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Density-functional theory study of structural and electronic properties of AgnAl(0,+1) (n = 1–7) clusters
Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
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Density-functional theory study of structural and electronic properties of AgnAl(0,+1) (n = 1–7) clusters FengLi Liu a,b, Gang Jiang a,* a b
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China College of Physical Science and Technology, Heilongjiang University, Harbin 150080, China
a r t i c l e
i n f o
Article history: Received 26 August 2009 Received in revised form 13 April 2010 Accepted 13 April 2010 Available online 22 April 2010 Keywords: Coinage-metal aluminum compound Density-functional theory Ground state structure Magic number Binding energy
a b s t r a c t Equilibrium geometric structures of coinage-metal aluminum compounds AgnAl(0,+1) (n = 1–7) are first predicted by density-functional theory calculations with relativistic pseudopotentials. The stability of the ground state structures of these clusters is examined via the analysis of the binding energies (BE) and second difference energy. In addition, adiabatic ionization potential (AIP), energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, possible dissociation channels are also presented and discussed. Remarkable odd–even alternation behaviors have been observed. The results show that n = 6 is the magic number for AgnAl+, and n = 5 is predicted as the magic number for AgnAl. Moreover, for neutral clusters, doping clusters are more stable than the corresponding pure clusters. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Coinage-metal (Cu, Ag and Au) clusters have attracted researchers due to their importance in basic research, as well as technological applications such as catalysis [1–5], photography [6–10], and nanoelectronics [11]. The impurity-doped coinage-metal clusters often represent more especial properties than the non-doped pure noble metals [12–16]. At the end of 20th century, some experiments have been reported on the properties of coinage metal clusters doped with group 13 atoms [17–19]. For example, Yamada et al. [17] produced metal alloy clusters including CunAlm, CunInm, AgnAlm and AgnInm by a gas aggregation source and investigated by time-of-flight mass spectrometry in 1992, they found these cluster ions have magic numbers which correspond to jellium shell closings. Heinebrodt and Bouwen et al. [18,19] produced the neutral and cationic clusters of AunXm(0,+1) (X = Al, In) in 1999 and their results show that the patterns are related to the magic numbers of the electronic shell model. Recently, Kumar [20,21] studied formation of aqueous Tl/Ag and Tl/Cu bimetallic clusters by gamma and electron irradiation. However, only a few theoretical studies of structures and electronic properties for coinage metal clusters doped with group 13 atoms are reported. Urban et al. [22] studied the binding of aluminum to coinage metals at the CCSD(T) theoretical level and indicated that the electron correlation and relativistic effects play an important role in the structure, stability and so on. * Corresponding author. E-mail address: [email protected] (G. Jiang). 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2010.04.016
Tunna Baruah et al. [23] obtained the candidate structures for the ground-state geometries of Al12M and Al13M (M = Cu, Ag and Au) and they found that the atomization energies of them are substantially larger than pure Al clusters. Wang Hong-Yan et al. [24] calculated electronic and structural properties of mixed AunXm (n + m = 4, X = Cu, Al, Y) at the B3LYP hybrid level. To our knowledge, no theoretical work for AgnAl(0,+1) (n = 1–7) clusters have been found. Based on our previous works [25,26], we investigate the geometrical structures and stabilities of the neutral and cationic AgnAl(0,+1) (n = 1–7) systematically using quantum-mechanical calculations. Binding energies, second difference energies, adiabatic ionization potentials (AIPs) and energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the ground state structures have been evaluated. The dissociation channels and the corresponding dissociation energies are also given. 2. Computational methods The density-functional theory (DFT) methods have been widely used to study structures of metal clusters as it predicts the VDE’s of coinage clusters quilt well [27]. Therefore, the geometry optimization and electronic structure calculation were carried out using the DFT with unrestricted B3LYP exchange–correlation potential [28,29] in this paper. The Ag atom was treated with 19-valence electron relativistic pseudopotentials (PPs) and the matched basis sets (8s7p6d)/[6s5p3d] given by Andrae et al. [30]. Pyykkö et al.
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F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
[31] pointed out that the diffuse f function is required for describing metallophilic attraction. So the f-type diffuse functions, which af = 0.22, was added to yield an overall basis set of (8s7p6d1f)/ [6s5p3d1f]. The Al atom was described with 6-311G* basis set. In order to examine the feasibility of the PPs and basis set for investigating this type of cluster, we first performed calculation on Ag+2 and Ag2. The results show that Ag–Ag bond lengths (2.590 Å), vibrational frequencies (178 cm1 for Ag2, 124 cm1 for Ag+2), and dissociation energies (1.53 eV for Ag2, 1.64 eV for Ag+2) are in good agreement with the corresponding experimental values (2.530 Å; 192 cm1 for Ag2 and 136 cm1 for Ag+2; 1.66 eV for Ag2 and 1.74 eV for Ag+2) [32,22]. This means that our PPs and basis sets used in this study are reasonable. The stabilities and geometries of the AgnAl(0,+1) (n = 1–7) cluster are reassured accurately by calculating on all possible structures, and the stable isomers are determined by vibrational analysis in the absence of negative frequencies. All calculations are performed using the GAUSSIAN 03 program package [34].
3. Results and discussion 3.1. Structures, energies and frequencies of AgnAl(0,+1) (n = 1–7) The spin multiplicities are 2S + 1 = 1 and 2S + 1 = 2 for even and odd number electron clusters, respectively. The systems with spin multiplicities of 3 and 4 are also calculated. The results show that the total energies of 3 and 4 are higher than of 1 and 2. Therefore, only the systems with spin multiplicities of 1 and 2 are considered in this paper. Fig. 1 shows the lowest-energy structures and low-lying isomers of the cationic clusters AgnAl+, while Fig. 2 displays those of neutral clusters AgnAl. The relative energies of the geometric structures are also given in Figs. 1 and 2. The nomenclature of isomers of each cluster is according to the relative energies. Since the values of relative energies are shown the order of stability thermodynamically, so the stability orders of each cluster are depicted by the order of letter, a > b > c > . The corresponding geometrical parameters and the symmetries of AgnAl+ and AgnAl are listed in Tables 1 and 2, respectively. The AgAl+ molecule has a bond length of 2.595 Å, while that of AgAl is 2.527 Å which is in accordance with the data of 2.474 ± 0.005 Å [35] experimentally. The Pauling’s electronegativity values for both Ag and Al are comparable. Mulliken total atomic charge analysis gives Al(0.2202)Ag(0.2202) for AgAl and Al(0.6468)Ag (0.3532) for AgAl+. This means that when an electron is removed from AgAl forming the cation AgAl+, the Al atom loses 0.4266 charges, and the Ag atom loses 0.5734 charges. The lowest-energy structure of Ag2Al+ cluster is linear with D1h 1P ( g) symmetry, while the low-lying isomer is a bent structure with Cs (1A’) symmetry (Fig. 1.2-a and b). The energy difference between the lowest-energy structure and the low-lying isomer is 0.607 eV. In the case of Ag2Al, both the lowest-energy structure (Fig. 2.2-a) and the low-lying isomer (Fig. 2.2-b) are all isosceles triangle with C2V (2A1) symmetry and C2V (2B2) symmetry, respectively. The energy difference of two Ag2Al isomers is 0.027 eV. The lowest-energy structures 2-a (both in Figs. 1 and 2) are predicted as the ground state structures of Ag2Al+ and Ag2Al, respectively. The structural changes in the ground state configuration of the ionized cluster relative to that of the neutral cluster are due to electronic reorganization during the ionizing process of the AgnAl clusters. Mulliken total atomic charge analysis gives Al(1.1168)Ag(0.0584) for the ground state structure of Ag2Al+, and Al(0.4749)Ag (0.2374) for Ag2Al. The Al atom loses 0.6419 charges, and an Ag atom loses 0.1791 charges for Ag2Al.
The lowest-energy structure of Ag3Al+ is Y shaped with the Al atom in the center (Fig. 1.3-a). The low-lying isomer (Fig. 1.3-b) is a planar rhombus, and the energy difference is 0.250 eV. The two isomers have same symmetry C2V (2B2). Contrarily, the lowest-energy structure of Ag3Al cluster (Fig. 2.3-a) is a planar rhombus with C2V (1A1) symmetry, while the low-lying isomer (Fig. 2.3-b) is Y shaped with D3h (1A0 1) symmetry. The energy difference of them is 0.165 eV. The lowest-energy structures 3-a (both in Figs. 1 and 2) are predicted as the ground state structures of Ag3Al+ and Ag3Al, respectively. Mulliken total atomic charge analysis gives Al(1.2674) 1Ag(0.0694)2Ag(0.0694)3Ag(0.1287) for the ground state structure of Ag3Al+, and Al(0.6496) 1Ag(0.3714)2Ag (0.0933)3Ag(0.3714) for Ag3Al. The Al atom loses 0.6179 charges for Ag3Al. Interestingly, the symmetry of the lowest-energy structure of Ag3Al+ is C2V rather than D3h (Fig. 1.3a), and Mulliken charges found in case of Ag3Al+ for Ag1 and Ag3 are different. This is mainly because for the ground state structure of neutron Ag3Al cluster Al atom will sp2 hybridise. There is a single valence electron for Ag atom which occupies an atomic orbital 5s. There are three valence electrons for Al atom which occupy atomic orbitals 3s23p1. For the Al atom, the 2s orbital ‘‘mixes” with the two available 2p orbitals to form three sp2 orbitals. The Al atom forms three r bonding orbital with Ag atoms by s–sp2 overlap all with 120° angles. Each bonding orbital has two electrons called r2 orbital as shown in Fig. 3a. When Ag3Al is ionized forming the cation Ag3Al+ one electron is removed from the one of three r2 orbitals, and this orbital has one electron named r1 orbital as shown in Fig. 3b. For this reason the symmetry of the cluster structure is reduced, and Mulliken charges in case of Ag3Al+ for Ag1 and Ag3 are different. Three stable configurations of Ag4Al+ have been found by geometry optimization. The lowest-energy structure of Ag4Al+ (Fig. 1.4-a) is a planar trapezoidal structure with C2V (1A1) symmetry. A planar and a three dimensional geometries (Fig. 1.4-b and c) are found for low-lying isomers, lying 0.192 and 0.476 eV above the lowest-energy structure. The lowest-energy structure for Ag4Al cluster is given in Fig. 2.4-a, which symmetry is C2V (2B1). A planar and two threedimensional low-lying isomers (Fig. 2.4-b–d) are found, lying 0.086, 0.149 and 0.220 eV above the lowest-energy structure. For both Ag4Al+ and Ag4Al clusters, the structures 4-a (both in Figs. 1 and 2) are predicted as the ground state structures. Mulliken total atomic charge analysis gives Al(1.4157)1Ag(0.1782)2Ag (0.0296)3Ag(0.0296)4Ag(-0.1782) for the ground state structure of Ag4Al+, and Al(0.6940)1Ag(0.2536)2Ag(0.0934)3Ag (0.2536) 4Ag(0.0934) for the ground state structure of Ag4Al, and the Al atom loses 0.7216 charges. The lowest-energy structure of Ag5Al+ (Fig. 1.5-a) is pyramidal with C5V (2A1) symmetry. The two other planar geometries (Fig. 1.5-b and c) are found to be low-lying isomers with energy differences being 0.346 and 0.635 eV, respectively. The lowest-energy structure of Ag5Al (Fig. 25-a) is a square bipyramid structure with C4V (1A1) symmetry. Three planar geometries (Fig. 2.5-b–d) are found to be the low-lying isomers with energy differences being 0.511, 1.200 and 1.246 eV, respectively. The structures 5-a (both in Figs. 1 and 2) are predicted as the ground state structures. Mulliken total atomic charge analysis gives Al(2.0105)Ag(0.2021) for the ground state structure of Ag5Al+, and Al(1.2501)1Ag(0.3600) 2Ag(-0.3600)3Ag (0.3600)4Ag(0.3600) 5Ag(0.1899) for the ground state structure of Ag5Al. The Al atom of Ag5Al loses 0.7603 charges. For Ag6Al+ cluster, the lowest-energy structure has C1 (1A) symmetry which slightly distorted C3V symmetry (Fig. 1.6-a), which is predicted the ground state structure. Two low-energy structural isomers are found. One is pentagonal bipyramid with C5V (1A1) symmetry and the Al atom being at the apex of Ag atoms (Fig. 1.6-b). The other isomer is a distorted planar pentagonal with C1(1A) symmetry (Fig. 1.6-c). Their energies are higher than that of the lowest-energy
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
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Fig. 1. Geometries and relative energies (DE) of AgnAl+ clusters. The shaded sphere represents the Ag atom. Structures are ordered in energy from the letter a–h, with the lowest-energy structure shown the letter a. The values of the geometric parameters are reported in Table 1.
structure by 0.064 and 0.669 eV, respectively. For Ag6Al cluster, interestingly, the lowest-energy structure has C1 (2A) symmetry and can be viewed as capping one Ag atom on the lowest-energy structure of Ag5Al (Fig. 2.6-a). This structure is predicted the ground state structure. There are three low-energy structural isomers (Fig. 2.6-b–d) and their energies are higher than the lowest-energy one by 0.043, 0.354 and 0.486 eV, respectively. For the ground state structure of Ag6Al+, Mulliken total atomic charge analysis gives Al (2.0570)1Ag(0.2905)2Ag(0.2994)3Ag(0.2842)4Ag(0.074 94) 5Ag(0.0878)6Ag(0.0200), and for Ag6Al Mulliken total atomic charge analysis gives Al (1.0336)1Ag(0.3155)2Ag(0.3158)3Ag (0.2837)4Ag(0.28 48)5Ag(0.2358)6Ag(0.0695). The Al atom of Ag6Al loses 1.0234 charges.
