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 9273
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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, 9274
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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 9275
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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 9276
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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 9277
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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 9278
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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. 9279
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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). ’ REFERENCES (1) West, P. S.; Johnston, R. L.; Barcaro, G.; Fortunelli, A. J. Phys. Chem. C 2010, 114, 19678–19686. (2) Tenney, S. A.; Ratliff, J. S.; Roberts, C. C.; He, W.; Ammal, S. C.; Heyden, A.; Chen, D. A. J. Phys. Chem. C 2010, 114, 21652–21663. (3) Zanti, G.; Peeters, D. J. Phys. Chem. A 2010, 114, 10345–10356. (4) Zhao, S.; Ren, Y. L.; Ren, Y. L.; Wang, J. J.; Yin, W. P. J. Phys. Chem. A 2010, 114, 4917–4923. (5) Nu~nez, S.; Johnston, R. L. J. Phys. Chem. C 2010, 114, 13255–13266.
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