J. Phys. Chem. A 2010, 114, 11691–11698
11691
Geometries, Stabilities, and Electronic Properties of Small Anion Mg-Doped Gold Clusters:
A Density Functional Theory Study
Yan-Fang Li,† Xiao-Yu Kuang,*,†,‡ Su-Juan Wang,† and Ya-Ru Zhao†
Institute of Atomic and Molecular Physics, Sichuan UniVersity, Chengdu 610065, China and International
Centre for Materials Physics, Academia Sinica, Shenyang 110016, China
ReceiVed: May 8, 2010; ReVised Manuscript ReceiVed: September 17, 2010
First-principle density functional theory is used for studying the anion gold clusters doped with magnesium
atom. By performing geometry optimizations, the equilibrium geometries, relative stabilities, and electronic
and magnetic properties of [AunMg]- (n ) 1-8) clusters have been investigated systematically in comparison
with pure gold clusters. The results show that doping with a single Mg atom dramatically affects the geometries
of the ground-state Aun+1- clusters for n ) 2-7. Here, the relative stabilities are investigated in terms of the
calculated fragmentation energies, second-order difference of energies, and highest occupied-lowest unoccupied
molecular orbital energy gaps, manifesting that the ground-state [AunMg]- and Aun+1- clusters with oddnumber gold atoms have a higher relative stability. In particular, it should be noted that the [Au3Mg]- cluster
has the most enhanced chemical stability. The natural population analysis reveals that the charges in [AunMg](n ) 2-8) clusters transfer from the Mg atom to the Au frames. In addition, the total magnetic moments of
[AunMg]- clusters exhibit an odd-even oscillation as a function of cluster size, and the magnetic effects
mainly come from the Au atoms.
1. Introduction
Clusters are formed by a few up to tens of thousands of atoms
occurring closely together, which may contain identical or different
elements in the periodic table. During the last several decades,
considerable interest has been focused on the small-sized clusters.1-12
As for simple small-sized clusters, the bimetallic clusters as a
suitable model for computational quantum chemistry often possess
marked properties different from both the atomic states and the
bulk materials.13-23 In particular, the gold-containing bimetallic
clusters are significant due to their special technical applications
in the fields of optics, magnetics, materials science, catalysis, and
solid-state chemistry.24-34 Because the properties of clusters depend
strongly upon the microscopic structure around the dopant, many
experimental techniques, such as cationic photofragmentation mass
spectrometry,35-38 anion photoelectron spectroscopy (PES),39-42 and
Knudsen-Effusion mass spectrometry (KEMS)43 have been used
to study the bimetallic systems. Among them, Li et al.42 presented
the first experimental observation and characterization of the
icosahedral [WAu12]- cluster, and the significant stability of this
cluster was revealed by the anion PES. Meanwhile, Li et al.42 also
predicted that a series of highly stable [MAu12]- clusters with M
) 4d elements might exist. Subsequently, cationic gold clusters
doped with one transition metal atom were investigated by Janssens
et al.37 using cationic photofragmentation mass spectrometry, and
strongly enhanced stabilities were found for [Au5X]+ (X ) V, Mn,
Cr, Fe, Co, Zn) clusters. In recent years, Koyasu et al.40 performed
a systematic investigation about the anion PES of small metaldoped bimetallic Au clusters, [AunM]- (n ) 2-7; M ) Pd, Ni,
Zn, Cu, and Mg).
The extensive experiments give important information about
the dopant in the gold clusters and form a useful starting point
* To whom correspondence should be addressed. E-mail: scu_kuang@
163.com.
†
Sichuan University.
‡
Academia Sinica.
to understand its significant role in the stabilities and chemical
activities. On the theoretical side, density functional theory
(DFT) has been regarded as an effective method to simulate
the chemical systems, because it can accurately estimate the
physicochemical properties of clusters with much less computational effort.44-50 As mentioned above, Koyasu et al.40
performed a systematic measure on the anion PES of [AunMg](n ) 2-7) clusters. Although the intermetallic molecules AuMg
and Au5Mg were studied by Balducci et al.43 and Majumder et
al.48 by employing DFT, respectively, few systematically
theoretical investigations on the bimetallic [AunMg]- (n ) 1-8)
clusters have been performed. Thus, in order to provide further
insight on [AunMg]- clusters, in this paper, we investigate the
geometrical structures, relative stabilities, electronic properties,
and magnetic properties of [AunMg]- (n ) 1-8) clusters by
using the first-principle method based on DFT. It is hoped that
our theoretical study not only would be useful in understanding
the influence of local structure on materials properties but also
can provide powerful guidelines for future experimental research.