Eight isomers are obtained for Ag7Al+ cluster (Fig. 1.7). The lowest-energy structure (Fig. 1.7-a) can be viewed as the additional Ag atom capping on the bottom of the lowest-energy structure for Ag6Al+ (Fig. 1.6-a), and is predicted as the ground state structure. The lowest-energy structure of Ag7Al cluster (Fig. 2.7-a) can be viewed as adding one Ag atom to the ground state structure of Ag6Al (Fig. 2.6-a), and is predicted as the ground state structure. There are six low-energy structural isomers for Ag7Al cluster. For the ground state structure of Ag7Al+, Mulliken total atomic charge analysis gives Al(1.9974)1Ag(0.3058)2Ag(0.3019)3Ag (0.2994)4Ag(0.0646) 5Ag(0.0656)6Ag(0.0617)7Ag(0.1017). For the ground state structure of Ag7Al, Mulliken total atomic charge analysis gives Al(1.4893)1Ag(0.2393)2Ag(0.2416)3Ag(0.3474)4Ag(0.3488)5
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F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
Fig. 2. Geometries and relative energies (DE) of AgnAl (n = 1–7) clusters the ground state geometry of Ag8Al. The shaded sphere represents the Ag atom. Structures are ordered in energy from the letter a–f, with the lowest-energy structure shown the letter a. The values of the geometric parameters are reported in Table 2. The ground state geometry of Ag8Al is shown in it.
Ag(0.1039)6Ag(0.0320)7Ag(0.3841). The Al atom of Ag7Al loses 0.5081 charges. According to the optimized equilibrium geometries of the Ag(0,+1) clusters, the growth pattern of the AgnAl(0,+1) clusters is nAl investigated. Theoretical results indicate that, for AgnAl+ clusters, the geometries of AgAl+, Ag2Al+, Ag3Al+ and Ag4Al+ clusters take planar shapes of linear, Y shaped and trapezoid. While the ground state clusters take three-dimensional structures when the size of AgnAl+ is bigger than 4. The doping atom Al prefers to bind more Ag atoms for n 6 5and at apex for n = 6, 7. For AgnAl clusters, the geometries of Ag–Al, Ag2Al, Ag3Al clusters are take planar shapes of linear, isosceles triangle, and rhombus. While the ground state clusters take three-dimensional structures when the size of AgnAl is bigger than 3. Many theoretical studies show that the ground state clusters of Agn take three-dimensional structures when the
size of Agn is bigger than 6 [36–42]. It is found that the Al atom occupies a peripheral position for AgnAl (n = 1–7) clusters. To aid future identification of the AgnAl(0,+1) clusters in the laboratory, the calculated vibrational frequencies and infrared intensities for the ground state structures of AgnAl(0,+1) are presented in Table 3. We can see that the dominant frequencies of AgnAl+ are 188, 368, 371, 242, 100, 85 and 170 cm1, respectively, with the corresponding infrared intensities 15.2, 7.9, 12.6, 3.3, 1.3, 0.7 and 0.7 km/mol. The dominant frequencies of AgnAl are 245, 309, 188, 210, 217, 219 and 144 cm1, respectively, with the corresponding infrared intensities 11.3, 9.5, 0.6, 1.4, 0.8, 2.8 and 1.3 km/mol. The frequency ranges and intensities of the ground state structures of AgnAl(0,+1) suggest that the IR species of these structures could be unambiguously differentiated experimentally. The infrared intensities of some vibrational frequencies are very small or close to zero.
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F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17 Table 1 Geometrical parameters (bond length in Å, bond angle and dihedral angle in deg) of the structures for AgnAl+(n = 1–7). Cluster AgAl
+
Ag2Al+
Ag3Al+
Ag4Al+
Ag5Al+
Ag6Al+
Ag7Al+
Structure
Symm
1-a
C1V
2-a
D1h
State 2P 1P g
2-b
Cs
1
3-a
C2V
2
3-b
C2V
2
4-a
C2V
1
4-b
Cs
1
4-c
C1
1
5-a
C5V
2
5-b
Cs
2
5-c
C2V
2
6-a
C1
1
6-b
C5V
1
6-c
C1
1
7-a
C1
2
7-b
C1
2
A
0
B2 B2 A1 A
0
A
A1 A
0
A1
A
A1
A
A
A
Bond length
Bond angle
Dihedral angle
Al-1Ag
2.595
Al-1Ag lAg-2Ag Al-1Ag lAg-2Ag
2.449 4.514 2.694 2.623
1Ag-Al-2Ag
180.0
2Ag-1Ag-Al
92.7
Al-1Ag lAg-3Ag Al-1Ag lAg-2Ag
2.528 2.442 2.619 2.731
1Ag-Al-3Ag
145.3
1Ag-Al-3Ag
68.9
Al-1Ag Al-2Ag Al-1Ag Al-3Ag Al-4Ag lAg-2Ag 2Ag-3Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag lAg-2Ag 2Ag-3Ag 3Ag-4Ag 4Ag-1Ag
2.462 2.596 2.517 2.739 2.599 2.745 2.709 2.590 3.260 2.590 3.264 2.901 2.900 2.902 2.902
1Ag-Al-4Ag 2Ag-Al-3Ag 1Ag-Al-3Ag 3Ag-Al-4Ag
148.9 63.4 70.2 61.1
1Ag-Al-2Ag 2Ag-Al-3Ag 3Ag-Al-4Ag 4Ag-Al-1Ag
58.1 58.1 58.1 58.1
1Ag-Al-2Ag-4Ag
73.9
Al-1Ag 1Ag-2Ag Al-1Ag Al-3Ag Al-4Ag Al-5Ag 1Ag-2Ag 2Ag-3Ag Al-1Ag 1Ag-2Ag lAg-3Ag
2.619 2.815 2.517 2.752 2.653 2.533 2.781 2.783 2.526 2.686 2.759
1Ag-Al-2Ag
65.0
Al-3Ag-2Ag-1Ag
28.7
1Ag-Al-5Ag 1Ag-2Ag-3Ag 3Ag-Al-4Ag 4Ag-Al-5Ag
166.4 61.9 60.7 67.3
Al-1Ag-2Ag 1Ag-2Ag-3Ag
86.6 62.2
Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-1Ag 4Ag-5Ag 5Ag-6Ag 4Ag-6Ag Al-1Ag lAg-2Ag lAg-6Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag 3Ag-5Ag 3Ag-6Ag
2.596 2.595 2.597 2.913 2.913 2.912 4.359 4.359 4.359 2.836 2.832 2.833 2.780 2.792 2.868 2.451 2.607 2.6271 2.603 2.775 2.723
1Ag-Al-2Ag 2Ag-Al-3Ag 1Ag-Al-3Ag 1Ag-2Ag-3Ag 2Ag-3Ag-1Ag 4Ag-5Ag-6Ag 5Ag-6Ag-4Ag
114.2 114.2 114.2 60.0 60.0 60.0 60.1
Al-2Ag-1Ag-3Ag 5Ag-4Ag-3Ag-6Ag
26.9 40.4
1Ag-Al-2Ag 1Ag-6Ag-2Ag
60.3 58.2
2Ag-1Ag-Al-3Ag 1Ag-2Ag-6Ag-3Ag
138.6 135.7
1Ag-Al-2Ag 2Ag-Al-3Ag 3Ag-Al-4Ag 5Ag-3Ag-6Ag
119.1 64.3 62.7 58.8
Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-1Ag 4Ag-5Ag 5Ag-6Ag 4Ag-6Ag 4Ag-7Ag 5Ag-7Ag Al-1Ag
2.608 2.608 2.609 2.982 2.980 2.981 4.350 4.349 4.351 2.842 2.842 2.842 2.860 2.861 2.594
1Ag-Al-2Ag 2Ag-Al-3Ag 1Ag-Al-3Ag 1Ag-2Ag-3Ag 2Ag-3Ag-1Ag 4Ag-5Ag-6Ag 5Ag-6Ag-4Ag 4Ag-7Ag-5Ag
113.0 113.0 113.0 60.0 60.0 60.0 60.0 60.0
Al-2Ag-1Ag-3Ag 5Ag-4Ag-3Ag-6Ag 3Ag-4Ag-5Ag-7Ag
29.3 40.7 155.8
1Ag-Al-2Ag
102.1
1Ag-2Ag-Al-3Ag
150.0
(continued on next page)
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F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
Table 1 (continued) Cluster
Structure
Symm
State
7-c
C1
2
7-d
C1
1
7-e
C5V
2
7-f
C1
2
7-g
C1
2
7-h
C1
2
A
A
A1
A
A
A
Bond length Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag 1Ag-7Ag 2Ag-7Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-1Ag 4Ag-5Ag 5Ag-6Ag 4Ag-6Ag 2Ag-7Ag 3Ag-7Ag Al-1Ag Al-2Ag Al-3Ag Al-5Ag Al-6Ag Al-7Ag 3Ag-4Ag 5Ag-4Ag Al-1Ag lAg-2Ag lAg-6Ag Al-7Ag Al-1Ag Al-5Ag Al-6Ag Al-7Ag 1Ag-6Ag 2Ag-6Ag 3Ag-6Ag 4Ag-6Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag 1Ag-6Ag 1Ag-7Ag 1Ag-2Ag 1Ag-Ag 1Ag-4Ag 1Ag-5Ag 1Ag-6Ag 2Ag-7Ag 6Ag-7Ag Al-7Ag
