Download Density functional theory study of AunMn(n=1–8) clusters

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Journal of Physics and Chemistry of Solids 71 (2010) 770–775
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Journal of Physics and Chemistry of Solids
journal homepage: www.elsevier.com/locate/jpcs
Density functional theory study of AunMn(n =1–8) clusters
Die Dong a,b,n, Kuang Xiao-Yu b,c,nn, Guo Jian-Jun a, Zheng Ben-Xia a
a
b
c
School of Physics and Chemistry, Xihua University, Chengdu 610039, China
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
International Centre for Materials Physics, Academia Sinica, Shengyang 110016, China
a r t i c l e in f o
a b s t r a c t
Article history:
Received 19 November 2009
Received in revised form
31 December 2009
Accepted 27 January 2010
Equilibrium geometries, relative stabilities, and magnetic properties of small AunMn (n = 1–8) clusters
have been investigated using density functional theory at the PW91P86 level. It is found that Mn atoms
in the ground state AunMn isomers tend to occupy the most highly coordinated position and the lowest
energy structure of AunMn clusters with even n is similar to that of pure Aun + 1 clusters, except for n =2.
The substitution of Au atom in Aun + 1 cluster by a Mn atom improves the stability of the host clusters.
Maximum peaks are observed for AunMn clusters at n =2, 4 on the size dependence of second-order
energy differences and fragmentation energies, implying that the two clusters possess relatively higher
stability. The HOMO–LUMO energy gaps of the ground state AunMn clusters show a pronounced odd–
even oscillation with the number of Au atoms, and the energy gap of Au2Mn cluster is the biggest
among all the clusters. The magnetism calculations indicate that the total magnetic moment of AunMn
cluster, which has a very large magnetic moment in comparison to the pure Aun + 1 cluster, is mainly
localized on Mn atom.
& 2010 Elsevier Ltd. All rights reserved.
Keywords:
A. Nanostructures
C. Ab initio calculations
D. Magnetic properties
1. Introduction
Previous experimental and theoretical work has demonstrated
that the introduction of a dopant atom in a small cluster can
significantly change the properties of the host cluster [1–4]. Gold
clusters doped with transition metal atoms (V, Cr, Fe, Co, Ni, etc.)
have been actively sought to tailor the desired structural,
electronic, optical, magnetic, and catalytic properties for potential
applications in solid state chemistry, materials science, microelectronics, biology, and nanotechnology [5–11]. For instance,
Yuan et al. [6] investigated the structure of AunM (n =1–7, M= Ni,
Pd, Pt) clusters and found that the dopant atoms can considerably
alter the geometric and electronic properties of the gold cluster.
Zhang et al. [7] reported that M@Au6 clusters (M =Sc–Ni), where
the transition metal atoms are located in the center of Au6 ring,
could be used as a new nanomaterials with tunable magnetic
moment. Graciani et al. [8] proved that the isolated V-doped Au12
cluster can bind a high number of oxygen molecules above pure
gold cluster and is an improved novel catalyst for CO oxidation.
Recently, the pure gold materials doped with manganese have
also been studied widely owing to their unique physical and
n
Corresponding author at: School of Physics and Chemistry, Xihua University,
Chengdu 610039, China.
nn
Corresponding author at: Institute of Atomic and Molecular Physics, Sichuan
University, Chengdu 610065, China
E-mail addresses: [email protected] (D. Dong), [email protected]
(K. Xiao-Yu).
0022-3697/$ - see front matter & 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jpcs.2010.01.015
chemical properties [12–15]. It was shown that the magnetocrystalline anisotropy energy of Mn@Au nanotube is dramatically
enhanced by one order of magnitude and this hybrid structure can
be used in ultrahigh density magnetic storage [12]. The icosahedral Au12 cage filled with single Mn atom, which has a large local
spin magnetic moment, shows unexpected large binding energy
compared with icosahedral Au13 cluster [13]. The positive charge
of cationic AunMn + clusters is mostly localized in Mn atom and
decreases when the size of the cluster increases [14]. Moreover,
these studies primarily focus on the ionic or special-size clusters.
To the best of our knowledge, there have been no reports
regarding small neutral Mn-doped gold clusters so far. On the
other hand, it is well-known that small metal clusters usually
exhibit extraordinary size-dependent properties, which should be
extremely different from those of the bulk, due to a large fraction
of surface atoms and a distinct electronic structure. Therefore, in
this paper, the geometric structures, relative stabilities, and
magnetic properties of AunMn (n= 1–8) clusters will be investigated systematically on the basis of density functional theory
(DFT). It is hoped that this work would be useful to understand
the influence of material structure on its properties and could
provide powerful guidelines for future experimental studies.
