ARTICLE
pubs.acs.org/JPCA
Determination of Structures, Stabilities, and Electronic Properties
for Bimetallic Cesium-Doped Gold Clusters: A Density Functional
Theory Study
Lu Cheng,*,†,‡ Kuang Xiao-Yu,§,|| Lu Zhi-Wen,† Mao Ai-Jie,§ and Ma Yan-Ming‡
†
Department of Physics, Nanyang Normal University, Nanyang 473061, China
National Lab of Superhard Materials, Jilin University, Changchun 130012, China
§
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China
International Centre for Materials Physics, Academia Sinice, Shenyang 110016, China
)
‡
ABSTRACT: The equilibrium geometric structures, stabilities,
and electronic properties of bimetallic AunCs (n = 110) and
pure gold Aun (n e 11) clusters have been systematically
investigated by using density functional theory with metageneralized gradient approximation. The optimized geometries
show that one Au atom capped on Aun1Cs structures and Cs
atom capped Aun structures for different sized AunCs (n =
110) clusters are two dominant growth patterns. Theoretical
calculated results indicate that the most stable isomers have
three-dimensional structures at n = 4 and 610. Averaged
atomic binding energies, fragmentation energies, and secondorder difference of energies exhibit a pronounced evenodd alternations phenomenon. The same evenodd alternations are found
in the highest occupiedlowest unoccupied molecular orbital gaps, vertical ionization potential, vertical electron affinity, and
hardnesses. In addition, it is found that the charge in corresponding AunCs clusters transfers from the Cs atom to the Aun host in the
range of 0.8511.036 electrons.
1. INTRODUCTION
Because of their unique electronic, magnetic, optical, and
mechanical properties, the bimetallic clusters have been one of
the most active areas of materials science research.17 The
exploration of physical properties of bimetallic clusters is of
remarkable interest, which gives us broadened views into the
essence of atomic binding in solids while greatly challenging our
instinctive understanding.817 Since the discovery of CsAu and
RuAu in 1959,18 many chemists and physicsts have worked with
growing interest on alkali metalgold alloy MAu (M = Li, Na, K,
Rb, and Cs). The major reason is due to the fact that they exhibit
particularly stable and strong intermetallic bonds, which are
related to an especially large electronegativity difference between
alkali metal and gold atom.
Experimentally, Norris and Walleden19 performed the photoemission spectra measurements on CsAu and RbAu and observed that structure in the electron energy distributions is
associated predominantly with transitions from bands derived
from the 6s and 5d states of Au. Wertheim et al.20 prepared the
X-ray photoemission spectra of CsAu and found that the charge
transfer to gold is in the range of 0.60.8 electrons. Tinelli and
Holcomb21 reported the nuclear magnetic resonance (NMR)
and X-ray diffraction measurements of granular samples of the
intermetallic compounds, CsAu and RbAu. Studies of X-ray line
intensities indicate that the excess Cs in the lattice is shown to be
r 2011 American Chemical Society
the primary source of conduction electrons. Busse and Weil22
reported a binding energy of 2.58 ( 0.04 eV in CsAu, but it is
revised to 2.53 eV by Fossgaard et al.23 By supersonic expansion
of a mixed metal vapor from a high-temperature, two-chamber
oven, Heiz et al.24 presented the thermodynamic stabilities together
with ionization potentials of NaxAu and CsxAu clusters. Also,
they carried out a quasi-relativistic density functional calculation.
Their theoretical results suggest that in NaxAu clusters the
various NaAu bonds are rather uniform and that the NaNa
interaction is rather strong, while in CsxAu clusters the CsAu
bonds may display large differences.
Several previous theoretical studies of the bimetallic clusters
are present in the literature, dealing mostly with the band
structure calculations. Ghanty et al.25 presented a theoretical
study on the ground state structures and electronic properties for
Au19X clusters (X = Li, Na, K, Rb, Cs, Cu, and Ag), by using an ab
initio scalar relativistic density functional theory based method.