This indicates these frequencies may be masked by background noise and difficult to be observed in experiments. 3.2. Stabilities Based on the binding energy per atom (BE) and the second difference of energy D2 E in their lowest-energy states, we have examined the stability of the neutral and cationic AgnAl(0,+1) (n = 1–7) clusters. Mulliken total atomic charge analysis for AgnAl+ shows that Al atom loses charges and becomes cationic Al+, so the BE for AgnAl+ is defined as Eb = (nE[Ag]+E[Al+] E[AgnAl+])/(n + 1). The BE for AgnAl is defined as Eb = (nE[Ag]+E[Al] E[AgnAl])/ (n + 1). The BE is presented in Fig. 4 as a function of cluster size. The ground structures of Ag+n+1 (n = 1–7) and Agn+1 (n = 1–7) are optimized by HuaLei Zhang and co-workers [42]. In order to detect
Bond angle 2.594 2.611 2.650 2.805 2.805 2.863 2.863 2.648 2.608 2.608 3.180 2.797 2.798 4.580 3.990 4.580 2.827 2.859 2.827 2.879 2.879 2.803 2.728 2.814 2.814 2.728 3.046 2.785 2.785 2.778 2.763 2.905 2.515 2.594 2.640 2.767 2.498 2.710 2.794 2.794 2.712 2.610 2.591 2.653 2.519 2.617 2.763 2.742 2.759 2.780 2.701 2.780 2.759 2.802 2.802 2.616
Dihedral angle
2Ag-Al-3Ag 3Ag-Al-1Ag 4Ag-Al-5Ag 5Ag-Al-6Ag 6Ag-Al-4Ag 1Ag-7Ag-2Ag
125.0 125.0 62.6 60.5 62.6 89.6
5Ag-4Ag-Al-6Ag 1Ag-Al-2Ag-7Ag
69.1 38.2
1Ag-Al-2Ag 2Ag-Al-3Ag 1Ag-Al-3Ag 1Ag-2Ag-3Ag 2Ag-3Ag-1Ag 4Ag-5Ag-6Ag 5Ag-6Ag-4Ag 2Ag-7Ag-3Ag
121.2 99.8 121.2 64.2 64.2 59.6 59.6 87.7
Al-2Ag-1Ag-3Ag 5Ag-4Ag-3Ag-6Ag 3Ag-2Ag-4Ag-7Ag
29.7 45.8 57.3
1Ag-Al-2Ag 1Ag-Al-6Ag 3Ag-Al-5Ag 2Ag-Al-3Ag 6Ag-Al-5Ag 2Ag-7Ag-6Ag 3Ag-4Ag-5Ag
61.5 61.5 59.1 60.6 60.6 103.8 59.8
3Ag-Al-2Ag-1Ag 1Ag-Al-6Ag-5Ag 2Ag-3Ag-Al-5Ag 5Ag-4Ag-3Ag-Al
140.0 140.0 139.4 33.0
1Ag-Al-2Ag 1Ag-6Ag-2Ag
59.6 56.8
2Ag-1Ag-Al-3Ag 1Ag-2Ag-6Ag-3Ag
37.5 133.7
1Ag-Al-6Ag 1Ag-6Ag-2Ag 2Ag-6Ag-3Ag 3Ag-6Ag-4Ag 4Ag-6Ag-5Ag
60.6 62.9 60.0 62.4 61.2
1Ag-Al-2Ag 2Ag-Al-3Ag 3Ag-Al-4Ag 4Ag-Al-5Ag 5Ag-Al-1Ag 6Ag-1Ag-7Ag
65.6 64.4 65.5 104.8 65.6 59.5
1Ag-2Ag-Al-3Ag 3Ag-4Ag-Al-5Ag 1Ag-2Ag-Al-3Ag 2Ag-1Ag-7Ag-6Ag
168.7 146.2 25.6 152.2
2Ag-1Ag-3Ag 3Ag-1Ag-4Ag 4Ag-1Ag-5Ag 5Ag-1Ag-7Ag 2Ag-1Ag-6Ag 2Ag-7Ag-6Ag 2Ag-7Ag-Al
61.2 62.7 62.7 61.2 63.2 62.1 146.8
1Ag-2Ag-3Ag-4Ag 1Ag-4Ag-5Ag-6A 6Ag-1Ag-2Ag-7Ag Al-7Ag-6Ag-2Ag
46.1 47.2 37.9 157.5
especial properties of doped cluster AgnAl(0,+1) (n = 1–7), we also calculated the BE of Agn+1(0,+1) (n = 1–7), using the optimized ground structures by HuaLei Zhang and co-workers [42], as shown in Fig. 4. In light of the stability of the present series, the HOMOs and LUMOs of AgnAl+ and AgnAl are displayed in Fig. 5. Observing Fig. 4, following trends can be gotten: (1) The BE of neutral clusters AgnAl (n = 1–7) are higher than the corresponding values of pure clusters Agþ1 (n = 1–7). n For example, the BE of the neutral AgAl is 1.971 eV, which is in good agreement with the experimental data [36], and larger than that of Ag2 by 0.437 eV, and so on. The BE for the doped clusters AgnAl are larger than the corresponding values of pure neutral clusters Agþ1 by 0.080–0.310 eV. It n is evident that the stability of neutral clusters is enhanced
13
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17 Table 2 Geometrical parameters (bond length in Å, bond angle and dihedral angle in deg) of the structures for AgnAl(n = 1–7). Cluster
Structure
Symm
State 1P
AgAl
1-a
C1V
Ag2Al
2-a
C2V
2
A1
2-b
C2V
2
B2
3-a
C2V
1
A1
3-b
D3h
1
A‘1
4-a
C2V
2
B1
4-b
Cs
2
A‘‘
4-c
C4V
2
A1
4-d
Cs
2
A‘
5-a
C4V
1
A1
5-b
Cs
1
A‘
5-c
C2V
1
A1
5-d
C2V
1
A1
6-a
C1
2
A
6-b
C1
2
A
6-c
C1
2
A
6-d
C2V
2
B2
Ag3Al
Ag4Al
Ag5Al
Ag6Al
Bond length
Bond angle
Dihedral angle
Al-1Ag
2.527 2.474a
Al-1Ag lAg-2Ag Al-1Ag lAg-2Ag
2.496 4.514 2.642 2.6543
1Ag-Al-2Ag
129.4
1Ag-Al-2Ag
60.3
Al-1Ag lAg-2Ag Al-1Ag
2.622 2.757 2.474
1Ag-Al-3Ag
116.5
1Ag-Al-2Ag
120.0
Al-1Ag Al-2Ag lAg-2Ag 2Ag-4Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-1Ag lAg-4Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag lAg-2Ag
2.622 2.868 2.805 2.816 2.655 2.584 3.033 2.655 2.526 2.946 2.575 4.853 3.029 2.583 2.797
1Ag-Al-3Ag
113.0
1Ag-3Ag-Al-2Ag
34.0
1Ag-Al-2Ag
107.0
Al-1Ag-2Ag-3Ag Al-1Ag-3Ag-4Ag
128.9 65.4
1Ag-Al-3Ag
111.1
1Ag-Al-2Ag-3Ag
121.0
1Ag-Al-3Ag Al-1Ag-2Ag
115.5 129.2
Al-1Ag Al-5Ag lAg-2Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag lAg-2Ag lAg-3Ag Al-1Ag 1Ag-2Ag lAg-3Ag Al-1Ag lAg-2Ag lAg-3Ag 2Ag-3Ag
2.601 3.428 2.953 2.549 4.716 2.858 2.585 2.520 2.732 2.757 2.581 2.648 2.832 2.866 2.760 2.886 2.723
1Ag-Al-3Ag
106.8
Al-1Ag-4Ag-3Ag
46.4
1Ag-Al-4Ag
120.7
Al-1Ag-2Ag 2Ag-1Ag-3 g
87.9 63.4
1Ag-Al-5Ag
55.1
Al-1Ag Al-2Ag Al-3Ag Al-4Ag 1Ag-5Ag 2Ag-5Ag 3Ag-5Ag 2Ag-5Ag 3Ag-6Ag 4Ag-6Ag 5Ag-6Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-4Ag 4Ag-5Ag 5Ag-6Ag Al-1Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-4Ag Al-1Ag Al-2Ag
2.640 2.640 2.640 2.641 2.805 2.804 2.873 2.874 2.908 2.906 2.779 2.660 2.680 2.778 2.660 2.778 2.680 2.867 2.737 2.833 4.575 2.737 2.552 2.757 2.580 2.499 2.767 2.725 2.787 3.133 2.683
1Ag-Al-2Ag 2Ag-Al-3Ag 3Ag-Al-4Ag 4Ag-Al-1Ag 1Ag-2Ag-3Ag 2Ag-3Ag-4Ag 3Ag-4Ag-1Ag 1Ag-5Ag-2Ag 2Ag-5Ag-3Ag 3Ag-5Ag-4Ag 3Ag-6Ag-4Ag 1Ag-Al-3Ag
68.6 66.6 66.8 66.0 89.3 90.6 90.7 64.0 60.9 60.8 60.0 114.5
Al-1Ag-4Ag-3Ag 4Al-2Ag-3Ag-1Ag 4Ag-1Ag-2Ag-3Ag 6Ag-3Ag-4Ag-5Ag
48.4 48.7 0.0 67.6
1Ag-5Ag-Al-3Ag
141.1
1Ag-Al-6Ag
160.9
2Ag-1Ag-Al-3Ag
0.02
2Ag-Al-6Ag
110.1 (continued on next page)
14
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
Table 2 (continued) Cluster
Ag7Al
a
Structure
Symm
State
7-a
C1
1
A
7-b
C1
1
A
7-c
C1
1
A
7-d
C1
1
A
7-e
C2V
1
A1
7-f
C1
1
A
Bond length
Bond angle
lAg-2Ag 1Ag-3Ag 1Ag-4Ag
2.718 2.704 2.841
Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-7Ag 1Ag-5Ag 1Ag-7Ag 2Ag-5Ag 3Ag-6Ag 4Ag-6Ag Al-1Ag Al-2Ag Al-3Ag Al-5Ag Al-6Ag Al-7Ag 3Ag-4Ag 5Ag-4Ag Al-1Ag Al-2Ag Al-7Ag 2Ag-3Ag 1Ag-3Ag 1Ag-4Ag 1Ag-5Ag 1Ag-6Ag 1Ag-7Ag Al-1Ag Al-6Ag Al-7Ag 1Ag-2Ag 2Ag-3Ag 3Ag-7Ag 3Ag-4Ag 4Ag-5Ag Al-1Ag Al-7Ag 1Ag-2Ag 2Ag-3Ag 3Ag-4Ag Al-1Ag 1Ag-2Ag 1Ag-3Ag 1Ag-4Ag 1Ag-5Ag 1Ag-6Ag 7Ag-2Ag 7Ag-3Ag
2.655 2.655 2.614 2.614 2.544 2.831 2.991 2.832 2.858 2.859 2.645 2.637 2.725 2.725 2.637 3.173 2.769 2.769 3.665 2.516 2.568 2.741 2.729 2.709 2.750 2.726 2.708 2.525 2.526 3.525 2.790 2.752 2.860 2.753 2.753 2.492 3.769 2.738 2.724 2.729 2.511 2.865 2.867 2.867 2.869 2.867 2.844 2.841
Dihedral angle
1Ag-Al-2Ag 1Ag-Al-7Ag 1Ag-5Ag-2Ag 3Ag-6Ag-4Ag
67.1 70.2 62.4 62.9
Al -1Ag-4Ag-3Ag 1Ag-2Ag-3Ag-4Ag 5Ag-1Ag-2Ag-3Ag 7Ag-2Ag-1Ag-Al 3Ag-4Ag-6Ag-5Ag
47.9 0.0 52.6 63.1 68.6
1Ag-Al-2Ag 1Ag-Al-6Ag 3Ag-Al-5Ag 2Ag-Al-3Ag 6Ag-Al-5Ag 2Ag-7Ag-6Ag 3Ag-4Ag-5Ag
65.7 65.7 61.2 64.5 64.5 91.1 60.1
3Ag-Al-2Ag-1Ag 1Ag-Al-6Ag-5Ag 2Ag-3Ag-Al-5Ag 5Ag-4Ag-3Ag-Al
167.1 167.1 133.3 29.0
1Ag-Al-7Ag 3Ag-1Ag-7Ag 4Ag-1Ag-6Ag
144.3 107.9 125.2
1Ag-Al-6Ag 1Ag-Al-7Ag 2Ag-1Ag-7Ag 2Ag-7Ag-3Ag 3Ag-7Ag-4Ag
55.8 111.5 56.8 58.8 57.5
1Ag-7Ag-3Ag-2Ag 3Ag-4Ag-5Ag-7Ag
21.8 13.0
1Ag-Al-7Ag 2Ag-1Ag-7Ag 2Ag-7Ag-3Ag
57.9 54.4 57.4
Al-1Ag-7Ag 2Ag-3Ag-4Ag 4Ag-5Ag-6Ag2Ag-7Ag-3Ag
179.5 108.0 108.0 59.1
2Ag-3Ag-4Ag-5Ag 4Ag-6Ag-5Ag-2Ag 7Ag-4Ag-3Ag-2Ag
0.1 0.0 38.9
Ref. [35].
