Journal of Nuclear and Radiochemical Sciences, Vol. 17, pp. 9-15, 2017

ArticlesRoles of d- and f-orbital electrons in the complexation of Eu(III) and Am(III) ions withalkyldithiophosphinic acid and alkylphosphinic acid using scalar-relativistic DFT
calculations
Masashi Kanekoa, Masayuki Watanabea,*, Sunao Miyashitab, Satoru Nakashimab, caNuclear Science and Engineering Center, Japan Atomic Energy Agency, 2-4, Shirakata, Tokai-mura, Naka-gun,Ibaraki-ken 319-1195, Japanb
Graduate School of Science, Hiroshima University, 1-3-1, Kagamiyama, Higashi-Hiroshima, Hiroshima-ken 7398526, Japanc
Natural Science Center for Basic Research and Development, Hiroshima University, 1-4-2, Kagamiyama,
Higashi-Hiroshima, Hiroshima-ken 739-8526, Japan
Received November 14, 2016; Accepted March 3, 2017; Published online March 21, 2017
Scalar-relativistic density functional calculations were applied to the complexation of Eu(III) and Am(III) ionswith alkyldithiophosphinic acid (S-donor) and alkylphosphinic acid (O-donor) from the viewpoint of the bonding
nature of valence orbitals of a metal ion. Two and four conformers for the S-donor and O-donor complexes,
respectively, were optimized at the ZORA-BP86 level. The stabilization energies by complex formation between
the metal ions and the ligands toward the hydrated metal ions were estimated at the ZORA-B2PLYP level; thesecalculations reproduced the experimental Am/Eu selectivities, where the S-donor ligand preferably coordinates toAm(III) ion rather than Eu(III) ion, whereas O-donor ligand selectively coordinates to Eu(III) ion rather than
Am(III) ion. Electron population analyses based on the molecular orbitals indicated that the d-orbital electrons inboth the Eu and Am complexes participate in bonding covalent interactions with donor atoms and have surprisingly similar contributions. This result suggests that the covalent interaction between the d-orbital electrons in
the metal ion and the ligands may be due to the geometrical similarity of the molecular structures of the Eu andAm complexes. In contrast, the contributions of the f-orbital electrons in the metal ions were different in the Eu
and Am complexes. In the case of the S-donor complexes, non-bonding and bonding contributions were observed
for the Eu and Am complexes, respectively, and in the case of the O-donor complex, bonding and anti-bonding
contributions were observed for the Eu and Am complexes, respectively. This result implies that the selectivities
of Eu(III) and Am(III) ions were determined by the difference in the participation of their f-orbital electrons, nottheir d-orbital electrons, in covalent interactions.

1. Introduction
High-level radioactive liquid waste (HLLW) containing
many types of metal ions is generated after the reprocessing ofspent nuclear fuel. Minor-actinides (MA: Am and Cm) havelong-term radiotoxicity due to their long half-lives andα-activities; thus, the partitioning and transmutation is a rational method for their disposal. In this method, MA ions are
separated from HLLW, followed by transmutation of the MA
ions to short-lived nuclides; this method was developed inorder to reduce their environmental loads.1 However, theselective separation of MA ions from lanthanide (Ln) ions isdifficult due to the similarity of their chemical properties, suchas their oxidation states, geometric structures, and chemical
stabilities in solution.2 To effectively separate MA ions, themolecular design of separation materials that have high selectivity for MA ions over Ln ions is desirable.
Solvent extraction has been employed for the separation of
MA ions from Ln ions.3-5 Selectivities for MA and Ln ionshave been investigated using various extraction reagents.
Previous studies indicated that S- and N-donor ligands such asalkyldithiophosphinic acid 6,7 (R 2 PS 2 H; Fig ure 1a) and
N,N,N’,N’-tetrakis(4-pyridylmethyl)ethylenediamine8 (TPEN),
respectively, preferably coordinate to MA ions over Ln ions,whereas O-donor ligands such as alkylphosphinic acid 6*Corresponding author. E-mail: watanabe.masayuki@jaea.go.jp(R 2PO2H; Figure 1b) selectively coordinate to Ln ions over
MA ions. This dependency of MA/Ln selectivity on donor
atoms has been explained using Pearson’s hard and soft acids
and bases (HSAB) rule.9 S- and N-donor atoms are softer
bases than O-donor atoms; they bond more strongly to MA
ions than Ln ions because MA ions are softer acids than Lnions due to the extended distribution of their electron orbitals
in the valence region.10 The difference in covalency between
MA and Ln complexes may determine the separation behaviors of MA ions from Ln ions; however, it is difficult to quantitatively discuss covalency using the HSAB rule.
Density functional theory (DFT) is a powerful tool tounderstand the chemical stabilities and electronic states of
f-block compounds,11-14 which has been successfully applied toevaluation of feasibility to separate MA ions from Ln ions.15
Discussion of the nature of the bonding between the metal ion
and ligands in Ln and MA complexes has been controversial.

