Journal of Nuclear and Radiochemical Sciences, Vol. 5, No. 2, pp. 27-31, 2004

Review
Theoretical Analysis of Electronic Structure for the Chemical Bonding of Pu and Am in MgOKumiko Tanaka,*, a, b Masaru Hirata,b and Rika SekineaaDepartment of Chemistry, Faculty of Science, Shizuoka University, 836 Ohya, Shizuoka 422-8529, Japan
Department of Materials Science, Japan Atomic Energy Research Institute, Tokai-mura, Naka-gun, Ibaraki
319-1195, Japanb

Received: September 8, 2004; In Final Form: October 18, 2004
The relativistic discrete-variational Dirac-Fock-Slater (DV-DFS) method was performed to investigate the electronic structure of MgO doped with Pu or Am atoms. The differences between these systems, in particular, theparticipation of d-electrons and f-electrons in chemical bonding, were clarified by calculating their electronic
structures. Substitution of actinide atoms was found to result in the effective charges of MgO becoming smaller,
with a large charge transfer occurring as far as the second layer. It was also found that the bonding feature
between the center atom and the surrounding oxygen atoms was extended to lower energy in the case of actinide(An) substituted systems. Moreover, the bonding characteristics were assigned; a bonding interaction for An6dO2p and an anti-bonding for An5f-O2p near the HOMO level. These complex effects were found to dominate thestrength of the covalent bonding between MgO and actinide atoms.

1. Introduction
The electronic structures of metal oxides containing actinide
atoms give essential information on the interaction between theactinide atoms and base metal oxides. In the field of nuclear
technology and science, magnesium oxide,1−4 zirconium oxide,4, 5
and spinel6, 7 are appropriate candidates for an inert matrix,
which acts as a mechanical support and diluent, used in transmutation of actinides (An), such as plutonium (Pu) and americium (Am).8 Early study9 indicated that magnesium oxide(MgO) was considered to be the most appropriate support
material for transmutation of Am because of its desirable properties, such as high melting point, relatively high thermal conductivity and high mobility of helium. 10 Researches of thethermophyisical properties of doped actinides in metal oxides
are accumulated so far, however less work has focused on theelectronic structures and chemical bonding nature of these systems to understand the physical and chemical properties.
The electronic configurations of the actinides also provide
insight into the properties of their compounds. The difference
between the electronic configuration of neutral Pu and Am atoms
is only one f-electron (Pu: 5f 66d 07s 27p0, Am: 5f 76d 07s 27p0);
however, the f-electrons of lighter actinides (Pa – Pu) are considered to have an itinerant trend,11, 12 on the other hand, the felectrons of transplutonium elements (Am – Cf) have localized
character and behave more like the lanthanides. It is known thata boundary of the chemical and physical properties lies between
Pu and Am.13 For example, Np and Pu metals have the uniqueproperties; such as low-symmetry of crystal structure (monoclinic) at room temperature, low melting point, and multiple
phase transition. On the other hand, transplutonium metals havemore symmetric hexagonal close-packed structure and relatively higher melting point than Np and Pu. Furthermore, alarge variation in stoichiometry is found in the actinide oxides.
The sesquioxide becomes the predominate oxide for the transplutonium elements, in contrast to the lighter actinides prefer tohave higher valence.
The present study is undertaken with the goal of advancing
our understanding of fundamental chemical bonding between*Corresponding author. E-mail: kumi-tnk@popx.tokai.jaeri.go.jp.
FAX: +81-29-282-6723.

actinide atom and metal oxides. The relativistic discrete-variational Dirac-Fock-Slater (DV-DFS) method was applied toinvestigate the electronic structure of MgO doped with Pu or
Am atoms. This method gives reliable information of chemical bonding even for heavy system such as the actinide series.
Although there are several theoretical studies of pure actinideoxides,14−18 the interaction between actinide atoms and an inert
matrix has not been well clarified until now. The current
investigation focused on the difference between these systems,
in particular, the participation of d-electrons and f-electrons in
the chemical bonding.
2. Computational Method
The DV-DFS molecular orbital (MO) method, based on the
Dirac-Fock-Slater (DFS) approximation, was used to perform
cluster calculations of pure MgO and actinide doped MgO.
This method provides a powerful tool for the study of the electronic structure of molecules and solids containing heavy
elements.14, 16, 19−23 The detailed procedure has been publishedelsewhere.24−26
The schematic representation of a model cluster of MgO isshown in Figure 1. MgO has NaCl structure and all bond length

Mg1

O
Mg
Figure 1. Model cluster for this study (5× 5 ×4 atoms with 1352 point
charges). An(Pu or Am) atom substituted for the center Mg1.

