A Deep Insight into the Selectivity Difference Between Y(III) and La(III) Ions Toward D2EHPA Ligand: Experimental and DFT Study

Abstract

The twofold extraction behavior of light and heavy rare earth elements transforms into a more selective extraction of heavy rare earth elements when Di-(2-ethylhexyl) phosphoric acid (D2EHPA), one of the commonest cation exchange extractants, is employed. However, why this phenomenon has not been fully investigated from the quantum perspective yet. To confirm and interpret the laboratory-observed selectivity results in the extraction of Y(III) over than La(III), this study utilized the Density Functional theory (DFT) connected with Born Haber thermodynamic besides importing the solvent effect through the Conductor-Like Screening Model (COSMO). The hydration reaction energies of La(III) and Y(III) were estimated at -383.7 kcal/mol and -171.83 kcal/mol according to the cluster solvation model. It was observed that, among other influential factors, hydration energy is a critical one in the rate of the extraction free energy of every rare earth element and its tendency to be transferred to the organic phase in reacting to the extractant ligand. It was shown that the experimental ∆∆G ext results (2.1 kcal/mol) enjoyed a proper consonance with the ∆∆G ext results of DFT calculations (1.3 kcal/mol). In the pursuit of discovering the reasons for this phenomenon, the orbital structure of every aqueous and organic complex was studied, and the significant differences in energy magnitudes were discussed. The current comprehensive design of experimental studies and calculations can give birth to a deeper understanding of the interactions of the D2EHPA extractant with La(III) and Y(III).

Full text

Page 1/23
A Deep Insight into the Selectivity Difference
Between Y(III) and La(III) Ions Toward D2EHPA
Ligand: Experimental and DFT Study
Shahab Alizadeh
Tarbiat Modares University
Mahmoud Abdollahy (  minmabd@modares.ac.ir )
Tarbiat Modares University
Ahmad Khodadadi Darban
Tarbiat Modares University
Mehdi Mohseni
Tarbiat Modares University
Research Article
Keywords: Born Haber Thermodynamic, D2EHPA, DFT, Extraction free Energy, Hydration Energy, Rare
Earth Elements
Posted Date: February 2nd, 2023
DOI: https://doi.org/10.21203/rs.3.rs-2525701/v1
License:   This work is licensed under a Creative Commons Attribution 4.0 International License. 
Read Full License

Page 2/23
Abstract
The twofold extraction behavior of light and heavy rare earth elements transforms into a more selective
extraction of heavy rare earth elements when Di-(2-ethylhexyl) phosphoric acid (D2EHPA), one of the
commonest cation exchange extractants, is employed. However, why this phenomenon has not been fully
investigated from the quantum perspective yet. To conrm and interpret the laboratory-observed
selectivity results in the extraction of Y(III) over than La(III), this study utilized the Density Functional
theory (DFT) connected with Born Haber thermodynamic besides importing the solvent effect through the
Conductor-Like Screening Model (COSMO). The hydration reaction energies of La(III) and Y(III) were
estimated at -383.7 kcal/mol and -171.83 kcal/mol according to the cluster solvation model. It was
observed that, among other inuential factors, hydration energy is a critical one in the rate of the
extraction free energy of every rare earth element and its tendency to be transferred to the organic phase
in reacting to the extractant ligand. It was shown that the experimental ∆∆Gext results (2.1 kcal/mol)
enjoyed a proper consonance with the ∆∆Gext results of DFT calculations (1.3 kcal/mol). In the pursuit of
discovering the reasons for this phenomenon, the orbital structure of every aqueous and organic complex
was studied, and the signicant differences in energy magnitudes were discussed. The current
comprehensive design of experimental studies and calculations can give birth to a deeper understanding
of the interactions of the D2EHPA extractant with La(III) and Y(III).
Highlights
Estimating the extraction free energy of lanthanum and yttrium with D2EHPA using experimental
studies and DFT calculations
Employing Born Haber thermodynamic procedure to calculate the extraction free energy
The higher hydration energy of La(III) compared to Y(III)
The excellent harmony between the laboratory-obtained results and quantum calculations
The higher selectivity of the Y(III) ionic complex when extracted by D2EHPA ligand, compared to
La(III) ionic complex
1. Introduction
Rare earth elements (REEs) comprise a 17-element group consisting of 15 elements that are the members
of the lanthanide group plus the two scandium and yttrium. Recently, the application of these elements
has been increased due to their use in modern technologies and so-called green energy resources [1].
Among the different metallurgy processes, hydrometallurgy methods are reckoned as the most applied
and conventional approaches used for purifying rare earth elements [2–5]. In the meantime, solvent
extraction is a proper alternative for separating rare earth elements from other elements of this group and
the impurities in the solutions obtained by leaching processes. The extraction of rare earth elements from
an aqueous phase is fullled by a ligand dissolved into the organic phase. By this method, the