S
HS

P
R

O
R

(a) alkyldithiophosphinic acid

HO

P
R

R

(b) alkylphosphinic acid

Figure 1. Molecular structures of (a) S- and (b) O-donor extraction
ligands.

© 2017 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 03/22/2017

10

J. Nucl. Radiochem. Sci., Vol. 17, 2017

Watanabe

16

MS6 and MO6 (M = Sm and Cm) environments for alkyldithiophosphinic and alkylphosphinic acids, respectively. 23 The
geometrical coordinates of the metal complexes were createdby referring to the single crystal X-ray diffraction data of thenona-hydrated complexes, [M(H2O)9]3+ (M = Eu and Am),24,25
and the S-donor complex, [Sm(R 2PS2)3] (R = cyclohexyl)26.
However, this could not be performed for the O-donor complexes, [M{(R 2PO2)2H}3], because their crystal structures are
not available.
Here, we considered simple models for both the S-donor andO-donor complexes in which all the alkyl chains of the phosphine group were replaced with methyl substituents. We
believe that the MA/Ln selectivity is primarily determined by
the coordination bond between the metal ion and the ligands,
not by the hydrophobic properties of the alkyl chains. This isbecause the length of the alkyl chain of an extraction ligand
affects its performance for extracting the metal ions but minimally affects its selectivity for MA/Ln ions, as indicated bysome studies.27,28 The stereoisomerism of f-block complexes
influences their spectroscopic properties29 and their Am/Eu
selectivities.30 Some stereoisomers exist for the S-donor andO-donor complexes based on the chelating effects of theligands (Figure 3). The S-donor complex, [M(Me2PS2)3], has
two geometrical isomers (Δ, Λ) that are crystallographicallyinequivalent, as observed in single crystal X-ray diffraction
experiments (Figure 3a).26 In the case of the O-donor complex, [M{(Me 2 PO 2) 2 H}3], we considered four conformers(Δ[δδδ], Δ[λλλ], Λ[δδδ], and Λ[λλλ]) based on the screwing
direction of the ligands toward the plane comprising a metal
ion and bidentate O-donor atoms, denoted as δ or λ, as well as
the Δ and Λ isomers (Figure 3b). In this case, assuming that
the O-donor complex has pseudo C3 symmetry as observed in
the case of the S-donor complex,26 we did not consider the δδλand λλδ conformers.
All DFT calculations were performed by the quantum
chemical calculation package ORCA ver. 3.0 developed by
Neese et al.31 The scalar-relativistic effect was considered by
the zeroth-order regular approximation (ZORA) Hamiltonian32
using the formalism implemented by Wüllen.33 The spin-orbit
coupling effect was included in the present calculations using
the Breit-Pauli perturbation method.34 The SARC basis set,
optimized for scalar-relativistic ZORA calculations, wasassigned to all atoms.19-21 The spin multiplicities of theAm(III) and Eu(III) complexes were set to the spin septet
state. The unrestricted Kohn-Sham method was applied to the
open-shell system. BP8635,36 and B2PLYP37 exchange-correlation functionals were employed for geometry optimization andsingle-point calculations, respectively, under gas conditions
because these methods have been confirmed in our previous
studies to reproduce the equilibrium structures, the strengths

