Electronic and structural properties in nanocluster Al n xNix
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Journal of Physics: Conference Series
PAPER • OPEN ACCESS
Electronic and structural properties in nanocluster Aln−x Nix
To cite this article: J Blanco et al 2021 J. Phys.: Conf. Ser. 1938 012002
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IV Workshop on Modeling and Simulation for Science and Engineering (IV WMSSE) IOP Publishing
Journal of Physics: Conference Series 1938 (2021) 012002 doi:10.1088/1742-6596/1938/1/012002
Electronic and structural properties in nanocluster
Aln−xNix
J Blanco1 , U Guevara2 , R Lozada3,4 , and O Castro1
1
Escuela de Ciencias, Universidad de Oriente, Cumaná, Venezuela
2
Facultad de Ciencias, Universidad de Tarapacá, Arica, Chile
3
Facultad de Ciencias Básicas, Universidad Católica del Maule, Talca, Chile
4
Facultad de Ciencias e Ingenierı́a, Universidad Tecnológica del Perú, Lima, Perú
E-mail: trobuyo@gmail.com
Abstract. In this paper, we study electronic isosurfaces and structural properties in
nanoclusters Aln−x Nix using Density Functional Theory, with the Local Density Approximation;
the density of state, the highest occupied molecular orbital and lowest unoccupied molecular
orbital were determined for different structures, obtaining different values of the energies. We
have obtained evidence of a contribution of d orbitals for pure Ni nanoclusters and Al-Ni
nanoclusters. In addition, an overlapping of the sp orbitals is evident. We also determined that
the structure with the greatest binding energy corresponded to Al10 , with a D2h symmetry, and
the structure with the minimum binding energy corresponded to Ni20 , with a C2v symmetry.
1. Introduction
Nanoscience and nanotechnology are important fields within scientific research mainly due
to the great expectations nanoparticles in the development and creation of new materials
that show increases and/or improvements in physical and chemical properties with potential
applications [1]. Numerous studies on metallic, semiconductor and even insulating materials can
be found in the literature. In general, it is considered that nanomaterials have to be crystalline,
as well as having a size and shape as monodisperse as possible [2]. In particular, considerable
effort has been put into the preparation of bimetallic AlNi nanoparticles, mainly due to recent
experimental studies reporting applications in biomedical therapies, clean energy enablers and
eco-friendly products [3].
Cotton [4] introduces the term cluster to designate compounds with metal-to-metal bonds
and in a sufficient number of atoms to define a polyhedral structure in three dimensions. The
atomic clusters are made up of groupings of atoms with well-defined compositions and only a
few stable geometrical structures, which is a first difference with respect to nanoparticles and a
similarity to molecules. After atoms, atomic clusters are the most elementary “atomic pieces”
in nature and are distinguished by a size equivalent to the Fermi wavelength of the electron,
which makes them the link between atoms and nanoparticles with ability that differ greatly
between the two systems. In these molecular type structures quantum effects are the ones that
cause their chemical, optical and electronic properties such as magnetism, photoluminescence,
photocatalytic and electrocatalytic activities [5–8].
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution
of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Published under licence by IOP Publishing Ltd 1
IV Workshop on Modeling and Simulation for Science and Engineering (IV WMSSE) IOP Publishing
Journal of Physics: Conference Series 1938 (2021) 012002 doi:10.1088/1742-6596/1938/1/012002
It is complicated to make accurate calculations of the electronic structure of metal clusters,
especially for the case of larger clusters when they are in dissolution and protected by a ligand
layer. In recent years, density functional theory has been used to determine structural and
electronic properties of different metal clusters, but there is little information in the literature on
theoretical studies with ab-initio methods of Al-Ni clusters, hence the great interest in carrying
out a study using computational methods to determine different properties in nanoclusters whose
compounds are Al and Ni.
The ab-initio methods provide a theoretical description of the electronic behavior by finding
the kinetic and potential energy of the system represented in the Hamiltonian. In the search
for the numerical solution, from the quantum point of view, the following methods have been
developed: Hartree-Fock, Quantum Monte Carlo, Embedded Atom Method, Density Functional
Theory, among others.
In this work, the structural and electronic properties of Aln−x Nix nanoclusters are studied
applying Density Functional Theory in the local density approximation to evaluate the density of
states, electronic density, binding energy, energy of highest occupied molecular orbital (HOMO)
and lowest unoccupied molecular orbital (LUMO), among others.
2. Computational method
To determine the density of states, electron density and the energies of the HOMO and LUMO
orbitals of the Aln−x Nix nanoclusters, density functional theory was used [9] with local density
approximation [10] using the functional developed by Perdew-Wang was used [11].
