Nano Research
Nano Res
DOI
10.1007/s12274-017-1637-9
1
Actinide endohedral boron clusters: A closed-shell
electronic structure of U@B40
Tianrong Yu1,2,§,Yang Gao1,2,§, Dexuan Xu1,2, and Zhigang Wang1,2 ()
Nano Res., Just Accepted Manuscript • DOI: 10.1007/s12274-017-1637-9
http://www.thenanoresearch.com on Apr. 19, 2017
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Nano Res.
64
Table of Contents (TOC)
Actinide
boron
endohedral
clusters:
a
closed-shell electronic
structure of U@B40
Tianrong Yuab+, Yang
Gaoab+, Dexuan Xuab,
Zhigang Wang*ab
a. Institute of Atomic
and Molecular Physics,
Jilin
University,
Changchun,
130012,
China.
b. Jilin Provincial Key
Laboratory of Applied
Atomic and Molecular
Spectroscopy,
Jilin
University, Changchun,
The molecular orbitals(MOs) energy levelsand electron density difference map, both of them exhibit
strong bonding character in U@B40.
130012, China.
+
These
authors
contributed equally to
this work.
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Nano Research
DOI (automatically inserted by the publisher)
Review Article/Research Article Please choose one
Actinide endohedral boron clusters: a closed-shell
electronic structure of U@B40
ab+
Tianrong Yu
,Yang Gao
ab+
ab
ab
, Dexuan Xu , Zhigang Wang* ()
a. Institute of Atomic and Molecular Physics, Jilin University, Changchun, 130012, China.
b. Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun, 130012,
China.
+
These authors contributed equally to this work.
Received: day month year
ABSTRACT
Revised: day month year
Actinide-containing clusters have received much attention in different subject
areas due to their distinctive electronic bonding properties. Herein, we propose
a unique actinide-encapsulated B40 cage structure, U@B40, based on density
functional theory (DFT) calculations. Our results revealed that U@B40 satisfies
the 32-electron principle of 1S21P61D101F14, in which all the s-, p-, d-, and f- type
valence shells of U atom are filled to form a closed-shell singlet-state
configuration. Furthermore, the binding energy of 8.22 eV calculated for this
cluster implies considerable stability. We also calculated the infrared and
Raman spectra, which exhibit active vibration modes of U-B40 stretching and
pure B40 breathing, respectively. These spectral characteristics may be helpful in
future experimental investigations. The current findings not only add a new
member for the superatomic family, but also provide a way to encapsulate
radioactive actinide-containing materials.
Accepted: day month year
(automatically inserted by
the publisher)
© Tsinghua University Press
and Springer-Verlag Berlin
Heidelberg 2014
KEYWORDS
actinide-containing
cluster,
32-electronprinciple,
superatomic orbital,
vibrational spectra,
DFT calculation.
Nano Res.
1. Instructions
Hollow cluster cages are capable of housing
atoms or small molecules forming a stable
core@shell system, thereby changing the
physicochemical properties of materials in the
nano realm[1-5]. Recently, an unprecedented
all-boron fullerene-like cluster, B40, was found by
photoelectron spectroscopy experimentally[6]. It
possesses unusual heptagonal faces and a slightly
smaller radius, in contrast to C60 fullerene, which
therefore could be a system that can house an
endohedral atom[7-10].
Currently, actinide-containing materials have
become a hotspot in different subject areas[11, 12],
owing to their hyperactive valence electrons and
interesting bonding properties. In particular, the
uranium and its compounds always play an
important role in advanced nuclear technology
and biomedicine, etc[12, 13]. Furthermore, the
endohedral uranium encapsulated in carbon
fullerenes
or
gold
cages
have
been
investigated[14-18]. Many of these clusters
exhibit strong spin polarization effect. In addition,
because of its special electronic shell, the central
uranium atom can be classified as “18-electron”
(1S21P61D10) or “32-electron” (1S21P61D101F14)
systems[19-22]. Thus, uranium as a typical
actinide atom could have the ability to present
the peculiar property of electronic structures
when it is encapsulated into B40 cage.
In the experiment, a series of experimental
techniques can achieve the synthesis of the
coating structures. Such as, arc discharge
techniques are the most widely used to
synthesize the carbon nanomaterials and
endohedral metallofullerenes (EMFs)[1, 23-25].