Cao et al. applied f-in-core relativistic effective core potential(RECP), which does not consider f-orbital electrons explicitly
but sets that their contributions using a projector operator, to
MA/Ln separation by alkyldithiophosphinic acid17 and alkylphosphinic acid.18 They suggested that the selectivity of MA
and Ln ions is determined by the contribution of s-, p-, andd-orbital electrons, not f-orbital electrons, in the metal ion.17
Meanwhile, our previous study using the segmented all-electron relativistic contracted (SARC) basis set,19-21 which explicitly includes f-orbital electrons, indicated that the difference inthe contribution of f-orbital electrons to metal-ligand bonding
between Eu(III) and Am(III) ions contributes to the Am/Eu
selectivity.22
This study elucidates the role of the atomic orbitals of themetal ions in the complexation behavior of Eu(III) andAm(III) ions with alkyldithiophosphinic acid and alkylphosphinic acid using DFT calculations. It focuses on the relative
stability of the metal ion by complexation reaction and discusses the covalent interactions of the atomic orbitals in themetal with the donor atoms of the ligands. More specifically,
the d- and f-orbital electrons of the metals and their major contributions to the electron populations were intensively studied
here. We aim to investigate the correlation between the covalency of f-block compounds and the separation mechanism of
MA ions from Ln ions. We also suggest an answer to thequestion of the origin of the selectivity of MA and Ln ions.
2. Calculations
In this study, we ignored the detailed reaction mechanism,
such as subsequently complex formation and dehydration processes, in order to simply correlate Am/Eu selectivity with relative stabilit y bet ween initial and f inal states. This
assumption is crude when estimating the absolute value ofGibbs free energy difference (ΔG), because the effect of solvation and dehydration entropy are not included. It is, however,valid for the comparison of the Gibbs free energy difference
between Eu and Am systems, because their coordinationgeometries are almost the same and the effect of stepwise
dehydration or formation is finally cancelled when estimating
the difference of ΔG between Eu and Am systems. We considered the stabilization of hydrated Eu(III) and Am(III) ions by
the formation of complexes and modeled the complexation
reactions, as illustrated in Figure 2. Solvent extraction experiments have reported that one metal ion of Ln or MA forms acomplex with three equivalents of monomeric R 2PS2H (R =2,4,4-trimethylpentyl) and dimeric R 2PO2H (R = 2,4,4-trimethylpentyl) ligands.23 The coordination geometries of thesecomplexes in solution, investigated by extended X-ray absorption fine structure (EXAFS) experiment, are suggested to be(a) S-donor
MIII(H2O)93+

+

Me
Me
3
P
S – S

S

Me2P SSMeMe P O
O

H O
–

Me
P Me
O

+ 9H2O

S
S
PMe2

O

(b) O-donor
MIII(H2O)93+ + 3

S
M

Me2
P

H

Me P
O
Me2 2
P
O
PMe2
O
O
O
M
H
O
O
O
P
PMe2
O
Me2
O
Me2P
O
H

+ 9H2O

Figure 2. Reaction models of the complexation of Eu(III) or Am(III) ion with (a) S- and (b) O-donor ligands in aqueous solution.

J. Nucl. Radiochem. Sci., Vol. 17, 2017

Roles of d- and f-orbital electrons in the complexation of Eu(III) and

11(a) S-donor complex [M(Me2PS2)3](b) O-donor complex [M{(Me2PO2)2H}3]













[]

[]

[]

[]

Figure 3. Three-dimensional descriptions of the conformers of (a) S- and (b) O-donor complexes. The black, purple, yellow, red, brown, andpink spheres represent metal, phosphorus, sulfur, oxygen, carbon, and hydrogen atoms, respectively.

of coordination bonds and the relative stabilities of complexation reactions of f-block compounds.22 Equilibrium structure
searches were performed without any geometrical constraints,
followed by normal vibrational frequency calculations.
Resolution of the identity (RI) approximations, Split-RI-J38
and RIJCOSX,39 were employed for all self-consistent field(SCF) calculations for the pure-DFT and hybrid-DFT computations, respectively. For the detailed computational conditions, such as the accuracy of self-consistent field calculations
and the level of basis sets, please refer to Reference 22.
3. Results and discussion
3.1. Comparison of stereoisomer. Normal vibrational frequency analysis after geometry optimization indicated that all
the obtained molecular structures were located in local minima. The three-dimensional geometries of the optimized
structures of the S- and O-donor complexes were visualizedusing VESTA 3.0 program40 and are shown in Figure 3. All
the S-donor complexes have distorted octahedral geometries,
whereas the MO 6 arrangement of the O-donor complexes
belongs to the pseudo O h point group. These results were dueto the difference in the bite angles between the monomeric
S-donor and dimeric O-donor ligands.17,18,23 Table 1 shows acomparison of the metal-ligand distances of the Eu and Am
complexes with S- and O-donor ligands. In the case of the
S-donor complexes, the distances between the metal ion and
the S atoms and between the metal ion and the P atoms wereca. 2.84 and 3.39 – 3.40 Å, respectively. In the case of theO-donor complexes, both the Eu and Am complexes have similar geometries wherein the metal-ligand distances were 2.31 –2.36 Å and 3.66 – 3.76 Å for M-O and M-P, respectively. The
variation of bond length among stereoisomers was small forboth S-donor and O-donor complexes. These bond lengths
were consistent with the experimental values for Sm and Cm
complexes.23
Gibbs free energy difference (ΔG) for the complexation
reaction was calculated as the energy difference in the sum of
Gibbs free energy values of the reactants and products, as
described in Figure 2. The Gibbs free energy (G) was divided
into total energy (Etot) obtained by single-point calculations at
the B2PLYP level and a thermal correction term of Gibbs freeenergy (G corr) obtained by calculating the normal vibration
modes at the BP86 level (eq 1). The Gcorr term includes a thermal correction for the enthalpy (Hcorr), the entropy term (S),TABLE 1: Calculated metal-ligand distances for Eu andAm complexes with S- and O-donor ligands
Complex