2. Computational method
DFT methods and an effective core potential LanL2DZ basis set,
as implemented in GAUSSIAN03 program package [16–18], have
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D. Dong et al. / Journal of Physics and Chemistry of Solids 71 (2010) 770–775
Table 1
The bond lengths (r) and dissociation energies (De) of ground state Au2 dimer
obtained by using different density functional methods.
Methods
r(Å)
De (eV)
LSDA
PW91P86
PW91PW91
PBEPBE
BLYP
Experimental (ref.25)
2.49
2.54
2.55
2.55
2.59
2.47
2.83
2.30
2.20
2.17
1.99
2.30
been employed for the calculations of structures and vibrational
frequencies. The exchange–correlation energies were treated
using PW91P86 functional of the generalized gradient approximation (GGA) [19,20]. The convergence thresholds were set to
1.5 10 5 Hartree/Bohr for the forces, 6.0 10 5 Å for the
displacement, and 10 6 Hartree for the energy change. To search
the lowest energy structures, lots of possible initial isomers,
which include one-, two- and three-dimensional configurations,
had been considered in geometry optimizations. Furthermore, the
number of possible initial isomers increases rapidly with the
increase in size of clusters. Due to the spin polarization, every
initial configuration was optimized at various possible spin
multiplicities. Each geometry optimization was followed by an
analysis of harmonic vibrational freqencies to confirm that the
optimized geometry corresponds to a local minimum.
The reliability of current computational method has been
tested by comparative calculations on gold dimer. The results are
listed in Table 1. It can be seen from Table 1 that the calculated
bond length and dissociation energy based on PW91P86 method
are in good agreement with experimental values. These indicate
the suitability of current computational method to describe small
AunMn (n = 1–8) clusters.
3. Results and discussion
3.1. Geometrical structures
For AunMn (n = 2–8) clusters, more than 300 initial configurations were optimized and many isomers have been obtained. The
ground state structure and three low-lying isomers for each
AunMn cluster are displayed in Fig. 1. According to the energies
from low to high, these isomers are designated by na, nb, nc, and
nd, where n represents the number of Au atoms in the AunMn
clusters. Their symmetry, spin multiplicity and energy difference
compared to each of ground state structures are also indicated in
the figure. Meanwhile, in order to examine the effects of dopant
Mn on gold clusters, geometry optimizations of Aun (n = 2–9)
clusters have been carried out using identical method and basis
set. The lowest energy structures of Aun clusters, as shown in
Fig. 1, were found. These structures are also in accord with the
results of Idrobo et al [21–25].
The calculated results for AuMn manifest that the total energy
of septet spin state is the lowest in all possible spin states. Hence,
the septet AuMn dimer with electronic state of 7Sg is the ground
state structure, and the bond length of ground state AuMn dimer
(2.45 Å) is shorter than that of Au2 (2.54 Å). This may be
attributed to the fact that the radius of Mn atom is smaller than
that of Au atom.
The linear 2a isomer with DNh symmetry is found to be the
most stable structure of Au2Mn cluster. The Au–Mn bond length is
2.43 Å and the corresponding electronic state is 6Sg. The 2b
771
isomer is a linear configuration with CNV symmetry and 1.33 eV
higher in energy than the 2a isomer. The trigonal 2c isomer in
octet spin state is another metastable isomer. The 2d isomer with
an apex angle of 119.21 is similar to the ground state structure of
Au3 cluster.
The lowest energy structure of Au3Mn cluster is the
3a isomer, which is obtained by distorting the geometry
starting from D3h to C2V symmetry. The electronic state for the
3a isomer is 5B2. The rhombus 3b and 3c isomers resemble the
most stable structure of Au4 cluster and are less stable than 3a
isomer by 0.20 and 1.02 eV, respectively. At the same time, the 3b
isomer can be seen as intermediate between 3a and 3c isomers.
The 3d isomer has the same spin multiplicity and structure as 3a
isomer. But Mn atom in 3d isomer is located at a lowly
coordinated position.
Similar to the configuration of ground state Au5 cluster,
the trapezoidal 4a isomer in electronic state of 6A1 is the
most stable structure of Au4Mn clusters. The planar 4b isomer
with an uncompact structure is energetically higher than
the 4a isomer by 0.16 eV. The sextet 4c isomer is a square
pyramid with Mn atom on the top and the first three-dimensional
(3D) configuration. The 4d isomer, which is 0.32 eV higher in
energy than the 3D 4c isomer, possesses a triangular bipyramid
structure. Other planar and 3D isomers are less stable than the
four isomers.