Heinebrodt et al.26 studied the bimetallic AunXm (X = Cu, Al, Y,
In, Cs) clusters and found the electronic shell effect. Belpassi
et al.27 reported a detailed analysis of spectroscopic constants for
the complete alkali auride series (LiAu, NaAu, KAu, RbAu,
Received: May 6, 2011
Revised:
July 18, 2011
Published: July 25, 2011
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Table 1. Properties of AuCs, Au2, and Cs2 Dimers Using TPSS with the Lanl2Dz Basis Set*
*
Experiment values are in parentheses. a Ref 23. b Ref 22. c Ref 44. d Ref 42. e Ref 41.
CsAu). Their results show that the intermetallic bond is highly
polar and is characterized by a large charge transfer from the
alkali metals to the gold atom. Koening et al.28 performed selfconsistent relativistic band structure calculations for the alkali
metalgold compounds, MAu (M = Li, Na, K, Rb, and Cs) in the
CsCl structure. The calculations suggest that RbAu undergoes an
insulatormetal transition at 30 kbar. Using a quaternion formulation of the DiracFock equations, Saue et al.29 calculated the
bonding in cesium auride and found an almost complete transfer
of one electron from cesium to gold in the AuCs dimer. More
recently, Jayasekharan and Ghanty30 studied the structures, stability,
energy partition analysis, and charge redistribution of X@Au32
clusters (X = Li+, Na+, K+, Rb+, Cs+). Additionally, they indicated
that the K+, Rb+, and Cs+ dopant ions occupy the central position
of the Au32 cage and retain the Ih symmetric structure of the Au32
cluster.
However, as far as we know, there are only a few reports on the
geometric structure and stability of cesium-doped gold clusters,
and the physical origin of its electronic properties is still not well
understood. An important question arises: are their structures
and properties greatly distinct from the pure gold clusters when a
single cesium atom is doped into gold clusters? Therefore, in the
present work, we have performed a systematical calculation on
the structure, stability, and electronic properties of the small size
bimetallic AunCs (n = 110) clusters. Our original motivation
for this work is 3-fold. Our first intention is to give a comprehensive study of the geometric structures for AunCs (n = 110)
clusters. The second is to probe the physical mechanism of the
growth behaviors. We are motivated, third, by the hope that such
a study might contribute some further understanding of the
structure and electronic properties of the bimetallic clusters and
other metallic clusters.
2. COMPUTATIONAL DETAILS
All optimizations of the Aun+1 and AunCs (n = 110) clusters
are performed by using density functional theory with meta-generalized gradient approximation, as implemented in the GAUSSIAN 03
program package.31 Because the meta-generalized gradient approximation (meta-GGA) functional includes the kinetic energy
density in the functional expression, the more accurate results for
both the atomization energy and the relative stability of competing
isomers are produced. In our calculations, the TaoPerdew
StaroverovScuseria (TPSS)32 meta-GGA functional was used
instead of the traditional GGA functional. For Au and Cs atoms,
full electron calculation is rather time consuming, so it is better to
introduce an effective core potential (ECP) Lanl2Dz basis set3335
to describe the outermost valence electrons. In searching for the
lowest-energy structures, lots of possible initial structures, which
include one-, two-, and three-dimensional configurations, are
considered, starting from the previous optimized Aun and XAun
geometries,7,1214,3640 and all clusters are relaxed fully without
any symmetry constraints. Toward nuclear displacement, all the
structures have real vibrational frequencies and therefore correspond to the potential energy minima.
To test the reliability of our calculations, we calculated the
total energies, bond lengths, dissociation energies, and vertical
ionization potential of AuCs, Au2, and Cs2 dimers. The results as
well as the experimental data are listed in Table 1. From Table 1,
we can see that the dissociation energy (2.55 eV), vertical
ionization potential (6.31 eV) for the AuCs dimer, and vertical
ionization potential (3.66 eV) for the Cs2 cluster are in good
agreement with the experimental results 2.53 ( 0.03, 6.6 ( 0.3,
and 3.69 eV.22,23,41,42 Furthermore, the bond length of Au2
molecular (2.537 Å) is also in good agreement with the previous
coupled-cluster calculation (2.512 Å)43 and the experimental
values (2.47 Å).44 The good agreement between them shows the
accuracy of the present theoretical calculation. So, in the following calculations, the highest occupiedlowest unoccupied molecular orbital (HOMOLUMO) energy gap, vertical ionization
potential (VIP), vertical electron affinity (VEA), and chemical
hardness of the most stable configurations are also performed
based on TPSS level.