M-Save or M-Oave / Å

M-Pave / Å

M=Eu

M=Am

M=Eu

M=Am

Δ

2.844

2.839

3.398

3.389

Λ

2.844

2.839

3.399

3.389

Exp.a

2.803
(M=Sm)

2.826(M=Cm)

3.40(M=Sm)

3.45(M=Cm)

2.312

2.355

3.711

3.730

M(Me2PS2)3

M{(Me2PO2)2H}3
Δ[δδδ]aΔ[λλλ]

2.319

2.357

3.663

3.689

Λ[δδδ]

2.319

2.354

3.685

3.748

Λ[λλλ]

2.311

2.352

3.718

3.764

Exp.a

2.301
(M=Sm)

2.32(M=Cm)

3.83(M=Sm)–

Reference 23.

and temperature (T), as shown in eq 2. The Hcorr and S terms
include contributions from vibration (vib), which is based on
the approximation of a strictly harmonic oscillator, rotation(rot). The rotation here is assumed as a rigid rotor, and translation (trans) (eqs 3 and 4). Sspin denotes the entropy term generated from the spin multiplicity of compound. All Gcorr values
were calculated under standard state condition (298.15 K, 1
atom).
G = Etot + Gcorr
Gcorr = Hcorr – TS
Hcorr = Htrans + Hvib + Hrot
S = Strans + Svib + Srot + Sspin

(1)
(2)
(3)
(4)

Table 2 shows the ΔEtot(M), ΔGcorr(M), and ΔG(M) values
for the S- and O-donor complexes. In the case of the S-donor
complexes, the ΔG(Am) values are more negative than theΔG(Eu) values for both Δ and Λ conformers. In the case of theO-donor system, the ΔG(Eu) values are smaller than the
ΔG(Am) values for the Δ[δδδ], Δ[λλλ], Λ[δδδ], and Λ[λλλ] conformers. Defining ΔΔG as ΔG(Eu) – ΔG(Am), none of the12

J. Nucl. Radiochem. Sci., Vol. 17, 2017

Watanabe

TABLE 2: ΔEtot(M), ΔGcorr(M), and ΔG(M) for M = Eu and Am complexes with S- and O-donor ligands and their averagevalues with standard deviations
Complex

ΔEtot(M) / kJ mol–1

ΔGcorr(M) / kJ mol–1

ΔG(M) / kJ mol–1

M=Eu

M=Am

M=Eu

M=Am

M=Eu

M=Am

Δ

–1928.42–1947.52–249.06–247.39–2177.48–2194.92

Λ

–1928.98–1945.78–250.44–253.25–2179.42–2199.03

Average–1928.70–1946.65–249.75–250.32–2178.45–2196.98

Std. dev.

0.28

0.87

0.69

2.93

0.97

2.06

Δ[δδδ]–2138.83–2122.46–261.72–258.06–2400.55–2380.51Δ[λλλ]–2135.75–2114.56–257.40–259.56–2393.16–2374.12

Λ[δδδ]–2134.49–2116.22–260.99–255.20–2395.48–2371.42

M(Me2PS2)3

M{(Me2PO2)2H}3

Λ[λλλ]–2141.88–2125.37–256.12–260.21–2398.00–2385.57

Average–2137.74–2119.65–259.06–258.25–2396.80–2377.91

Std. dev.