The software used was Materials Studio 5.0 implementing the DMOL3 code. For the
calculation of the energy gap (Eg), The Koopmans Theorem [12] for Hartree-Fock calculations
was used [9].
There are a large number of frameworks possessing different atomic disposition in a given
geometry. Typically, it is difficult to optimize all possible topological isomers for large groups
and with a high doping concentration, which is why an artificial structural construction is
necessary. The designed structures of the clusters can be linear, planar, Y-shaped, square
pyramid, pentagonal pyramidal, tetrahedron, octahedron, hexagonal, prism configurations. For
the calculuses, nanoclusters were designed with a size between 10 and 20 atoms, for each
structure the atoms were varied under the condition n ≥ x.
3. Results and discussions
The Figure 1, Figure 2 and Figure 3 show the density of state for the nanocluster Al10 , Al5 Ni5
and Ni1 0 respectively. In Figure 1 it can be seen that around the Fermi level (dotted line) the
highest electronic contribution is offered by the 3p orbital of aluminum, below the Fermi level
(between −0.40 and −0.3 Ha) it can be observed that the contribution is represented by the 3s
orbitals. The Figure 1 shows that the structure for this nanocluster is a double hexagonal ring
with D2 symmetry.
In Figure 2, for the Al5 Ni5 nanocluster, it is observed that around the Fermi energy the
greatest electronic contribution is offered by the 3d orbitals of Ni, in the energy interval −0.50
and −0.25 Ha, it is evident that the contribution in the system is given by the 3s, 3p orbitals of
aluminum and the 4s orbitals of nickel, it is also indicated that the structure for this nanocluster
is a double hexagonal ring with Cs symmetry.
The Figure 3 shows that the major contribution is provided by the 3d orbitals of Ni around
the Fermi level, also very little contribution is observed from the 4s orbitals, also the structure
for this nanocluster is double hexagonal ring with D2h symmetry.
The density of states of the Al15 , Al7 Ni8 and Ni15 nanoclusters are shown in Figure 4,
Figure 5, and Figure 6, respectively. In Figure 4, is shown that around the Fermi level the
major contribution is by the 3p orbitals of the Al atoms, above and below the Fermi level a
2
IV Workshop on Modeling and Simulation for Science and Engineering (IV WMSSE) IOP Publishing
Journal of Physics: Conference Series 1938 (2021) 012002 doi:10.1088/1742-6596/1938/1/012002
contribution from the 3p orbitals is also observed, furthermore in Figure 4 it is indicated that
the structure for this nanocluster has a Cs symmetry.
For the Al7 Ni8 nanocluster, the density of states indicates that there is a greater contribution
of the 3d orbitals of nickel around the Fermi level. In addition, it is observed that there is a
medium contribution from the 3p orbitals of aluminum, and very little contribution from the
3s orbitals of Al and 4s orbitals of Ni. The Figure 5, it is indicated that the structure for this
nanocluster has a Cs symmetry.
The density of state of Ni15 shows the largest contribution from the 3d orbitals around the
Fermi level and very little contribution from the 3p and 4s orbitals, in Figure 6 it is observed
that the structure for this nanocluster has a Cs symmetry.
500
350
450 s
Density of States (electrons / Ha)
Density of States (electrons / Ha)
s 300 p
400
p d
350 Sum Sum
250
300
200
250
200 150
150
100
100
50
50
0 0
-0,50 -0,25 0,00 0,25 -0,50 -0,25 0,00 0,25
Energy (Ha) Energy (Ha)
Figure 1. Density of states of Al10 with Figure 2. Density of states of Al5 Ni5
double hexagonal ring structure and D2h with double hexagonal ring structure and Cs
symmetry. symmetry.
550
600
500
s 550
Density of States (electrons / Ha)
s
450 p
Density of States (electrons / Ha)
500 p
d
400 450 Sum
Sum
350 400
300 350
250 300
200 250
150
200
150
100
100
50
50
0
-0,50 -0,25 0,00 0,25 0
-0,50 -0,25 0,00 0,25
Energy (Ha)
Energy (Ha)
Figure 3. Density of states of Ni10 with
Figure 4. Density of states of Al15 with Cs
double hexagonal ring structure and D2h
symmetry.
symmetry.
3
IV Workshop on Modeling and Simulation for Science and Engineering (IV WMSSE) IOP Publishing
Journal of Physics: Conference Series 1938 (2021) 012002 doi:10.1088/1742-6596/1938/1/012002
550 800
s 750 s
500
p 700 p
Density of States (electrons / Ha)
Density of States (electrons / Ha)
450 d 650 d
Sum 600 Sum
400
550
350 500
450
300
400
250 350
200 300
250
150
200
100 150
100
50
50
0 0
-0,50 -0,25 0,00 -0,50 -0,25 0,00
Energy (Ha) Energy (Ha)
Figure 5. Density of states of Al7 Ni8 with Figure 6. Density of states of Ni15 with
Cs symmetry. Cs symmetry.
