Physics Letters A 375 (2011) 1877–1882
Contents lists available at ScienceDirect
Physics Letters A
www.elsevier.com/locate/pla
Geometries, stabilities, and electronic properties of gold–magnesium (Aun Mg)
bimetallic clusters
Yan-Fang Li a , Xiao-Yu Kuang a,b,∗ , Su-Juan Wang a , Yang Li c , Ya-Ru Zhao a
a
b
c
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
International Centre for Materials Physics, Academia Sinica, Shenyang 110016, China
Department of Opto-Electronics Science and Technology, Sichuan University, Chengdu 610065, China
a r t i c l e
i n f o
Article history:
Received 26 December 2010
Received in revised form 10 March 2011
Accepted 20 March 2011
Available online 30 March 2011
Communicated by R. Wu
Keywords:
Aun Mg cluster
Density functional theory
Relative stability
Natural population analysis
a b s t r a c t
The geometrical structures, relative stabilities, and electronic properties of bimetallic Aun Mg (n = 1–8)
clusters have been systematically investigated by means of first-principle density functional theory. The
results show that the ground-state isomers have planar structures for n = 1–7. Here, the calculated fragmentation energies, the second-order difference of energies, the highest occupied–lowest unoccupied
molecular orbital energy gaps, and the hardness exhibit a pronounced odd–even alternation, manifesting
that the clusters, especially Au2 Mg, with even-number gold atoms have a higher relative stability. On the
basis of natural population analysis, the charge transfer and magnetic moment are also discussed.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
During the last decade, noble-metal Au has been a considerable topic in experimental and theoretical studies due to its special
technical applications in the fields of optics, materials science, and
solid-state chemistry [1–7]. Especially, gold-based catalysts have
attracted more attention for their fascinating catalytic activity exhibited by Au particles supported on metal oxide surfaces [8–12].
As for simple small-sized clusters, the gold clusters are formed by
a few up to tens of thousands of atoms occurring closely together,
which represent a bridge between atomic state and bulk material.
Gold is known to be particularly convenient for spectroscopic
studies due to the closed d-shell electronic configuration 5d10 6s1 .
The alkali atoms have the same s1 unpaired electron. They all
can be viewed as “simple” s-only metals, which are easily characterized experimentally and investigated with less computational
effort. It is well known that an electronic shell model (jellium
model), in which valence electrons move freely in an averaged
electronic potential, successfully explains size-dependent features
of both coinage and alkali metal clusters. Solving the Schrödinger
equation for the potential results in an electronic shell structure
*
Corresponding author at: Institute of Atomic and Molecular Physics, Sichuan
University, Chengdu 610065, China.
E-mail address: [email protected] (X.-Y. Kuang).
0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.physleta.2011.03.036
1s2 , 1p6 , 1d10 , 2s2 , 2p6 , 1f14 , . . . . So when the number of valence electrons in the clusters is just enough to complete one of
the electronic shells, the corresponding clusters exhibit enhanced
stability. Meanwhile, because an especially large electronegativity
exists between alkali metal and gold atom, the alkali–gold series
are found to be particularly stable. Therefore, alloys of gold with
various alkali metals have roused interest of both chemists and
physicists [13–18]. For example, the complete alkali auride series
(LiAu, NaAu, KAu, RbAu, CsAu) have been studied by Belpassi et al.
