reactions with n = 0 and 1 for eq 1 and n = 1 for eq 2 in contrast to ΔG°(M) and ΔEtotal(M). This might be ascribed to underestimation of the total energy of charged compounds, such as [M(TMDGA)3]3+ or NO3−, under the gas phase condition. Consideration of the COSMO solvation method for determining total energies improves the underestimation and the sign of the present complexation reactions to some extent, but it imparts a positive sign to the ΔG°(M) and ΔEtotal(M) values obtained using eq 3. Although the reason behind this positive sign remains unknown and will be pursued in a future work, we think it can possibly be ascribed to the exclusion of the long alkyl chains in ADAAM ligand, and explicit solvent molecules may alleviate stabilization of the metal−ADAAM complex or destabilization of the metal−TMDGA complex. By defining ΔΔG° as eq 8, we can judge the relative stability in the complexation reaction, and by extension, the Am(III)/ Cm(III) selectivity by evaluating the sign of ΔΔG°. A negative sign means Am(III) selectivity over Cm(III), whereas a positive sign means Cm(III) selectivity over Am(III). In the case of the reactions for n = 0, Am(III) selectivity was observed

Am(III) and Cm(III) complexes indicated that most of the bond lengths between the Am(III) ion and the donor atoms are consistent within the standard deviation values or larger than those between the Cm(III) ion and the donor atoms. This is comparable to the results of several DFT works that calculated the bond lengths of Am(III) and Cm(III) complexes with Cyanex-301, 5 8 Cyanex-272, 5 9 bis(chalcogenophosphinyl)imine series,60 2,6-bis(1,2,4-triazin-3yl)pyridine,61,62 and DGA63 ligands, and it is also supported by the result that Shannon’s ionic radii of Am(III) and Cm(III) ions are 0.975 and 0.97 Å, respectively.54 The exception that the Am−ligand length is shorter than the Cm−ligand length was observed in case of the metal−nitrogen(amine) length in the ADAAM complex. Similar examples have been published in DFT studies on organo-actinide compounds, MIIICp364 and MIVCp465 (M = Am, Cm; Cp− = cyclopentadienyl), and in studies on Am(III)/Cm(III) separation using the diaza-18crown-666 and N,N,N′,N′-tetrakis[(6-carboxylpyridin-2-yl)methyl]ethelene-diamine ligand.67 These studies indicated that the stronger interaction of Am(III) ion with the ligand compared to the Cm(III) ion in the f-electron orbital originates from the shortening of the Am−ligand length.64,65 This difference in the trend, that is, the Am−TMDGA length being longer than the Cm−TMDGA length but the Am− ADAAM length being shorter than the Cm−ADAAM length, implies that the Am−ADAAM bond has stronger covalency compared to that of the Am−TMDGA bond. This might be caused by the fact that the metal ion recognizes the hardness or softness of the donor atoms in the ligand. This difference will be discussed in the following sections. 3.2. Complexation Reactions of [M(TMDGA)3]3+ and [M(ADAAM)(NO3)3(H2O)]. The calculated Gibbs energy differences, ΔG°(M), for M = Am and Cm systems, based on eqs 1−3, are listed in Table 2. In addition, we have listed the total energy differences, ΔEtotal(M), which depend only on single-point energy terms, not thermodynamic properties, such as vibrational, rotational, and translational terms. In the calculations of ΔG° and ΔEtotal, we assumed the G°(M) and Etotal(M) values of [M(TMDGA)3]3+ and [M(ADAAM)(NO3)3(H2O)] as the averages of the energies between each pair of two isomers, because the stability was almost the same between the isomers, and our previous studies have indicated that the selectivity of the Am(III) ion over the Eu(III) ion does not depend on the difference between optical or conformational isomers.14,15 Numerical data of the Etotal and G° values of all compounds are given in Table S1. A comparison of the ΔG°(M) and ΔEtotal(M) values between E


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Inorganic Chemistry Table 3. Electron Configuration and Spin Population Values of the Metal Ion by Natural Population Analyses

natural spin population/electrons complexes [M(TMDGA)3]3+ (Δ) [M(TMDGA)3]3+ (Λ) [M(ADAAM)(NO3)3(H2O)] (cis) [M(ADAAM)(NO3)3(H2O)] (trans)

natural electron configuration M M M M M M M M

= = = = = = = =

Am Cm Am Cm Am Cm Am Cm

6.21

0.68

0.16

[Rn]5f 6d 7s [Rn]5f7.076d0.687s0.17 [Rn]5f6.216d0.687s0.16 [Rn]5f7.076d0.687s0.17 [Rn]5f6.266d0.827s0.20 [Rn]5f7.116d0.807s0.20 [Rn]5f6.276d0.797s0.19 [Rn]5f7.116d0.797s0.20