Among the Au5Mn isomers, the lowest energy structure is the
planar 5a isomer with electronic state of 5B2 and C2V symmetry.
The Mn atom is surrounded by five Au atoms. But the isomer
belonged to point group of D5h is not obtained in geometry
optimizations. The 5b, which relates to the most stable structure
of Au6 cluster, is found as a low-lying isomer, with 0.45 eV higher
than the lowest energy structure. The 5c isomer in quintet spin
state is energetically lower than the same structure with other
spin states. The septet 5d isomer with C4V symmetry is an
octahedral configuration, where the tetrahedrally coordinated Mn
atom occupies the vertex position. In addition, several planar
isomers, which are not displayed in Fig. 1, have a big energy
difference relative to the forgoing four isomers.
In the case of Au6Mn clusters, seven isomers, such as 6a in
Fig. 1, show a similar structure to that of the ground state Au7
cluster and their energies decrease as the coordinated number of
Mn atom increases. The 6a isomer with electronic state of 6A0 is
the most stable structure in all isomers. Other six isomers, which
are not plotted in Fig. 1, are significantly higher in energy than the
6a isomer. The 6b isomer with Mn atom at the center of Au6 ring
is a high-symmetry planar structure, which was expected to be
the lowest energy structure. But its energy is higher by 0.13 eV
than that of the 6a isomer. The 6c and 6d isomers, whose energies
are closed to the 6b isomer, are more stable than other 3D
configurations. Due to the Jahn–Teller effect, Mn atom in the 6c
isomer with C3V symmetry is shifted along the C3 axis of D3h
symmetry.
The quintet planar 7a isomer with electronic state of 5B2 is the
lowest energy structure of Au7Mn cluster. However, our results
show that this configuration corresponds to the metastable
isomer of Au8 cluster. The 7b isomer with Au–Mn-Au bond angle
of 161.31, which is the most stable 3D configuration, is still
0.33 eV less stable than the 7a isomer. The 7c and 7d isomers are
two low-lying planar structures and have a large structural
distortion relative to the most stable Au8 cluster. For the 7c
isomer, the septet spin state is energetically lower than the
quintet spin state by 0.09 eV. The 7d geometry in septet spin state
turns into the 7c isomer.
With regard to Au8Mn cluster, 30 odd isomers were found and
the low-lying isomers evidently favor planar structures, as shown
in Fig. 1. The 8a and 8b isomers, which exhibit a configuration
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D∞h, 6
2a
C∞V, 6, 1.33 eV
2b
C2V, 8, 1.69eV
2c
C2V, 2, 2.97eV
2d
D2h, 1
Au4
C2V, 5
3a
C2V, 5, 0.20eV
3b
C2V, 5, 1.02eV
3c
C2V, 5, 1.48eV
3d
C2V, 2
Au5
C2V, 6
4a
C2V, 6, 0.16eV,
4b
C4V, 6, 0.53eV
4c
C3V, 6, 0.85eV
4d
D3h, 1
Au6
C2V, 5
5a
C2V, 5, 0.45eV
5b
CS, 5, 0.62eV
5c
C4V, 7, 0.98eV
5d
CS, 2
Au7
CS, 6
6a
D6h, 4, 0.13eV
6b
C3V, 6, 0.19eV
6c
C2V, 6, 0.27eV
6d
D4h, 1
Au8
C2V, 5
7a
C2V, 5, 0.33eV
7b
C2V, 7, 0.50eV
7c
C2V, 5, 0.60eV
7d
C2V, 2
Au9
C2V, 6
8a
C2V, 6, 0.22eV
8b
D2h, 6, 0.30eV
8c
CS, 6, 0.37eV
8d
C2V, 2
Au3
Fig. 1. The lowest energy structures of Aun + 1 and AunMn (n= 2–8) clusters, and three low-lying isomers for doped clusters. Bond lengths are in Å. Their symmetry,
multiplicity, and energy difference compared to each of the ground state structures are given below them. The yellow and blue balls represent Au and Mn atoms,
respectively. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.
similar to the ground state structure of Au9 cluster, are more
stable than other isomers. The former with electronic state of 6A1
is lower in energy than the latter and the lowest energy structure.
The 8c isomer is a rhombus structure with D2h symmetry. Mn
atom in the 8c isomer is at the center of this structure. The 8d
isomer with CS symmetry is above the lowest energy structure by
0.37 eV. Nevertheless, the 8d-like configuration with Mn atom at
the center was found to be an unstable structure. As for the 3D
isomers of Au8Mn cluster, their energies are higher than the
planar 8d isomer.