For example, in 1990, Krätschmer et al.
accomplished the synthesis of C60 by evaporating
graphite rods via resistive heating with helium
atmosphere[26, 27]. For the preparation process
of EMFs, a graphite anode are packed with the
desired metal is burned together with a graphite
rods/block as cathode in the presence of helium
fabricated by using a carbon rod containing
radiotracers of 237U with lanthanum as a
carrier[29]. Besides, BN nanomaterials (B99N99
nanotube, B36N36 cluster) are usually produced by
this method, which is similar to that used for
carbon nanomaterials, with specific conducting
electrodes (HfB2, ZrB2) in a nitrogen
atmosphere[30-32]. In addition, the theoretically
predicted W@Au12 (Mo@Au12) was produced
experimentally using laser vaporization[33]. The
boron clusters (B8, B40) were also fabricated by
this method[6, 34]. Thus, it is conceivable to
synthesize the uranium- embedded B40 cage
based on these or related synthetic protocols.
For our study of the systems containing U
and other actinide elements, the practical
experimental research is very difficult because of
the toxicity and radioactivity of actinides,
therefore theoretical calculations have been
employed as effective tools in the investigations
of actinide-containing systems, including the
design, bonding and spectral characterisitics, as
well as their intriguing properties. In this study,
the geometries and electronic structure of U@B40
is predicted by employing density functional
theory (DFT) methods. The detailed analyses are
performed for the orbitals, electron density
difference and charge transfer of the
nanostructure. Surprisingly, we found that the
U@B40 satisfies the 32-electron principle to form a
closed-shell electronic structure, indicating that it
could be a stable cluster.
2. Computational methods
In the present work, both Amsterdam
Density Functional package (ADF, 2012.01)[35]
and Gaussian 09 program[36] were employed to
performed the relevant calculations with no
global search. In order to make the reliability of
the
obtained
structures,
the
geometry
optimizations have been performed without
imposing any symmetry constraint. In ADF, the
geometries
were
optimized
using
Address correspondence to Zhigang Wang, [email protected].
argon and then annealed[23, 28]. Such as, the
uranium metallofullerenes (U@C82, U2@C80) were
Perdew-Burke-Ernzerhof (PBE)[37], Perdew and
Wang
(PW91)[38]
generalized
gradient
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approximation exchange-correlation functionals.
And then the frequency calculations were
performed at the PBE level based on the
optimized structure to determine the stability of
structures. The single-point calculations were
performed to employ the hybrid functional
PBE0[39] and B3LYP[40-42] based on PBE
geometries. The scalar and spin-orbit relativistic
effects were included via zeroth-order regular
approximations (ZORA) method. The TZ2P
Slater basis sets (relativistic valence triple-ζ with
two polarization functions were employed, and
the frozen-core approximation was applied for
the 1s-4d electrons of uranium atom). In
Gaussian 09, the geometries were optimized
using PBE, BP86[43], PBE0 and B3LYP functionals.
Furthermore,
the
single-point
MP2[44]
calculations were also performed based on ADF’s
PBE geometries. The small core RECP (including
60 core electrons) with its corresponding
(14s13p10d8f6g)/ [10s9p5d4f3g] valence basis
set[45] and 6-31G* basis set[46, 47] were used for
the U and B atoms, respectively.
3. Results and Discussion.
The optimized B40 structure possesses a
singlet state at PBE/TZ2P level, which is
consistent with the recent report[6]. Moreover,
considering various initial cage structures via
changing the U position in B40, we obtained an
endohedral metal cluster, U@B40, that U atom is
located at the center of B40 and adopts a D2d symmetry
with singlet ground electronic state using the PBE
functional in both ADF and Gaussian programs.
These results were checked by the other
functionals (PW91, BP86, PBE0 and B3LYP).
Furthermore, the electronic correlation energies
were
also
calculated
by
second-order
Møller-Plesset perturbation theory (MP2) method
based on ADF’s PBE geometries, the qualitative
results of these are consistent with that of DFT.