Fig. 3. Three sp2 orbitals (a) Ag3Al;(b) Ag3Al+.
because of doping Al atom. The trend could be explained as the formation of an inert AgAl molecule unit in the clusters. The unit is known to have relatively high dissociation energy of 2.220 eV [35] as compared to Ag2 (1.660 eV) [33].
(2) The BE of the cationic clusters AgnAl+ (n = 1–7) are lower than the corresponding values of pure clusters Agþ nþ1 . For example, the BE of AgAl+ is 1.059 eV, which is lower than that of Agþ 2 by 1.639 eV, and so on. The BE for the doped clusters AgnAl+ are lower than the corresponding values of pure þ clusters Agþ nþ1 by 0.476–1.949 eV. The pure clusters Agnþ1 is + more stable than the doping clusters AgnAl (n = 1–7). This could be explained that Ag+2 is more stable than AgAl+, and Agþ 2 has relatively high dissociation energy of 1.740 eV [32] as compared to AgAl+ (1.059 eV). There is a single valence electron for Ag atom which occupies atomic orbital 5s. There are two valence electrons for Al+ atom which occupy an atomic orbital 3s. For neutral Ag2, the two 5s atomic orbitals combine to form two molecular orbitals, one bonding (r) and one antibonding (r*). The bonding molecular orbital is of lower energy than the two 5s atomic orbitals, and the two valence electrons go into the bonding
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
molecular orbital to form lowest potential energy for the molecule. If one electron is removed forming the cation Agþ 2 , the bonding molecular orbital has an unpaired electron. For AgAl+, there are three valence electrons. The 5s atomic orbital of Ag atom and the 3s atomic orbital of Al atom also combine to form two molecular orbitals, one bonding (r) and one antibonding (r*). Two electrons occupy the bonding molecular orbital and one valence electron goes into the antibonding molecular orbital. The energy of antibonding molecular orbital is greater than that of the 5s atomic orbital of Ag atom. This is good agreement with the calculated results. Fig. 5 shows that the highest occupied molecular orbital (HOMO) of Agþ 2 is a bonding molecular orbital r, whereas the HOMO of AgAl+ is an antibonding molecular + orbital r*. So Agþ 2 is more stable than AgAl . (3) Both curves of BE for the cationic and neutral clusters doping Al atom show odd–even variations obviously except Ag2Al. For cationic clusters AgnAl+, the curve shows peaks when it has an even number of Ag atoms, but for neutral clusters AgnAl, the peaks appears when it has an odd number of Ag atoms. It indicates that clusters with even-electron are more stable than odd–electron neighbors. This is mainly due to the pairing properties of the molecular orbitals. For odd-electron systems, the HOMO is single occupied and can easily accept or lose electron (as shown in Fig. 5). Furthermore, Ag6Al+ and Ag5Al have the highest BE compared with the corresponding cationic or neutral clusters. It is well known that the stability of pure Agn clusters can be explained by the spherical jellium model (SJM). The SJM predicts that the clusters with 2,8,20,, valence electrons are more stable because of the closing of electronic shells. It is interesting that the stability of Ag6Al+ and Ag5Al can be explained by SJM. Silver has a valence electronic configuration of 5s1 and aluminum has 3s23p1. Ag5Al has the shell closing with 8 valence electrons. For Ag6Al+, Mulliken total atomic charge analysis shows that when Ag6Al is ionized, the Al atom loses about 1 charge, so Ag6Al+ has the shell closing with 8 valence electrons as well. The n = 5 is predicted to be the magic number for AgnAl clusters, and n = 6 is the magic number for AgnAl+ clusters. Even though there is no experiment data for AgnAl clusters, but our calculated result that the n = 6 is the magic number is in good agreement with the mass spectrum of AgnAl+ clusters [17]. The second difference of cluster energy (SDE), defined by 0;þ1
D2 E½Agn Al
ð0;þ1Þ
¼ E½Agnþ1 Al
ð0;þ1Þ
þ E½Agn1 Al
ð0;þ1Þ
2E½Agn Al
;
also indicates the relative stability of the cluster with respect to its neighbors. The calculated values of SDE for both series are presented in Fig. 6. Fig. 6b is also shown the point corresponding to n = 7 for AgnAl. The calculated ground state structure of Ag8Al is dis-
Fig. 4. Binding energy per atom vs. cluster size for the ground state structures.
played in Fig. 2. Higher value of SDE indicates that the geometry of AgnAl(0,+1) is the most stable one compared to its neighbors Agn+1Al(0,+1) and Agn-1Al(0,+1). Cationic AgnAl+ (n = 2, 4, 6) and neutral AgnAl (n = 3, 5, 7) with even numbers of valence electrons have relatively large SDE, and the highest SDE of Ag6Al+ or Ag5Al proves again that n = 6 for AgnAl+ or n = 5 for AgnAl is the magic number. 3.3. HOMO–LUMO gaps It is well known that the energy gap Eg between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) reflects the relative chemical reactivity of clusters. Since the unrestricted B3LYP method was used in this paper, the clusters AgnAl(0,+1) (n = 1–7) have both a-states and b-states. The HOMO, LUMO, and Eg values of the systems studied are tabulated in Table 4. Some interesting features follow from this table: (1) the gaps exhibit significant even–odd oscillation behavior just as that of pure Agn(0,+1) clusters [42]. The higher gaps are exhibited by cationic AgnAl+ clusters with even numbers of Ag atoms and neutral AgnAl clusters with odd numbers of Ag atoms, respectively. This means that these clusters have even numbers of electrons, and they are more stable and have lower chemical reactivities. On the other hand, Ag7Al+ and Ag6Al clusters are less stable and have stronger chemical reactivity due to smaller energy gaps. (2) For odd number of electrons clusters, the gap of the a-states is relativity smaller than that of the b-states, except Ag4Al cluster. 3.4. Adiabatic ionization potentials The variation of adiabatic ionization potentials (AIPs) for the lowest-energy structures with cluster size is plotted in Fig. 7. The
Table 3 Harmonic vibrational frequencies (cm1), and infrared intensities (km/mol) (parentheses) of the ground state structures for AgnAl(0,+1) (n = 1–7). Cations
Frequencies (infrared intensity)
Neutrals
Frequencies (infrared intensity)
AgAl+ Ag2Al+ Ag3Al+ Ag4Al+
188(15.2) 90(1.5),90(1.5),120(0.0),368(7.9) 30(0.3),79(2.3),92(0.0),121(0.1),166(0.7),371(12.6) 32(0.0),44(0.7),44(0.7),86(0.0),98(0.1),114(0.3), 136(0.0), 242 (3.3), 366(1.2) 17(0.0),17(0.0),71(0.0),71(0.0),98(0.0),100(1.3), 100(1.3),113(0.0),113(0.0),202(0.0), 255(0.1), 255(0.1) 31(0.0),31(0.0), 66(0.2),75(0.0),75(0.0), 80(0.0), 85(0.7),85(0.7),101(0.0),125(0.10),125(0.1),131(0.5), 172(0.2),242(0.0),243(0.0) 27(0.0),27(0.0),55(0.4),55(0.4),59(0.3),73(0.1), 74(0.1),76(0.0),91(0.0),91(0.0),93(0.2),118(0.1), 121(0.2),122(0.2),143(0.2),170(0.7),230(0.2), 231(0.2)
AgAl Ag2Al Ag3Al Ag4Al
245(11.3) 55(0.5),180(0.0),309(9.5) 50(0.0),56(0.0),116(0.0),133(0.3),188(0.6), 246.(0.3) 42(0.1),50(0.0),86(0.0),87(0.0),89(0.1),124(0.2), 38(0.1),210(1.4),221(0.4) 39(0.0),39(0.0),64(0.0),72(0.5),75(0.0),92(0.0), 113(0.0),113(0.0),137(0.0), 217(0.8), 217(0.8), 239(0.0) 39(0.1),44(0.1),60(0.0),63(0.2),67(0.6),72(0.1), 82(0.0),85(0.5),94(0.2),110(0.0),133(0.3),141(0.8), 189(0.9),196(0.5),219(2.8) 38(0.0),39(0.0),51(0.0),51(0.1),61(0.0),68(0.5), 74(0.0),79(0.0),82(0.1),87(0.2),94(0.3),104(0.8), 114(0.0),137(0.6),144(1.3),200(1.1),213(0.1), 287(0.2)
Ag5Al+ Ag6Al+
Ag7Al+
15
Ag5Al Ag6Al
Ag7Al
16
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
Ag2+
AgAl+
Ag2Al+
Ag3Al+
Ag4Al+
Ag5Al+
Ag6Al+
Ag7Al+
AgAl
Ag2Al
Ag3Al
Ag4Al
Ag5Al
Ag6Al
Ag7Al
LUMO
HOMO
LUMO
HOMO
Fig. 5. HOMOs and LUMOs of Ag2+, AgnAl and AgnAl clusters.
Fig. 6. Second difference of energy (a) AgnAl+, and (b) AgnAl vs. cluster size for the ground state structures.
Table 4 Calculated HOMO, LUMO energies (in hartrees) and HOMO–LUMO gap (Eg) energies (in eV) of the ground state structures for AgnAl(0,+1) (n = 1–7). Clusters
HOMO (a)
LUMO (a)
Eg (a)
HOMO (b)
HUMO (b)
Eg(b)
AgAl+ Ag2Al+ Ag3Al+ Ag4Al+ Ag5Al+ Ag6Al+ Ag7Al+ AgAl Ag2Al Ag3Al Ag4Al Ag5Al Ag6Al Ag7Al
0.3962 0.3885 0.3405 0.3537 0.3281 0.3527 0.2929 0.1766 0.1673 0.1970 0.1787 0.2001 0.1576 0.1762
0.2767 0.2657 0.2629 0.2541 0.2409 0.2349 0.2291 0.0862 0.0880 0.0868 0.0979 0.0881 0.0966 0.1003
3.2518 3.3394 2.1124 2.7113 2.3726 3.2071 1.7366 2.4602 2.1568 3.0000 2.1990 3.0477 1.6580 2.0678
0.5071 0.3885 0.3840 0.3537 0.3691 0.3527 0.3605 0.1766 0.2037 0.1970 0.1963 0.2001 0.2026 0.1762
0.3284 0.2657 0.2824 0.2541 0.2700 0.2349 0.2457 0.0862 0.1111 0.0868 0.1258 0.0881 0.1101 0.1003
4.8619 3.3394 2.7639 2.7113 2.6964 3.2071 3.1233 2.4602 2.5190 3.0000 1.9198 3.0477 2.5179 2.0678
AIP is defined as the energy difference between the cationic and þ neutral clusters: AIP ¼ Eþ n En , where En is the total energy of the lowest-energy structures of the cationic cluster and En is of neutral one.
Fig. 7. Adiabatic ionization potentials vs. cluster size for the ground state structures of the neutral AgnAl clusters.