3. RESULTS AND DISCUSSIONS
3.1. Bare Gold Clusters Aun (n = 211). To investigate the
effects of impurity atoms on gold clusters, we first perform
some optimizations and discussions on pure gold clusters Aun
(n = 211) by using an identical method and basis set. Taking
lots of possible initial structures into account, the most stable
isomers for each size are only selected and shown in Figure 1. It is
interesting to note that the geometric structures and electronic
states are in good agreement with the previous results.7,12,38,39 In
addition, the averaged atomic binding energies, fragmentation
energies, the second-order difference of energies, VIP, and VEA of
gold clusters are also calculated and compared with the available
experimental values in the following.
3.2. Bimetallic CalciumGold Clusters AunCs (n = 110).
For AunCs (n = 110) clusters, the spin multiplicities are 2S + 1
= 1 and 2S + 1 = 2 for even and odd number electron clusters,
respectively. The systems with higher spin multiplicities of 3 and
4 are also taken into account. The calculated results show that the
isomers with spin multiplicities of 1 and 2 have lower total
energies than those of 3 and 4. Therefore, only the isomers with
spin multiplicities of 1 and 2 are considered in this paper. Figure 1
also shows the lowest-energy isomers and few low-lying structures
of the AunCs (n = 110) clusters for each size. The nomenclature of isomers of each cluster is according to the relative
energies. According to the relative energies from low to high,
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Figure 1. Lowest-energy structures of AunCs and Aun+1 (n = 110) clusters and a few low-lying isomers for doped clusters. The yellow and violet balls
represent Au and Cs atoms, respectively.
the stability orders of each cluster are designated by order of
letter, na > nb > nc > nd (n is the number of Au atoms in the
AunCs clusters). Meanwhile, the symmetries, electronic states,
and relative energies compared to each of the lowest-energy
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Table 2. Electronic States, HOMO and LUMO Energies (au), and Vibration Frequencies (cm1) of the Lowest-Energy Isomers
and Few Low-Lying Structures of AunCs (n = 110) Clusters
isomer
state
HOMO
LUMO
AuCs
Au2Cs
1a
2a
0.12803
0.11990
0.06678
0.09507
92
50, 82, 131
2b
0.18383
0.17669
14, 42, 85
3a
0.17264
0.08664
27, 36, 40, 85, 114
3b
0.13792
0.11276
38, 38, 77, 86, 86, 137
3c
0.16526
0.16267
11, 12, 25, 37, 82, 156
4a
0.14502
0.12442
6, 30, 45, 47, 61, 81, 93, 125, 183
4b
0.17230
0.15788
9, 10, 15, 26, 45, 65, 97, 139, 167
4c
4d
0.14156
0.15612
0.12545
0.14261
30, 39, 41, 64, 64, 78, 98, 139, 140
8, 10,10, 28, 29, 40, 70, 148, 152
Au3Cs
Au4Cs
Au5Cs
Au6Cs
Au7Cs
Au8Cs
Au9Cs
Au10Cs
frequency
5a
0.19549
0.11435
3, 34, 34, 39, 41, 55, 62, 78, 89, 115, 170, 193
5b
0.15992
0.10691
20, 27, 39, 45, 49, 53, 77, 80, 84, 122, 143, 177
5c
0.17591
0.10996
12, 19, 25, 33, 40, 48, 73, 78, 87, 129, 155, 180
5d
0.16124
0.13351
28, 28, 41, 45, 44, 52, 70, 79, 84, 122, 122, 156
6a
0.13145
0.11902
14, 14, 26, 43, 43, 53, 53, 69, 69, 73, 107, 113, 138, 166, 166
6b
0.16691
0.15651
16, 16, 29, 32, 36, 46, 50, 65, 76, 78, 91, 115, 116, 163, 171
6c
6d
0.16561
0.16172
0.15346
0.14490
14, 16, 23, 28, 31, 48, 54, 65, 72, 86, 94, 115, 132, 151, 177
14, 23, 25, 31, 39, 46, 54, 61, 64, 76, 82, 99, 118, 173, 192
7a
0.16970
0.12126