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Fig. 2. Size dependence of the averaged binding energies for the ground state
structures of AunMn and Aun + 1 clusters.
773
Fig. 3. Size dependence of the second-order energy differences for the ground
state structures of AunMn and Aun + 1 clusters.
From the above discussions, it is obvious that the ground state
structures of AunMn (n= 1–8) clusters favor the linear structures
for n = 1–2 and planar structures for n =3–8. The Mn atom in the
most stable AunMn clusters tend to occupy the most highly
coordinated position. On the other hand, for n= 3–8, the ground
state geometries of AunMn clusters with even n are similar to
those of pure Aun + 1 clusters.
3.2. Relative stabilities
In this part, compared with the pure Aun + 1 clusters, the
relative stabilities of AunMn (n = 1–8) clusters for the most stable
structures are analyzed based on the atomic averaged binding
energies, second-order difference of energies, fragmentation
energies, and energy gaps between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital
(LUMO).
The atomic averaged binding energies (Eb) of AunMn and Aun + 1
clusters are defined as [26]
Eb ½Aun Mn ¼ ðnE½Au þ E½MnE½Aun MnÞ=ðn þ1Þ
ð1Þ
Eb ½Aun þ 1 ¼ fðn þ1ÞE½AuE½Aun þ 1 g=ðn þ 1Þ
ð2Þ
where E represents the energies of the corresponding systems.
The calculated binding energies per atom for the most stable
AunMn and Aun + 1 clusters are shown in Fig. 2. As seen from Fig. 2,
the substitution of Au atom by an Mn atom enhances the stability
of the host clusters. For AunMn clusters, the averaged binding
energy of AuMn dimer is much smaller than those of other AunMn
(n= 2–8) clusters. A local visible peak occurs at n = 2. This hints
that the Au2Mn cluster is more stable than its neighboring
clusters. From n4 3, the Eb of AunMn clusters increase with n, but
finally tends to saturate.
In cluster physics, the second-order difference of energies
(D2E), which can be compared with the relative abundances
determined in mass spectroscopy experiment, are a quite
sensitive quantity that reflects the relative stability of clusters
[27]. For the most stable AunMn and Aun + 1 clusters, it can be
estimated as follows
D2 E½Aun Mn ¼ E½Aun þ 1 Mn þE½Aun1 Mn2E½Aun Mn
ð3Þ
D2 E½Aun ¼ E½Aun þ 1 þ E½Aun1 2E½Aun ð4Þ
where E is the energy of the ground state clusters. Fig. 3 illustrates
the size dependence of the second-order energy differences for
the most stable AunMn and Aun + 1 clusters. It is clear from this
Fig. 4. The fragmentation energies of the ground state structures of AunMn and
Aun + 1 clusters via loss of an Au atom.
figure that the even-numbered gold clusters are more stable than
the odd-numbered ones. However, the presence of Mn atom
changes the stable pattern of the host clusters. For AunMn
clusters, two conspicuous maxima are found at n =2 and 4.
Accordingly, it can be deduced that Au2Mn and Au4Mn clusters
possess relatively higher stability and are magic clusters.
The relative stability of the most stable AunMn and Aun + 1
clusters can also be investigated by examining the fragmentation
energy [27], which involves the energy that an Au atom is
separated from these clusters. In this case, the fragmentation
energy (DE) can be calculated as
DE½Aun Mn ¼ E½Aun1 Mn þE½AuE½Aun Mn
ð5Þ
DE½Aun þ 1 ¼ E½Aun þE½AuE½Aun þ 1 ð6Þ
where E is the energy of the lowest energy clusters or atom. For
the most stable AunMn and Aun + 1 clusters, the fragmentation
energy as a function of the cluster size is displayed in Fig. 4.
Obviously, the results are also in accord with the above analysis
based on the second-order difference of energies.
The HOMO–LUMO energy gap (Eg), which relies on the
eigenvalues of the HOMO and LUMO energy levels, is always
considered to be a significant parameter that characterizes
chemical stability of small clusters. A big energy gap usually
relates to a high chemical stability. For the most stable AunMn and
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Aun + 1 clusters, the energy gaps are plotted in Fig. 5. The AunMn
and Aun + 1 clusters show a strong odd–even oscillations in their
energy gap spectrum. The energy gap of AunMn clusters is smaller
for odd n and larger for even n than that of the corresponding
Aun + 1 clusters. Although the energy gaps do not correlate directly
with the second-order difference of energies and fragmentation
energy, it can be seen from Fig. 5 that the magic clusters, Au2Mn,
has a particularly large energy gap. In other words, the Au2Mn
cluster is less reactive and could be useful as building block for
constructing the cluster-assembled materials. The AuMn dimer
has a very small energy gap (0.01 eV) relative to other clusters.