Page 3/23
hydrophobe complexes of ligand – rare earth elements are formed, and their transmission to the organic
phase becomes possible [6].
For rare earth elements extraction and separation, diverse extractants, including D2EHPA [7–10], Cyanex
272 [11–14], Cyanex 921 [15–16], PC88A [17–20], TBP [21–24], EHEHPA [25–28], and various ionic
liquids [29–32], have been utilized in operational conditions and different aqueous sulfate, chloride, and
nitrate mediums. All trivalent lanthanide ions have extremely similar properties owing to the coverage of
4f electrons. Various trivalent lanthanide complexes are usually of an isostructural ligand, and the
ultimate structure of each is transformable to other lanthanides. Therefore, the selective extraction of
these elements from one another is very complicated [33]. Extractants with organophosphorus acid
ligands, such as Di-(2-ethylhexyl) phosphoric acid (D2EHPA), are introduced as very ecient extractants
of rare earth elements [34]. Among the unique features of the processes wherein D2EHPA is employed as
a rare earth element extractant, we can refer to saponication-freeness and the difference in the stability
of the LREE-D2EHPA and HREE-D2EHPA ligand complexes. These features lead to the separation of the
rare earth elements in a leachate aqueous solution into two distinct groups, containing light rare earth
elements and heavy rare earth elements, in fewer than two extraction stages and even in more acidic pHs.
Likewise, they raise the possibility of accessing the ultimate product with high purity. However, besides
these favorable characteristics, a need for more severe stripping conditions, along with environmental
pollutions resultant from harmful P or S elements in the chemical compounds of these extractants, are
among the disadvantages of this extractant [35]. In addition, the structure of the extractant and the type
of atom-donor electrons play signicant roles in making decisions about the separation behavior of metal
ions [36]. Hence, a more thorough comprehension of the reasons for such phenomena in solvent
extraction, especially on a molecular scale, enables us to optimize the structure of this extractant in
addition to developing and fabricating newer extractants to achieve more favorable operational
conditions.
Nowadays, with respect to emerged advancements, computational chemistry is an ecient tool for
understanding the structures and interactions of lanthanide complexes and various extractants [37–40].
Among the most outstanding investigations, we can refer to studies on the reason for the differences in
the stability of the Nd(III) and Dy(III) complexes with D2EHPA in a chloride medium and the physio-
chemical properties of the interface between aqueous and organic phases in this process using the
molecular dynamics method [41–42].
Alizadeh and co-workers determined the effect of nitrate counter ions on the coordination and hydration
of La(III) and Y(III) ions using the simultaneous combination of two methods, including molecular
dynamics simulation and experimental studies. The analysis of the results of the Radial Distribution
Function clearly showed the presence of one and two nitrate ligands, respectively, in the rst hydration
shells of lanthanum and yttrium. Considering the effect of nitrate anion, the identied ionic complexes of
the rare earth elements in the electrolyte were [LaNO3.(H2O)7]2+ and [Y(NO3)2.(H2O)4] +. The overlap
between the results of slope analysis and molecular dynamics elucidated that two and one ligands from
the Di-(2-Ethylhexyl) phosphoric acid extractant were required for the complete extraction of lanthanum

Page 4/23
and yttrium ionic complexes, respectively. Stated stoichiometry of lanthanum and yttrium in extraction by
the D2EHPA ligand from a nitrate medium due to the quite similar conditions in both researches, are
considered in pursuing of our study as below [43]:
1
2
Many experimental studies have addressed the extraction of different rare earth elements from varying
aqueous systems by the D2EHPA extractant in laboratory conditions. These investigations have
employed experimental factors, such as distribution coecients and separation factors, to determine
thermodynamic parameters and analyze the different extraction results. However, to the best of our
knowledge, no work has adopted a quantum perspective to delve into the selectivity mechanism of rare
earth elements extraction by the D2EHPA extractant in a nitrate system. Additionally, yttrium does not
take a stable position at similar times in the lanthanides group, it is called an itinerant element. Thus,
studying the extraction chemistry of yttrium in diverse extraction systems is of utmost value [44].
This paper aimed at using a computational instrument to acquire a deep perception of the difference in
the selectivity of the phosphoric acid ligand during the extraction process of the La(III) and Y(III) ions. In
this process, La(III) represented a light rare earth element, and Y(III) was an itinerant rare earth element.
We reached a better understanding of the extraction process mechanism in a nitrate medium employing
the synergy of two experimental and theoretical routes. The experimental free energy (∆Gexp) was
determined by examining the effect of temperature via solvent extraction experiments for the comparison
of the results of quantum computations. This research employed the cluster solvation model and explicit
solvation method to calculate hydration energy and extraction free energy (∆Gext), respectively, using the
Born Haber thermodynamic cycle for large-complex molecular systems with D2EHPA in the presence of
nitrate anions. We systematically evaluated structures, bonding, and thermodynamic parameters for the
free ligand, hydrated metal ion, and ligand-ion metal system using Density Functional Theory (DFT), as
well as the effect of water and organic solvents using the Conductor-Like Screening Model (COSMO).
Eventually, the difference in the reactivity of the present complexes was discussed by the calculation of
the chemical parameters with molecular orbitals.
2. Experimental Studies
2.1. Materials
(
LaNO
3)2+
aq
+ (HA)2
org
= (LaN
O
3.A2)
org
+ 2
H
+
aq
(Y(
NO
3)2)+
aq
+ 0.5(HA)2
org
= (Y(N
O
3)2.A)
org
+
H
+
aq