12, 15, 19, 25, 43, 49, 52, 63, 69, 69, 72, 89, 106, 106, 114
7b
0.17777
0.12595
29, 32, 34, 44, 50, 53, 62, 64, 70, 75, 91, 94, 103, 132, 135
7c
0.17036
0.11668
19, 19, 37, 37,52, 52, 64, 68, 68, 81, 90, 106, 117, 144, 157
7d
0.20516
0.12623
9, 10, 18, 23, 31, 40, 46, 56, 62, 73, 83, 85, 101, 117, 163
8a
0.14841
0.13998
9, 13, 18, 25, 47, 47, 52, 62, 63, 63, 66, 71, 101, 101, 106
8b
0.15941
0.15020
11, 14, 21, 24, 35, 41, 43, 51, 59, 65, 66, 73, 78, 80, 115
8c
8d
0.15787
0.14222
0.14849
0.13050
8, 11, 17, 25, 27, 29, 38, 40, 49, 58, 61, 68, 74, 85, 92
10, 13, 21, 29, 30, 34, 36, 47, 52, 55, 62, 71, 77, 88, 99
9a
0.18300
0.11788
13, 22, 26, 36, 41, 44, 61, 63, 64, 64, 71, 71, 76, 90, 111
9b
0.19080
0.11566
8, 17, 28, 36, 41, 48, 60, 65, 71, 73, 77, 99, 103, 110, 118
9c
0.17036
0.11731
5, 18, 23, 28, 32, 41, 57, 62, 63, 65, 69, 75, 82, 90, 93, 97
9d
0.16996
0.11849
11, 23, 29, 37, 39, 45, 55, 59, 64, 65, 67, 74, 80, 83, 89, 92
10a
0.15256
0.14333
13, 20, 22, 23, 34, 39, 41, 45, 53, 58, 61, 62, 67, 68, 73, 78
10b
0.15620
0.14725
12, 16, 24, 27, 33, 34, 39, 43, 44, 50, 59, 61, 64, 66, 74, 75
10c
10d
0.14744
0.16278
0.13706
0.15438
15, 20, 27, 29, 31, 35, 38, 44, 48, 56, 58, 61, 64, 66, 71, 76
12, 20, 26, 29, 35, 38, 42, 43, 50, 52, 61, 62, 64, 68, 71, 74
isomers are also presented in Figure 1, and the vibration frequencies
are listed in Table 2.
The possible Au2Cs geometries such as C2v and D∞h isomers
are optimized as the stable structures. According to the calculated
results, it is worth to note that the lowest-energy isomer is an
acute-angle triangular structure (2a) with C2v symmetry, a 44.2°
angle, and 3.57 Å of AuCs bonds. Another stable isomer (2b) is
a linear structure with D∞h symmetry, in which AuCs bond
lengths are also 3.57 Å. However, this isomer is higher in energy
than that of the triangular structure by 0.77 eV. For Au3Cs
clusters, a planar fanlike structure (3a) is found to be the most
stable structure. This structure, with C2v symmetry and different
AuCs bonds (3.45 and 3.97 Å), is obtained when the Au atom
is added to the 2a isomer. The calculations show that the trigonal
bipyramid structure (3b), with 3A1 electronic state, is 1.18 eV
higher in energy than that of the 3a structure. In the 3b isomer,
the AuCs bond length elongates to 3.67 Å. After one Au atom
adds to a 2b isomer, another planar structure 3c is obtained. In
addition, there are two derived structures (4a and 4b) of ground
state Au3Cs clusters when one Au atom is capped on the 3a
isomer. In these isomers, we find that the 3D structure 4a is more
stable than the planar structure 4b because the total energy of 4a
is 0.01 eV lower than that of 4b. Due to the JahnTeller effects,
the symmetry of the quadrangular pyramid structure (4c) is
lowered to be C2v from the C4v point group. With regard to the
Au5Cs clusters, three derived isomers (5b, 5c, and 5d) are
obtained after one Au capping on different sites of the quadrangular pyramid structure (4c). However, the total energy
calculations show that all of them are less stable than the planar
structure (5a), and the relative energies for them compared with
5a are 0.20, 0.39, and 1.21 eV, respectively. Isomer 5a as the
lowest-energy structure of Au5Cs clusters can be generated when
a Au atom is capped on the 4b isomer. Among Au5Cs clusters,
5a has the largest HOMOLUMO gap and VIP value. The
theoretical values are 2.21 and 8.40 eV, respectively. These