2. Computational Details
Geometrical structures, together with the frequency analysis
of [AunMg]- (n ) 1-8) clusters, are optimized with the
GAUSSIAN 03 program.51 For the Au atom, the full electron
calculation is rather time consuming, so the effective core
potentials including relativistic effects (RECP) are introduced.
Then, the Stuttgart/Dresden double-ζ SDD52 (ECP60MWB)
basis set is adopted to describe the Au atom in our calculation.
The gradient-corrected exchange and correlation functional of
Perdew-Wang (PW91PW91)53 has been used successfully for
the magnesium-doped gold cluster in the early literature,48 so
all the calculations are performed at the level of the PW91PW91
method (SDD for the Au atom and 6-311+G* for the Mg atom)
in our paper. In searching for the lowest-energy structures of
[AunMg]- (n ) 1-8) clusters, lots of possible initial configurations are considered starting from the previous optimized Aun-
10.1021/jp104206m  2010 American Chemical Society
Published on Web 10/11/2010
11692
J. Phys. Chem. A, Vol. 114, No. 43, 2010
geometries, and all clusters are relaxed fully without any
symmetry constraints. Considering the spin polarization, different spin multiplicities are also taken into account for every
initial configuration. Here, spin-restricted (RPW91PW91) calculations are employed for the singlet states, while spinunrestricted (UPW91PW91) calculations are used for the other
electronic states. For the small clusters, the default convergence
thresholds are used. When the clusters are large, the convergence
thresholds of the maximum force, root-mean-square (rms) force,
maximum displacement of atoms, and rms displacement are set
to 0.00045, 0.0003, 0.0018, and 0.0012 au, respectively. In this
way, a large number of optimized isomers for [AunMg]- (n )
1-8) clusters are obtained, but here we report only the few
energetically low-lying isomers. Toward nuclear displacement,
all the structures reported here have real vibrational frequencies
(see Supporting Information) and therefore correspond to the
potential energy minima. In addition, the vertical electron
detachment energy (VDE ) Eneutral at optimized anion geometry Eoptimized anion), highest occupied-lowest unoccupied molecular
orbital (HOMO-LUMO) energy gap, and natural population
analysis (NPA) of the stable configurations for [AunMg]- (n )
1-8) clusters are also performed based on the PW91PW91
method.
3. Results and Discussion
A number of optimized low-energy configurations for [AunMg]- (n ) 1-8) clusters are shown in Figure 1, where na, nb,
nc, nd, and ne (n is the number of Au atoms in [AunMg]clusters) are designated to different isomers according to the
total energy from low to high. In order to understand the effect
of doping impurity on the pure gold clusters, the low-lying
configurations of Aun+1- (n ) 1-8) clusters are also optimized
by using the identical theoretical method (PW91PW91/SDD),
and the lowest energy configurations are shown in Figure 1.
Meanwhile, Table 1 lists the electronic states, symmetries,
relative energies, HOMO and LUMO energies, as well as natural
charge populations (NCP) of the Mg atom for [AunMg]- (n )
1-8) clusters.
3.1. Equilibrium Geometry. The biatomic [AuMg]- cluster
with the singlet electronic state (1Σ) is the ground-state structure,
and the equilibrium bond length is 2.683 Å, which is longer
than that of Au2- (2.681 Å). Its VDE is calculated as 1.60 eV.
Besides, the theoretical results of the bond length (2.496 Å),
frequency (287 cm-1), dissociation energy (1.82 eV), and
ionization energy (6.99 eV) of the neutral form are in good
agreement with the experimental results of 2.443 Å,54 307.9
cm-1,55 1.818 eV,56 and 6.7 ( 0.3 eV,43 respectively. Such a
testing calculation indicates that it is reliable to investigate the
small gold-magnesium clusters by using the GAUSSIAN 03
package at the PW91PW91 (SDD for the Au atom and
6-311+G* for the Mg atom) level.
All possible initial structures of [Au2Mg]- clusters, i.e., linear
structures (D∞h, C∞V), and triangle structures (acute angle or
obtuse angle), are optimized at the PW91PW91 level with the
different spin multiplicities. The calculated results illustrate that
isomer 2a with C2V symmetry is the lowest energy structure.