[17] using the G-spinor basis set in the program BERTHA. The intermetallic bond that occurs in these series is characterized by a
large charge transfer from the alkali metals to gold atom. Besides,
because the electronegativity difference is larger in sodium–gold
cluster than that of sodium–silver cluster, Heiz et al. [14] have
found that this leads to a higher polarization and more directionalities of the metal–metal bonds for sodium–gold system. In recent
years, the intermetallic bond in gold–alkaline earth molecules is
also found to be particularly stable [19–22]. Among them, it is obtained that the bond energy of AuBe and AuCa is 5%–10% higher
than that of the gold dimer Au2 while 30%–40% higher compared
with the species AuMg, and the doping Mg atom hardly deforms
the electronic structure of Aun− clusters for n = 2–4 [20,22]. Since
the chemical and physical properties of clusters depend strongly
upon the microscopic structure around the dopant, we have made
significant efforts to understand the structural and electronic properties of Aun Mg− clusters recently [23]. A good agreement between
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Y.-F. Li et al. / Physics Letters A 375 (2011) 1877–1882
Fig. 1. The lowest energy structures and low-lying isomers for Aun Mg (n = 2–8) clusters, and the ground-state structures of pure gold clusters Aun+1 (n = 2–8) have been
listed on the left. The yellow and green balls represent Au and Mg atoms, respectively. (For interpretation of the references to color in this figure legend, the reader is referred
to the web version of this Letter.)
theoretical and experimental results suggests good calculations of
the physical structures. Although the intermetallic molecules AuMg
and Au5 Mg have been studied by Balducci et al. [20] and Majumder et al. [21] by employing density functional theory (DFT),
respectively, there is no systematically theoretical study on neutral gold–magnesium clusters until now. Are their structures and
properties greatly distinct from the anionic ones? How does the
dopant affect the bare gold clusters? These open questions are still
unsolved, so it is urgent to understand the geometries, stabilities,
and electronic properties of Aun Mg clusters.
In the current work, we systematically investigate the small
neutral gold clusters doped by a single-impurity magnesium atom,
Aun Mg (n = 1–8), using the first-principle method based on DFT.
The Letter is organized as follows: Section 2 gives a brief description of the computational details. Then, the equilibrium geometry,
relative stability, and natural population analysis (NPA) are given
in Section 3. Lastly, the conclusions are summarized in Section 4.
2. Computational methods
In this work, all geometrical optimizations of Aun Mg (n = 1–8)
clusters are performed by using a DFT-based GAUSSIAN 03 package [24]. While calculations involving full electrons are rather time
consuming due to the gold being a heavy atom, the effective
core potentials including relativistic effects (RECP) are introduced
to describe the inner core electrons. In this connection, the basis set labeled GEN (SDD for the Au atom and 6-311G* for the
Mg atom) is adopted at the level of the PW91PW91 method [25,
26]. In searching for the lowest energy structures, lots of possible
initial structures have been extensively explored without any symmetry constraint, and different spin multiplicities are also taken
into account. Here, the configurations are regarded as optimized
when the convergence thresholds of the maximum force, rootmean-square (RMS) force, maximum displacement of atoms, and
RMS displacement of atoms are set to 0.00045, 0.0003, 0.0018,
and 0.0012 a.u., respectively. Furthermore, harmonic vibrational
frequency calculations are performed to guarantee the optimized
structures correspond to the potential energy minima. The highest
occupied–lowest unoccupied molecular orbital (HOMO–LUMO) energy gaps, hardness (η ), and NPA of the stable configurations are
also obtained based on PW91PW91/GEN method.
3. Results and discussions
A large number of optimized isomers for Aun Mg (n = 1–8) clusters have been considered, but here we report only the few energetically low-lying ones in Fig. 1. According to the total energy
from low to high, these isomers are designated by na, nb, nc, nd,
and ne (n is the number of Au atoms in Aun Mg clusters). Meanwhile, the corresponding electronic states, symmetries, relative energies, HOMO and LUMO energies are summarized in Table 1. In
order to discuss the effects of doping impurity on gold clusters,
we also performed optimizations for Aun+1 (n = 1–8) clusters by
using PW91PW91/SDD method, and the lowest energy configura-
Y.-F. Li et al. / Physics Letters A 375 (2011) 1877–1882
1879
Table 1
Electronic states, symmetries, relative energies ( E), HOMO energies, and LUMO energies for Aun Mg (n = 1–8) clusters.
State
1a
2a
2b
2c
3a
3b
3c
3d
4a
4b
4c
4d
4e
5a
5b
5c
5d
2
Σ
Σg
1
Σ
1
3
B2
B2
A1
2
B2
2
B2
1
A1
1
A1
1 A
1
A1
1
A1
2
B2
2
A1
2 A
2 A
2
2
Symm.