The adiabatic ionization potentials show odd–even oscillations, and decrease with increasing of the cluster size. The variation of the AIPs is in the range of 5.165–6.935 eV. It was observed that the AIP of the neutral clusters with odd Ag atoms is the highest one among their neighboring clusters with even Ag atoms. The reason of variation of the calculated IP values with the cluster size is mainly due to the sum of valence electrons of all atoms. The AIPs with even electrons are higher than those with odd electrons, indicating that it is more difficult for even-electron clusters to lose electron than odd–electron neighbors. The AIP of Ag6Al with nine valence electrons is the lowest (5.165 eV). This means that Ag6Al cluster is easily to lose an electron and transform to Ag6Al+ with eight valence electrons. It proves again that Ag6Al+ cluster is more stable. 3.5. Dissociation channels Table 5 lists the lowest dissociation energies of cationic and neutral clusters AgnAl(0,+1) (n = 1–7). The dissociation energy is defined as XY = X + Y. In all cases, the energetically lowest fragmentation channel is monomer Ag ejection for odd-electron clusters and dimmer Ag ejection for even-electron clusters. The result is similar to the theoretical [43] and experimental results [44,45] for pure clusters Agn. A general odd–even behavior in the dissociation ener-
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17 Table 5 Energetically preferred dissociation channels of the ground state structures for AgnAl+ and AgnAl, 1 6 n 6 7. Cations
E (eV)
Neutrals
E (eV)
AgAl+ ? Ag + Al+ Ag2Al+ ? Ag2+Al+ Ag3Al+ ? Ag + Ag2Al+ Ag4Al+ ? Ag2 + Ag2Al+ Ag5Al+ ? Ag + Ag4Al+ Ag6Al+ ? Ag2 + Ag4Al+ Ag7Al+ ? Ag + Ag6Al+
1.059 3.008 1.018 1.615 1.330 2.017 0.917
AgAl ? Ag + Al Ag2Al ? Ag + AgAl Ag3Al ? Ag2 + AgAl Ag4Al ? Ag + Ag3Al Ag5Al ? Ag2 + Ag3Al Ag6Al ? Ag + Ag5Al Ag7Al ? Ag2 + Ag5Al
1.971 1.139 1.577 1.100 1.639 0.895 1.172
gies indicates that even-electron clusters are usually more stable than their odd–electron neighbors. AgAl+ prefers to dissociate to Ag atom and Al+ ion. This proves again it is available that the BE for AgnAl+ is defined as Eb = (nE[Ag]+E[Al+] E[AgnAl+])/(n + 1). Additionally, we found that Ag7Al+ prefers to dissociate to Ag atom and Ag6Al+ cluster. And Ag6Al prefers to dissociate to Ag atom and Ag5Al. The dissociation energies for Ag6Al+ and Ag5Al are the largest of all cationic and neutral clusters, which are 2.017 and 1.639 eV, respectively. Ag7Al+ and Ag6Al have the lowest dissociation energies, which is 0.917 and 0.895 eV, respectively. These results suggest that Ag6Al+ and Ag5Al clusters are more stable which is consistent with the fact that Ag6Al+ and Ag5Al have larger calculated binding energies and the second difference of energies. It also consist with our conclusion that n = 6 and 5 are magic numbers for cationic clusters and neutral clusters, respectively. 4. Conclusion The equilibrium structures and electronic properties of AgnAl(0,+1) (n = 1–7) clusters have been studied using a density-functional method (B3LYP) with the relativistic PPs and corresponding basis sets. The ground state structures and their isomers are first predicted. The results show that binding energies (BE), second differences (SDE), HOMO–HUMO gaps, adiabatic ionization potentials (AIPs) of the ground state structures of AgnAl(0,+1) (n = 1–7) clusters show remarkable odd–even alternation behaviors, which reveal that even-electron clusters are more stable than odd-electron clusters. Moreover, the satiability of AgnAl (n = 1–7) are enhanced by doping the Al atom. Odd-electron clusters prefer to eject monomer Ag and even-electron clusters prefer to eject dimmer Ag. The n = 6 is the magic number of AgnAl+ (n = 1–7) and more stable. The n = 5 is predicted as the magic number of AgnAl (n = 1–7) and more stable. Acknowledgment The authors acknowledge to the support by Heilongjiang Education Department Foundation of China (Grant No. 11533046). References [1] M. Valden, X. Lai, D.W. Goodman, Science 281 (1998) 1647–1650. [2] M.B. Kinickelbein, Annu. Rev. Phys. Chem. 50 (1999) 79–115.
17
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Journal of Molecular Structure: THEOCHEM journal homepage: www.elsevier.com/locate/theochem
Density-functional theory study of structural and electronic properties of AgnAl(0,+1) (n = 1–7) clusters FengLi Liu a,b, Gang Jiang a,* a b
Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China College of Physical Science and Technology, Heilongjiang University, Harbin 150080, China
a r t i c l e
i n f o
Article history: Received 26 August 2009 Received in revised form 13 April 2010 Accepted 13 April 2010 Available online 22 April 2010 Keywords: Coinage-metal aluminum compound Density-functional theory Ground state structure Magic number Binding energy
a b s t r a c t Equilibrium geometric structures of coinage-metal aluminum compounds AgnAl(0,+1) (n = 1–7) are first predicted by density-functional theory calculations with relativistic pseudopotentials. The stability of the ground state structures of these clusters is examined via the analysis of the binding energies (BE) and second difference energy. In addition, adiabatic ionization potential (AIP), energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital, possible dissociation channels are also presented and discussed. Remarkable odd–even alternation behaviors have been observed. The results show that n = 6 is the magic number for AgnAl+, and n = 5 is predicted as the magic number for AgnAl. Moreover, for neutral clusters, doping clusters are more stable than the corresponding pure clusters. Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction Coinage-metal (Cu, Ag and Au) clusters have attracted researchers due to their importance in basic research, as well as technological applications such as catalysis [1–5], photography [6–10], and nanoelectronics [11]. The impurity-doped coinage-metal clusters often represent more especial properties than the non-doped pure noble metals [12–16]. At the end of 20th century, some experiments have been reported on the properties of coinage metal clusters doped with group 13 atoms [17–19]. For example, Yamada et al. [17] produced metal alloy clusters including CunAlm, CunInm, AgnAlm and AgnInm by a gas aggregation source and investigated by time-of-flight mass spectrometry in 1992, they found these cluster ions have magic numbers which correspond to jellium shell closings. Heinebrodt and Bouwen et al. [18,19] produced the neutral and cationic clusters of AunXm(0,+1) (X = Al, In) in 1999 and their results show that the patterns are related to the magic numbers of the electronic shell model. Recently, Kumar [20,21] studied formation of aqueous Tl/Ag and Tl/Cu bimetallic clusters by gamma and electron irradiation. However, only a few theoretical studies of structures and electronic properties for coinage metal clusters doped with group 13 atoms are reported. Urban et al. [22] studied the binding of aluminum to coinage metals at the CCSD(T) theoretical level and indicated that the electron correlation and relativistic effects play an important role in the structure, stability and so on. * Corresponding author. E-mail address: [email protected] (G. Jiang). 0166-1280/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2010.04.016
Tunna Baruah et al. [23] obtained the candidate structures for the ground-state geometries of Al12M and Al13M (M = Cu, Ag and Au) and they found that the atomization energies of them are substantially larger than pure Al clusters. Wang Hong-Yan et al. [24] calculated electronic and structural properties of mixed AunXm (n + m = 4, X = Cu, Al, Y) at the B3LYP hybrid level. To our knowledge, no theoretical work for AgnAl(0,+1) (n = 1–7) clusters have been found. Based on our previous works [25,26], we investigate the geometrical structures and stabilities of the neutral and cationic AgnAl(0,+1) (n = 1–7) systematically using quantum-mechanical calculations. Binding energies, second difference energies, adiabatic ionization potentials (AIPs) and energy gaps between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the ground state structures have been evaluated. The dissociation channels and the corresponding dissociation energies are also given. 2. Computational methods The density-functional theory (DFT) methods have been widely used to study structures of metal clusters as it predicts the VDE’s of coinage clusters quilt well [27]. Therefore, the geometry optimization and electronic structure calculation were carried out using the DFT with unrestricted B3LYP exchange–correlation potential [28,29] in this paper. The Ag atom was treated with 19-valence electron relativistic pseudopotentials (PPs) and the matched basis sets (8s7p6d)/[6s5p3d] given by Andrae et al. [30]. Pyykkö et al.
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F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
[31] pointed out that the diffuse f function is required for describing metallophilic attraction. So the f-type diffuse functions, which af = 0.22, was added to yield an overall basis set of (8s7p6d1f)/ [6s5p3d1f]. The Al atom was described with 6-311G* basis set. In order to examine the feasibility of the PPs and basis set for investigating this type of cluster, we first performed calculation on Ag+2 and Ag2. The results show that Ag–Ag bond lengths (2.590 Å), vibrational frequencies (178 cm1 for Ag2, 124 cm1 for Ag+2), and dissociation energies (1.53 eV for Ag2, 1.64 eV for Ag+2) are in good agreement with the corresponding experimental values (2.530 Å; 192 cm1 for Ag2 and 136 cm1 for Ag+2; 1.66 eV for Ag2 and 1.74 eV for Ag+2) [32,22]. This means that our PPs and basis sets used in this study are reasonable. The stabilities and geometries of the AgnAl(0,+1) (n = 1–7) cluster are reassured accurately by calculating on all possible structures, and the stable isomers are determined by vibrational analysis in the absence of negative frequencies. All calculations are performed using the GAUSSIAN 03 program package [34].
3. Results and discussion 3.1. Structures, energies and frequencies of AgnAl(0,+1) (n = 1–7) The spin multiplicities are 2S + 1 = 1 and 2S + 1 = 2 for even and odd number electron clusters, respectively. The systems with spin multiplicities of 3 and 4 are also calculated. The results show that the total energies of 3 and 4 are higher than of 1 and 2. Therefore, only the systems with spin multiplicities of 1 and 2 are considered in this paper. Fig. 1 shows the lowest-energy structures and low-lying isomers of the cationic clusters AgnAl+, while Fig. 2 displays those of neutral clusters AgnAl. The relative energies of the geometric structures are also given in Figs. 1 and 2. The nomenclature of isomers of each cluster is according to the relative energies. Since the values of relative energies are shown the order of stability thermodynamically, so the stability orders of each cluster are depicted by the order of letter, a > b > c > . The corresponding geometrical parameters and the symmetries of AgnAl+ and AgnAl are listed in Tables 1 and 2, respectively. The AgAl+ molecule has a bond length of 2.595 Å, while that of AgAl is 2.527 Å which is in accordance with the data of 2.474 ± 0.005 Å [35] experimentally. The Pauling’s electronegativity values for both Ag and Al are comparable. Mulliken total atomic charge analysis gives Al(0.2202)Ag(0.2202) for AgAl and Al(0.6468)Ag (0.3532) for AgAl+. This means that when an electron is removed from AgAl forming the cation AgAl+, the Al atom loses 0.4266 charges, and the Ag atom loses 0.5734 charges. The lowest-energy structure of Ag2Al+ cluster is linear with D1h 1P ( g) symmetry, while the low-lying isomer is a bent structure with Cs (1A’) symmetry (Fig. 1.2-a and b). The energy difference between the lowest-energy structure and the low-lying isomer is 0.607 eV. In the case of Ag2Al, both the lowest-energy structure (Fig. 2.2-a) and the low-lying isomer (Fig. 2.2-b) are all isosceles triangle with C2V (2A1) symmetry and C2V (2B2) symmetry, respectively. The energy difference of two Ag2Al isomers is 0.027 eV. The lowest-energy structures 2-a (both in Figs. 1 and 2) are predicted as the ground state structures of Ag2Al+ and Ag2Al, respectively. The structural changes in the ground state configuration of the ionized cluster relative to that of the neutral cluster are due to electronic reorganization during the ionizing process of the AgnAl clusters. Mulliken total atomic charge analysis gives Al(1.1168)Ag(0.0584) for the ground state structure of Ag2Al+, and Al(0.4749)Ag (0.2374) for Ag2Al. The Al atom loses 0.6419 charges, and an Ag atom loses 0.1791 charges for Ag2Al.