2.86

4.42

2.36

1.93

2.76

5.52

ΔΔG were dependent on the conformations of the S-donor andO-donor complexes. The average ΔΔG values were 18.5 ± 1.1
kJ mol –1 for the S-donor system and –18.9 ± 4.2 kJ mol –1 for
the O-donor system. These results reproduced the experimental selectivities and relative stabilities of Am(III) and Eu(III)ions; bis-(2,4,4-trimethylpentyl)-dithiophosphinic acid andbis-(2,4,4-trimethylpentyl)phosphinic acid showed separation
factors (DAm /D Eu) of 5900 7 and 0.058,6 respectively, corresponding to ΔΔG = 21.5 and –7.1 kJ mol –1, respectively.
Furthermore, the difference of the ΔGcorr(M) values between
the Eu and Am systems was smaller than that of the ΔEtot(M)values. For example, in the case of the O-donor complex, theaverage ΔGcorr(M) values were –259.1 ± 2.4 and –258.3 ± 1.9
kJ mol –1 for M = Eu and Am, respectively. In contrast, theaverage ΔEtot(M) values were –2396.8 ± 2.8 and –2377.9 ± 5.5
kJ mol–1 for M = Eu and Am, respectively. This indicates thatthe dominant contribution to the estimation of ΔG(M) is
ΔE tot (M) which based on the orbital interactions, and not
ΔGcorr(M). In other words, the Am/Eu selectivity in this caseshould be determined by the difference between the orbital
interactions of the Eu and Am complexes, i.e., the chemicalbonding.
3.2. Orbital interactions by population analysis. To discuss the orbital interactions in Eu and Am complexes with Sand O-donor ligands, the atomic spin population of the metal
ions, ρ spin (M), was estimated using Mulliken’s procedure(Table 3).41 The absolute values of ρ spin (M) of the S-donor
complex were greater than those of the O-donor complex for
both the Eu and Am systems. This may be explained by thefact that the decomposition of the electronic degeneracy oforbital levels caused by the decrease of the octahedral symmetry of the S-donor complexes, which belong to the pseudo-D3
point group, resulted in an increase of the orbital overlap
between the center metal and donor atoms. In all the cases,
the f-orbital electrons made a dominant contribution toρspin(M). Comparing the atomic orbital components of ρspin(M)between the Eu and Am complexes, the contributions of the dand f-orbital electrons of the Am complexes were greater thanthose of the Eu complexes, whereas the contributions of the sand p-orbital electrons to ρ spin(M) did not vary significantly
between the Eu and Am complexes for both the S- andO-donor systems. This indicates that the difference in thecontributions of d- and f-type atomic orbital electrons ofEu(III) and Am(III) ions to their complexes may correlate with
Am/Eu selectivity. Figure 4 shows selected MO surface

TABLE 3: Mulliken’s atomic spin population of Eu andAm ions for S- and O-donor complexesρspin(M) / electrons

Complex

all

s

p

d

f

M(Me2PS2)3 (Δ)
M=Eu

6.129 0.015 0.027 0.097 5.990

M=Am

6.138 0.024 0.033 0.134 5.948

M{(Me2PO2)2H}3 (Δ[δδδ])
M=Eu

6.038 0.006 0.016 0.047 5.969

M=Am

6.020 0.011 0.015 0.068 5.926(a) d-type MOs(b) f-type MOs

 





M=Eu

M=Am





Figure 4. Selected MO surface descriptions of (a) d-type and (b)f-type MOs for S-donor complexes were visualized at 2.5 × 10 –5 electrons/bohr3.

descriptions for S-donor complexes. In the case of d-type
MOs, the bond overlap between metal ion and donor atoms
was indicated to be same for Eu and Am systems. In the caseof f-type MOs, there was no overlap between Eu 3+ ion anddonor atoms, whereas the explicit orbital interaction between
Am 3+ ion and donor atoms was observed. This result suggested that the orbital overlap between metal ion and donor

J. Nucl. Radiochem. Sci., Vol. 17, 2017

Roles of d- and f-orbital electrons in the complexation of Eu(III) and(a) S-donor& ' 

0.10

2.0

0.02

1.0

0.00

0.0

-0.05

-1.0
 

-0.10

-2.0
-20

-15



-10

-5

 


0.05

1.0

0.00

0.0
-1.0

-0.05

0.01

0.5

0.00

0.0

-0.01

-0.5
 

-0.02

-1.0
-20

-15

-10

   
1.0

0.02

0.01

0.5

0.00

0.0
-0.5

-0.01

 

 
-2.0

-0.10
-20

-15



-10

-5

 %

2.0

0.10

 %! " 

1.0# $ 

0.05# $ 

M=Am

! " 

M=Eu

13

-1.0

-0.02

-5

-20

 

-15

-10

-5

   

Figure 5. Partial density of states (PDOS) curves of the d-orbital electrons of metal ions (black solid line) and MO overlap population (MOOP)
curves between the d-orbital of the metal ions and the donor-atoms of the ligands (blue broken line) with orbital energy level (black bar) in thevalence α-spin MO region for Eu and Am complexes with S- and O-donor ligands.