© 2004 The Japan Society of Nuclear and Radiochemical Sciences
Published on Web 11/11/2004

28

TanakaJ. Nucl. Radiochem. Sci., Vol. 5, No. 2, 2004

Mg2
O1

Mg1

O2
Mg3

O
O3

Mg

Figure 2. Magnification of a part of model cluster. The center Mg1
was substituted by Pu or Am atom.

between Mg and O is fixed to 210.6 pm. The calculation, when
performed for insulators such as magnesium oxides, is difficult
because of the long-range Coulomb interactions even fromdistant atoms. In order to represent the effect, 1352 points of+2 and –2 point charges (PC) were placed at the lattice positions around the cluster model. These PC guaranteed that the
Madelung potential inside the cluster was properly reproduced.
Figure 2 shows a part of the model cluster, cutting away thesubstituted center atom and surrounding atoms from Figure 1.
The Pu or Am doped MgO system was also calculated, using
the model cluster with substitution of an An atom for the center
Mg1 atom as shown in Figure 2. For the initial charge, An
atoms were assigned as trivalent and the other atoms as divalent, in other words, the electronic configurations were Pu:
5f 5 6d 0 7s 0 7p 0 , Am: 5f 6 6d 0 7s 0 7p 0 , Mg: 2s 2 2p 6 3s 0 3p 0 , and O:
2s22p63s03p0. The bond length of Pu-O2 and Am-O2 were estimated from the ionic radius of the trivalent atom, and were
determined to be 238.39 pm and 235.91pm, respectively. The
lattice relaxation caused by An substitution was not consideredin the present calculation, therefore, only the bond lengths
between metals (Mg1, Pu, or Am) and adjacent oxygens (O1,
O2) were changed.

to have a higher oxidation state than Am. It is known that
MgO is a strongly ionic system, and therefore the HOMOLUMO gap of Mg+MgO is calculated as 4.18 eV; however,that of the Pu+MgO (0.55 eV) and Am+MgO (0.02 eV)
systems were found to be small in this study. This indicatesthat the ionic bonding strength becomes weak and the systems
become unstable as a result of An substitution.
Table 2 shows the occupation number of the valence orbitals
for the Mg+MgO, Pu+MgO, and Am+MgO systems. When
comparing the final orbital occupations with the initial ones, thenumber of electrons of Mg3s, Mg3p, An6d, An7s, and An7p
orbitals increase and only that of the 5f orbital slightly decrease.
A significant change in the orbital population was observed in
the increase of the 6d electron for the An+MgO system. The
Pu6d orbital receives 1.84 electrons from the surrounding
oxygen atoms, while the Am6d orbital receives 1.79 electrons.
It follows from these results that the number of electrons in the
5f orbital is directly proportional to the atomic number, but thatof the 6d orbital is inversely proportional in the MgO environment. The occupation numbers of O2s and O2p become smallerwith An substitution. The O12s, O12p, O22s, and O22p orbitals
release 0.07, 0.47, 0.05, and 0.40 electrons, respectively, in the
Pu+MgO system, and 0.06, 0.46, 0.05, and 0.40, respectively,in the Am+MgO system. This indicates that charge transfer
occurs mainly from the O2p oribtal to An6d orbital. The occupation of the Pu6d orbital is larger than that of Am6d, however,
the total charge transfer between Am and the surrounding
oxygen (+2.50), and also that for Pu (+2.46).
3.2. Analysis of Covalent Bonding. In order to evaluate
covalent interactions between substituted Pu, Am, and thesurrounding oxygens, bond overlap population (BOP) analyses
were obtained, as shown in Table 3. After substitution of An for
Mg, the interaction between the An atom and the surrounding
oxygen (O1, O2) becomes larger than that for Mg. The BOP
for Pu+MgO is slightly larger than Am+MgO. On the other
hand, the bonding of Mg2-O1, Mg3-O1, and Mg3-O2 becomes
weak, because electrons move to the surrounding of An and astrong interaction between An and oxygen is generated by An
substitution.
TABLE 2: Orbital Occupations of Valence Orbitals