results indicate that the 5a isomer is the most stable structure
in Au5Cs clusters. For n = 6, no planar structures are found in the
theoretical calculations due to the effects of the doped Cs atom. It
is interesting to point out that the lowest-energy isomer (6a) of
Au6Cs clusters is optimized after a Au atom top-capping on the
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ground state Au6 structure. As effects of the Cs atom, the six Au
atoms in the 6a isomer are not coplanar, but they still keep the C3v
symmetry. At the same time, it can be seen from Figure 1 that the
derived structure of 5a is higher in energy than that of 6a by
0.33 eV. Among the stable isomers of Au7Cs clusters, a new
structure (7a), with Cs symmetry, is proved to be the ground state
structure. The higher symmetry isomer (7b) is described as two
Au atoms capped on the 5d structure. When one Au atom is
capped on the ground state Au6Cs clusters, another higher
symmetry isomer (7c) is generated. However, both 7b and 7c
are less stable than that of 7a, and the energy differences are 0.30
and 0.34 eV, respectively. Similarly, the lowest-energy structure
(8a) of Au8Cs clusters is formed by top-capping the Cs atom on
the ground state Au8 cluster. This isomer can also be viewed as
the Au atom capped on the 7a structure. In the 8a structure, the
inner Au4 square ring exhibits a contractive trend due to the
effects of the doped Cs atom. Interestingly, for n = 9 and 10, the
lowest-energy structure (9a) of Au9Cs clusters evolves from 8a
when the Au atom is bottom-capped on the 8a isomer and the
10a structure is formed from 9a as the same growth pattern.
From the above discussion, it is remarkable that the lowestenergy structures of AunCs clusters for n = 4 and 610 favor the
three-dimensional (3D) structure. Although Au2,3,5Cs clusters have
planar structure, they are not similar structures to those of the pure
gold clusters. This indicates that the doped Cs atom dramatically
affects the geometries of the ground state of Aun clusters. In
addition, one Au atom capped on Aun1Cs structures and Cs atom
capped Aun structures for different sized AunCs (n = 110) clusters
are two dominant growth patterns. In light of the geometries of
other alkali atom-doped gold clusters,8,9 we conclude that for
AunX and in the case when the dopant (X) is an alkali atom, the
gold geometry, Aun, is more planar than in the case of doping
with other type of atoms, such as transition metals (X = TM).
3.3. Relative Stabilities. To predict relative stabilities of the
AunCs clusters, the averaged atomic binding energies Eb(n),
fragmentation energies ΔE(n), and the second-order difference
of energies Δ2E(n) for different-sized AunCs and corresponding
Aun clusters are calculated. For AunCs clusters, Eb(n), ΔE(n),
and Δ2E(n) are defined as the following
Eb ðnÞ ¼ ½nEðAuÞ þ EðCsÞ EðAun CsÞ=n þ 1
ð1Þ
ΔEðnÞ ¼ EðAun1 CsÞ þ EðAuÞ EðAun CsÞ
ð2Þ
Δ2 EðnÞ ¼ EðAun1 CsÞ þ EðAunþ1 CsÞ 2Eð3Aun CsÞ
ð3Þ
where E(Aun1Cs), E(Au), E(Cs), E(AunCs), and E(Aun+1Cs)
denote the total energy of the Aun1Cs, Au, Cs, AunCs, and Aun
+1Cs clusters, respectively. For Aun clusters, Eb(n), ΔE(n), and
Δ2E(n) are defined as
Eb ðnÞ ¼ ½nEðAuÞ EðAun Þ=n
ð4Þ
ΔEðnÞ ¼ EðAun1 Þ þ EðAuÞ EðAun Þ
ð5Þ
Δ2 EðnÞ ¼ EðAun1 Þ þ EðAunþ1 Þ 2EðAun Þ
ð6Þ
where E(Aun1), E(Au), E(Aun), and E(Aun+1) denote the total
energy of the Aun1, Au, Aun, and Aun+1 clusters, respectively.