(a) S-donor& ' 

1.0

1.0

1.0

1.0


-0.5-0.5 

-1.0

-1.0
-20

-15



-10

-5

 
1.0

1.0
0.5

0.5

0.0

0.0

-0.5

-0.5

0.5

0.0

0.0

-0.5

-0.5
 

-1.0

-1.0
-20

-1.0

-1.0
-20

-15



-10

-5

 

-10

-5

   
1.0

1.0

0.5

0.5

0.0

0.0

-0.5
 

-15 %!! " 

0.0

0.5

# $! 0.0

 %

M=Am

0.5

# $! 

M=Eu

0.5

!! " 

-0.5 

-1.0

-1.0

-1.5

-1.5
-20

-15

-10

-5

   

Figure 6. Partial density of states (PDOS) curves of the f-orbital electrons of metal ions (black solid line) and MO overlap population (MOOP)
curves between the f-orbital of the metal ions and the donor-atoms of the ligands (blue broken line) with orbital energy level (black bar) in thevalence α-spin MO region for Eu and Am complexes with S- and O-donor ligands.

atoms was a critical factor to understand the Am/Eu selectivity.
Molecular orbital overlap population (MOOP), whichenables us to evaluate the strength and sign of the bonding
overlap between AOs in each MO, was applied to these complexes.42 Recently, this analysis was employed in computat ion a l st ud ie s of t he b ond i ng prop e r t ie s of f-blo ck
compounds.43-45 The MOOP of the ith MO, termed OPi, can be
described in terms of eq 5:
OPi = 2 Σ μΣνcμicνiSμν(5)where cμ and cν denote the MO coefficients of the basis func-

tions χ μ and χ ν, respectively, and S μν denotes the overlap integral between χμ and χ ν. To discuss the property of the bonding
between the d- or f-orbital of the metal ion and the donor
atoms, μ was defined as belonging to the set of the d- or f-typebasis functions in the metal ion, and ν was defined as belonging to the set of all basis functions in the donor atoms. The
partial density of states (PDOS) curves of the AOs in the metal
ion, with MOOP between the AOs in the metal ion and thedonor atoms in the valence α-spin orbital region and withselected MO surfaces, are shown in Figures 5 and 6. These
curves can be described as a Gaussian line shape profile convoluted with a half-width of 0.5 eV using the single-point calculation results of the Δ conformer of [M(Me2PS2)3] and the14