Page 5/23
The aqueous solution was prepared by the direct dissolution of the lanthanum nitrate salt and yttrium
oxide in HNO3, manufactured by Sigma Aldrich and Merck companies, respectively. In this study, the Di-(2-
Ethylhexyl) phosphoric acid (D2EHPA) extractant and kerosene, needed for preparing the organic phase,
were supplied from an industrial grade.
2.2. Extraction Experiments
In every extraction experiment, 20ml of the extractant-containing organic solution and 20ml of the
aqueous solution containing the lanthanum and yttrium ions were mixed for 30 minutes by a magnetic
stirrer. A hot water bath was used for keeping the temperature constant in every experiment. Then, the
obtained mixtures were separated by the decanter. The concentration of rare earth ions in the aqueous
solution was analyzed by Inductively Coupled Plasma Emission Spectroscopy (ICP-AES), the Agilent 735
model. The concentration of metal in the organic phase was calculated by the mass balance approach.
The distribution coecient is determined as below:
3
Where, and are the concentrations of nitrate
complexes containing rare earth metals in aqueous and organic phases, respectively. The
n
value
indicates the electric charge of rare earth elements, i.e. +3, and the
x
value depicts the number of nitrate
anions in the ionic complex. This value equals 2 and 1, respectively, for lanthanum and yttrium with
regard to the previous studies of this group. The solvent extraction experiments were accomplished at
different temperatures (298–333 K) by the synthesis of a solution, wherein lanthanum and yttrium
concentrations equaled 515.18 ppm and 526.17 ppm at the pH of 1.79 as the aqueous phase, and 2 ml
of the D2EHPA extractant was dissolved in 18 ml of kerosene, as the organic phase.
3. Thermodynamic Calculations
If the general extraction reaction is considered as Relation 4, the reaction equilibrium constant will be
computable by Relation 5.
4
D
=[(
M
.(
NO
3)
x
)(
n
−
x
)+
org
]
Org
[(
M
.(
NO
3)
x
)(
n
−
x
)+
aq
]
aq
[(
M
.(
NO
3)
x
)(
n
−
x
)+
aq
]
aq
[(
M
.(
NO
3)
x
)(
n
−
x
)+
org
]
Org
(
M
.(
NO
3)
x
)(
n
−
x
)+
aq
+
(
m
(
HR
)2
)
org K
↔
(
M
.
(
NO
3)
xRn
(
HR
)2
m
−
n
)
org
+
nH
+
aq
Keq
= =
[
(
M
.(
NO
3)
xRn
(
HR
)2
m
−
n
)
org
]
.[
H
+]
n
[
(
M
.(
NO
3)
x
)(
n
−
x
)+
aq
]
.[(
HR
)2
org
]
m
D
[
H
+
aq
]
n
[(
HR
)2
org
]
m

Page 6/23
5
Where,
aq
and
org
indicate the aqueous and organic phases, respectively. A factor with maximum impact
on the thermodynamic of systems is the effect of temperature. The variations in the equilibrium constant
(Keq) due to temperature can be explained by Van’t Hoff’s Relation:
6
In the following, a change in the system enthalpy can now be explained with the help of Relations 5 and
6.
7
As a result, the variations in Gibbs free energy (∆G) and entropy (∆S) are estimated as below:
8
9
4. Quantum Computational Details
The Density Functional Theory (DFT) was computed by the use of Gradient-Corrected Functionals (GGA-
PW91) in combination with the correlation functional of Becke et al. (BLYP) via the application of DMol3.
It is necessary to mention that rstly some of the initial structures had been simulated with different
levels of theory like B3LYP to make a decision for selecting the level of calculations. But due to the lack of
signicant differences in outputs, BLYP of theory was selected for decreasing computational costs to
optimize all needed structures. All electrons were used for the entire atoms in computations, and no
treatment was exerted on the core. The optimization convergence criterion was employed in the energy
matrix of 10− 6. All structures were optimized in the absence of symmetry constraints and by the
minimization of vibrational analysis. The effects of organic and aqueous solvents in the energetics were
incorporated by the approach of Conductor–Like Screening Model (COSMO) [39, 45]. The dielectric
constant (ε) of the water and organic solvents was considered at 78.54 and 1.89 in computations. In this
study, the considered structures were optimized in the entertained solvent, and the optimal geometry of
logKeq
= − +
ΔH
2.3
RT
ΔS
2.3
R
=
∂
logD
∂1
T
−
ΔH
2.303
R
ΔG
= −
RTlnKeq
ΔS
=
ΔH
−
ΔG
T