3. Results and Discussion

Mg+MgO

3.1. Effective Charge and Ionic Interaction. Table 1 showsthe effective charges on substituted Pu (Pu+MgO), Am (Am+
MgO) and the surrounding Mg and O with reference to the pure
MgO (Mg+MgO). The positions of these atoms are indicated in
Figure 2. The Mulliken population analysis27 is known to have abasis set dependence; however, the analysis provides qualitative
aspects of the chemical bonding. In this calculation, numericalbasis sets28 were generated for Pu, Am, Mg, and O atoms, withthe same conditions, so that the effect of the basis set on theorbital population was negligible. As shown in Table 1, theeffective charges of Mg and O became fairly small in consequence of the An substitution, and a large charge transfer to thesecond layer occurred. Plutonium has a slightly larger effective
charge (0.53) than Am (0.50) and this indicates that Pu prefers
TABLE 1: Effective Charge of Center Atom (Mg1, Pu, orAm) and Neighbor Mg and O
Mg(An)1
Mg2
Mg3
O1
O2
O3

Mg+MgOPu+MgO

Am+MgO

0.71
0.72
0.64
-0.74
-0.70
-0.72

0.53
0.37
0.28
-0.21
-0.25
-0.37

0.50
0.38
0.29
-0.23
-0.26
-0.38

Mg1 3sMg1 3p1/2
Mg1 3p3/2
O1 2s
O1 2p1/2
O1 2p3/2
O2 2s
O2 2p1/2
O2 2p3/2

0.48
0.27
0.54
1.80
1.65
3.29
1.78
1.64
3.28

Pu+MgO

Am+MgO

3.90
0.95
0.77
1.07
0.39
0.22
0.20
1.73
1.50
2.97
1.73
1.51
3.01

4.74
1.16
0.75
1.04
0.40
0.23
0.21
1.74
1.50
2.98
1.73
1.51
3.01

An 5f5/2
An 5f7/2
An 6d3/2
An 6d5/2
An 7s
An 7p1/2
An 7p3/2
O1 2s
O1 2p1/2
O1 2p3/2
O2 2s
O2 2p1/2
O2 2p3/2

TABLE 3: Bond Overlap Population between Center Atom
(Mg1, Pu, or Am) and Neighbor Oxygen (O1, O2)
Mg+MgO
O1
O2
Mg(An)1 0.32
0.65
Mg2
0.24
Mg3

0.26
-0.20
1.23

Pu+MgO
O1
O2

Am+MgO
O1
O2

0.55
0.46
0.18

0.54
0.47
0.20

0.39
-0.10
1.03

0.38
-0.10
1.04

J. Nucl. Radiochem. Sci., Vol. 5, No. 2, 2004

Theoretical Analysis of Electronic Structure

29

TABLE 4: Orbital Overlap Population between Valence Orbital of Center Atom (Mg1, Pu, or Am) and O1 and O2
O1 2s