The corresponding electronic state is 2A1 with a bond length
(Au-Mg) of 2.585 Å, and its apex angle is 140.0°. However,
the ground-state bare gold cluster is found to be a linear structure
in the present study. The linear structure 2b with the Mg atom
at one end is the next isomer and 0.61 eV higher in energy
than the 2a isomer. Isomer 2c with an apex angle of 126.5°
possesses Cs symmetry, which is also a triangle structure. For
[Au2Mg]- clusters, the calculated VDE values are 1.55 eV (2a),
1.89 eV (2b), and 1.91 eV (2c), respectively.
Li et al.
In the case of [Au3Mg]- clusters, the ground-state structure
(3a) and the other three low-lying isomers (3b, 3c, 3d) are
obtained in the energy range 1.43 eV. The lowest energy
structure 3a with the magnesium atom occupying the center
position of the Au3 equilateral triangle is a high-symmetry planar
structure, which has D3h symmetry. This structure, with three
equal Au-Mg bonds (2.560 Å), is lower in energy than 3b, 3c,
and 3d by 0.44, 0.90, and 1.43 eV, respectively. Isomer 3b in
the singlet spin state is a linear structure. The C2V rhombus
isomer 3c is another stable configuration with a Au-Mg-Au
apex angle of 125.4°, which is similar to the lowest energy
structure of Au4.47 Y-like isomer 3d, in which the Mg atom
lies in the apex position, is the least stable structure. In summary,
the planar or linear structures are the preferred geometrical
configurations for n ) 3. The VDE of the 3a configuration is
4.22 eV, which is satisfactorily in line with the experimental
result (4.17 ( 0.03 eV),40 while other isomers clearly underestimate the VDE (3.20 eV for 3b, 2.31 eV for 3c, and 2.38 eV
for 3d).
Guided by addition of one Au atom to the different isomers
of [Au3Mg]- clusters or substitution of the impurity in Au5clusters, scoop-shaped structure (4a), A-shaped structure (4b,
4e), square pyramid structure (4c), and chain structure (4d) are
found for [Au4Mg]- clusters, as seen in Figure 1. Adding one
gold atom to the rhombus structure 3c, the most stable isomer
4a with Cs symmetry can be yielded and the electronic state is
2
A′. Its calculated VDE value is 2.47 eV. The planar isomers
4b and 4e have a similar geometrical structure in which the
impurity atom occupies different positions. Therefore, different
relative energies (0.18 eV, 0.68 eV), symmetries (Cs, C2V),
electronic states (2A′, 2A1), and VDE (2.53 eV, 3.06 eV) exist
between them. As for the three-dimensional (3D) stable isomer
4c, it is a regular square pyramid isomer possessing four
identical Au-Mg bonds (2.691 Å), whose energy is 0.50 eV
higher than that of isomer 4a. Frequency analysis indicates that
isomer 4d in the doublet spin multiplicity state is another stable
structure. For 4c and 4d isomers, the VDE are 2.57 and 2.87
eV, respectively. In our calculation, the trapezoidal configuration
of the [Au4Mg]- cluster, which is similar to the ground-state
Au5-, is significantly higher by 4.82 eV in energy than the 4a
isomer. Thus, it is not displayed in our present work.
With regard to [Au5Mg]- clusters, numerous possible initial
geometries are optimized. According to the calculated results,
it should be pointed out that the lowest energy structure is also
a planar configuration. It is consistent with the result of the
neutral Au5Mg cluster.45 As shown in Figure 1, the groundstate structure 5a with a singlet electronic state 1A′ can be
regarded as the overlap of two rhombus structures. The closest
isomer 5b is a 3D structure, whereas it is almost degenerate in
energy for the planar isomer 5a (0.06 eV). The planar 5c isomer
in the 1A1 electronic state is energetically higher than the groundstate structure 5a by 0.11 eV, which can be viewed as two Au
atoms capping on the apex positions of the C2V rhombus structure
[Au3Mg]- (3c). The 3D isomer and planar triangular isomer,
labeled as 5d and 5e, are 0.31 and 0.71 eV higher in energy
than the most stable isomer 5a, respectively. As for the 5d lowlying isomer, the Mg atom sitting inside the gold tetrahedron is
a complicated 3D structure. The least stable isomer 5e can be
performed by locating the impurity on one side of the equilateral
triangle structure, which is similar to the ground-state configuration Au6- cluster. However, in order to reach the minimum
of the potential surface, the impurity atom shifts along the
direction of the gold-apex position, so D3h symmetry distorts
Small Anion Mg-Doped Gold Clusters
J. Phys. Chem. A, Vol. 114, No. 43, 2010 11693
Figure 1. Lowest energy structures and low-lying isomers for [AunMg]- (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 bond lengths are in Angstroms. The yellow and green balls represent Au and Mg atoms,
respectively.
to C2V. Our calculated VDE values are 3.16 (5a), 3.47 (5b),
3.91 (5c), 5.90 (5d), and 2.46 eV (5e).