Page 7/23
every one of them was delineated in the gas phase. Population analysis was also applied to the ultimate
optimized structures for bonding analysis. Different chemical parameters, such as ionization potential
(IP), electron anity (EA), electronegativity (X), chemical hardness (η), and chemical softness (S), were
addressed via below relations, using the Highest Occupied Molecular Orbital (HOMO) and the Lowest
Unoccupied Molecular Orbital (LUMO) in every optimized structure [46–49]:
(10)
(11)
(12)
(13)
(14)
5. Results And Discussion
5.1. The effect of temperature on extraction
Temperature is a complicated factor impacting solvent extraction processes. The dehydration of species
enhances at high temperatures, while this factor reversely impacts the stability of metal complexes in an
aqueous phase. Figure1 illustrate the logD diagram to for both lanthanum and yttrium metals.
Figure1. Graphs of logD against ( ) (K) for extracting of lanthanum and yttrium
As Fig.1 depict, temperature rise decreases extraction, and this relationship is linear. The under-study
system shows that the stability of the extracted D2EHPA ligand-rare earth elements complexes decreases
as temperature enhances. The effect of this factor is more dominant at higher temperatures compared to
the effect of the dehydration factor. Hence, the downward trend of extraction is achieved by temperature
enhancement. Table1 summarizes the thermodynamic parameters using the explained relations and
results obtained from experimental studies. The extraction equilibrium constant displays that yttrium
extraction by D2EHPA is more favorable than lanthanum extraction.
IP = − (HOMO)
EA = − (LUMO)
x =
( )
IP+EA
2
η
=IP−EA
2
S
=1
η
1000
T
1000
T

Page 8/23
Table 1
Extraction thermodynamic parameters at 298 K
Complex Keq ∆H (kcal/mol) ∆Gexp (kcal/mol) ∆S (cal/mol.K)
[La.NO3.2D2EHPA] 6.46 × 10− 4 -6.67 4.34 -36.97
[Y.(NO3)2.D2EHPA] 467.68 × 10− 3 -1.74 0.45 -7.33
With regard to Table1, ∆H values show the exothermic nature of lanthanum and yttrium extraction
reactions. Accordingly, the enthalpy magnitudes of extraction reaction equal − 6,67 kcal/mol and − 1,74
kcal/mol, respectively, for lanthanum and yttrium complexes in the aqueous phase. Compared to yttrium,
temperature variations have the highest effect on lanthanum extraction under the experimental
conditions, such that as the temperature increases from 298K to 333K, the distribution coecient of
lanthanum decreases from 0.77 to 0.22. However, regarding the high extraction percentage of yttrium (>
99%), no sensible decline is observed due to temperature variations for this element, and extraction
eciency is still elevated at higher temperatures. The negative value of ∆S indicates that the degree of
disorder decreases during the extraction of La(III) and Y(III) ions in a nitrate medium. This issue may be
due to complex formation. The quantitative comparison between the entropy of lanthanum (-36.97
kcal/mol) and yttrium (-7.33 kcal/mol) extractions denotes that further disorder happens in the system
due to yttrium extraction. This issue is one of the factors in the more selective extraction of yttrium than
that of lanthanum. The positive values of Gibbs free energy conrm the non-spontaneous feasibility of
the process and the unfavorable nature of the extraction reaction. As Table1 displays, extraction by
D2EHPA ligand is much more favorable for Y(III) (∆Gexp=0.45 kcal/mol) than La(III) (∆Gexp=4.34
kcal/mol).
5.2. Hydration Energy
The estimation of hydration free energy for ions is a challenging task since continuum dielectric solvent
models are often insucient when they deal with ionic solutes that have concentrated charge densities
with strong local solute-solvent interactions. Researchers perceived that the published methodologies
bring about systematic errors in the computed free energies because of the incorrect accounting of the
standard state corrections for water molecules or water clusters present in the thermodynamic cycle [50].
With respect to the coordination of water molecules and nitrate anions in the rst cluster surrounding
every metal, we can consider the hydration reaction of yttrium and lanthanum ions on the basis of the
three schemes discussed in the following. It should be noted that according to the formed complexes of
lanthanum and yttrium in aqueous and organic phases sequentially [La.NO3.(H2O)7]2+ and [Y.NO3.
(H2O)4]+, [La.NO3.(D2EHPA)2] and [Y.(NO3)2.D2EHPA] that had been proved by Alizadeh and co-workers
[43], by reason of exactly similar conditions, we applied these complexes hereafter for our simulations.
Scheme 1- This scheme is based on the implicit solution model, such that the bare metal ion is solved
directly in the continuum solvent by the use of the COSMO solvation model.