Mg1 3s -0.01
Mg1 3p 0.07

Mg+MgO
O1 2p
O2 2s

0.12
0.16

O2 2p

0.00
0.01

An 5f
An 6d
An 7s
An 7p

0.06
0.06

O1 2s

Pu+MgO
O1 2p
O2 2s

O2 2p

O1 2s

Am+MgO
O1 2p
O2 2s

O2 2p

0.01
0.05
0.01
0.10

0.10
0.28
0.07
0.07

0.02
0.09
0.05
0.03

0.01
0.05
0.01
0.11

0.08
0.27
0.07
0.07

0.01
0.09
0.05
0.03

The analysis of orbital contributions to the chemical bondingis useful to understand the nature of 6d and 5f electrons in theactinide systems. Table 4 provides the orbital overlap populations between the valence orbitals of An-O1 and An-O2. The
main difference between the Pu+MgO and Am+MgO systems
are the An5f-O2p and An6d-O2p orbital overlap populations.
Both of the orbital overlap populations for Pu5f-O2p and Pu6dO2p are larger than those for Am5f-O2p and Am6d-O2p. This
causes a larger interaction between Pu and O1, than that for
Am; however such a discrepancy is obscure in the case of An
and O2. As indicated in Table 2, the number of 6d electrons
directly influences the An6d-O2p orbital overlap population,
however the influence of 5f occupation reveals an opposite
trend. In order to sufficiently examine the contribution of 6dand 5f orbitals toward chemical bonding, the participation of
the valence orbitals was analyzed for bonding features.
Figure 3 illustrates the bonding features of the central Mg
atom with neighboring O1 or O2 for the Mg+MgO system versus
the molecular orbital (MO) energy. The figures consist of thecalculated partial density of states (PDOS) for O2p, Mg3s, andMg3p, which are main components of the valence band, together
with the BOP between Mg and O1 or O2. Vertical lines shown in
the figures of PDOS are the energy levels of each component. In
these figures, the HOMO level, was calibrated to be 0 eV, andpositive and negative values of the BOP signify bonding andanti-bonding features, respectively, for the corresponding MO.
The valence band of Mg+MgO contains mainly an O2p component plus some components of Mg3p and Mg3s, implying that
Mg+MgO is a strongly ionic system. From these figures, thebonding features show a similar trend to the PDOS for the O2p
orbital in both the Mg-O1 and Mg-O2 cases. Moreover, thestrengths of covalent bonding for Mg-O1 and Mg-O2 are almost
the same, although the dominant bonding features appear atdifferent energy levels.
The principal features of BOP and PDOS of corresponding
energy are indicated as arrows and categorize into five parts.
The small Mg3p orbital is distributed from the HOMO to

1.0

1.0

1.0

0.0

0.0

0.0

0.0

0.3

0.3

6.0

0.1

0.0

0.0

0.6
0.4

0.6
0.4

e

dc b

0.2

Mg1-O2 BOP

0.1

a

0.0
-0.2

-6.0

-4.0

-2.0

Energy /eV

0.0

1.0
0.8
0.6
0.4
0.2
0.0

Mg1 3p

b
c

e
d

0.2

a

0.0
-0.2
-6.0

-4.0

-2.0

0.0

Energy /eV

Figure 3. Bond overlap population of Mg1-O1 and Mg1-O2.
a, b: Mg3p-O2p interaction, c: Mg3s-O2p interaction,d: Mg3s-Mg3p-O2p hybridization and e: Mg3p-O2p andMg3p-O2p interaction

4.0
2.0

O2 2p

Pu 5f
x5

0.0
1.0
0.8
0.6
0.4
0.2
0.0

Pu 6d

0.6

Pu-O1 BOP

0.2

x5

0.0

0.3

Mg1 3p

2.0

6.0

Pu 5f

4.0

PDOS

0.1
0.0

0.3
0.2

Mg1 3s

c
b

0.4
0.2
0.0
-0.2
-10.0

-8.0

Pu 6d

0.6

Pu-O2 BOP

0.1

0.2

PDOS

Mg1 3s0.0

Mg1-O1 BOP

2.0

O1 2p

O2 2p

1.0

0.2

0.00
0.01
0.01
0.01

about –1.5 eV, and has bonding interaction (b) with the O2p
orbital, while anti-bonding interaction indicated as feature (a)is predominant around the HOMO level. The Mg3s orbital
appears from about –1.5 eV, and has bonding interaction (c)with the O2p orbital in Mg-O1 and in Mg-O2. The Mg3p andthe Mg3s orbitals are hybridized from about –2.5 to –3.5 eV,and have bonding interaction (d) with the O2p orbital. The
Mg3p and the Mg3s orbitals appear again from approximately–3.5 eV and –5.0 eV, respectively, and have bonding interaction (e) with the O2p orbital. It is noted that almost all interactions of O2p-Mg3s, O2p-Mg3p, and O2p-Mg3s-Mg3p indicate
bonding features, but the MO close to the HOMO level shows
anti-bonding features, which appear clearly in the bonding of
Mg-O2, than that of Mg-O1.
The valence band of the Pu+MgO system mainly contains an
O2p component plus some Pu5f and Pu6d components. The
PDOS of O2p, Pu5f, and Pu6d together with the BOP between
Pu and O1 or O2 are illustrated in Figure 4. From these figures,
it can be presumed that almost all bonding features mainly
consist of Pu6d-O2p interactions. The O12p and O22p orbitals
appear around 3.0 eV deeper in energy than the case of Mg+
MgO, with the shift caused by the charge transfer between Pu
and oxygen. The covalent bonding of Pu-O1 becomes stronger
than that of Pu-O2 , and consequently, the reinforcement oflateral bonding arises from Pu substitution for Mg. The orbital
interaction can be approximately divided into three parts, as
shown in these figures. The large components of Pu5f are
distributed around the HOMO, and have anti-bonding interaction (a) with the O2p orbital in Pu-O 2. The Pu5f and Pu6d
orbitals are distributed from about –0.5 to –6.5 eV, and interact
with the O2p orbital in both bonding and anti-bonding characteristics (b). The Pu5f, Pu6d, and O2p orbitals are well hybridized
and the largest BOP in Pu-O2 is due to this hybridization. The
Pu6d orbital is also distributed from about –6.5 to –8.0 eV, andinteracts with the O2p orbital as large bonding features (c), as
shown in Figure 4. The overlap of the O2p and Pu6d orbitals
becomes large, because of the shift of O2p orbitals toward
2.0