As for [Au6Mg]- clusters, we find four planar isomers and
one 3D isomer with the same spin multiplicity. Adding the Mg
atom to the center of the Au6 ring, the lowest energy structure
6a is obtained. Due to the Jahn-Teller effect, the symmetry of
the Au6 ring is lowered, that is, distorting from D6h to D2h. In
this way, the two-dimensional (2D) structure 6a has two
different Au-Mg bonds, as shown in Figure 1, which are 2.677
and 2.766 Å, respectively. Its corresponding electronic state is
2
Ag. Other four isomers 6b, 6c, 6d, and 6e within 0.57 eV are
all higher in energy than 6a. The planar isomers, 6b and 6d,
are also stable structures for [Au6Mg]- clusters. The former is
energetically higher than 6a by 0.14 eV, but the latter is 0.53
eV. With the impurity substituting the different positions of the
ground-state structure of the Au7- cluster, surprisingly, we find
11694
J. Phys. Chem. A, Vol. 114, No. 43, 2010
Li et al.
TABLE 1: Electronic States, Symmetries, Relative Energies
(∆E), HOMO Energies, LUMO Energies, and Natural
Charge Populations (NCP) of the Mg Atom for [AunMg](n ) 1-8) Clusters
isomer state symmetry ∆E (eV)
1a
2a
2b
2c
3a
3b
3c
3d
4a
4b
4c
4d
4e
5a
5b
5c
5d
5e
6a
6b
6c
6d
6e
7a
7b
7c
7d
7e
8a
8b
8c
8d
8e
1
Σ
A1
2
Σ
2
A′
1
A 1′
1
Σ
1
A1
1
A′
2
A′
2
A′
2
A1
2
A
2
A1
1
A′
1
A
1
A1
1
A′
3
B2
2
Ag
2
A′
2
B2
2
A′
2
A1
1
A1
1
A1
1
A1
1
A1
1
A1
2
A1
2
A1
2
Bu
2
A1
2
A
2
C∞V
C2V
C∞V
Cs
D3h
C∞V
C2V
Cs
Cs
Cs
C4V
C1
C2V
Cs
C1
C2V
Cs
C2V
D2h
Cs
C2V
Cs
C4V
C2V
C2V
C2V
C2V
C2V
C2V
C2V
C2h
C2V
C1
0.00
0.00
0.61
0.75
0.00
0.44
0.90
1.43
0.00
0.18
0.50
0.58
0.68
0.00
0.06
0.11
0.31
0.71
0.00
0.14
0.31
0.53
0.57
0.00
0.03
0.37
0.62
0.65
0.00
0.33
0.43
0.67
0.71
HOMO
(hartree)
LUMO
(hartree)
NCP of
Mg (e)
0.01483
0.01932
0.00083
0.00080
-0.06370
-0.04045
-0.01103
-0.01800
-0.02109
-0.02268
-0.01954
-0.03990
-0.04490
-0.04933
-0.05758
-0.07211
-0.07670
-0.02574
-0.04909
-0.02745
-0.05600
-0.03329
-0.05079
-0.08175
-0.06149
-0.07867
-0.05125
-0.06044
-0.05226
-0.04791
-0.05821
-0.04189
-0.06503
0.07323 -0.137
0.04356
0.302
0.02309
0.126
0.01940
0.135
0.03437
0.499
0.02947
0.603
0.02418
0.315
0.00710
0.232
-0.00786
0.440
-0.00829
0.651
0.00865
0.214
-0.02751
0.613
-0.01314
0.587
-0.00188
0.557
-0.00592
0.239
-0.00572
0.511
-0.02003
0.414
-0.01342
0.633
-0.04161
0.561
-0.01440
0.609
-0.04690
0.616
-0.02091
0.625
-0.03940
0.281
-0.04342
0.665
-0.01447
0.728
-0.01805
0.477
-0.02056
0.620
-0.01744
0.621
-0.04337
0.726
-0.03991
0.682
-0.05071
0.771
-0.03336
0.600
-0.05610
0.297
that 6b and 6d isomers are similar to each other. In addition,
they also possess identical structural symmetry (Cs) and
electronic state (2A′). The distorted trapezoidal structure 6c is
the third stable isomer, which is another planar structure, and
its symmetry is C2V. Torch-shaped 3D isomer 6e has high
geometrical symmetry (C4V); however, its total energy is higher
by 0.57 eV than that of the 6a isomer. This indicates that isomer
6e is not the ground-state configuration in our optimized results.