C ∞v
D ∞h
C ∞v
C 2v
C 2v
C 2v
C 2v
C 2v
C 2v
C 2v
Cs
C 4v
C 2v
C 2v
C 2v
Cs
Cs
E
(eV)
HOMO
(hartree)
LUMO
(hartree)
0.00
0.00
1.23
1.48
0.00
0.17
0.88
1.40
0.00
0.18
0.28
0.69
1.48
0.00
0.16
0.27
0.35
−0.16596
−0.21318
−0.19508
−0.17276
−0.19357
−0.17331
−0.18585
−0.15517
−0.18556
−0.24655
−0.21471
−0.19751
−0.20283
−0.19264
−0.14696
−0.19600
−0.19025
−0.12999
−0.10837
−0.13769
−0.15983
−0.17282
−0.15649
−0.16843
−0.14661
−0.12583
−0.17147
−0.13923
−0.14459
−0.16543
−0.18267
−0.14068
−0.18376
−0.17922
tions are shown in Fig. 1. It is worth pointing out that the most
stable structures of bare gold clusters we obtained are overall in
good agreement with the published literature [27].
State
2
5e
6a
6b
6c
6d
6e
7a
7b
7c
7d
7e
8a
8b
8c
8d
8e
B2
1 Symm.
C 2v
Cs
C 2v
C 3v
Cs
C 2v
C 2v
C 2v
C 2v
C 2v
Cs
C2
C 2v
C 2v
C1
Cs
A
1
A1
1
A1
1 A
1
A1
2
B2
2
A1
2
A1
2
A2
2 A
1
A
1
A1
1
A1
1
A
1 A
E
(eV)
HOMO
(hartree)
LUMO
(hartree)
0.65
0.00
0.31
0.43
0.51
0.97
0.00
0.22
0.41
0.45
0.57
0.00
0.19
0.37
0.41
0.45
−0.17254
−0.19758
−0.20248
−0.19213
−0.19910
−0.20548
−0.20526
−0.17350
−0.17234
−0.17042
−0.17358
−0.21904
−0.20261
−0.20016
−0.20739
−0.20082
−0.16259
−0.15215
−0.14646
−0.14577
−0.16464
−0.18284
−0.19667
−0.16558
−0.16503
−0.16257
−0.16429
−0.16826
−0.16360
−0.15816
−0.14937
−0.15519
mers 8b and 8c, with the same symmetry (C 2v ) and electronic
state (1 A1 ), resemble the ground-state configuration of Au9 cluster; however, isomer 8c is located at a lowly coordinated position.
Therefore, the former is more stable than later by 0.18 eV.
3.1. Equilibrium geometry
3.2. Relative stability
The biatomic AuMg cluster with 2Σ electronic state is the
ground-state structure, which bond length (2.496 Å) is shorter than
that of Au2 (2.557 Å). Besides, the dissociation energy (1.82 eV)
and ionization energy (6.99 eV) agree well with experimental data:
1.818 eV [19] and 6.7 ± 0.3 eV [20], respectively. Thus, we believe
the functional and basis set used in the current DFT-package is
reasonably good to describe the small gold–magnesium clusters.
The lowest energy structures of Aun Mg clusters with three to
eight atoms are found to adopt planar forms. For Au2 Mg, the linear structure 2a with Mg atom at the middle is 1.23 and 1.48 eV
in energy lower than the other two low-lying isomers (2b, 2c).
By substituting the impurity on different positions of groundstate configuration Au4 , the C 2v rhombus isomers 3b and 3c can
be yielded; however, their total energies are higher by 0.17 and
0.88 eV than that of Y-shaped structure 3a. The optimized groundstate structure (4a) of Au4 Mg is a trapezia with C 2v symmetry,
which is similar to the bare metal cluster. Meanwhile, an early appearance of three-dimensional (3D) configuration starts at n = 4
(4d). This isomer has a high geometrical symmetry (C 4v ), but it is
0.69 eV energetically higher than 4a. Besides, as one, two, or three
gold atoms being surface capped on different sides of 4d isomer,
the other three 3D isomers (5d, 6b, 7d) are obtained, respectively.