Page 9/23
Scheme 2- This scheme, recognized as the monomer cycle, is based on the explicit solvation model,
similar to what Dolg et al. mentioned [51]. For the monomer cycle, the ionic solute reacts with
n
separated
water molecules. The gas phase metal ion is solvated in the rst solvation sphere water molecules as
below:
15
16
Scheme 3- The cluster method applied by Goddard et al. is used in the cluster cycle, such that, unlike the
monomer cycle, a cluster of
n
water molecules reacts with the ionic solute in the cluster cycle. These
clusters are used for geometry optimization and total energy computation [50]:
17
18
Table2 presents the hydration energy (HE) of every metal in each scheme. This value is estimated by the
energy difference between the ultimate hydrated complex and the sum of the energies of the water
molecules and metal ionic complex.
Table 2
Calculated values of hydration energy (kcal/mol) and reaction free energy (kcal/mol) of La(III) and
Y(III) ions
Energy Hydration of La ions Hydration of Y ions
Scheme 1 Scheme 2 Scheme 3 Scheme 1 Scheme 2 Scheme 3
HE (kcal/mol) -265.74 -296.10 -383.70 -96.58 -137.98 -171.83
∆G (kcal/mol) 0.40 75.18 16.30 0.09 42.03 16.70
∆∆G (kcal/mol) -0.31 -33.15 0.40   
As these values illuminate, according to all three schemes, the hydration energy for the formation of
lanthanum hydrated complex is more than the rate for the yttrium hydrated complex. Thus, we can
conclude that the stability of the lanthanum ionic complex is more than that of the yttrium ionic complex
[
La
.
NO
3]2+
(
g
)+ 7[
H
2
O
](
aq
)= [
La
.
NO
3.(
H
2
O
)7]2+
(
aq
)
[
Y
.(
NO
3)2]+
(
g
)+ 4[
H
2
O
](
aq
)= [
Y
.(
NO
3)2.(
H
2
O
)4]+
(
aq
)
[
La
.
NO
3]2+
(
g
)+ [
H
2
O
]7(
aq
)= [
La
.
NO
3.(
H
2
O
)7]2+
(
aq
)
[
Y
.(
NO
3)2]+
(
g
)+ [
H
2
O
]4(
aq
)= [
Y
.(
NO
3)2.(
H
2
O
)4]+
(
aq
)

Page 10/23
in the aqueous phase, and a more stable species of lanthanum is formed in the aqueous solution
compared to yttrium. Furthermore, the analysis of free energy among three schemes shows that the
results obtained from the free energy difference (∆∆G = 0.4 kcal/mol) of scheme 3 approximate to what
is observed in reality compared to similar values in the other schemes. In reality, it is observed that the
lanthanum complex further tends to be present in the aqueous solution compared to yttrium. Hence, the
selectivity of water solvent is higher for solvating lanthanum complexes than those of yttrium.
5.3. Extraction Selectivity
Similar to what has been mentioned in some references, this study also showed that the binding energy
of the gas phase was not a suitable tool for showing the higher experimental selectivity of Y(III) ions than
that of La(III) ions towards the D2EHPA ligand. The reason for this issue is the ignorance of considering
the solvent effect in both aqueous and organic phases. Metal ions should be extracted from the aqueous
environment, wherein they severely take hydrated forms. Hence, it is necessary to calculate the solvation
energy of lanthanum and yttrium ions in an aqueous environment to achieve an accurate estimation of
extraction energy. To correctly estimate the manner of extraction selectivity and complexation studies in
solvent extraction processes, we can employ thermodynamic calculations. As Fig.2 illustrates, Born-
Haber thermodynamic cycle is used for computing the solvent phase free energy of complexations [52].
Figure2. Thermodynamic cycle for the calculation of extraction free energy (M = La(III) or Y(III) ion, L =
D2EHPA−, and x = 1 and 2 for La(III) and Y(III), respectively)
Complexation selectivity for metal ions can be modeled by use of the extraction reaction presented below
:
19
In the following, the free energy of the above reaction complexation (∆Gext) is estimated by the
thermodynamic cycle method, being highly successful in estimating the solution phase selectivity.
(20)
(21)
(22)
(
M
.
xNO
3)(3−
x
)+
(
aq
)+
mL
(
org
)→ (
M
.
xNO
3.
mL
)(
org
)
ΔGext
=
ΔGg
+
ΔΔGsol
ΔGg
=
G
(
M
.
xNO
3.
mL
)(
g
)−
(
G
(
M
.
xNO
3)
(3−
x
)+
(
g
)+
mGL
(
g
)
)
ΔΔGsol
=
ΔGsol
[
M
.
xNO
3.
mL
]−
(
ΔGsol
[(
M
.
xNO
3)(3−
x
)+]+
mΔGsol
[
L
]
)