5f

6d

7s

5.742 6.792 5.743 6.790 5.731 6.737 5.750 6.750

0.023 0.023 0.023 0.022 0.034 0.030 0.031 0.028

0.005 0.004 0.005 0.004 0.007 0.005 0.005 0.005

(H2O)8]3+ to [M(NO3)(H2O)6]2+ as well, in which the coordination number was assumed as eight (the ΔG(M) and ΔEtotal(M) values are shown in Table S2). This might be because the natural spin population variation from [M(H2O)9]3+ to [M(NO3)(H2O)7]2+ was 5.818−5.808 electrons for M = Am system and 6.898−6.875 electrons, indicating that the coordination bond in [Cm(NO3)(H2O)7]2+ compared to [Cm(H2O)9]3+ is relatively stronger than that in [Am(NO3)(H2O)7]2+. Notably, prediction of the Am(III)/Cm(III) selectivity can be improved by considering the hydrated species accurately. However, the difference in the selectivity between the DGA and the ADAAM ligands is not mentioned yet. In the following section, we demonstrate the chemical bonding analysis between the metal ion and the ligand by using the model complexes, [M(TMDGA)3]3+ and [M(ADAAM)(NO3)3(H2O)], to approach the origin of this selectivity.

in both eqs 1 and 2, whereas in the case of the reactions for n = 1, we observed Cm(III) selectivity in eq 1 and Am(III) selectivity in eq 2. This indicates that Am(III)/Cm(III) selectivity with DGA and ADAAM can be reproduced by considering the relative stability in the complexation reaction toward [M(NO3)(H2O)7]2+, not [M(H2O)9]3+. Furthermore, we estimated the separation factors between Am(III) ions and Cm(III) ions, SFAm/Cm, by using eq 9, where R denotes the gas constant. The results indicate that the calculated values reproduce well the experimental values. The SFAm/Cm values obtained in the calculation/experiment were 0.24/0.38, 6.2/5.5 and 26/5.7−41 in the cases of DGA, ADAAM, and a combination of DGA and ADAAM, respectively. To the best of our knowledge, the difference in Am(III)/Cm(III) selectivity between DGA and ADAAM ligands has never been reproduced using quantum chemical calculations. When comparing the ΔΔEtotal and ΔΔEtotal,gas values, which are also listed in Table 2 with the ΔΔG° values, the absolute values remained unchanged compared to the ΔΔG° values. This means that Am(III)/Cm(III) selectivity does not depend on the difference in the correction terms by vibrational frequency mode analysis and COSMO solvation between the Am(III) and the Cm(III) systems. We have also tried to estimate the SFAm/Cm values when the different metal−ADAAM complex with nine-coordinated sphere, [M(ADAAM)(NO3)3], was used. Although the calculated values were 0.86 and 3.6 for ADAAM and the DGA and ADAAM combination, respectively, and were indicated to be somehow underestimated, the higher Am(III) selectivity of ADAAM than DGA can be reproduced. It was also indicated that selectivity depends strongly on the choice of hydration model of the metal ion complex because the coordination of one nitrate ion with an aqua complex, as has been suggested by a UV−vis titration study of nitrate ions into an Am(III) aqueous solution,17 was necessary to reproduce the Am(III)/Cm(III) selectivity, although this idea has already been employed in a DFT study on the separation of Am(III) ion from Eu(III) and Cm(III) ions by Shi and co-workers.62,63,68,69 The Nona-aqua complex [M(H2O)9]3+ is considered a suitable hydration model to predict Am(III) selectivity over Ln(III) ions in the complexation reaction by means of DFT calculation,12−15,70,71 but it might be unsuitable for determining the selectivity between Am(III) and Cm(III) ions owing to the higher similarity. A comparison of the variation of ΔEtotal(M) from n = 0 to n = 1 for both eqs 1 and 2 between M = Am and Cm systems showed that the coordination of the nitrate ion with [M(H2O)9]3+ yielded [M(NO3)(H2O)7]2+, resulting in destabilization of the hydrated Am(III) species by ca. 2 kcal mol−1 relative to the hydrated Cm(III) species. This destabilization was observed in the variation from [M-