J. Nucl. Radiochem. Sci., Vol. 17, 2017Δ[δδδ] conformer of [M{(Me2PO2)2H}3].
The MOOP curve between the d-orbital in the metal ion andthe donor atoms correlates to the PDOS of the d-orbital in themetal ion with a positive linearity in all systems (Figure 5),
indicating that the d-orbital in either the Eu(III) ion or Am(III)ion participates in a bonding covalent interaction with the Sand O-donor atoms, as observed in the MO surface descriptions. The bonding interaction strength of the O-donor
complex was 3 to 4 times greater than that of the S-donor complex. It was because, in O h symmetry, d-type AOs and p-type
AOs belong to different irreducible representation, whereas, inD 3 symmetry, d-type AOs (x 2 –y 2 , xy, xz and yz) and p-type
AOs (x and y) belong to same irreducible representation. It is
indicated that the mixing of d-type AOs of metal ion andp-type AOs of donor atoms leads to the increase of MOOP for
S-donor complex. Interestingly, there were no differences inthe bonding properties of the Eu and Am complexes in either
S- or O-donor systems. This suggests that the analogous contribution of d-type AOs to the interaction between the metal
ion and the donor atoms results in the formation of similarequilibrium structures in the Eu and Am complexes. In contrast, in the case of f-type AOs, the bonding properties weresignificantly different depending on the metal ion and ligands,
as shown in Figure 6. In the case of the Eu complex, there was
no overlap with the S-donor atoms and weakly positive overlap
with the O-donor atoms, indicating a non-bonding interactionin the S-donor complex and a bonding interaction in the
O-donor complex, as observed in the MO surface descriptions.
Meanwhile, the f-orbital of Am(III) ion has a positive overlap
with the S-donor atoms and a strongly negative overlap with
the O-donor atoms, indicating a bonding interaction in the
S-donor complex and an anti-bonding interaction in the
O-donor complex. This suggests that the bonding interaction
between the 5f-orbital in Am(III) ion and the S-donor atoms
stabilized [Am(Me2PS2)3] relative to [Eu(Me2PS2)3]. In contrast, the anti-bonding interaction between the 5f-orbital in
Am(III) ion and the O-donor atoms and the bonding interaction between the 4f-orbital in Eu(III) ion and the O-donor
atoms may result in destabilization of [Am{(Me2PO2)2H}3] relative to [Eu{(Me2PO2)2H}3]. This difference in the f-orbital
contributions to covalent interactions was a key factor in
determining the Am/Eu selectivity of S- and O-donor ligands,
although the correlation between the orbital contribution tocovalency and the relative stability of the Am/Eu system wasas yet undetermined and should be discussed carefully in our
future work.
4. Conclusion
Relativistic DFT calculations were applied to the chemical
separation of Am(III) complex from Eu(III) complex with Sand O-donor ligands to elucidate the correlation between thebonding properties and the Am/Eu selectivity. The computational stabilization energies of complexation with S- andO-donor ligands reproduced the experimentally observed
selectivity, where S-donor ligands selectively coordinate toAm(III) ion rather than Eu(III) ion and O-donor ligands preferably coordinate to Eu(III) ion rather than Am(III) ion
regardless of the conformers of their complexes. Mulliken’s
atomic spin population analysis revealed that the d- andf-orbital electrons in the metal ions majorly contribute to thechemical bonding. MOOP analysis implied that the contributions of d-orbital electrons are almost same for Eu(III) andAm(III) complexes, whereas the contributions of the f-orbital
electrons are significantly different. The similar interactionsof the d-orbital electrons in both the Eu and Am complexes aresuggested to contribute to the analogous geometries of the Eu
and Am complexes. The difference in the contributions of the
f-orbital electrons of Eu and Am ions is implied to be the ori-

Watanabegin of the Am/Eu selectivity. It is interesting to note that both
the d- and f-orbital electrons in the metal ions play importantroles in formation of covalent bonding; however, their functions are different. We hope that the present work will be usef ul to elucidate the separation behavior of MAs f rom
lanthanides and will contribute to the improvement and optimization of partitioning and transmutation technologies.
References(1) H. Oigawa, K. Nishihara, S. Nakayama, Y. Morita,
Proceedings of Actinide and Fission Product Partitioning
and Transmutation 10th Information Exchange Meeting(OECD/NEA, San Francisco, California, USA, 2012),
p.123.
(2) K. L. Nash, Solvent Extr. Ion Exch. 11, 729 (1993).
(3) Z. Kolarik, Chem. Rev. 108, 4208 (2008)(4) S. Tachimori, Y. Morita, Ion Exchange and Solvent
Extraction: A Series of Advances, Volume 19, edited by B.
A. Moyer (Routledge, 2009).
(5) S. A. Ansari, P. N. Pathak, P. K. Mohapatra, V. K.
Manchanda, Chem. Rev. 112, 1751 (2012).
(6) M. P. Jensen, A. H. Bond, Radiochim. Acta 90, 205 (2002).
(7) Y. Zhu, Y. Chen, R. Jiao, Solvent Extr. Ion Exch. 14, 61(1996).
(8) M. Watanabe, R. Mirvaliev, S. Tachimori, K. Takeshita, Y.
Nakano, K. Morikawa, R. Mori, Chem. Lett. 12, 1230
(2002).
(9) R. G. Pearson, Chemical Hardness (Wiley-VCH Verlag
GmbH, Weinheim, 1997).
(10) Y. Nagame, M. Hirata, H. Nakahara, Handbook of Nuclear
Chemistry, Vol. 2, 2nd edition, edited by A. Vértes, S. Nagy,
Z. Klencsár, R. G. Lovas, F. Rösch (Springer Verlag,2011).
(11) N. Kaltsoyannis, Chem. Soc. Rev. 32, 9 (2003).
(12) G. Schreckenbach, G. A. Shamov, Acc. Chem. Rev. 43, 19(2010).
(13) C. Platas-Iglesias, A. Roca-Sabio, M. Regueiro-Figueroa,
D. Esteban-Gomez, A. de Blas, T. Rodriguez-Blas, Curr.
Inorg. Chem. 1, 91 (2011).
(14) D. Wang, W. van Gunsteren, Z. Chai, Chem. Soc. Rev. 41,5836 (2012).
(15) J. Lan, W. Shi, L. Yuan, J. Li, Y. Zhao, Z. Chai, Coord.
Chem. Rev. 256, 1406 (2012).
(16) X. Cao, A. Weigand, Computational Methods in
Lanthanide and Actinide Chemistry, edited by M. Dolg
(John Wiley & Sons, Ltd., 2015).
(17) X. Cao, D. Heidelberg, J. Ciupka, M. Dolg, Inorg. Chem.
49, 10307 (2010).
(18) X. Cao, J. Zhang, D. Weissmann, M. Dolg, X. Chen, Phys.
Chem. Chem. Phys. 17, 20605 (2015).
(19) D. A. Pantazis, X. Chen, C. R. Landis, J. Chem. Theory
Comput. 4, 908 (2008).
(20) D. A. Pantazis, F. Neese, J. Chem. Theory Comput. 5,2229 (2009).
(21) D. A. Pantazis, F. Neese, J. Chem. Theory Comput. 7, 677(2011).
(22) M. Kaneko, S. Miyashita, S. Nakashima, Inorg. Chem. 54,7103 (2015).
(23) M. P. Jensen, A. H. Bond, J. Am. Chem. Soc. 124, 9870
(2002).
(24) S. Chatterjee, E. N. Maslen, K. Watson, J. Acta
Crystallogr. Sect. B 44, 381 (1996).
(25) P. Lindqvist-Reis, C. Apostolidis, J. Rebizant, A.
Morgenstern, R. Klenze, O. Walter, T. Fanghänel, R. G.
Haire, Angw. Chem. Int. Ed. 46, 919 (2007).
(26) Y. Meseri, A. A. Pinkerton, G. Chapuis, J. Chem. Soc.
Dalton Trans., 725 (1977).
(27) G. Tian, Y. Zhu, J. Xu, Solvent Extr. Ion Exch. 19, 993