2.0

O1 2p

PDOS

PDOS

2.0

0.00
0.01
0.01
0.01

-6.0

-4.0

Energy /eV

-2.0

0.0

b

0.4

c
a

0.2
0.0
-0.2
-10.0

-8.0

-6.0

-4.0

-2.0

0.0

Energy /eV

Figure 4. Bond overlap population of Pu-O1 and Pu-O2.
a: Pu5f-O2p interaction, b: Pu5f-Pu6d-O2p hybridizationand c: Pu6d-O2p interaction

2.0

O2 2p

0.0

0.0

6.0

6.0

2.0

Am 5f
x5

0.0

Mg-O1

0.15

Pu-O1

4.0
2.0

1.0
0.8
0.6
0.4
0.2
0.0

Am 6d

c

0.6
0.4

b

a

0.2
0.0

-0.2
-10.0

-8.0

-6.0

-4.0

-2.0

Energy /eV

0.0

Pu

0.10

Mg

Am 5f
x5

0.6

b
c

a

0.2
0.0
-8.0

Am-O1

Am

Mg

0.00

0.00

-0.50

-0.50

200

150

100

50

0.0

200

150

100

50

0.0

r /pm

Figure 6. Cross sectional view of the difference in charge density for
Pu-O1 and Am-O1 comparing with Mg1-O1. Atomic unit (au) is Bohrradius, which corresponds to 52.9 pm.

Am 6d

-0.2
-10.0

Mg-O1

0.15

0.05

r /pm

0.4

0.20

0.10

0.05

0.0

Am-O2 BOP

1.0
0.8
0.6
0.4
0.2
0.0

0.25

0.20

1.0

PDOS

PDOS

1.0

4.0

0.25

2.0

O1 2p

Am-O1 BOP

TanakaJ. Nucl. Radiochem. Sci., Vol. 5, No. 2, 2004

ρ /e·au-3

30

-6.0

-4.0

-2.0

0.0

Energy /eV

Figure 5. Bond overlap population of Am-O1 and Am-O2.
a: Am5f-O2p interaction, b: Am5f-Am6d-O2p hybridizationand c: Am6d-O2p interaction