ΔΔG° = ΔG°(Am) − ΔG°(Cm)

(8)

SFAm/Cm = exp( −ΔΔG°/RT )

(9) 3+

3.3. Chemical Bond Analyses of [M(TMDGA)3] and [M(ADAAM)(NO3)3(H2O)] Models. Table 3 lists the values of the natural electron configuration and spin population of the metal ion for the complexes. The result indicates that the contribution of the 6d and 5f orbital electrons are large. It was also suggested that when comparing the spin population values between the Am(III) and Cm(III) complexes in the same conformers, the 6d electron contribution was almost same, however, the 5f electron contribution was different. The 5f electron population of the Am(III) complexes was smaller than that of the Cm(III) complex by ca. 0.05 electrons for [M(TMDGA)3]3+, whereas those values of the Am(III) and Cm(III) complexes were consistent within a deviation of 0.006 electrons for [M(ADAAM)(NO3)3(H2O)]. Because previous publications correlated the atomic spin population to the Mössbauer isomer shift values as an indicator of covalency, the present result might indicate that the Am−TMDGA bond has a stronger covalency compared to the Cm−TMDGA bond. We also analyzed the partial density of states of the metal atom in the complex, PDOS(M), as well as the bond overlap density of states between the metal d or f orbital and the donor atoms, BODOS(d) or BODOS(f). The DOS value of MO number i, N(i), was calculated using eq 10, where Pμν(i) and Sμν denote the density matrix and the overlap matrix between the basis functions φμ and φν, respectively. The PDOS(M) value was obtained by inserting the basis functions, which belong to the metal atom, into both φμ and φν. The BODOS(d or f) value was obtained by inserting the basis functions, which belong to the metal d or f orbital and the donor atoms, into φμ and φν, respectively. Only α-spin basis functions were used for F


Article

Inorganic Chemistry

Figure 3. PDOS(M) and BODOS(d) curves of [M(TMDGA)3]3+ (a) and [M(ADAAM)(NO3)3(H2O)] (b), which were convoluted as Gaussian lines with the half-width value of 0.5 eV. The black bars, black broken lines, and solid lines show the α orbital energy level, PDOS(M) curves, and BODOS(d) curves, respectively.

Figure 4. PDOS(M) and BODOS(f) curves of [M(TMDGA)3]3+ (a) and [M(ADAAM)(NO3)3(H2O)] (b), which were convoluted as Gaussian lines with the half-width value of 0.5 eV. The black bars, black broken lines and solid lines show the α orbital energy level, PDOS(M) curves, and BODOS(f) curves, respectively.

focusing on the region, where the negative BODOS(f) of M−O(amide) is distributed in Figure 4, the contribution of PDOS(Am) to the peak of BODOS(f) is larger than that of PDOS(Cm), especially for [M(TMDGA)3]3+, indicating that the back-donation of the Am 5f orbital electrons toward the O(amide) atoms is larger than that of the Cm 5f orbital electrons with the antibonding overlap. The stronger antibonding nature of Am−O(amide) might have originated in the smaller atomic spin population of [Am(TMDGA)3]3+ compared to that of [Cm(TMDGA)3]3+ in Table 3. When comparing the BODOS(f) curves between [M(TMDGA)3]3+ and [M(ADAAM)(NO3)3(H2O)], we observed that the absolute values of BODOS(f) decreased from M−O(ether) to M−N(amine). To clarify this difference in the increase between Am(III) and Cm(III) systems, we analyzed the selected MO surfaces, which contributed significantly to the PDOS(M) of the metal 5f orbital and the BODOS(f) of M− O(ether) or M−N(amine) bond.

calculating the DOS values because the basis functions are adequate for considering the coordination bonds between the metal atom and the donor atoms in the valence region. N (i) = ΣμΣνPμν(i)Sμν

(10)