Roles of d- and f-orbital electrons in the complexation of Eu(III) and(2001).
(28) E. A. Mowafy, H. F. Aly, Solvent Extr. Ion Exch. 20, 177(2002).
(29) R. Carr, N. H. Evans, D. Parker, Chem. Soc. Rev. 41, 7673
(2012).
(30) K. Ishimori, M. Watanabe, T. Kimura, T. Yaita, T. Yamada,Y. Kataoka, S. Shinoda, H. Tsukube, Chem. Lett. 34, 1112
(2005).
(31) F. Neese, WIREs Comput. Mol. Sci. 2, 73 (2012).
(32) E. van Lenthe, E. J. Baerends, J. G. Snijders, J. Chem.
Phys. 89, 4597 (1993).
(33) C. van Wüllen, J. Chem. Phys. 109, 392 (1998).
(34) K. G. Dyall, K. Fægri Jr., Introduction to Relativistic
Quantum Chemistry, edited by K. G. Dyall, K. Fægri Jr.
(Oxford University Press, 2007).
(35) A. D. Becke, Phys. Rev. A 38, 3098 (1989).

J. Nucl. Radiochem. Sci., Vol. 17, 201715(36) J. P. Perdew, Phys. Rev. B 33, 8822 (1986).
(37) S. Grimme, J. Chem. Phys. 124, 034108 (2006).
(38) F. Neese, J. Comput. Chem. 24, 1740 (2003).
(39) F. Neese, F. Wennmohs, A. Hansen, U. Becker, Chem.
Phys. 356, 98 (2009).
(40) K. Momma, F. Izumi, J. Appl. Crystallogr. 41, 653 (2008).
(41) R. S. Mulliken, J. Chem. Phys. 23, 1833 (1955).
(42) R. S. Mulliken, J. Chem. Phys. 23, 2338 (1955).
(43) M. P. Jensen, R. Chiarizia, I. A. Shkrob, J. S. Ulicki, B. D.
Splindler, D. J. Murphy, M. Hossain, A. Roca-Sabio, C.
Platas-Iglesias, A. de Blas, T. Rodríguez-Blas, Inorg.
Chem. 53, 6003 (2014).
(44) M. Kaneko, S. Miyashita, S. Nakashima, Croat. Chem.
Acta 88, 347 (2016).
(45) M. Kaneko, M. Watanabe, T. Matsumura, Dalton Trans.
45, 17530 (2016).