The lowest-energy structure of Ag3Al+ is Y shaped with the Al atom in the center (Fig. 1.3-a). The low-lying isomer (Fig. 1.3-b) is a planar rhombus, and the energy difference is 0.250 eV. The two isomers have same symmetry C2V (2B2). Contrarily, the lowest-energy structure of Ag3Al cluster (Fig. 2.3-a) is a planar rhombus with C2V (1A1) symmetry, while the low-lying isomer (Fig. 2.3-b) is Y shaped with D3h (1A0 1) symmetry. The energy difference of them is 0.165 eV. The lowest-energy structures 3-a (both in Figs. 1 and 2) are predicted as the ground state structures of Ag3Al+ and Ag3Al, respectively. Mulliken total atomic charge analysis gives Al(1.2674) 1Ag(0.0694)2Ag(0.0694)3Ag(0.1287) for the ground state structure of Ag3Al+, and Al(0.6496) 1Ag(0.3714)2Ag (0.0933)3Ag(0.3714) for Ag3Al. The Al atom loses 0.6179 charges for Ag3Al. Interestingly, the symmetry of the lowest-energy structure of Ag3Al+ is C2V rather than D3h (Fig. 1.3a), and Mulliken charges found in case of Ag3Al+ for Ag1 and Ag3 are different. This is mainly because for the ground state structure of neutron Ag3Al cluster Al atom will sp2 hybridise. There is a single valence electron for Ag atom which occupies an atomic orbital 5s. There are three valence electrons for Al atom which occupy atomic orbitals 3s23p1. For the Al atom, the 2s orbital ‘‘mixes” with the two available 2p orbitals to form three sp2 orbitals. The Al atom forms three r bonding orbital with Ag atoms by s–sp2 overlap all with 120° angles. Each bonding orbital has two electrons called r2 orbital as shown in Fig. 3a. When Ag3Al is ionized forming the cation Ag3Al+ one electron is removed from the one of three r2 orbitals, and this orbital has one electron named r1 orbital as shown in Fig. 3b. For this reason the symmetry of the cluster structure is reduced, and Mulliken charges in case of Ag3Al+ for Ag1 and Ag3 are different. Three stable configurations of Ag4Al+ have been found by geometry optimization. The lowest-energy structure of Ag4Al+ (Fig. 1.4-a) is a planar trapezoidal structure with C2V (1A1) symmetry. A planar and a three dimensional geometries (Fig. 1.4-b and c) are found for low-lying isomers, lying 0.192 and 0.476 eV above the lowest-energy structure. The lowest-energy structure for Ag4Al cluster is given in Fig. 2.4-a, which symmetry is C2V (2B1). A planar and two threedimensional low-lying isomers (Fig. 2.4-b–d) are found, lying 0.086, 0.149 and 0.220 eV above the lowest-energy structure. For both Ag4Al+ and Ag4Al clusters, the structures 4-a (both in Figs. 1 and 2) are predicted as the ground state structures. Mulliken total atomic charge analysis gives Al(1.4157)1Ag(0.1782)2Ag (0.0296)3Ag(0.0296)4Ag(-0.1782) for the ground state structure of Ag4Al+, and Al(0.6940)1Ag(0.2536)2Ag(0.0934)3Ag (0.2536) 4Ag(0.0934) for the ground state structure of Ag4Al, and the Al atom loses 0.7216 charges. The lowest-energy structure of Ag5Al+ (Fig. 1.5-a) is pyramidal with C5V (2A1) symmetry. The two other planar geometries (Fig. 1.5-b and c) are found to be low-lying isomers with energy differences being 0.346 and 0.635 eV, respectively. The lowest-energy structure of Ag5Al (Fig. 25-a) is a square bipyramid structure with C4V (1A1) symmetry. Three planar geometries (Fig. 2.5-b–d) are found to be the low-lying isomers with energy differences being 0.511, 1.200 and 1.246 eV, respectively. The structures 5-a (both in Figs. 1 and 2) are predicted as the ground state structures. Mulliken total atomic charge analysis gives Al(2.0105)Ag(0.2021) for the ground state structure of Ag5Al+, and Al(1.2501)1Ag(0.3600) 2Ag(-0.3600)3Ag (0.3600)4Ag(0.3600) 5Ag(0.1899) for the ground state structure of Ag5Al. The Al atom of Ag5Al loses 0.7603 charges. For Ag6Al+ cluster, the lowest-energy structure has C1 (1A) symmetry which slightly distorted C3V symmetry (Fig. 1.6-a), which is predicted the ground state structure. Two low-energy structural isomers are found. One is pentagonal bipyramid with C5V (1A1) symmetry and the Al atom being at the apex of Ag atoms (Fig. 1.6-b). The other isomer is a distorted planar pentagonal with C1(1A) symmetry (Fig. 1.6-c). Their energies are higher than that of the lowest-energy
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
9
Fig. 1. Geometries and relative energies (DE) of AgnAl+ clusters. The shaded sphere represents the Ag atom. Structures are ordered in energy from the letter a–h, with the lowest-energy structure shown the letter a. The values of the geometric parameters are reported in Table 1.
structure by 0.064 and 0.669 eV, respectively. For Ag6Al cluster, interestingly, the lowest-energy structure has C1 (2A) symmetry and can be viewed as capping one Ag atom on the lowest-energy structure of Ag5Al (Fig. 2.6-a). This structure is predicted the ground state structure. There are three low-energy structural isomers (Fig. 2.6-b–d) and their energies are higher than the lowest-energy one by 0.043, 0.354 and 0.486 eV, respectively. For the ground state structure of Ag6Al+, Mulliken total atomic charge analysis gives Al (2.0570)1Ag(0.2905)2Ag(0.2994)3Ag(0.2842)4Ag(0.074 94) 5Ag(0.0878)6Ag(0.0200), and for Ag6Al Mulliken total atomic charge analysis gives Al (1.0336)1Ag(0.3155)2Ag(0.3158)3Ag (0.2837)4Ag(0.28 48)5Ag(0.2358)6Ag(0.0695). The Al atom of Ag6Al loses 1.0234 charges.
Eight isomers are obtained for Ag7Al+ cluster (Fig. 1.7). The lowest-energy structure (Fig. 1.7-a) can be viewed as the additional Ag atom capping on the bottom of the lowest-energy structure for Ag6Al+ (Fig. 1.6-a), and is predicted as the ground state structure. The lowest-energy structure of Ag7Al cluster (Fig. 2.7-a) can be viewed as adding one Ag atom to the ground state structure of Ag6Al (Fig. 2.6-a), and is predicted as the ground state structure. There are six low-energy structural isomers for Ag7Al cluster. For the ground state structure of Ag7Al+, Mulliken total atomic charge analysis gives Al(1.9974)1Ag(0.3058)2Ag(0.3019)3Ag (0.2994)4Ag(0.0646) 5Ag(0.0656)6Ag(0.0617)7Ag(0.1017). For the ground state structure of Ag7Al, Mulliken total atomic charge analysis gives Al(1.4893)1Ag(0.2393)2Ag(0.2416)3Ag(0.3474)4Ag(0.3488)5
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F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
Fig. 2. Geometries and relative energies (DE) of AgnAl (n = 1–7) clusters the ground state geometry of Ag8Al. The shaded sphere represents the Ag atom. Structures are ordered in energy from the letter a–f, with the lowest-energy structure shown the letter a. The values of the geometric parameters are reported in Table 2. The ground state geometry of Ag8Al is shown in it.
Ag(0.1039)6Ag(0.0320)7Ag(0.3841). The Al atom of Ag7Al loses 0.5081 charges. According to the optimized equilibrium geometries of the Ag(0,+1) clusters, the growth pattern of the AgnAl(0,+1) clusters is nAl investigated. Theoretical results indicate that, for AgnAl+ clusters, the geometries of AgAl+, Ag2Al+, Ag3Al+ and Ag4Al+ clusters take planar shapes of linear, Y shaped and trapezoid. While the ground state clusters take three-dimensional structures when the size of AgnAl+ is bigger than 4. The doping atom Al prefers to bind more Ag atoms for n 6 5and at apex for n = 6, 7. For AgnAl clusters, the geometries of Ag–Al, Ag2Al, Ag3Al clusters are take planar shapes of linear, isosceles triangle, and rhombus. While the ground state clusters take three-dimensional structures when the size of AgnAl is bigger than 3. Many theoretical studies show that the ground state clusters of Agn take three-dimensional structures when the
size of Agn is bigger than 6 [36–42]. It is found that the Al atom occupies a peripheral position for AgnAl (n = 1–7) clusters. To aid future identification of the AgnAl(0,+1) clusters in the laboratory, the calculated vibrational frequencies and infrared intensities for the ground state structures of AgnAl(0,+1) are presented in Table 3. We can see that the dominant frequencies of AgnAl+ are 188, 368, 371, 242, 100, 85 and 170 cm1, respectively, with the corresponding infrared intensities 15.2, 7.9, 12.6, 3.3, 1.3, 0.7 and 0.7 km/mol. The dominant frequencies of AgnAl are 245, 309, 188, 210, 217, 219 and 144 cm1, respectively, with the corresponding infrared intensities 11.3, 9.5, 0.6, 1.4, 0.8, 2.8 and 1.3 km/mol. The frequency ranges and intensities of the ground state structures of AgnAl(0,+1) suggest that the IR species of these structures could be unambiguously differentiated experimentally. The infrared intensities of some vibrational frequencies are very small or close to zero.