With regard to Au5 Mg, the planar triangular structure (5b) and deformed isomer (5e) are in consistency with the calculated results
of Majumder et al. [21], but the configuration 5a has a favorable
lowest energy. This structure is fivefold coordinated Au atoms, and
is almost degenerate in energy for 5b. The lowest energy structure 6a and low-lying configuration 6d of Au6 Mg are derived by
replacing one Au atom on different sites by impurity Mg atom in
the pure cluster, thus they look like each other together with pure
gold cluster Au7 . As for the 3D isomer 6c, possessing two different
Au–Mg bonds (2.613 Å, 2.896 Å), which can be viewed as three
gold atoms symmetrically bi-capped on the triangular pyramid. In
the case of 7a, the single magnesium atom assumes central position and therefore is highly coordinated, which is still a planar
structure. The other four low-lying isomers (7b, 7c, 7d, 7e) are obtained in the energy range 0.35 eV. When the number of Aun Mg
cluster is up to 9, surprisingly, a 2D → 3D structural transition occurs for the most stable configuration 8a. This is different from
the anionic Au8 Mg cluster. Among Au8 Mg clusters, the planar iso-
In order to investigate the relative cluster stabilities, we therefore carry out the calculations of atomic average binding energies
E b , fragmentation energies 1 E (with respect to removing one Au
atom from cluster), and second-order difference of energies 2 E.
For Aun Mg (n = 1–8) clusters, the corresponding E b , 1 E, and 2 E
are defined as
E b (n) = nE (Au) + E (Mg) − E (Aun Mg) /(n + 1),
1 E (n) = E (Aun−1 Mg) + E (Au) − E (Aun Mg),
2 E (n) = E (Aun−1 Mg) + E (Aun+1 Mg) − 2E (Aun Mg),
(1)
while for Aun+1 (n = 1–8) clusters, which can be expressed as
E b (n + 1) = (n + 1) E (Au) − E (Aun+1 ) /(n + 1),
1 E (n + 1) = E (Aun ) + E (Au) − E (Aun+1 ),
2 E (n + 1) = E (Aun ) + E (Aun+2 ) − 2E (Aun+1 ),
(2)
where E (Au), E (Mg), E (Aun Mg), E (Aun−1 Mg), E (Aun+1 Mg),
E (Aun+1 ), E (Aun ), and E (Aun+2 ) represent the total energies of
the lowest energy clusters or atoms for Au, Mg, Aun Mg, Aun−1 Mg,
Aun+1 Mg, Aun+1 , Aun , and Aun+2 , respectively.
Based on the above formulas, we now discuss the size dependence of atomic average binding energies, fragmentation energies,
and second-order difference of energies. The corresponding relationships of E b , 1 E, and 2 E with respect to cluster size are
plotted in Figs. 2(a), (b), and (c). The primary features are concluded: (i) For Aun+1 clusters, Fig. 2(a) illustrates that the atomic
average binding energies have an increasing tendency with the
cluster size growing, which agrees with the previous works [27].
(ii) Meanwhile, a stair-step increasing tendency is also found for
gold–magnesium clusters, but the curve increases sharply up to
1.61 eV as the size going from n = 1 to 2. (iii) As for the fragmentation energies and second-order difference of energies, although
the doping Mg atom makes the stable pattern of host cluster
contrary, Figs. 2(b) and (c) clearly exhibit odd–even alternations
in the region of n = 1–8. This means that the clusters containing even-number gold atoms have a higher relative stability than
the neighbors. It is against the conclusions about Aun Mg− clusters
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Y.-F. Li et al. / Physics Letters A 375 (2011) 1877–1882
Fig. 2. Size dependence of (a) the atomic average binding energies, (b) the fragmentation energies, (c) the second-order difference of energies, and (d) the HOMO–LUMO
energy gaps for the lowest energy structures of Aun Mg and Aun+1 (n = 1–8) clusters.