Besides, we calculate the VDE, which are, 3.92 (6a), 2.57 (6b),
3.36 (6c), 2.66 (6d), and 3.25 eV (6e).
According to the theoretical results of [Au7Mg]- clusters, it
is interesting to find that those five low-lying isomers possess
the same geometrical symmetry (C2V) and electronic state (1A1).
Meanwhile, VDE ) 3.25 (7a), 3.46 (7b), 3.90 (7c), 2.96 (7d),
and 3.13 eV (7e) can also be obtained. As seen from the
sequence of the relative energies in Table 1, one can find that
isomer 7a, with a planar structure, is the lowest isomer in the
total energy. Therefore, it is the most stable structure among
the investigated [Au7Mg]- clusters, which can be described as
one gold atom capping on one side of the Au6 ring in the
[Au6Mg]- (6a). Consequently, this planar structure distorts from
D2h to C2V symmetry and is found similar to the lowest energy
structure of neutral Au7Pd and Au7Pt clusters or the second most
stable configuration of the Au7Ni cluster in ref 30. Additionally,
adding one Au atom to [Au6Mg]- cluster 6c, isomer 7b is
generated. According to Table 1, it is clear that the stability of
the planar isomer 7b is weaker than that of the lowest energy
structure by only 0.03 eV, which are almost degenerate, whereas
the calculated VDE values are 3.25 and 3.46 eV. The different
VDE values between 7a and 7b may be caused by the difference
in the coordinates of the component atoms. Among [Au7Mg]clusters, boat-shaped isomer 7c, which is the most stable 3D
configuration, is 0.37 eV higher in energy than the planar isomer
7a. The last two planar isomers 7d and 7e, whose energies are
close to each other, resemble the ground-state configuration of
the Au8- cluster.
When the number of [Au8Mg]- clusters is up to 9, we still
find a planar structure to be the potential energy minima. This
configuration (8a) is a trapezoidal structure, which is similar to
the ground-state structure of the Au9- cluster, and it can be
obtained by substituting one Mg atom in the ground-state Au9cluster centrally. The similar planar isomers 8b and 8d have
identical C2V symmetry and 2A1 electronic state as the most stable
isomer 8a, but their relative energy is different (0.34 eV), which
may originate from the fact that the impurity atom occupies
different positions in the isomers. The Mg atom in the more
stable isomer 8b holds a more highly coordinated position,
which can be seen in Figure 1. In our optimization, arranging
two extra gold atoms to the hexagonal ring [Au6Mg]- (6a), the
rhombus isomer 8c with C2h symmetry and 2Bu electronic state
is obtained, which is 0.43 eV higher in energy than that of the
ground-state structure. In addition, a 3D low-lying structure 8e,
with a Mg atom at the center of the heptagonal pyramid, is the
least stable isomer for the [Au8Mg]- cluster. Its energy is higher
than the 8a configuration by 0.71 eV. On the basis of the above
optimized structures, the single-point energy of the neutral
isomers with the same anion geometries are calculated, so the
corresponding VDE values are obtained, which are 2.96 (8a),
2.95 (8b), 3.23 (8c), 2.80 (8d), and 3.51 eV (8e).
From the above discussion, it is remarkable that the lowest
energy configurations of pure and magnesium-doped gold
clusters favor the planar structures and prefer the lowest spin
multiplicity. In the case of [AunMg]- (n ) 2-7) clusters, the
most stable structures are found to be different from the groundstate structures for pure gold clusters. This may be due to the
fact that the Mg atom has a closed-shell electronic configuration
3s2; on the contrary, the single 6s outermost valence electron
corresponds to the Au atom, so the electronic shell of Aun+1is not similar to that of [AunMg]-. As for the experimentally
measured VDE, the values have been presented by Koyasu et
al.40 for n ) 2-4 (1.69 ( 0.01, 4.17 ( 0.03, and 2.35 ( 0.02
eV). According to our calculations, it is also worth pointing
out that the ground-state configurations (2a, 3a, 4a) give a much
smaller deviation from the experimental measurements than
those of the other isomers. Unfortunately, owing to the extremely
weak signals for PES spectra, there are no experimental VDE
values for the larger clusters. Thus, it is hoped that our
theoretical results will provide powerful guidelines for further
experiments aiming at defining the spectral features for [AunMg]- clusters.