This means that AuMn dimer has lower chemical stability.
Table 2
The charge and local magnetic moment of 3d, 4s, and 4p states for Mn atoms in
AunMn clusters
Cluster
AuMn
Au2Mn
Au3Mn
Au4Mn
Au5Mn
Au6Mn
Au7Mn
Au8Mn
Mn—3d
Mn—4s
Mn—4p
Q (e)
m (mB)
Q (e)
m (mB)
Q (e)
m (mB)
5.23
5.32
5.43
5.44
5.54
5.47
5.53
5.47
4.77
4.62
4.49
4.51
4.30
4.47
4.37
4.47
1.20
0.80
0.76
0.70
0.58
0.69
0.65
0.67
0.70
0.18
0.14
0.14
0.08
0.09
0.09
0.10
0.16
0.31
0.06
0.08
0.89
0.08
0.10
0.09
0.10
0.01
0
0
0.03
0
0.01
0.01
3.3. Magnetic properties
The total magnetic moment of the most stable AunMn (n = 1–8)
clusters has been calculated and the results are presented in Fig. 6,
where we have also plotted the total magnetic moment of the
host clusters. The ground state Aun + 1 clusters show a pronounced
odd–even alternations with the number of Au atoms in the total
magnetic moment. When an Mn atom substitutes for an Au atom
in Aun + 1 cluster, the AunMn clusters generate a very large
magnetic moment. In particular, the AuMn dimer, which is
more chemically active, has the biggest magnetic moment (6mB)
among all the AunMn clusters. For n = 2–8, the total magnetic
moments of AunMn clusters keep the same pattern of oscillation
with the pure gold clusters and are 5mB for even n and 4mB for odd
n. Simultaneously, it is also evident from the magnetic moment
calculations that the doping by an Mn atom augments the
magnetism of gold clusters.
In order to understand the magnetic properties further, we have
performed the natural bond orbital analysis for the most stable
AunMn (n =1–8) clusters [28]. The local magnetic moments on Mn
atoms are shown in Fig. 6. It can be seen from Fig. 6 that the total
magnetic moment of the clusters is mainly localized in Mn atom.
Small amount of magnetic moments are found in Au atoms. The Au
atoms in AunMn clusters exhibit antiferromagetic alignment for
n=3, 5, and 7 and ferromagetic alignment for even n and n=1 with
respect to Mn atom’s magnetic moment. The charge and magnetic
moment on 3d, 4s, and 4p states of Mn atom in AunMn clusters
were listed in Table 2. It is found that the partially filled 3d orbital
play an important role in determining the magnetism of Mn atom.
The magnetic moment provided by 3d orbital is about 4.30–4.77mB.
The 4s and 4p subshells, which are non-magnetic for a free Mn
atom, contribute a little of magnetic moment. This may be ascribed
to the internal charge transfer from 4s orbital to 3d and 4p states.
Namely, the 4s orbital lose 0.80–1.42 electrons, while the 3d and
4p states obtain 0.23–0.54 and 0.06–0.89 electrons, respectively.
At the same time, the magnetic moment of 4s and 3d orbitals
decreases gradually with the increase in charge transfer.
4. Conclusions
Fig. 5. Size dependence of the HOMO–LUMO energy gaps of ground state AunMn
and Aun + 1 clusters.
Equilibrium geometries, relative stabilities, and magnetic
properties of AunMn (n=1–8) clusters have been studied by firstprincples density functional calculations. The geometric optimizations indicate that Mn atoms in ground state AunMn isomers tend
to occupy the most highly coordinated position and the most
stable structure of AunMn clusters with even n resembles that of
pure Aun + 1 clusters, except for n=2. The substitution of Mn atom
for an Au atom in Aun + 1 cluster enhances the stability of the host
clusters. The analyses of the second-order energy differences and
fragmentation energies indicate that Au2Mn and Au4Mn clusters
are magic clusters. We also found from the HOMO–LUMO gaps
that Au2Mn cluster have high chemical stability. The magnetism
calculations show that the total magnetic moments of AunMn
cluster are 4 or 6mB larger than those of pure Aun + 1 clusters. Mn
atom in these clusters carries most of the magnetic moment.
Acknowledgements
Fig. 6. Total magnetic moment of the ground state AunMn and Aun + 1 clusters, and
local magnetic moment on Mn atom.
This project was supported by Xihua University (No.
Zg0723304) and the Education Department of Sichuan Province
(No. 2006B042).
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