The Eb(n), ΔE(n), and Δ2E(n) values of the lowest-energy
AunCs and Aun+1 (n = 110) clusters against the corresponding
number of Au atoms are plotted in Figure 2. As shown in
Figure 2, some interesting results can be obtained. First, the
averaged atomic binding energies of AunCs and Aun+1 clusters
have an increasing tendency and show slight oddeven oscillations with increasing cluster size. Two visible peaks occur at n = 3
and 5, indicating that the Au3Cs and Au5Cs isomers are relatively
more stable than its neighboring clusters. Second, Eb(n) values of
AunCs clusters are higher than those of Aun+1 clusters, which
hints that the impurity of Cs atoms can enhance the stability of
gold clusters. Third, the fragmentation energies and the secondorder difference of energies of AunCs and Aun+1 clusters exhibit
obvious oddeven alternations. This means that clusters containing an even number of atoms have higher relative stability
than their neighbors. Lastly, as shown in Figure 2, the Au5Cs
isomer corresponds to the local maxima of ΔE(n), and the Au3Cs
isomer is a local peak of Δ2E(n), which are 2.84 and 1.27 eV,
respectively. This is in accord with the above analysis based on
Eb(n) of AunCs clusters. Furthermore, it is worth pointing out
that the calculated results for pure gold clusters are found to be in
good agreement with the previous works.38,39
To confirm the stability of the AunCs clusters, we calculated
the energy differences Edis(n) for each size. Generally speaking,
the energy differences Edis(n) can be expressed as
Edis ðnÞ ¼ EðAun Þ þ EðCsÞ EðAun CsÞ
ð7Þ
where E(Aun), E(Cs), and E(AunCs) denote the total energy of
the ground state Aun, Cs, and AunCs clusters, respectively. The
energy difference curves as a function of size n for various clusters
are presented in Figure 3. Similar to ΔE(n) and Δ2E(n), Edis(n)
also displays a remarkable characteristic oscillation effect, which
implies that the Au1,3,5,7Cs clusters have higher adsorption
energies than the Au2,4,6,8Cs clusters. Moreover, a local peak of
Edis(n) is found in the Au3Cs isomer, which is 3.63 eV. This
indicates that the Au3Cs cluster is relatively more stable than its
neighboring clusters.
3.4. HOMOLUMO Gaps and Charge Transfer. The electronic properties of cluster can be reflected by highest occupiedlowest unoccupied molecular orbital (HOMOLUMO)
energy gaps, VIP, VEA, chemical hardness, and polarizability.
Among them, the HOMOLUMO gap is considered to be an
important criterion in terms of the electronic stability of
clusters.45 It represents the ability of a molecule to participate
in chemical reaction to some degree. A large value of the
HOMOLUMO energy gap is related to an enhanced chemical
stability. For the low-lying configuration of AunCs clusters,
HOMO and LUMO energies at each cluster size are listed in
Table 2. From Table 2, we can obtain that the HOMOLUMO
energy gaps are 1.67, 0.68, 2.34, 0.56, 2.21, 0.34, 1.32, 0.23, 1.77,
and 0.25 eV for the lowest-energy isomers of the AunCs clusters
from n = 1 to n = 10, respectively. Meanwhile, the HOMO
LUMO gaps for the most stable AunCs clusters as well as Aun+1
are listed in Figure 4. From Figure 4, we can see that the
HOMOLUMO gaps have an oscillating behavior, similar to
the fragmentation energies and the second-order difference of
energies of AunCs and Aun+1 (n = 110) clusters. Specifically,
the clusters with an even number of atoms have larger HOMO
LUMO energy gaps and are less reactive than clusters with an
odd number of atoms. This may be due to that clusters with an
even number of atoms have closed-shell electron configuration,
which always produces extra stability. Besides, it is found that the
HOMOLUMO gaps of the AunCs cluster are larger than those
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Figure 2. Size dependence of the averaged atomic binding energies Eb(n), fragmentation energies ΔE(n), and the second-order difference of energies
Δ2E(n) for the lowest-energy structure of AunCs and Aun+1 (n = 110) clusters.