11
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17 Table 1 Geometrical parameters (bond length in Å, bond angle and dihedral angle in deg) of the structures for AgnAl+(n = 1–7). Cluster AgAl
+
Ag2Al+
Ag3Al+
Ag4Al+
Ag5Al+
Ag6Al+
Ag7Al+
Structure
Symm
1-a
C1V
2-a
D1h
State 2P 1P g
2-b
Cs
1
3-a
C2V
2
3-b
C2V
2
4-a
C2V
1
4-b
Cs
1
4-c
C1
1
5-a
C5V
2
5-b
Cs
2
5-c
C2V
2
6-a
C1
1
6-b
C5V
1
6-c
C1
1
7-a
C1
2
7-b
C1
2
A
0
B2 B2 A1 A
0
A
A1 A
0
A1
A
A1
A
A
A
Bond length
Bond angle
Dihedral angle
Al-1Ag
2.595
Al-1Ag lAg-2Ag Al-1Ag lAg-2Ag
2.449 4.514 2.694 2.623
1Ag-Al-2Ag
180.0
2Ag-1Ag-Al
92.7
Al-1Ag lAg-3Ag Al-1Ag lAg-2Ag
2.528 2.442 2.619 2.731
1Ag-Al-3Ag
145.3
1Ag-Al-3Ag
68.9
Al-1Ag Al-2Ag Al-1Ag Al-3Ag Al-4Ag lAg-2Ag 2Ag-3Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag lAg-2Ag 2Ag-3Ag 3Ag-4Ag 4Ag-1Ag
2.462 2.596 2.517 2.739 2.599 2.745 2.709 2.590 3.260 2.590 3.264 2.901 2.900 2.902 2.902
1Ag-Al-4Ag 2Ag-Al-3Ag 1Ag-Al-3Ag 3Ag-Al-4Ag
148.9 63.4 70.2 61.1
1Ag-Al-2Ag 2Ag-Al-3Ag 3Ag-Al-4Ag 4Ag-Al-1Ag
58.1 58.1 58.1 58.1
1Ag-Al-2Ag-4Ag
73.9
Al-1Ag 1Ag-2Ag Al-1Ag Al-3Ag Al-4Ag Al-5Ag 1Ag-2Ag 2Ag-3Ag Al-1Ag 1Ag-2Ag lAg-3Ag
2.619 2.815 2.517 2.752 2.653 2.533 2.781 2.783 2.526 2.686 2.759
1Ag-Al-2Ag
65.0
Al-3Ag-2Ag-1Ag
28.7
1Ag-Al-5Ag 1Ag-2Ag-3Ag 3Ag-Al-4Ag 4Ag-Al-5Ag
166.4 61.9 60.7 67.3
Al-1Ag-2Ag 1Ag-2Ag-3Ag
86.6 62.2
Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-1Ag 4Ag-5Ag 5Ag-6Ag 4Ag-6Ag Al-1Ag lAg-2Ag lAg-6Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag 3Ag-5Ag 3Ag-6Ag
2.596 2.595 2.597 2.913 2.913 2.912 4.359 4.359 4.359 2.836 2.832 2.833 2.780 2.792 2.868 2.451 2.607 2.6271 2.603 2.775 2.723
1Ag-Al-2Ag 2Ag-Al-3Ag 1Ag-Al-3Ag 1Ag-2Ag-3Ag 2Ag-3Ag-1Ag 4Ag-5Ag-6Ag 5Ag-6Ag-4Ag
114.2 114.2 114.2 60.0 60.0 60.0 60.1
Al-2Ag-1Ag-3Ag 5Ag-4Ag-3Ag-6Ag
26.9 40.4
1Ag-Al-2Ag 1Ag-6Ag-2Ag
60.3 58.2
2Ag-1Ag-Al-3Ag 1Ag-2Ag-6Ag-3Ag
138.6 135.7
1Ag-Al-2Ag 2Ag-Al-3Ag 3Ag-Al-4Ag 5Ag-3Ag-6Ag
119.1 64.3 62.7 58.8
Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-1Ag 4Ag-5Ag 5Ag-6Ag 4Ag-6Ag 4Ag-7Ag 5Ag-7Ag Al-1Ag
2.608 2.608 2.609 2.982 2.980 2.981 4.350 4.349 4.351 2.842 2.842 2.842 2.860 2.861 2.594
1Ag-Al-2Ag 2Ag-Al-3Ag 1Ag-Al-3Ag 1Ag-2Ag-3Ag 2Ag-3Ag-1Ag 4Ag-5Ag-6Ag 5Ag-6Ag-4Ag 4Ag-7Ag-5Ag
113.0 113.0 113.0 60.0 60.0 60.0 60.0 60.0
Al-2Ag-1Ag-3Ag 5Ag-4Ag-3Ag-6Ag 3Ag-4Ag-5Ag-7Ag
29.3 40.7 155.8
1Ag-Al-2Ag
102.1
1Ag-2Ag-Al-3Ag
150.0
(continued on next page)
12
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
Table 1 (continued) Cluster
Structure
Symm
State
7-c
C1
2
7-d
C1
1
7-e
C5V
2
7-f
C1
2
7-g
C1
2
7-h
C1
2
A
A
A1
A
A
A
Bond length Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag 1Ag-7Ag 2Ag-7Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-1Ag 4Ag-5Ag 5Ag-6Ag 4Ag-6Ag 2Ag-7Ag 3Ag-7Ag Al-1Ag Al-2Ag Al-3Ag Al-5Ag Al-6Ag Al-7Ag 3Ag-4Ag 5Ag-4Ag Al-1Ag lAg-2Ag lAg-6Ag Al-7Ag Al-1Ag Al-5Ag Al-6Ag Al-7Ag 1Ag-6Ag 2Ag-6Ag 3Ag-6Ag 4Ag-6Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag 1Ag-6Ag 1Ag-7Ag 1Ag-2Ag 1Ag-Ag 1Ag-4Ag 1Ag-5Ag 1Ag-6Ag 2Ag-7Ag 6Ag-7Ag Al-7Ag
This indicates these frequencies may be masked by background noise and difficult to be observed in experiments. 3.2. Stabilities Based on the binding energy per atom (BE) and the second difference of energy D2 E in their lowest-energy states, we have examined the stability of the neutral and cationic AgnAl(0,+1) (n = 1–7) clusters. Mulliken total atomic charge analysis for AgnAl+ shows that Al atom loses charges and becomes cationic Al+, so the BE for AgnAl+ is defined as Eb = (nE[Ag]+E[Al+] E[AgnAl+])/(n + 1). The BE for AgnAl is defined as Eb = (nE[Ag]+E[Al] E[AgnAl])/ (n + 1). The BE is presented in Fig. 4 as a function of cluster size. The ground structures of Ag+n+1 (n = 1–7) and Agn+1 (n = 1–7) are optimized by HuaLei Zhang and co-workers [42]. In order to detect
Bond angle 2.594 2.611 2.650 2.805 2.805 2.863 2.863 2.648 2.608 2.608 3.180 2.797 2.798 4.580 3.990 4.580 2.827 2.859 2.827 2.879 2.879 2.803 2.728 2.814 2.814 2.728 3.046 2.785 2.785 2.778 2.763 2.905 2.515 2.594 2.640 2.767 2.498 2.710 2.794 2.794 2.712 2.610 2.591 2.653 2.519 2.617 2.763 2.742 2.759 2.780 2.701 2.780 2.759 2.802 2.802 2.616
Dihedral angle
2Ag-Al-3Ag 3Ag-Al-1Ag 4Ag-Al-5Ag 5Ag-Al-6Ag 6Ag-Al-4Ag 1Ag-7Ag-2Ag
125.0 125.0 62.6 60.5 62.6 89.6
5Ag-4Ag-Al-6Ag 1Ag-Al-2Ag-7Ag
69.1 38.2
1Ag-Al-2Ag 2Ag-Al-3Ag 1Ag-Al-3Ag 1Ag-2Ag-3Ag 2Ag-3Ag-1Ag 4Ag-5Ag-6Ag 5Ag-6Ag-4Ag 2Ag-7Ag-3Ag
121.2 99.8 121.2 64.2 64.2 59.6 59.6 87.7
Al-2Ag-1Ag-3Ag 5Ag-4Ag-3Ag-6Ag 3Ag-2Ag-4Ag-7Ag
29.7 45.8 57.3
1Ag-Al-2Ag 1Ag-Al-6Ag 3Ag-Al-5Ag 2Ag-Al-3Ag 6Ag-Al-5Ag 2Ag-7Ag-6Ag 3Ag-4Ag-5Ag
61.5 61.5 59.1 60.6 60.6 103.8 59.8
3Ag-Al-2Ag-1Ag 1Ag-Al-6Ag-5Ag 2Ag-3Ag-Al-5Ag 5Ag-4Ag-3Ag-Al
140.0 140.0 139.4 33.0
1Ag-Al-2Ag 1Ag-6Ag-2Ag
59.6 56.8
2Ag-1Ag-Al-3Ag 1Ag-2Ag-6Ag-3Ag
37.5 133.7
1Ag-Al-6Ag 1Ag-6Ag-2Ag 2Ag-6Ag-3Ag 3Ag-6Ag-4Ag 4Ag-6Ag-5Ag
60.6 62.9 60.0 62.4 61.2
1Ag-Al-2Ag 2Ag-Al-3Ag 3Ag-Al-4Ag 4Ag-Al-5Ag 5Ag-Al-1Ag 6Ag-1Ag-7Ag
65.6 64.4 65.5 104.8 65.6 59.5
1Ag-2Ag-Al-3Ag 3Ag-4Ag-Al-5Ag 1Ag-2Ag-Al-3Ag 2Ag-1Ag-7Ag-6Ag
168.7 146.2 25.6 152.2
2Ag-1Ag-3Ag 3Ag-1Ag-4Ag 4Ag-1Ag-5Ag 5Ag-1Ag-7Ag 2Ag-1Ag-6Ag 2Ag-7Ag-6Ag 2Ag-7Ag-Al
61.2 62.7 62.7 61.2 63.2 62.1 146.8
1Ag-2Ag-3Ag-4Ag 1Ag-4Ag-5Ag-6A 6Ag-1Ag-2Ag-7Ag Al-7Ag-6Ag-2Ag
46.1 47.2 37.9 157.5
especial properties of doped cluster AgnAl(0,+1) (n = 1–7), we also calculated the BE of Agn+1(0,+1) (n = 1–7), using the optimized ground structures by HuaLei Zhang and co-workers [42], as shown in Fig. 4. In light of the stability of the present series, the HOMOs and LUMOs of AgnAl+ and AgnAl are displayed in Fig. 5. Observing Fig. 4, following trends can be gotten: (1) The BE of neutral clusters AgnAl (n = 1–7) are higher than the corresponding values of pure clusters Agþ1 (n = 1–7). n For example, the BE of the neutral AgAl is 1.971 eV, which is in good agreement with the experimental data [36], and larger than that of Ag2 by 0.437 eV, and so on. The BE for the doped clusters AgnAl are larger than the corresponding values of pure neutral clusters Agþ1 by 0.080–0.310 eV. It n is evident that the stability of neutral clusters is enhanced
13
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17 Table 2 Geometrical parameters (bond length in Å, bond angle and dihedral angle in deg) of the structures for AgnAl(n = 1–7). Cluster
Structure
Symm
State 1P
AgAl
1-a
C1V
Ag2Al
2-a
C2V
2
A1
2-b
C2V
2
B2
3-a
C2V
1
A1
3-b
D3h
1
A‘1
4-a
C2V
2
B1
4-b
Cs
2
A‘‘
4-c
C4V
2
A1
4-d
Cs
2
A‘
5-a
C4V
1
A1
5-b
Cs
1
A‘
5-c
C2V
1
A1
5-d
C2V
1
A1
6-a
C1
2
A
6-b
C1
2
A
6-c
C1
2
A
6-d
C2V
2
B2
Ag3Al
Ag4Al
Ag5Al
Ag6Al
Bond length
Bond angle
Dihedral angle
Al-1Ag
2.527 2.474a
Al-1Ag lAg-2Ag Al-1Ag lAg-2Ag
2.496 4.514 2.642 2.6543
1Ag-Al-2Ag
129.4
1Ag-Al-2Ag
60.3
Al-1Ag lAg-2Ag Al-1Ag
2.622 2.757 2.474
1Ag-Al-3Ag
116.5
1Ag-Al-2Ag
120.0
Al-1Ag Al-2Ag lAg-2Ag 2Ag-4Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-1Ag lAg-4Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag lAg-2Ag
2.622 2.868 2.805 2.816 2.655 2.584 3.033 2.655 2.526 2.946 2.575 4.853 3.029 2.583 2.797
1Ag-Al-3Ag
113.0
1Ag-3Ag-Al-2Ag
34.0
1Ag-Al-2Ag
107.0
Al-1Ag-2Ag-3Ag Al-1Ag-3Ag-4Ag
128.9 65.4
1Ag-Al-3Ag
111.1
1Ag-Al-2Ag-3Ag
121.0
1Ag-Al-3Ag Al-1Ag-2Ag
115.5 129.2
Al-1Ag Al-5Ag lAg-2Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag lAg-2Ag lAg-3Ag Al-1Ag 1Ag-2Ag lAg-3Ag Al-1Ag lAg-2Ag lAg-3Ag 2Ag-3Ag
2.601 3.428 2.953 2.549 4.716 2.858 2.585 2.520 2.732 2.757 2.581 2.648 2.832 2.866 2.760 2.886 2.723
1Ag-Al-3Ag
106.8
Al-1Ag-4Ag-3Ag
46.4
1Ag-Al-4Ag
120.7
Al-1Ag-2Ag 2Ag-1Ag-3 g
87.9 63.4
1Ag-Al-5Ag
55.1
Al-1Ag Al-2Ag Al-3Ag Al-4Ag 1Ag-5Ag 2Ag-5Ag 3Ag-5Ag 2Ag-5Ag 3Ag-6Ag 4Ag-6Ag 5Ag-6Ag Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-4Ag 4Ag-5Ag 5Ag-6Ag Al-1Ag Al-4Ag Al-5Ag Al-6Ag lAg-2Ag 2Ag-3Ag 3Ag-4Ag Al-1Ag Al-2Ag
2.640 2.640 2.640 2.641 2.805 2.804 2.873 2.874 2.908 2.906 2.779 2.660 2.680 2.778 2.660 2.778 2.680 2.867 2.737 2.833 4.575 2.737 2.552 2.757 2.580 2.499 2.767 2.725 2.787 3.133 2.683
1Ag-Al-2Ag 2Ag-Al-3Ag 3Ag-Al-4Ag 4Ag-Al-1Ag 1Ag-2Ag-3Ag 2Ag-3Ag-4Ag 3Ag-4Ag-1Ag 1Ag-5Ag-2Ag 2Ag-5Ag-3Ag 3Ag-5Ag-4Ag 3Ag-6Ag-4Ag 1Ag-Al-3Ag
68.6 66.6 66.8 66.0 89.3 90.6 90.7 64.0 60.9 60.8 60.0 114.5
Al-1Ag-4Ag-3Ag 4Al-2Ag-3Ag-1Ag 4Ag-1Ag-2Ag-3Ag 6Ag-3Ag-4Ag-5Ag
48.4 48.7 0.0 67.6
1Ag-5Ag-Al-3Ag
141.1
1Ag-Al-6Ag
160.9
2Ag-1Ag-Al-3Ag
0.02
2Ag-Al-6Ag
110.1 (continued on next page)
14
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
Table 2 (continued) Cluster
Ag7Al
a
Structure
Symm
State
7-a
C1
1
A
7-b
C1
1
A
7-c
C1
1
A
7-d
C1
1
A
7-e
C2V
1
A1
7-f
C1
1
A
Bond length
Bond angle
lAg-2Ag 1Ag-3Ag 1Ag-4Ag