[23]; however, both neutral and anionic gold–magnesium clusters
with paired s valence electrons are more stable than those of unpaired ones due to the closed-shell configuration always produces
extra stability. These results indicate that the alternation is determined by the total number of s valence electrons. According to
jellium model, some of the magic sizes (Au2 , Au8 , Au6 Mg) can be
associated with occupation of the electronic shell 1s2 , 1p6 . As for
magic number ten for Au8 Mg cluster, it appears that the 1d and
2s levels are reversed, that is, 1s2 , 1p6 , 2s2 . This feature is also
found theoretically for Nan Al, Nan Au, and Nan Mg. (iv) As can be
seen from the plots, a maximum value at n = 2 is found for 1 E
(3.02 eV) and 2 E (1.57 eV), respectively, suggesting the Au2 Mg
cluster keeps the highest stability, which may come from a strong
s–s σ bonding interaction.
The highest occupied–lowest unoccupied molecular orbital
(HOMO–LUMO) energy gap reflects the ability of an electron to
jump from occupied orbital to unoccupied orbital, which can provide an important criterion to reflect the chemical stability of
clusters. For the low-lying configurations of Aun Mg clusters, the
HOMO and LUMO energies are summarized in Table 1; meanwhile,
the corresponding HOMO–LUMO energy gaps for the ground-state
structures are plotted in Fig. 2(d) compared to the bare gold clusters. It can be seen that the HOMO–LUMO energy gaps exhibit an
approximate odd–even oscillations as 1 E and 2 E, interestingly,
the significant peak (2.85 eV) is also localized at n = 2. Therefore, it
can be concluded that the clusters with even-number gold atoms,
particularly Au2 Mg, are related to a weaker chemical activity.
3.3. Vertical ionization potential, vertical electron affinity, and hardness
The vertical ionization potential (VIP) and the vertical electron
affinity (VEA) are the useful quantities for determining the stability
of clusters, which are defined as
VIP = E cation at optimized neutral geometry − E optimized neutral
and
VEA = E optimized neutral − E anion at optimized neutral geometry .
Our calculated VIPs and VEAs for the ground-state configurations
are listed in Table 2. It is found that the VIPs and VEAs of Aun Mg
clusters exhibit an odd–even alternation for the cluster size n =
1–8, and the large values of VIP suggest a high stability for the
clusters with an even number of gold atoms, especially Au2 Mg. In
view of these clusters with large VEAs, according to jellium model,
they are short of one electron to form a closed electronic shell and
therefore having a greater tendency to accept an extra electron. As
shown in Table 2, although the calculated VIP values of pure gold
clusters do not show a visible oscillatory behavior, they are in line
with the experimental result as expected [28].
Y.-F. Li et al. / Physics Letters A 375 (2011) 1877–1882
With the calculations of VIP and VEA, the chemical hardness η
has been studied. Hardness has been established as an electronic
quantity which may be used in characterizing the relative stability of molecules and aggregate through the principle of maximum
hardness proposed by Pearson [29]. The finite-difference approximation leads to η ≈ (VIP − VEA)/2. The calculated results are given
in Table 2, and the size dependence of η for the most stable Aun Mg
and Aun+1 clusters are shown in Fig. 3. The two curves in Fig. 3
present an oscillating behavior, and the local maxima occur at
n = 2, 4, and 6 for Aun Mg and n = 3, 5, and 7 for Aun+1 . This
reflects that these configurations with even-number valence electrons are harder than their neighboring clusters, in other words,
they are more stable structures. Here, Au2 Mg configuration shows
the largest chemical hardness of 3.70 eV, which confirms the conclusions based on the VIP, E b , 1 E, 2 E, and HOMO–LUMO energy gap. In addition, the calculated VEAs of Aun Mg clusters are
Fig. 3. Size dependence of the hardness for the lowest energy structures of Aun Mg
and Aun+1 (n = 1–8) clusters.