Figure 3. Size dependence of the energy difference for the lowestenergy structure of AunCs clusters.
Figure 4. Size dependence of the HOMOLUMO gaps for the lowestenergy structure of AunCs and Aun+1 (n = 110) clusters.
of Aun+1 clusters except for AuCs and Au5Cs isomers. This
means that the doped Cs atom can enhance the chemical stability
of gold clusters. In particular, the largest HOMOLUMO gap
difference (1.24 eV) exists between clusters Au3Cs and Au4,
which illustrates that the corresponding cluster Au3Cs has
dramatically enhanced chemical stability.
The net Mulliken populations (MPs) can provide reliable
charge-transfer information. Here, the Mulliken populations of
the most stable AunCs (n = 110) clusters are listed in Table 3.
As shown in Table 3, the MP values for the Cs atoms in the
AunCs clusters are positive, indicating that the charge in the
corresponding clusters transfers from the Cs atom to Aun frames
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Table 3. Mulliken Charge Populations of the Lowest-Energy AunCs (n = 110) Clusters
cluster
Cs
Au-1
Au-2
Au-3
Au-4
Au-5
Au-6
Au-7
Au-8
Au-9
AuCs
0.851
0.851
Au2Cs
1.028
0.514
0.514
Au3Cs
1.019
0.451
0.451
0.118
Au4Cs
1.021
0.265
0.418
0.480
0.142
Au5Cs
0.965
0.120
0.496
0.120
0.213
Au6Cs
1.015
0.031
0.369
0.369
0.369
0.031
0.031
Au7Cs
1.036
0.253
0.168
0.168
0.370
0.370
0.146
0.146
Au8Cs
Au9Cs
1.025
1.016
0.081
0.209
0.338
0.366
0.338
0.366
0.081
0.209
0.338
0.366
0.338
0.366
0.081
0.209
0.081
0.209
0.386
Au10Cs
0.969
0.193
0.387
0.387
0.193
0.413
0.413
0.305
0.365
0.354
Au-10
0.496
0.382
Table 4. Chemical Hardness, Vertical Electron Affinity
(VEA), and Vertical Ionization Potential (VIP) of the LowestEnergy AunCs and Aun+1 (n = 110) Clusters
AunCs
Aun+1
cluster
η
VEA
VIP
η
VEA
VIP
VIP42
n=1
5.75
0.56
6.31
7.59
1.86
9.45
9.20
n=2
5.01
0.65
5.66
5.09
3.40
8.49
7.50
n=3
6.18
0.83
7.01
5.52
2.42
7.94
8.60
n=4
4.52
1.52
6.04
4.49
2.99
7.48
8.00
n=5
7.03
1.37
8.40
6.50
2.02
8.52
8.80
n=6
n=7
3.75
4.83
1.58
1.61
5.33
6.44
4.00
5.72
3.15
2.68
7.15
8.40
7.80
8.65
n=8
3.45
2.21
5.66
3.67
3.35
7.02
7.15
n=9
5.03
1.66
6.69
4.74
2.79
7.53
8.20
n = 10
3.43
2.33
5.76
3.41
3.60
7.01
7.28
owing to larger electronegativity of the Au than that of the Cs
atom. This feature is consistent with the case of AuCs systems by
X-ray photoelectron spectroscopy (XPS) measurements.46
Moreover, we can also find that the MP values of the Cs atoms
are in the range of 0.8511.036e, which agree well with the
results of HartreeFock calculations.29
3.5. Vertical Ionization Potential, Vertical Electron Affinity, and Chemical Hardness. Vertical ionization potential and
vertical electron affinity are the most important characteristics
reflecting the size-dependent relationship of electronic structure
in cluster physics. The VIP and VEA can be defined as
VIP ¼ Ecationatoptimizedneutralgeometry Eoptimizedneutral
ð8Þ
VEA ¼ Eoptimizedneutral Eanionatoptimizedneutralgeometry
ð9Þ
Next, we have calculated the vertical ionization potential and
vertical electron affinity of AunCs and Aun+1 (n = 110) clusters.