3.2. Relative Stability. In order to investigate the stabilities
of [AunMg]- (n ) 1-8) clusters, the atomic average binding
energy Eb is introduced in the present work, which can be
expressed as
Eb(n) )
E(Mg) + (n - 1)E(Au) + E(Au-) - E([AunMg]-)
n+1
(1)
It is well known that the fragmentation energies ∆1E and secondorder difference of energies ∆2E have also proved to be a
Small Anion Mg-Doped Gold Clusters
J. Phys. Chem. A, Vol. 114, No. 43, 2010 11695
powerful tool to reflect the relative stabilities of the clusters.
For [AunMg]- clusters, the corresponding ∆1E (with respect to
removing one Au atom from the [AunMg]-cluster) and ∆2E are
defined as
∆1E(n) ) E([Aun-1Mg]-) + E(Au) - E([AunMg]-)
∆2E(n) ) E([Aun-1Mg]-) + E([Aun+1Mg]-) 2E([AunMg]-) (2)
where E(Mg), E(Au), E(Au-), E([AunMg]-), E([Aun-1Mg]-),
and E([Aun+1Mg]-), respectively, are the total energies of the
most stable Mg, Au, Au-, [AunMg]-, [Aun-1Mg]-, and
[Aun+1Mg]-.
Considering the influence of the impurity atom on small pure
clusters, the atomic average binding energies Eb, fragmentation
energies ∆1E (with respect to removing one Au atom from the
Aun+1- cluster), and second-order difference of energies ∆2E
of Aun+1- clusters are also studied, which can be expressed as
the following formulas
Eb(n + 1) )
Figure 2. Size dependence of the atomic average binding energies
for the lowest energy structures of [AunMg]- and Aun+1- (n ) 1-8)
clusters.
E(Au-) + nE(Au) - E(Aun+1
)
n+1
∆1E(n + 1) ) E(Aun ) + E(Au) - E(Aun+1)
∆2E(n + 1) ) E(Aun ) + E(Aun+2) - 2E(Aun+1)
(3)
where E(Au-), E(Au), E(Aun+1-), E(Aun-), and E(Aun+2-)
represent the total energies of the lowest energy clusters or atoms
for Au-, Au, Aun+1-, Aun-, and Aun+2-, respectively.
With the use of above formulas, we obtain Eb ) 0.49 ([AuMg]-),
1.24 ([Au2Mg]-), 1.73 ([Au3Mg]-), 1.74 ([Au4Mg]-), 1.88
([Au5Mg]-), 1.94 ([Au6Mg]-), 2.05 ([Au7Mg]-), and 2.08 eV
([Au8Mg]-) for [AunMg]- (n ) 1-8) clusters and 0.95 (Au2-),
1.57 (Au3-), 1.57 (Au4-), 1.76 (Au5-), 1.81 (Au6-), 1.94 (Au7-),
1.98 (Au8-), and 2.04 eV (Au9-) for Aun+1- (n ) 1-8) clusters.
In order to investigate the dependence of the atomic average binding
energies on the cluster size, the relationships of Eb versus n are
plotted in Figure 2. For Aun+1- clusters, Figure 2 illustrates that
the atomic average binding energies have an increasing tendency
with the clusters size growing. This reflects the fact that the bigger
the clusters, the more stable the molecular properties, which is in
accord with previous theoretical works.7 Meanwhile, a similar
increasing tendency is also found for Mg-doped clusters, and the
curve increases sharply as the size of [AunMg]- clusters goes from
n ) 1 to 3.
As for the fragmentation energies and second-order difference
of energies, the calculated results for both pure and doped gold
clusters are obtained by using eqs 2 and 3. The corresponding
trends of ∆1E and ∆2E with respect to cluster size are plotted
in Figures 3 and 4, respectively. Both Figures 3 and 4 show
that the cluster stabilities exhibit pronounced odd-even alternations. However, it is clearly found that the doping impurity atom
makes the stable pattern of the host cluster contrary. In Figure
3, the local peaks occur at n ) 3, 5, 7 for [AunMg]- clusters
and n ) 2, 4, 6 for pure gold clusters, while the local maxima
are found at n ) 3, 5 ([AunMg]-) and n ) 2, 4, 6 (Aun+1-) in
Figure 4. This means that the clusters containing odd-number
Figure 3. Size dependence of the fragmentation energies for the lowest
energy structures of [AunMg]- (n ) 2-8) and Aun+1- (n ) 1-8)
clusters.
gold atoms have a higher relative stability compared to the
neighbors. In other words, the clusters with even-number valence
electrons are more stable than those with odd-number valence
electrons. In particular, the significant peaks of the fragmentation
energies and second-order difference of energies as a function
of cluster size localize at n ) 3, indicating that the [Au3Mg]cluster keeps the highest stability in the size range of n ) 1-8
for [AunMg]- clusters, which is also proved by our calculated
results of VDE. With regard to the [Au3Mg]- cluster, its strong
stability may be related to a high-symmetry structure (D3h).