Page 11/23
∆Gg is calculated by the use of the free energy relevant to the structures optimized in the gas phase, and
other terms associated with ∆Gsol in the solvent phase are computed by the use of these structures in the
gas phase. The solvation energy rate of La(III) and Y(III) ions in the aqueous phase is determined by the
cluster solvation model at this stage of computations. The selectivity of the D2EHPA ligand for the rare
earth metal ions can be explained as the exchange reaction of metal cation, described below:
23
Hence, selectivity can be explained by the difference in the free energy of extraction energy (∆∆Gext) as
shown below (52–53):
24
Table3 shows the values of the calculated free energies. A positive value of ∆∆Gext (+ 10.9 kcal/mol)
indicates the selectivity of Y(III) ions to the D2EHPA ligand is more than that of La(III) ions. Thus, the
selectivity process observed in the experimental studies was also conrmed in calculations. Compared to
the energy of the metal ionic solvation, the solvation energy rate of the ligand and ligand-metal ion is very
small. Hence, we can claim that aqueous solvation energy plays a paramount role in determining the
selectivity process.
Table 3
Calculated free energy (kcal/mol) for extracting of La(III) and Y(III) with D2EHPA ligand at BLYP
level of theory
Reaction ∆Gg∆∆Gsol ∆Gext ∆∆Gext
22.9 -17.3 5.6 10.9
16.47 -21.77 -5.3 
It should be reminded that the thermodynamic parameters obtained by Van’t Hoff methods may not
ideally be rational due to experimental uncertainties (54). Therefore, there may sometimes be
contradictions between the results obtained by Van’t Hoff methods and computer computations.
However, with respect to the results presented by both experimental studies (∆Gexp) and quantum
calculations (∆Gext), there is an excellent correlation among the results of this study. The selectivity trend
observed in the laboratory concerning rare earth elements extraction by the D2EHPA extractant can
[
Y
.(
NO
3)2.
L
](
org
)+ [
La
.
NO
3]2+
(
aq
)+
L
−
(
org
)→ [
Y
.(
NO
3)2](
aq
)+ [
La
.
NO
3.2
L
](
org
)
ΔΔGext
=
ΔG
[
La
.
NO
3]2+ −
ΔG
[
Y
.(
NO
3)2]+
(
La
.
NO
3)
2+
(
aq
)+ 2
L
−
(
org
)→ (
La
.
NO
3.2
L
)(
org
)
(
Y
.(
NO
3)2)
+
(
aq
)+
L
−
(
org
)→ (
Y
.(
NO
3)2.
L
)(
org
)

Page 12/23
depend on different factors, including a difference in the ionic potential, ionic radius, the interaction of
these elements with counter ions in the aqueous solution, and the hydration of the aqueous complexes of
rare earth elements. However, regarding the theoretical computations of this study, it seems that the
difference in the hydration of rare earth element complexes can be a key factor in their extraction
selectivity with the D2EHPA extractant.
5.4. Bonding Analysis and Reactivity
When the interaction energy of the extraction reactions was calculated regardless of the solvent effect in
the gas phase, it was observed that the value of this energy was larger for La(III) (-452.68 kcal/mol) than
that of Y(III) (-192.35 kcal/mol). This trend counters the extractability trend observed in the extraction free
energy calculations. To better perceive the reason for this event and better comprehend the metal-ligand
complexes bonding, we studied the energy of the frontier molecular orbitals (LUMOs and HOMOs) and
charge transfer on metal ions in the relevant complexes using population analysis. Table4 displays the
Mulliken charge and occupied orbitals for the related complexes. The charges of lanthanum and yttrium
ions equal + 3 in the free state. It can be seen that the positive charge of lanthanum and yttrium ions
decreases in the formed aqueous complex. This issue shows that electrons are transferred from the
existing nitrate ligand in the aqueous solution to the lanthanum and yttrium ions and form coordination
bonds. Due to the transfer of more electrons because of the further coordination of the nitrate ions with
yttrium (two coordination positions), the partial charge of yttrium (+ 1.86) experiences more reduction
compared to the free state and the partial charge of Lanthanum (+ 1.91).
Table 4
Calculated values of Mulliken charges (Q) and occupied
orbitals (s, p, d, and f) at BLYP level of theory
Complex s p d f Q
[LaNO3.(H2O)7]2+ 12.2 26.8 29.9 14.1 1.91
[LaNO3.(D2EHPA)2]12.1 26.5 30.1 14 1.65
[Y(NO3)2.(H2O)4]+10.4 24.7 24.6 0 1.86
[Y(NO3)2.D2EHPA] 10.5 23.4 22.9 0 1.69
The charge transfer is larger for La(III) than that of Y(III) in their complexes extracted by the D2EHPA
ligand. This trend is consistent with the lower interaction energy of Y(III) than that of La(III) in the gas
phase. Furthermore, the value of the Mulliken charge on the atom center of La(III) is larger than this value
for the Y(III) atom center. This denotes the lower covalent character of La(III) complex than that of Y(III).
In the DFT studies, no treatment was applied to electrons, and all electrons were considered as ground
state valence in calculations. The crowdedness of electrons in the s, p, and d orbitals of the lanthanum
and yttrium ions reects the covalent nature of bonding after complexations in the aqueous nitrate
medium and complexations with D2EHPA.