The density of states for Al20 , Al10 Ni10 and Ni20 nanoclusters are shown in Figure 7,
Figure 8 and Figure 9, respectively. Around the Fermi level in the density of states for Figure 7
shows a higher contribution from the 3p orbitals of the Al atoms, moreover it is observed that
around the interval between −0.50 and −0.30 Ha there is a contribution from the 3s orbitals.
The Figure 7 indicates a planar triangular structure for this nanocluster, with a C2v symmetry.
In Figure 8 for the Al10 Ni10 nanocluster, the density of states indicates that there is a major
contribution from the 3d orbitals of nickel around the Fermi level. In addition, it is observed that
there is a medium contribution from the 3p orbitals of aluminum, and very little contribution
from the 3s orbitals of Al and 4s orbitals of Ni, only a small contribution from these orbitals
is observed above the 3d orbitals of Ni and 3p orbitals of Al near the energy value of −0.50
Ha. Also, the Figure 8 indicates a planar triangular structure for this nanocluster, with a Cs
symmetry.
800 800
750
s
750
s p
700 700
Density of States (electrons / Ha)
Density of States (electrons / Ha)
p d
650 650
Sum Sum
600 600
550 550
500 500
450 450
400 400
350 350
300 300
250 250
200 200
150 150
100 100
50 50
0 0
-0,50 -0,25 0,00 -0,50 -0,25 0,00
Energy (Ha) Energy (Ha)
Figure 7. Density of states of Al20 with Figure 8. Density of states of Al10 Ni10
C2v symmetry. with symmetry Cs.
The density of state of Ni20 (Figure 9) shows the major contribution from the 3d orbitals
around the Fermi level and very little contribution from the 3p and 4s orbitals of Ni. Figure 9
indicates a planar triangular structure for this nanocluster, with C2v symmetry.
4
IV Workshop on Modeling and Simulation for Science and Engineering (IV WMSSE) IOP Publishing
Journal of Physics: Conference Series 1938 (2021) 012002 doi:10.1088/1742-6596/1938/1/012002
1000
950
s
900 p
d
Density of States (electrons / Ha)
850 Isosurface1
800 Sum 3.084e-3
750
700 -1.804e-3
650
600 -6.692e-3
550
500
-1.158e-2
450 -1.647e-2
400
350
Isosurface1
300 3.253e-1
250
200
-2.018
150
100
-4.362
50 -6.705
0
-0,50 -0,25 0,00
-9.048
Energy (Ha)
Figure 9. Density of states of Ni20 with C2v
Figure 10. Electronic isosurfaces of Al10 .
symmetry.
The Figure 10 and Figure 11 represent the projection in the XY plane of the electronic
isosurfaces for the Al10 and Ni10 nanoclusters, respectively. In Figure 10, the blue colored area
indicates a lower density of bonded electrons with the electrons located in the center of the Al10
nanocluster structure, while the orange area indicates a higher density of bonded electrons, the
highest electronic contribution for this nanocluster is given by the 3p orbitals.
Figure 11 also shows that the lowest density of non-bonded electrons is located in the center
of the structure (blue zone), while the highest density of bonded electrons, orange zone, are
located at the edge of the structure, the largest contribution for this nanocluster is provided by
the 3d orbitals.
The Figure 12 shows that the lowest density of non-bonded electrons is in the blue zone, while
in the orange zone where aluminum atoms are located, the highest density of bonded atoms is
found, the highest electronic contribution for the Al7 Ni8 structure is offered by the 3d orbitals
of Ni with a medium contribution of the 3p orbitals of Al.
Isosurface1 Isosurface1
-2.127e-3 1.115e-3
-3.362e-3 -1.683e-3
-4.596e-3 -4.482e-3
-5.831e-3 -7.281e-3
-7.066e-3 -1.008e-2
Isosurface1 Isosurface1
7.449e-1 1.985
-5.695 -5.361e-1
-1.214e1 -3.057
-1.858e1 -5.579
-2.502e1 -8.100
Figure 11. Electronic isosurfaces of Ni10 . Figure 12. Electronic isosurfaces of Al7 Ni8 .
In the case of the isosurfaces presented in Figure 13, it can be seen that the blue zone, which
is shared by Ni and Al atoms, has the lowest density of non-bonded electrons, while the orange
zone has the highest density of bonded electrons. The largest electronic contribution in this
structure is provided by the 3d orbitals of Ni.