The highest occupied-lowest unoccupied molecular orbital
(HOMO-LUMO) energy gap reflects the ability of an electron
to jump from an occupied orbital to an unoccupied orbital, which
represents the ability of the molecule to participate in the
chemical reaction in some degree. A large value of the
HOMO-LUMO energy gap is related to an enhanced chemical
stability; on the contrary, a small one corresponds to a high
chemical activity. In a sense it can provide an important criterion
to reflect the chemical stability of clusters. For the low-lying
configurations of [AunMg]- (n ) 1-8) clusters, the HOMO
and LUMO energies at each cluster size are summarized in
Table 1; meanwhile, the corresponding HOMO-LUMO energy
gaps ranging from 0.20 to 2.67 eV can be obtained. Here, the
size dependence of the HOMO-LUMO energy gaps for the
11696
J. Phys. Chem. A, Vol. 114, No. 43, 2010
Figure 4. Size dependence of the second-order difference of energies
for the lowest-energy structures of [AunMg]- (n ) 2-7) and Aun+1(n ) 1-7) clusters.
Li et al.
Figure 6. Size dependence of the natural charge populations of the
Mg atom for the lowest energy structures of [AunMg]- (n ) 1-8)
clusters.
TABLE 2: Natural Electron Configuration and Magnetic
Moment of 3s, 3p, and 3d States for the Mg Atom in the
Lowest Energy [AunMg]- (n ) 1-8) Clusters
natural electron configuration
Q (e)
Figure 5. Size dependence of the highest occupied-lowest unoccupied
molecular orbital energy gaps for the lowest energy structures of
[AunMg]- and Aun+1- (n ) 1-8) clusters.
lowest energy isomers is plotted in Figure 5. We note in Figure
5 that the HOMO-LUMO energy gaps of [AunMg]- and
Aun+1- (n ) 1-8) clusters exhibit an odd-even oscillatory
behavior, indicating that [Au3Mg]- (Au3-), [Au5Mg]- (Au5-),
and [Au7Mg]- (Au7-) have large HOMO-LUMO energy gaps.
Therefore, it can be concluded that the clusters with odd-number
gold atoms are relatively more stable in chemical reactions than
the neighboring ones, which is in accord with the behavior of
the fragmentation energies and second-order difference of
energies versus n, respectively, as discussed above. Besides, it
is worth pointing out that the largest HOMO-LUMO energy
gap of 2.67 eV is found for the most stable configuration of
[Au3Mg]- cluster, so this structure has a higher chemical
stability among all the [AunMg]- (n ) 1-8) clusters.
3.3. Natural Population Analysis. Aiming at probing into
the localization of the negative charge in [AunMg]- (n ) 1-8)
clusters, the natural population analysis (NPA) has been performed
in this part. It is found that there are -0.137-0.771e charges at
the Mg atom, which are listed in Table 1.The NPA results, except
for [AuMg]-, clearly show that the NCP values for the Mg atom
are positive for n ) 2-8, suggesting that the charges transfer from
the Mg atom to the Aun frames, which may be caused by a different
electronegativity between Mg (1.31) and Au (2.54). Among the
low-lying isomers of [AunMg]- (n ) 1-8) clusters with the same
magnetic moment
µ (µB)
cluster
3s
3p
3d
3s
3p
3d
[AuMg][Au2Mg][Au3Mg][Au4Mg][Au5Mg][Au6Mg][Au7Mg][Au8Mg]-
1.85
1.22
0.81
0.71
0.76
0.47
0.45
0.47
0.28
0.47
0.67
0.83
0.04
0.95
0.04
0.78
0
0.01
0.01
0.01
0.01
0.01
0.01
0.01
0
0.45
0
0.03
0
-0.01
0
0.02
0
0.15
0
0.03
0
0
0
0
0
-0.01
0
0
0
0
0
0
n, interestingly, one can see that the 3D structure corresponds to
the smallest NCP value, such as 4c (0.214), 5b (0.239), 6e (0.281),
7c (0.477), and 8e (0.297). In addition, the natural charge of the
Mg atom for the lowest energy configuration at each cluster size
is plotted in Figure 6. We find that the charge transfer from the
Mg atom to the Au atoms increases as the number of Au atoms
increases from 1 to 8, and the local peak corresponds to [Au3Mg]cluster. Furthermore, in order to understand the internal charge
transfer, the natural electron configuration of the impurity atom is
also taken into account on the basis of NPA. For the Mg atom, the
charge transfer occurs at the outer electronic orbitals, while the
1s22s22p6 interior electronic shell is mostly unchanged. The charges
of the 3s, 3p, and 3d states for the Mg atom in the lowest energy
configurations of [AunMg]- (n ) 1-8) clusters are summarized
in Table 2. It is shown that the 3s states lose electrons 0.15-1.55
while the 3p states get 0.04-0.95 electrons, and the contribution
from the 3d states is nearly zero.