Page 13/23
The energy levels of HOMO and LUMO, recognized as frontier molecular orbitals and the reactivity
controllers of molecular complexation, were also estimated for the hydrated complexes of these metals.
LUMO modies the ability of the molecule for accepting electrons in any structure, while HOMO shows
the electron-donating ability of the molecule. The difference between the energy values of HOMO and
LUMO is called the HOMO-LUMO energy gap, which shows the probable charge transfer interaction that
occurred within a molecule. Molecules with a small energy gap are generally accompanied by high
chemical reactivity and low kinetic stability besides being considered as soft molecules. However,
molecules with a large energy gap possess higher stability and are recognized as hard molecules. It is
because they oppose their charge transfer, distribution changes, and electron density. In Table5, some
chemical properties of the studied structures were computed by the use of DFT studies at the BLYP level
of theory. Concerning the difference in the number of nitrate ligands in the rst coordination clusters of
the lanthanum and yttrium, the amount of the energy released due to electron addition to the aqueous
complex of these elements also differs. The electron anity amount for the aqueous complex of yttrium
(0.24 eV) is smaller than that of lanthanum (0.43 eV) due to the addition of the second electron to the
hydrated complex. Hence, the value of the electron anity is larger for the hydrated complex of
lanthanum owing to the addition of a single electron to its structure.
Table 5
Calculated chemical parameters for studying of the reactivity of the
complexes
Complex IP (eV) EA (eV) X (eV) η (eV) S (eV)
[LaNO3.(H2O)7]2+ 0.48 0.43 0.46 0.02 42.18
[LaNO3.(D2EHPA)2]0.24 0.14 0.19 0.05 20.85
[Y(NO3)2.(H2O)4]+0.39 0.24 0.31 0.07 13.77
[Y(NO3)2.D2EHPA] 0.26 0.13 0.20 0.06 15.60
As observed, the hardness of yttrium hydrated complex (0.072 eV) is more than that of the lanthanum
hydrated complex (0.024 eV). This means that, in the presence of an electric eld, the electron cloud of
the yttrium-containing molecule is less distorted than that of lanthanum. The chemical softness of the
lanthanum complex extracted by D2EHPA (20.85 eV) is higher than that of the yttrium complex extracted
similarly (15.6 eV). This indicates that lanthanum forms a more unstable complex in the organic phase
compared to yttrium. Therefore, we can conclude that yttrium forms a stronger bond with the D2EHPA
ligand than that of lanthanum. This issue can be reckoned as one of the reasons for the experimental
observations respecting the harder chemical conditions needed for yttrium stripping for the transfer of
ions from the organic to the aqueous phase compared to the lanthanum stripping. Likewise, the larger
ionization potential of the extracted lanthanum complex (0.24 eV) denotes that the energy rate needed for
removing an electron from yttrium is more than the rate needed for lanthanum. That is why we can claim
that yttrium forms a more stable complex in the organic phase, and it is more dicult to omit the D2EHPA

Page 14/23
ligand, as an electron donor, from the extracted structure. Furthermore, the higher electronegativity of the
lanthanum aqueous complex (0.46 eV) than that of the yttrium aqueous complex (0.31 eV) shows the
further capability of this molecule in attracting the electron towards itself during bond formation. Figure3
illustrates the levels of the frontier molecular orbitals and their related shapes for the considered
combinations.
Figure3. Shapes of frontier molecular orbitals for lanthanum complexes, yttrium complexes, and D2EHPA
extractant at BLYP level of theory
As observed, the D2EHPA ligand contributes to the HOMO shapes of the extracted complexes of rare
earth elements, and lanthanum and yttrium contribute to the LUMO shapes of those complexes. For the
formation of a bond between D2EHPA and every one of the yttrium and lanthanum ionic complexes, an
electron should move from the highest occupied molecular orbital ; i.e., the HOMO related to the D2EHPA
ligand, to the lowest unoccupied molecular orbital; i.e., the LUMO related to every metal ionic complexes.
For this reason, as the energy level difference of these orbitals (∆Eorbital) becomes smaller, the electron
transfer is simpler, and the reactivity is higher. This difference in the energy level equals 0.4 eV and 0.21
eV for the bonding of D2EHPA with the lanthanum and yttrium ionic complexes, respectively. Hence, this
result implies that the formation of a bond between D2EHPA and the yttrium ionic complex is simpler
than that of the lanthanum ionic complex. In this condition, a more stable complex is formed. Table6
shows the Mayer bond order analysis at the BLYP level of theory and its results.
Table 6
Mayer bond orders of D2EHPA molecule after the
formation of extracted complexes of La(III) and Y(III)
Complex Bonds Mayer Bond Order
[LaNO3.(D2EHPA)2]P = O 1.25
P-O−1.23
[Y(NO3)2.D2EHPA] P = O 1.14
P-O−1.19
Compared to La(III), the smaller values of the bond order for the electron donor head group in the D2EHPA
ligand in the extracted Y(III) complex show the weakening of these bonds due to the formation of a
stronger bond of the ligand with the relevant metal. This issue qualitatively interprets the selectivity and
stronger bond of the yttrium metal with the extractant ligand compared to lanthanum. Besides, the partial
charge distribution shows that oxygen atoms have a higher negative charge in D2EHPA. Since the
electron density of the double bond oxygen atom is higher than that of the single bond oxygen atom
connected to the phosphor atom in the D2EHPA structure, and the single bond oxygen atom is a weaker
donor atom, both lanthanum and yttrium form a chelating bond with this extractant.