Table 2
Hardness (η ), vertical ionization potential (VIP), and vertical electron affinity (VEA)
of the lowest energy Aun+1 and Aun Mg (n = 1–8) clusters.
Cluster
size
Aun+1
Aun Mg
η
VIP
VEA
Expt.a
η
VIP
VEA
n=1
n=2
n=3
n=4
n=5
n=6
n=7
n=8
3.75
2.54
2.72
2.25
3.18
2.01
2.59
1.83
9.50
8.45
8.28
7.61
8.56
7.27
8.04
7.13
2.00
3.38
2.76
3.12
2.20
3.25
2.87
3.47
9.50
7.50
8.60
8.00
8.80
7.80
8.65
7.15
2.80
3.70
2.34
2.88
2.06
2.53
1.92
2.66
7.02
8.48
6.88
7.61
6.89
7.37
7.05
8.18
1.43
1.08
2.20
1.85
2.77
2.32
3.21
2.87
1881
smaller than the corresponding adiabatic electron affinity (AEA)
values. Unfortunately, there are no further experimental researches
for them. Thus, it is hoped that our theoretical results will provide a useful guideline in order to define the spectral features of
gold–magnesium system.
3.4. Natural population analysis
In order to understand the electronic properties of Aun Mg (n =
1–8) clusters, the natural population analysis (NPA) has been performed in this part, which can give a reasonable explanation of the
charge transfer within the cluster. Our NPA results for the lowest
energy isomers are summarized in Table 3. Due to a larger difference in electronegativity of magnesium (1.31) and gold (2.54), NPA
clearly shows an ionic character for Mg–Au bond in these clusters, in which magnesium atoms possess 0.510–0.776e charges for
n = 1–8. This indicates that the charges transfer from the Mg atom
to the Aun frames, namely, magnesium acts as electron donor in
all Aun Mg clusters. Also, it can be clearly seen that natural charge
of Mg atom exhibits an odd–even oscillatory behavior (except for
n = 4), and a local peak also corresponds to Au2 Mg cluster. In
addition, as shown in Table 3, one can see that the charge distribution is dependent on the symmetry of the cluster. Meanwhile,
aiming at probing into the internal charge transfer in details, the
natural electron configuration of Mg atom is taken into account
on the basis of NPA. We find that the charge transfer occurs at
the outer electronic orbital, while the 1s2 2s2 2p6 interior electronic
shell can be viewed as a core orbital. Here, the charges of 3s, 3p,
and 3d states for the Mg atom in the lowest energy configurations
are shown in Table 4. It is shown that the 3s states lose 0.72–
1.54 electrons, while the 3p states obtain 0.20–0.95 electrons, and
the contribution from the 3d states is mostly zero. This result is
consistent with the well-known fact in chemistry that the internal
charge transfer mainly happens between Mg 3s and 3p states. Furthermore, the internal charge transfer increases as the number of
Au atoms increasing from 1 to 8.
Based on the lowest energy structures, we further investigate
the size evolution of the electronic properties of Aun Mg (n = 1–8)
clusters by examining the magnetic moment. The total magnetic
moments of Aun Mg and Aun+1 as well as the local magnetic moTable 4
Natural electron configuration and magnetic moment of 3s, 3p, and 3d states for
Mg atom in the lowest energy Aun Mg (n = 1–8) clusters.
Expt.b
1.55(2)
3.69(13)
1.93(6)
a
Experimental values of VIP for Aun+1 clusters, Ref. [28].
Experimental values of adiabatic electron affinity (AEA) for Aun Mg clusters,
Ref. [22].
b
Magnetic moment
μ (μ B )
Cluster
Natural electron
configuration Q (e)
3s
3p
3d
3s
3p
3d
AuMg
Au2 Mg
Au3 Mg
Au4 Mg
Au5 Mg
Au6 Mg
Au7 Mg
Au8 Mg
1.28
0.85
0.76
0.65
0.58
0.55
0.47
0.46
0.20
0.36
0.55
0.77
0.89
0.81
0.95
0.86
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0.60
0
0
0
0
0
0.01
0
0.11
0
0.09
0
0.01
0
0.01
0
0
0
0
0
0
0
0.01
0
Table 3
Natural charge populations of the lowest energy Aun Mg (n = 1–8) clusters.