On the other hand, the HOMO-LUMO gap of
U@B40 value (0.76 eV) at PBE level is small in
comparison with the larger gap 1.77 eV at PBE
level[8] and 3.13 eV at PBE0 level[6] for the
reported empty B40, but the value is at least as
large as those of M@B40 (M=Sc, Y, La)[8],
conferring an indication of the stability for
U@B40.
Next, considering the ionization potential (IP)
and electron affinity (EA) values could estimate
inoxidizability and anti-reductive of the
structures, respectively, so we calculated its
vertical and adiabatic ionization potential (VIP
and AIP), vertical and adiabatic electron affinity
(VEA and AEA) to facilitate future experimental
validation. They are 6.05 eV, 2.23 eV, 5.99 eV and
2.24 eV for VIP, VEA, AIP and AEA, respectively.
The specific calculations for details see
supporting information (SI) part 1. Next, the
estimated binding energy of U@B40 is about 8.22
eV (see part 1 of SI), it is greater than the reported
binding energies for Y@B40 (5.90 eV) and La@B40
(5.88 eV)[8], once again, suggesting the U@B40 is a
rather stable, viable cluster.
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Figure 1. MOs energy diagrams and electron density difference map (lower right corner) for U@B40 at PBE/TZ2P level.
The red and blue denote electron densities gained and lost, respectively (Isovalue=0.002).
Figure 2. The shapes of superatomic MOs for U@B40 at
PBE/TZ2P level (Isovalue=0.02).
For the isolated U atom, its electronic
configuration is [Rn]5f36d17s2, which exhibits a
quintet spin ground state[48]. When the U atom
is confined into the B40 cage, the electronic
ground state of U@B40 is found to be a singlet,
indicating that B40-confinement induces spin
polarization of U atom. In order to achieve a
better understanding of the electronic structure
of U@B40, the orbitals energy diagram between
the U atom and B40 is shown in Figure 1. We can
see that the strong participation of atomic orbitals
of U in 16 MOs of U@B40, involving 32 electrons,
and their spatial shapes have also been shown in
Figure 2. Specifically, there are seven molecular
orbitals (MOs) mainly origins from the
combination of U-5f and B40 orbitals, i.e. 29e, 19b2,
19a1, 9a2 and 27e, the percentage of U-5f
contributions are 44.50%, 33.23%, 13.51%, 15.23%
and 9.61%, respectively. The 17b2, 18a1, 10b1 and
25e MOs related to the interaction of U-6d and B40
orbitals, and the orbital compositions percentage
of U-6d are 22.55%, 26.07%, 19.35% and 21.33%,
respectively. In the low-lying energy levels, the
three (24e and 15b2) and one (14a1) MOs
correspond to the U-7p and U-7s atomic orbitals
interact with B40 orbitals, respectively, each of
them is bound to B40 cage. Actually, the covalent
interaction also can be reflected through the
electron density difference map (see the lower
right corner of Figure 1), the whole valence
electrons exhibit obvious accumulation behavior
(red areas) between the U atom and the cage in
the center, indicating strong bonding character.
Hence, according to the energetic sequence and
the nodal shape of the MOs, we can identify a
series of superatomic orbitals in the sequence 1S,
1P, 1D, 1F. To sum up, the extent to which the
central atoms participate in bonding is similar to
the
previously
reported
superatom
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systems[19-21], which reveals the present
actinide endohedral B40 cluster is a new example
of the 32-electron system.
On the other hand, charge transfer also plays
a crucial role in the binding of the U@B40 system.
So the Mulliken, Voronoi deformation density
(VDD), Hirshfeld charge analyses were employed
in here, the results show that the charge
transferred from the U atom to the B40 cage
originates primarily from the 5f, 6d, 7s and 7p
shell electrons. As an illustration, the Mulliken
populations in U@B40 were found to be
5f3.716d0.827s0.257p0.69 on U (approximate electron
occupation). It can be seen that the 7p shell,
which is originally unoccupied, is also involved
in strong electron correlation. This provides
direct evidence for the existence of 32-electron
principle in U@B40. Furthermore, the charge of
the central U atom was calculated to be 0.53, 0.69,
and 0.59 based on Mulliken, VDD and Hirshfeld
charge analyses, respectively. The cationic
character of the encapsulated U atom can be
understood in terms of the electronegativity
difference between U (1.38) and B (2.04).