Page 15/23
6. Conclusion
This research employed the theory route of DFT calculations and experimental studies and showed that
the selectivity mechanism of the yttrium ions with the D2EHPA cationic extractant, which led to the
twofold behavior in the extraction of lanthanides, was higher than that of lanthanum ions. In this
research, yttrium was an itinerant rare earth element, and lanthanum was considered as a light rare earth
element. An examination of the hydration energy of lanthanum and yttrium ions by different schemes in
an aqueous phase revealed that the cluster method was suitable for describing the hydration that
happened in the reality observed in solvent extraction experimental studies. Therefore, the results properly
showed the more tendency of the lanthanum ionic complex for presence in water compared to the yttrium
ionic complex. The hydration energy directly affected the free energy of each complex’s extraction from
the aqueous phase. With the help of the Born Haber thermodynamic cycle, the extraction free energy
(∆Gext) was estimated at 5.6 kcal/mol and − 5.3 kcal/mol for the stoichiometry of lanthanum and yttrium
reactions at the BLYP level of theory. ∆∆Gext obtained by DFT computations was a selectivity factor
between La(III) and Y(III) and exhibited an excellent harmony with the results obtained from experimental
studies. Thus, at this level of computations, the Di- (2-ethylhexyl) phosphoric acid (D2EHPA) extractant
preferred the Y(III) ionic complex more than that of La(III).
A comparison of the value of Mulliken charge on the center of metal atoms uncovered the lower covalent
character of the La (III) complex than that of Y(III). The chemical parameters, including chemical
hardness, chemical softness, electronegativity, electron anity, and ionization potential, were computed
for the purpose of inspecting the reactivity of the complexes containing La(III) and Y(III) ions in the nitrate
aqueous solution and loaded organic phase. The comparison of the chemical softness of the
[Y(NO3)2.D2EHPA] (15.6 eV) and [LaNO3.(D2EHPA)2] (20.85 eV) complexes led to the conclusion that
Y(III) formed a stronger bond with D2EHPA than La(III) in the organic phase. Hence, it seems that,
compared to La(III), more dicult conditions are needed for Y(III) stripping in order to transfer it from the
organic phase to the aqueous phase. Moreover, a comparison between the ionization potentials of La(III)
(0.24 eV) and Y(III) (0.26 eV) conrmed the higher stability of yttrium complexes in the organic phase.
The orbital energy value (∆Eorbital) estimated by the energy levels of frontier molecular orbitals for the
complexation of rare earth elements with the extractant ligand equaled 0.4 eV and 0.21 eV for La(III) and
Y(III), respectively. The difference between these values indicated the simpler extraction and more stable
complex formation of Y(III) than that of La(III). The conduction of Mayer bond order analysis exhibited
the complexation covalent nature that occurred during the extraction process of rare earth metals with the
D2EHPA ligand. The computational method applied in the present study can be used for properly
interpreting the difference in the extraction selectivity of lanthanides with diverse extractants at the
theoretical level and designing extractants with favorable extraction properties. Furthermore, using BLYP
level of theory caused not only the favorable coordination between the results of laboratory and
simulation studies but also consuming the minimum time cost.
Declarations

Page 16/23
Acknowledgment
Not applicable.
Funding
Not applicable.
Conict of Interest/ Competing Interests
On behalf of all authors, the corresponding author states that there is no conict of interest.
Ethics Approval
Not applicable.
Consent to participate
Not applicable.
Consent for publication
Not applicable.
Availability of data and material
Data available on request from the authors.
Code Availability
Data available on request from the authors.
Authors’ Contributions
Shahab Alizadeh: Writing- original draft, Designed the analysis, Performed the analysis, Methodology,
Validation. Mahmoud Abdollahy: Writing- review & editing, Methodology, Validation. Ahmad Khodadadi
Darban: Writing- review & editing, Methodology, Validation. Mehdi Mohseni: Writing- review & editing,
Methodology, Investigation, Validation.
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Schemes
Schemes 1-3 are not available with this version
Figures

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Figure 1
See image above for gure legend.
Figure 2
Thermodynamic cycle for the calculation of extraction free energy (M= La(III) or Y(III) ion, L=D2EHPA-, and
x=1 and 2 for La(III) and Y(III), respectively)

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Figure 3
Shapes of frontier molecular orbitals for lanthanum complexes, yttrium complexes, and D2EHPA
extractant at BLYP level of theory
Supplementary Files
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GA.jpg