lower energy, which was caused by the charge transfer between
Pu and oxygen, and consequently, a largest bonding featurearises. From these results, it has been clarified that O2p-Pu6d
interaction plays an important role for the bonding of Pu-O 1
and Pu-O2.
The PDOS of O2p, Am5f, and Am6d, for the Am+MgO
system, together with the BOP between Am and O1 or O2, areshown in Figure 5. The valence band of the Am+MgO system,
like Pu+MgO, mainly contains an O2p component plus someAm5f and Am6d components, and the general trends are nearly
similar to the Pu+MgO system. In order to analyze the discrepancy between these two systems, the principal features of BOP
and PDOS of corresponding energy were indicated as arrows
for the Am+MgO. The orbital interaction can be divided into
three parts. The large components of the Am5f orbital are
distributed from the HOMO to –1.0 eV, and have anti-bonding
interaction (a) with the O2p orbital. The Am5f and Am6d
orbitals are distributed from –1.0 to –6.5 eV, and interact
toward the O2p orbital with both bonding and anti-bonding
characteristics (b). The Am5f, Am6d, and O2p orbitals arewell hybridized, however these hybridized MOs are fewer thanthose of the Pu system. The hybridization also produces thelargest bonding feature in Am-O2, while it contributes a small
anti-bonding feature in Am-O1. The Am6d orbital is distributed from –6.55 to –8.0 eV, and has bonding interaction (c)with the O2p orbital. The intensity of the O2p-Am6d interaction is similar to that of O2p-Pu6d, however the orbital occupation of Am6d is less than that of Pu6d, as shown in Table 2.
That is, Am-O1 and Am-O2 interactions are weaker than thoseof Pu-O1 and Pu-O2. The most important difference between
the Pu+MgO and Am+MgO systems is the electronic structures
around the Fermi energy, which are assigned to O2p-An5f
interaction. Apparently, the overlap of Am5f-O2p is larger thanthat for Pu, in proportion to the orbital occupation of An5f, but
this interaction has anti-bonding characteristic, and therefore
the chemical bonding for Am-O 1 and Am-O2 is weaker thanthat for Pu-O1 and Pu-O2.
Consideration of the charge density of an ideally isolated ion
is subtracted from that of the cluster (the difference in charge
density) of the interatomic region can provide additional insight
into clarifying the covalent bonding in these systems.29 The
difference in charge densities of Pu-O1 and Am-O1 are shown in
Figure 6, compared with those of Mg1-O1. The Mg, Pu, and Am
atomic positions are at r = 0.0 pm, and O1 is at r = 210.6 pm.
From the difference in charge density of Mg1-O1, no electronsbinding two nuclei are exhibited to generate covalent bonding.

On the other hand, the charge densities for the Pu-O1 and AmO1 bonds increase in the interatomic region. The difference inthe charge densities of Mg, Pu, and Am are 0.004, 0.021 and
0.020 at the ionic radius of the metal atom (Pu(III) = 114.0 pm,
Am(III) = 111.5 pm, Mg(II) = 86.0 pm),30 respectively. This
indicates that ionic bonding dominates the chemical bondingof Mg1-O1, and covalent bonding dominates in the chemicalbonding of An-O1. In the case of An-O1, increases of the difference in charge density inside the An atoms are appreciable.
The increase implies that the An5f electron participates inshielding the nuclear charge, which makes the effective chargeof the An atom small. Moreover, a remarkable discrepancy
between the bonding nature of Pu-O1 and Am-O1 is recognizedin this shielding.
4. Conclusions
In order to investigate the electronic structure of MgO dopedwith Pu or Am atoms, the relativistic discrete-variational DiracFock-Slater (DV-DFS) method was performed. It was foundthat the effective charges of Mg and O become small, in consequence of the An substitution, in addition to a large chargetransfer that reached to the second layer. Furthermore, the effective charge of Pu (0.53) and Am (0.50) indicated that Pu prefers
to have a higher oxidation state than Am. Using a combinationof PDOS for the main components of the valence band of the
Mg+MgO, Pu+MgO, and Am+MgO systems, and the BOP
between the Metal (Mg, Pu, or Am)-O1 and Metal-O2 versus the
MO energy, the contribution of these atomic orbitals to thechemical bonding was clarified. In the case of the Mg+MgO
system, almost all interactions for O2p-Mg3s, O2p-Mg3p, andO2p-Mg3s-Mg3p exhibited bonding features, although those forO2p-Mg3p near the HOMO level showed anti-bonding features.
Conversely, in the case of the An+MgO system, the largest
bonding feature is produced from interactions of An6d-O2p, andthe reinforcement of lateral bonding occurred by an An substitution for Mg. One of the essential results of this calculation is theinterpretation of the chemical bonding nature of An doped MgO.
The interaction of An6d-O2p plays an important role, however,that of An5f-O2p is also effective for determining the bonding
strength between An and the surrounding oxygens, because of
their anti-bonding feature. Furthermore, it was revealed that thestrength of both the ionic and covalent bonding are stronger in
the Pu+MgO system than the Am+MgO system, and theseresults implied that the stability of Pu in MgO is higher than Am
in MgO. The difference in the charge density of An-O1 exhibited an increase in density inside the An atoms, which implied acontribution of the An5f electron in screening the charges. In
the present study, the participation of d- and f-electrons in chemical bonding was evaluated, and the results suggest that charge
screening occurred due to An5f electrons.
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