5
IV Workshop on Modeling and Simulation for Science and Engineering (IV WMSSE) IOP Publishing
Journal of Physics: Conference Series 1938 (2021) 012002 doi:10.1088/1742-6596/1938/1/012002
The Figure 14 shows the average binding energy for a cluster of pure Ni n nanoclusters and
doped monoatomic AlNin−1 nanoclusters for n = 10 − 20. Here a linear behavior is shown where
it is observed that the average energies for the AlNin−1 group clusters are larger than the values
of the corresponding pure Ni n clusters, indicating that when introducing an Al atom this energy
presents an increase. For this case, the structure with the highest binding energy of the AlNin−1
group is the AlNi9 nanocluster, as the cluster size increases the average binding energy decreases
until reaching the nanocluster with the lowest energy AlNi19 , something similar happens with
the pure Ni nanoclusters, where the Ni10 structure is the one with the highest energy and the
one with the lowest energy corresponds to the structure for Ni20 .
Isosurface1
1.559e-3
Average Binding Energy (ev)
-1.390e-3
-4.339e-3
-7.289e-3
-1.024e-2
Isosurface1
6.164e-1
2.843e-2
-5.595e-1
-1.147
-1.735
Cluster Size (n)
Figure 13. Electronic isosurfaces of Figure 14. The average binding energy as
Al10 Ni10 . a function of nanocluster size.
The average binding energy, varying the concentration of Ni atoms for Aln−x Nix nanoclusters
(for n = 10, 15, 18, 20 with x ≤ n) is shown in Figure 15, for fixed values of n and increasing
x (increasing Ni concentration) futhermore, it is observed that the average binding energy
decreases linearly. On the other hand, for fixed values of x and increased cluster size, the
binding energies are observed to gradually decrease as n increases. Generally, the structure with
the highest energy is the Al10 nanocluster and the one with the lowest binding energy is Ni20 .
Based on the results obtained from the electronic transition energies which mostly do not
exceed 1 ev, the semiconducting character of the studied nanoclusters can be observed, except
for the particular case of the Al6 Ni14 nanocluster which has a value Eg = 0.058 eV tending to
be more conductive than all the other structures.
-10
-20
-30
-40
Average Binding Energy (ev)
-50
-60
-70
-80
-90
-100
-110
-120
-130 n=10
-140 n=15
-150 n=18
-160 n=20
-170 Figure 15. Average binding energy as a function
-2 0 2 4 6 8 10 12 14 16 18 20 22
of Ni atom variation for Aln−x Nix nanoclusters of
Number of Ni atoms (x) sizes n = 10, 15, 18, 20 with x ≤ n.
6
IV Workshop on Modeling and Simulation for Science and Engineering (IV WMSSE) IOP Publishing
Journal of Physics: Conference Series 1938 (2021) 012002 doi:10.1088/1742-6596/1938/1/012002
4. Conclusions
Noble metal nanoparticles, such as Ni, have been one of the most researched nanomaterials in
nanoscience and nanotechnology. Their electrical and magnetic properties make these particles
a good candidate for numerous applications in the field of electronics and computer science. In
this paper, we study electronic isosurfaces and structural properties in nanoclusters Aln−x Nix
using density functional theory. The main study results are summarized as follows.
(i) For the different structures studied the densities of partial and electronic states evidence a
contribution of the d orbitals of the nickel atoms and an overlap of the sp orbitals when the
nanoclusters are composed of Al-Ni.
(ii) The binding energy of the structure for pure nickel nanoclusters decreases as the size of the
structure increases and the energy increases when an aluminum impurity atom is added to
it.
(iii) It is found that the binding energy for a fixed size nanocluster decreases as the nickel
concentration increases, and there is also a decrease in the binding energy in this structure
when the number of nickel atoms is fixed and the number of aluminum atoms is increased.
(iv) For all the structures studied, it was determined that the nanocluster with the highest
binding energy is Al10 and the structure with the lowest average binding energy is Ni20 .
Based on the results obtained for the electronic transition energy (gap) for the different
nanoclusters studied, these structures are semiconducting.
(v) In general the large clusters, consisting of a core of between 14 and 20 atoms and a protective
layer of strong ligands, and the small clusters, consisting of a smaller number of atoms,
approximately between 2 and 13, which do not need strong stabilizing ligands and have
all their atoms on the surface, present discrete energy levels and a band-gap that increases
with decreasing size.
(vi) It should be considered that it is interesting to establish the stability of the nanocluster
structures as a function of the Gibbs free energy.
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