We also performed spin-orbit coupling (SOC)
calculations on U@B40 (see Figure S1 of SI Part 2
for details). The results show that the splits of the
MO energy levels are very small (<0.04 eV), and
the energy gap value has decreased from 0.75 eV
to 0.49 eV. This suggests that SOC does not have
much effect on the ground-state molecular
properties of U@B40 cluster.
Figure 3. Calculated Infrared (IR) and Raman spectra
for U@B40 at PBE/TZ2P level. Spectra are broadened by
the Lorentzian function with a width of 10 cm−1. Pink
and green shadow areas denote regions of two
vibration modes.
To
assist
future
experimental
characterizations, we computed the vibrational
spectra of U@B40. As shown in Figure 3, there are
two regions IR-active frequencies (in the vicinity
of 82 cm-1and 441 cm-1, respectively). These
modes can be assigned to combined motions of
the central U atom and B40 cage. Two degenerate
peaks correspond to the U-B40 cage-stretching
mode in 82 cm-1 region is IR-active, but
Raman-inactive. In contrast, the pure B40
breathing vibration mode in the region of 441
cm-1 with a1 symmetry is IR-inactive and
Raman-active. These modes could be used as
diagnostic fingerprints for U-B bonding in IR and
Raman spectroscopic characterizations.
4. Conclusions.
The U@B40 cluster has a closed-shell
singlet-state
electronic configuration.
The
electronic structure analysis reveals that U@B40
qualifies as a 32-electron system. The 7s, 7p, 6d,
and 5f orbitals of U atom all hybridize with the
B40 cage orbitals. Moreover, vibration spectra
indicate that the U-B40 cage-stretching mode in
the vicinity of 82 cm-1 is IR-active and
Address correspondence to Zhigang Wang, [email protected].
Raman-inactive.
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The study of actinides-encapsulated systems
has attracted a great deal of attentions, because
they have important application values in nuclear
science and biomedicine[12, 13]. However, due to
inherent toxicity and radioactivity of actinide
elements make experimental detection has
received a large degree of restrictions, therefore,
the theoretical research is necessary. We hope the
current theoretical research can afford a useful
reference for the design and synthesis of
actinide-containing materials.
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Nano Res.
Electronic Supplementary Material
Actinide endohedral boron clusters: a closed-shell
electronic structure of U@B40
ab+
Tianrong Yu
ab+
, Yang Gao
ab
ab
, Dexuan Xu , Zhigang Wang* ()
a. Institute of Atomic and Molecular Physics, Jilin University, Changchun, 130012, China.
b. Jilin Provincial Key Laboratory of Applied Atomic and Molecular Spectroscopy, Jilin University, Changchun, 130012,
China.
+
These authors contributed equally to this work.
Supporting information to DOI 10.1007/s12274-****-****-* (automatically inserted by the publisher)
Contents:
Part 1. Related calculation details.
Part 2. Scalar relativistic and spin–orbit coupling effects.
101
Nano Res.
1.
Related calculation details.
We calculated the binding energy by using PBE functional in Gaussian 09 program. The
ionization potential (IP) and electron affinity (EA) via using PBE level functional in ADF program.
The binding energy is defined as the difference between the sum of total energies of the separated
empty B40 cage and encapsulated U atom and the total energy of U@B40. The values of vertical
ionization potential (VIP), vertical electron affinity (VEA), adiabatic ionization potential (AIP) and
adiabatic electron affinity (AEA) are defined as EVIP = E+(sp) – E0(opt), EVEA = E0(opt) – E−(sp), EAIP =
E+(opt) – E0(opt) and EAEA = E0(opt) – E−(opt) (where E0(opt) is the total bonding energy of the neutral
U@B40; E+(opt) and E−(opt) represent total bonding energies of the cation and the anion on their
respective optimized geometries; E+(sp) and E−(sp)represent total bonding energies of the cation and
the anion in single-point geometries, respectively).
2. Scalar relativistic and spin–orbit coupling effects.
Figure S1. Molecular orbitals energy diagrams for the U@B40 with (right) and without (left) spin–orbit
coupling calculated using the PBE functional in ADF.
102