The calculated results are listed in Table 4. It can be seen from
Table 4 that the VIP of AunCs and Aun+1 clusters with even
number atoms is the highest one among the neighboring clusters
with odd number atoms, except for the Au3 isomer. The reason of
variation of the VIP with cluster size is mainly due to the sum of
valence electrons of all atoms. Namely, it is more difficult for
even-electron clusters to lose an electron than odd-electron
neighbors. In addition, VIP values of AunCs clusters are markedly
lower than those of Aun+1 clusters except for the Au5Cs isomer. It
is worthwhile noticing that the calculated VIP values of the pure
Figure 5. Size dependence of the chemical hardnesses for the lowestenergy structure of AunCs and Aun+1 (n = 110) clusters.
gold cluster agree well with experimental data as expected.42 By
comparison with VIP, we find an inverse oscillatory behavior of
VEA. For AunCs clusters, the VEA values decrease with increasing cluster size.
Chemical hardness has been established as an electronic
quantity which may be applied in characterizing the relative
stability of molecules and aggregates through the principle of
maximum hardness (PMH) proposed by Pearson.47 On the basis
of a finite-difference approximation and the Koopmans
theorem,48 the chemical hardness η is expressed as
η ¼ VIP VEA
ð10Þ
In Table 4, we list the calculated results of the hardness for AunCs
and Aun+1 (n = 110) clusters. The relationships of η vs n are
plotted in Figure 5. From Figure 5, it is found that the η for each
cluster shows an obvious oddeven oscillation with the increasing cluster size. Through the PMH of chemical hardness, the
behaviors indicate that the even-numbered isomers with higher
hardness are more stable than their neighboring odd-numbered
isomers. Among even-numbered isomers, the values of η for
Au3Cs, Au5Cs, and Au9Cs clusters are higher than those of Au4,
Au6, and Au10 clusters. It shows that the doped Cs atoms can
enhance the chemical hardness of Au3Cs, Au5Cs, and Au9Cs
clusters. Specially, the Au5Cs cluster has the largest chemical
hardness of 7.03 eV.
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The Journal of Physical Chemistry A
4. CONCLUSIONS
The geometrical structures, stabilities, growth behaviors,
HOMOLUMO gaps, charge transfer, VIPs, VEAs, and hardnesses of the AunCs and Aun+1 (n = 110) clusters have been
investigated by the metal-GGA functional at the TPSS level. The
results are summarized below:
(i) The optimized geometries show that one Au atom capped
on Aun-1Cs structures and Cs atom capped Aun structures
for different sized AunCs (n = 110) clusters are two
dominant growth patterns. The lowest-energy structures
of AunCs clusters favor the 3D structure at n = 4 and 610.
Although Au2,3,5Cs clusters have planar structures, their
structures are not similar to the corresponding pure gold
clusters.
(ii) The averaged atomic bonding energies, fragmentation
energies, energy differences, second-order difference of
energies, and HOMOLUMO gaps of the most stable
AunCs clusters exhibit the same oscillatory behavior as a
function of cluster size. According to the calculated
results, it is found that the planar Au3Cs and Au5Cs
structures are the most stable geometries for AunCs
(n = 110) clusters. Moreover, we also conclude that
for AunX and in the case where the dopant (X) is an alkali
atom, the gold geometry, Aun, is more planar than in the case
of doping with other types of atoms, such as transition
metals (X = TM).
(iii) On the basis of the calculated Mulliken populations, it is
found that the charge in corresponding AunCs clusters
transfers from the Cs atom to the Aun host. In addition,
the vertical ionization potential, vertical electron affinity,
and chemical hardness display an evenodd alternation
with cluster size. Theoretical results indicate that the
clusters with an even number of atoms, especially Au5Cs
isomers, have enhanced chemical stabilities compared
with their neighbors.
’ AUTHOR INFORMATION
Corresponding Author
*E-mail: [email protected].
’ ACKNOWLEDGMENT
This work was supported by the National Natural Science
Foundation of China (No.10974138), Doctoral Education Foundation of Education Ministry of China (No.20050610011), China
Postdoctoral Science Foundation Funded Project, Natural Science
Foundation of Science and Technology Department of Henan
Province (No.102300410209), Natural Science Foundation of
Education Department of Henan Province (No.2011B140015),
and Nanyang Normal University Science Foundation (No.
zx20100011).
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