For the ground-state structures of [AunMg]- (n ) 1-8)
clusters, the size dependence of the magnetic moment as well
as that of Aun+1- (n ) 1-8) clusters are plotted in Figure 7, in
which the distinct odd-even oscillations are observed, that is,
both [AunMg]- and Aun+1- clusters with even-number gold
atoms have a total magnetic moment of 1 µB. When the number
of gold atoms is odd, the cluster is a closed-shell system, whose
R and β spin orbitals are degenerate, so the corresponding
magnetic moment is zero. Notice that for [AunMg]- (n ) 1-8)
clusters, the magnetic moment is mainly coming from the gold
atoms while the magnetic effect of the impurity atom can be
neglected (see Table 2).
Small Anion Mg-Doped Gold Clusters
J. Phys. Chem. A, Vol. 114, No. 43, 2010 11697
[AunMg]- (n ) 1-8) clusters. This material is available free
of charge via the Internet at http://pubs.acs.org.
References and Notes
Figure 7. Size dependence of the total magnetic moment for the lowest
energy structures of [AunMg]- and Aun+1- (n ) 1-8) clusters.
4. Conclusions
In summary, we extensively investigated the geometrical
structures, relative stabilities, and natural population analysis
of [AunMg]- (n ) 1-8) clusters, combining with anionic gold
clusters for comparison, by using the first-principle method at
the PW91PW91 (SDD for the Au atom and 6-311+G* for the
Mg atom) method level. We find several interesting results. (1)
The equilibrium geometries of [AunMg]- (n ) 1-8) clusters
are optimized. The calculated results show that all ground-state
structures prefer the lowest spin multiplicity, and the lowest
energy configurations of Mg-doped clusters are different from
those of pure Aun+1- clusters for n ) 2-7. (2) The different
size dependence of the fragmentation energies, second-order
difference of energies, and highest occupied-lowest unoccupied
molecular orbital energy gaps of the most stable configurations
are discussed separately. It is worth pointing out that contrary
odd-even oscillations exist for [AunMg]- and Aun+1- clusters,
suggesting that [Au3Mg]- (Au3-), [Au5Mg]- (Au5-), and
[Au7Mg]- (Au7-) clusters have a higher relative stability than
the neighboring ones. In particular, the [Au3Mg]- cluster shows
the most enhanced chemical stability. Meanwhile, the calculated
atomic average binding energies indicate that the stabilities are
generally increasing as the size of pure and doped gold cluster
increases. (3) Natural population analysis reveals that the charges
transfer from the Mg atom to Au atoms in the low-lying
configurations of [AunMg]- (n ) 2-8) clusters, and the 3D
(4c, 5b, 6e, 7c, and 8e) structures have the smallest NCP values.
As for the ground-state structures, the charge localization at the
Mg atom exhibits an increasing behavior when the number of
Au atoms added, and the local maximum corresponds to
[Au3Mg]- cluster. (4) Considering the influence of the cluster
size on the magnetic moment, we find a pronounced odd-even
oscillatory phenomenon. Moreover, the ground-state configurations of [AunMg]- and Aun+1- (n ) 1-8) clusters with evennumber gold atoms have a total magnetic moment of 1 µB, while
the zero value corresponds to the odd-number ones. In [AunMg](n ) 1-8) clusters, it must be pointed out that the magnetic
effects mainly come from the Au atoms.
Acknowledgment. This work was supported by the Doctoral
Education Fund of the Education Ministry of Chain (No.
20050610011) and the National Natural Science Foundation of
China (No. 10774103).
Supporting Information Available: Calculated frequencies
of the lowest energy structures and low-lying isomers for
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