Figures 3 and 4 show the BODOS(d) and BODOS(f) curves, respectively, along with the PDOS(M) curves for [M(TMDGA)3]3+ (Λ) and [M(ADAAM)(NO3)3(H2O)] (trans) in the valence region. All curves were convoluted as Gaussian lines with the half-width value of 0.5 eV. In Figure 3, the BODOS(d) curves between the metal ion and the donor atoms were distributed with mainly positive values for both M = Am(III) and Cm(III) systems, regardless of the ligand, indicating that the unoccupied 6d orbital of the metal atom acts as the electron acceptor from the donor atoms with bonding-type overlap. A comparison of the BODOS(d) curves between the Am(III) and Cm(III) systems showed that the pattern of the curves remains almost unchanged. When G


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Inorganic Chemistry

Figure 5. Three-dimensional descriptions of selected α-MO surfaces with MO numbers in parentheses, and values of PDOS(M) of 5f orbital (%) and BODOS(f) of M−O(ether) or M−N(amine) bond (× 10−2) for [M(TMDGA)3]3+ (a) and [M(ADAAM)(NO3)3(H2O)] (b). The lower and upper parts show the representative MO surfaces with bonding- and antibonding-type interactions between the metal ion and the O(ether) or N(amine) atom, respectively.

Table 4. Calculated Binding Energies, Ediss, between Metal Ion and Ligand Ediss (kcal mol−1)

Ediss (kcal mol−1)a

ligand

M = Am

M = Cm

ΔEdiss (kcal mol−1)

M = Am

M = Cm

ΔEdiss (kcal mol−1)a

TMDGA ADAAM

399.14 408.59

395.51 403.46

3.62 5.12

393.99 402.55

389.76 397.42

4.23 5.13

a

The values include the basis set superposition error correction using counterpoise method.

evaluation of selectivity of Am(III) ion over Ln(III) ions by using the contribution of the valence f orbital to the covalent interaction with the donor atoms can be explored to the elucidation of the selectivity among trivalent actinide ions. To confirm a significance of the 5f orbital contribution, we also computed the complexation free energies and the DOS analyses in the case of Nd(III)/Eu(III) pair, which has similar ionic radii to Am(III)/Cm(III) pair, by the same procedure to Am(III)/Cm(III) system. The ΔΔG°(Nd/Eu) values, defined as ΔG°(Nd) − ΔG°(Eu), were estimated as 0.14 and 0.33 kcal mol−1 for TMDGA and ADAAM systems, respectively, indicating that the both ligands have Eu(III) selectivity over Nd(III) unlike the Am(III)/Cm(III) selectivity. This might be explained by the difference in the orbital contribution to the metal−ligand covalent interaction between Nd/Eu and Am/ Cm pairs. As shown in Figures S1 and S2, the f orbital contribution for Nd/Eu system had only bonding-type interaction and is quite smaller than that for Am/Cm system, although the d orbital contribution was almost the same as that of the Am/Cm system. This implies that the 5f orbital contribution has a significant role on actinide ions selectivity compared to the 4f orbital contribution on lanthanide ions selectivity. Our present work not only supports the previous works in relation to the covalency in the series of trivalent actinide complexes64,65,72 but also adds a new finding that the degree and the type of orbital mixing of the metal 5f orbital and the donor atoms is a key factor determining the selectivity

Figure 5 shows the three-dimensional descriptions of the MO surface visualized at 2.5 × 10−5 and 4.0 × 10−5 electrons bohr − 3 for [M(TMDGA) 3 ] 3 + and [M(ADAAM)(NO3)3(H2O)], respectively, with the values of PDOS(M) of 5f orbital (%)/BODOS(f) of M−O(ether) or M−N(amine) (×10−2). Bonding- and antibonding-type MO surfaces are shown in the bottom and upper parts, respectively. In Figure 5a, the 5f orbital population of M = Cm is larger than that of M = Am for the bonding-type MO, whereas that of M = Am is similar to than that of M = Cm for the antibonding-type MO. However, the significant difference in the tendency of 5f orbital population between the M = Am and the M = Cm systems cannot be observed in Figure 5b. This implies that the balance of 5f orbital population between the bonding- and the antibonding-type MOs changes depending on the Am(III)/ Cm(III) ion and the O(ether)/N(amine) atom. When focusing on the values of BODOS(f) for [M(ADAAM)(NO3)3(H2O)], those of Cm(III) system are close to zero. This was also indicated in that there was no overlaps between Cm 5f orbital and N(amine) atoms in the corresponding MO surfaces. In contrast, Am 5f orbital has the larger overlap with the N(amine) atoms. This result implies that the relatively stronger covalency in the Cm(f)−O(ether) and the Am(f)− N)amine) originates in the difference in the relative stability of [M(TMDGA)3]3+ and [M(ADAAM)(NO3)3(H2O)]. This discovery is comparable to the findings of our recent studies on Am(III)/Eu(III) selectivity,12−15 indicating that the H