Cluster
Mg
Au-1
Au-2
Au-3
Au-4
Au-5
Au-6
Au-7
Au-8
AuMg
Au2 Mg
Au3 Mg
Au4 Mg
Au5 Mg
Au6 Mg
Au7 Mg
Au8 Mg
0.510
0.776
0.666
0.562
0.517
0.627
0.556
0.664
−0.510
−0.388
−0.164
−0.085
−0.122
−0.222
−0.080
−0.165
−0.388
−0.164
−0.196
−0.122
−0.013
−0.080
−0.165
−0.338
−0.085
−0.099
−0.172
−0.193
−0.157
−0.196
−0.099
−0.064
−0.193
−0.028
−0.075
−0.162
−0.019
−0.028
0.007
−0.019
−0.157
0.027
0.018
0.018
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Y.-F. Li et al. / Physics Letters A 375 (2011) 1877–1882
shows the strongest stability due to its local peak in all the curves
of E b , 1 E, 2 E, HOMO–LUMO energy gap, and hardness.
(III) Natural population analysis reveals that the charges in
Aun Mg (n = 1–8) clusters transfer from Mg atom to Au atoms
in the most stable configurations, and the local maximum also
corresponds to n = 2. As for magnetic moment, we find a pronounced odd–even oscillatory phenomenon as a function of cluster size. Consequently, the ground-state configurations of Aun Mg
and Aun+1 (n = 1–8) clusters with odd-number gold atoms have
the total magnetic moments of 1μ B , while even-number clusters
correspond to zero value, and it should be pointed out that the
magnesium is nonmagnetic for n = 2–8.
Acknowledgements
This work was supported by the Doctoral Education Fund of Education Ministry of China (No. 20050610011) and the National Natural Science Foundation of China (Nos. 10774103 and 10974138).
Fig. 4. Total magnetic moment for the lowest energy structures of Aun Mg and Aun+1
(n = 1–8) clusters, and local magnetic moment on Mg atom.
ments of Mg atom in Aun Mg cluster are plotted in Fig. 4. As
shown in Fig. 4, the total magnetic moments of both Aun Mg
and Aun+1 clusters show pronounced odd–even alternative phenomenon, that is, the clusters with odd-number gold atoms have
a total magnetic moment of 1μ B . However, this is contrary to
the anionic Aun Mg (n = 1–8) clusters [23], which may be ascribed to one excess electron. When clusters correspond to evennumber gold atoms, for which α and β spin orbital are degenerate,
the total magnetic moments are zero. Notice that in the Aun Mg
(n = 2–8) clusters where the magnetic moments are mainly come
from the gold atoms while the Mg atom is nonmagnetic (see Table 4).
4. Conclusions
By using the fist-principle method at PW91PW91/GEN (SDD for
the Au atom and 6-311G* for the Mg atom) level, we have presented a systematic study of geometries, stabilities, and electronic
properties of bimetallic Aun Mg (n = 1–8) clusters and comparison
with pure gold systems. The main conclusions can be made as follows.
(I) The DFT calculations reveal that the ground-state Aun Mg
configurations adopt the planar structures for n = 1–7, and a 3D
transition is obtained up to nine atoms. Mg-substituted Aun+1 clusters, as well as Au-capped Aun−1 Mg clusters, are dominant growth
pattern for the small gold–magnesium clusters and the Mg atom
favors higher coordination.
(II) For Aun Mg and Aun+1 clusters, the contrary odd–even
alternation behaviors are found in the fragmentation energies,
the second-order difference of energies, the HOMO–LUMO energy
gaps, and the hardness of the most stable structures, indicating
that Au2, 4, 6 Mg and Au4, 6, 8 clusters keep a higher relative stability than their neighboring ones. In particular, the Au2 Mg cluster
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