Article

Inorganic Chemistry

coordination compounds, as well as to applied chemical aspects, such as accelerating the MA partitioning process by theoretically designing extraction reagents with high and efficient MA selectivity.

rather than localization of the 5f orbital energy. More recently, Huang et al. indicated in a DFT study on the Am/Cm separation with N,N,N′,N′-tetrakis[(6-carboxylpyridin-2-yl)methyl]ethelene-diamine ligand that the Am−N bond strength is stronger than the Cm−N bond strength; however, the Am− O bond strength is weaker than the Cm−O strength.69 It might be also correlated by the difference in the 5f orbital contribution to the metal−ligand bonds. Furthermore, we demonstrated to estimate simply the ionic bond dissociation energy, Ediss, which is assumed as the difference in the gaseous single-point energy for the equation, ML3+ → M3+ + L (M = Am, Cm; L = TMDGA, ADAAM). Those values in kcal mol−1 were 399.1/395.5 (Am/Cm) for L = TMDGA and 408.6/ 403.5 (Am/Cm) for L = ADAAM in Table 4. This indicated that the bond dissociation energies of AmL3+ were stronger than those of CmL3+ by 3.6 and 5.1 kcal mol−1 for L = TMDGA and ADAAM, respectively, and the relative Am− ADAAM bond to Cm−ADAAM bond was stronger than the relative Am−TMDGA bond to Cm−TMDGA bond by 1.5 kcal mol−1. This might be also one origin of the difference in the relative stability of [M(TMDGA)3]3+ and [M(ADAAM)(NO3)3(H2O)]. Finally, we succeeded in elucidating that the difference in the contribution of metal 5f orbital to M− O(ether) in TMDGA and M−N(amine) in ADAAM between Am(III) and Cm(III) produces the difference in selectivity of the Am(III) ion over the Cm(III) ion between TMDGA and ADAAM ligands.

■

ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.8b01624.

■

Listings of numerical data of energies, complexation reaction (PDF) Cartesian coordinates for all complexes (ZIP)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Masashi Kaneko: 0000-0001-5428-2144 Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This work was supported by JSPS KAKENHI Grant Number JP17K14915.

4. CONCLUSION We presented the origin of selectivity of the Am(III) ion over the Cm(III) ion with two types of diamide ligands, DGA and ADAAM, which are thought to be among the most reliable candidates for achieving mutual separation between MA(III) ions, by means of scalar-relativistic DFT calculations. After modeling the equilibrium structures of the complexes by referring to the corresponding single-crystal X-ray diffraction experiments [M(TMDGA) 3 ] 3 + and [M(ADAAM)(NO3)3(H2O)] for DGA and ADAAM complexes, respectively, we calculated the complexation reactions of Am(III) and Cm(III) ions with the ligands based on the previously reported reaction schema and the standard Gibbs energies. The relative stability of the complexation reactions between Am(III) and Cm(III) complexes reproduced the Am(III)/Cm(III) selectivity with DGA and ADAAM reagents, in which DGA selects Cm(III) ion over Am(III) ion and ADAAM selects Am(III) ion over Cm(III) ion, considering the coordination of a nitrate ion with the hydration species. In addition, we performed metal−ligand bond analyses by using the model complexes, [M(TMDGA)3]3+ and [M(ADAAM)(NO3)3(H2O)], to understand the fundamental differences in Am(III)/Cm(III) selectivity between the ligands. The differences in the degree of overlap and the degree of orbital mixing between the metal 5f orbital and the O(ether) or N(amine) atom were discussed. We suggested that the Am(III)/Cm(III) selectivity with the two practical ligands can be explain the participation of the valence d and f orbitals in the covalent interaction with the donor atoms. We will extend the present prediction and analytical methods for MA(III) selectivity to integrated prediction procedures for the selectivity of MA(III) ions over Ln(III) ions by combining the results of our present works and the HSAB rule. We expect the present work to contribute to fundamental chemical aspects, such as understanding the bonding properties of f-block

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