2.718 2.704 2.841
Al-1Ag Al-2Ag Al-3Ag Al-4Ag Al-7Ag 1Ag-5Ag 1Ag-7Ag 2Ag-5Ag 3Ag-6Ag 4Ag-6Ag Al-1Ag Al-2Ag Al-3Ag Al-5Ag Al-6Ag Al-7Ag 3Ag-4Ag 5Ag-4Ag Al-1Ag Al-2Ag Al-7Ag 2Ag-3Ag 1Ag-3Ag 1Ag-4Ag 1Ag-5Ag 1Ag-6Ag 1Ag-7Ag Al-1Ag Al-6Ag Al-7Ag 1Ag-2Ag 2Ag-3Ag 3Ag-7Ag 3Ag-4Ag 4Ag-5Ag Al-1Ag Al-7Ag 1Ag-2Ag 2Ag-3Ag 3Ag-4Ag Al-1Ag 1Ag-2Ag 1Ag-3Ag 1Ag-4Ag 1Ag-5Ag 1Ag-6Ag 7Ag-2Ag 7Ag-3Ag
2.655 2.655 2.614 2.614 2.544 2.831 2.991 2.832 2.858 2.859 2.645 2.637 2.725 2.725 2.637 3.173 2.769 2.769 3.665 2.516 2.568 2.741 2.729 2.709 2.750 2.726 2.708 2.525 2.526 3.525 2.790 2.752 2.860 2.753 2.753 2.492 3.769 2.738 2.724 2.729 2.511 2.865 2.867 2.867 2.869 2.867 2.844 2.841
Dihedral angle
1Ag-Al-2Ag 1Ag-Al-7Ag 1Ag-5Ag-2Ag 3Ag-6Ag-4Ag
67.1 70.2 62.4 62.9
Al -1Ag-4Ag-3Ag 1Ag-2Ag-3Ag-4Ag 5Ag-1Ag-2Ag-3Ag 7Ag-2Ag-1Ag-Al 3Ag-4Ag-6Ag-5Ag
47.9 0.0 52.6 63.1 68.6
1Ag-Al-2Ag 1Ag-Al-6Ag 3Ag-Al-5Ag 2Ag-Al-3Ag 6Ag-Al-5Ag 2Ag-7Ag-6Ag 3Ag-4Ag-5Ag
65.7 65.7 61.2 64.5 64.5 91.1 60.1
3Ag-Al-2Ag-1Ag 1Ag-Al-6Ag-5Ag 2Ag-3Ag-Al-5Ag 5Ag-4Ag-3Ag-Al
167.1 167.1 133.3 29.0
1Ag-Al-7Ag 3Ag-1Ag-7Ag 4Ag-1Ag-6Ag
144.3 107.9 125.2
1Ag-Al-6Ag 1Ag-Al-7Ag 2Ag-1Ag-7Ag 2Ag-7Ag-3Ag 3Ag-7Ag-4Ag
55.8 111.5 56.8 58.8 57.5
1Ag-7Ag-3Ag-2Ag 3Ag-4Ag-5Ag-7Ag
21.8 13.0
1Ag-Al-7Ag 2Ag-1Ag-7Ag 2Ag-7Ag-3Ag
57.9 54.4 57.4
Al-1Ag-7Ag 2Ag-3Ag-4Ag 4Ag-5Ag-6Ag2Ag-7Ag-3Ag
179.5 108.0 108.0 59.1
2Ag-3Ag-4Ag-5Ag 4Ag-6Ag-5Ag-2Ag 7Ag-4Ag-3Ag-2Ag
0.1 0.0 38.9
Ref. [35].
Fig. 3. Three sp2 orbitals (a) Ag3Al;(b) Ag3Al+.
because of doping Al atom. The trend could be explained as the formation of an inert AgAl molecule unit in the clusters. The unit is known to have relatively high dissociation energy of 2.220 eV [35] as compared to Ag2 (1.660 eV) [33].
(2) The BE of the cationic clusters AgnAl+ (n = 1–7) are lower than the corresponding values of pure clusters Agþ nþ1 . For example, the BE of AgAl+ is 1.059 eV, which is lower than that of Agþ 2 by 1.639 eV, and so on. The BE for the doped clusters AgnAl+ are lower than the corresponding values of pure þ clusters Agþ nþ1 by 0.476–1.949 eV. The pure clusters Agnþ1 is + more stable than the doping clusters AgnAl (n = 1–7). This could be explained that Ag+2 is more stable than AgAl+, and Agþ 2 has relatively high dissociation energy of 1.740 eV [32] as compared to AgAl+ (1.059 eV). There is a single valence electron for Ag atom which occupies atomic orbital 5s. There are two valence electrons for Al+ atom which occupy an atomic orbital 3s. For neutral Ag2, the two 5s atomic orbitals combine to form two molecular orbitals, one bonding (r) and one antibonding (r*). The bonding molecular orbital is of lower energy than the two 5s atomic orbitals, and the two valence electrons go into the bonding
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
molecular orbital to form lowest potential energy for the molecule. If one electron is removed forming the cation Agþ 2 , the bonding molecular orbital has an unpaired electron. For AgAl+, there are three valence electrons. The 5s atomic orbital of Ag atom and the 3s atomic orbital of Al atom also combine to form two molecular orbitals, one bonding (r) and one antibonding (r*). Two electrons occupy the bonding molecular orbital and one valence electron goes into the antibonding molecular orbital. The energy of antibonding molecular orbital is greater than that of the 5s atomic orbital of Ag atom. This is good agreement with the calculated results. Fig. 5 shows that the highest occupied molecular orbital (HOMO) of Agþ 2 is a bonding molecular orbital r, whereas the HOMO of AgAl+ is an antibonding molecular + orbital r*. So Agþ 2 is more stable than AgAl . (3) Both curves of BE for the cationic and neutral clusters doping Al atom show odd–even variations obviously except Ag2Al. For cationic clusters AgnAl+, the curve shows peaks when it has an even number of Ag atoms, but for neutral clusters AgnAl, the peaks appears when it has an odd number of Ag atoms. It indicates that clusters with even-electron are more stable than odd–electron neighbors. This is mainly due to the pairing properties of the molecular orbitals. For odd-electron systems, the HOMO is single occupied and can easily accept or lose electron (as shown in Fig. 5). Furthermore, Ag6Al+ and Ag5Al have the highest BE compared with the corresponding cationic or neutral clusters. It is well known that the stability of pure Agn clusters can be explained by the spherical jellium model (SJM). The SJM predicts that the clusters with 2,8,20,, valence electrons are more stable because of the closing of electronic shells. It is interesting that the stability of Ag6Al+ and Ag5Al can be explained by SJM. Silver has a valence electronic configuration of 5s1 and aluminum has 3s23p1. Ag5Al has the shell closing with 8 valence electrons. For Ag6Al+, Mulliken total atomic charge analysis shows that when Ag6Al is ionized, the Al atom loses about 1 charge, so Ag6Al+ has the shell closing with 8 valence electrons as well. The n = 5 is predicted to be the magic number for AgnAl clusters, and n = 6 is the magic number for AgnAl+ clusters. Even though there is no experiment data for AgnAl clusters, but our calculated result that the n = 6 is the magic number is in good agreement with the mass spectrum of AgnAl+ clusters [17]. The second difference of cluster energy (SDE), defined by 0;þ1
D2 E½Agn Al
ð0;þ1Þ
¼ E½Agnþ1 Al
ð0;þ1Þ
þ E½Agn1 Al
ð0;þ1Þ
2E½Agn Al
;
also indicates the relative stability of the cluster with respect to its neighbors. The calculated values of SDE for both series are presented in Fig. 6. Fig. 6b is also shown the point corresponding to n = 7 for AgnAl. The calculated ground state structure of Ag8Al is dis-
Fig. 4. Binding energy per atom vs. cluster size for the ground state structures.
played in Fig. 2. Higher value of SDE indicates that the geometry of AgnAl(0,+1) is the most stable one compared to its neighbors Agn+1Al(0,+1) and Agn-1Al(0,+1). Cationic AgnAl+ (n = 2, 4, 6) and neutral AgnAl (n = 3, 5, 7) with even numbers of valence electrons have relatively large SDE, and the highest SDE of Ag6Al+ or Ag5Al proves again that n = 6 for AgnAl+ or n = 5 for AgnAl is the magic number. 3.3. HOMO–LUMO gaps It is well known that the energy gap Eg between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) reflects the relative chemical reactivity of clusters. Since the unrestricted B3LYP method was used in this paper, the clusters AgnAl(0,+1) (n = 1–7) have both a-states and b-states. The HOMO, LUMO, and Eg values of the systems studied are tabulated in Table 4. Some interesting features follow from this table: (1) the gaps exhibit significant even–odd oscillation behavior just as that of pure Agn(0,+1) clusters [42]. The higher gaps are exhibited by cationic AgnAl+ clusters with even numbers of Ag atoms and neutral AgnAl clusters with odd numbers of Ag atoms, respectively. This means that these clusters have even numbers of electrons, and they are more stable and have lower chemical reactivities. On the other hand, Ag7Al+ and Ag6Al clusters are less stable and have stronger chemical reactivity due to smaller energy gaps. (2) For odd number of electrons clusters, the gap of the a-states is relativity smaller than that of the b-states, except Ag4Al cluster. 3.4. Adiabatic ionization potentials The variation of adiabatic ionization potentials (AIPs) for the lowest-energy structures with cluster size is plotted in Fig. 7. The
Table 3 Harmonic vibrational frequencies (cm1), and infrared intensities (km/mol) (parentheses) of the ground state structures for AgnAl(0,+1) (n = 1–7). Cations
Frequencies (infrared intensity)
Neutrals
Frequencies (infrared intensity)
AgAl+ Ag2Al+ Ag3Al+ Ag4Al+
188(15.2) 90(1.5),90(1.5),120(0.0),368(7.9) 30(0.3),79(2.3),92(0.0),121(0.1),166(0.7),371(12.6) 32(0.0),44(0.7),44(0.7),86(0.0),98(0.1),114(0.3), 136(0.0), 242 (3.3), 366(1.2) 17(0.0),17(0.0),71(0.0),71(0.0),98(0.0),100(1.3), 100(1.3),113(0.0),113(0.0),202(0.0), 255(0.1), 255(0.1) 31(0.0),31(0.0), 66(0.2),75(0.0),75(0.0), 80(0.0), 85(0.7),85(0.7),101(0.0),125(0.10),125(0.1),131(0.5), 172(0.2),242(0.0),243(0.0) 27(0.0),27(0.0),55(0.4),55(0.4),59(0.3),73(0.1), 74(0.1),76(0.0),91(0.0),91(0.0),93(0.2),118(0.1), 121(0.2),122(0.2),143(0.2),170(0.7),230(0.2), 231(0.2)
AgAl Ag2Al Ag3Al Ag4Al
245(11.3) 55(0.5),180(0.0),309(9.5) 50(0.0),56(0.0),116(0.0),133(0.3),188(0.6), 246.(0.3) 42(0.1),50(0.0),86(0.0),87(0.0),89(0.1),124(0.2), 38(0.1),210(1.4),221(0.4) 39(0.0),39(0.0),64(0.0),72(0.5),75(0.0),92(0.0), 113(0.0),113(0.0),137(0.0), 217(0.8), 217(0.8), 239(0.0) 39(0.1),44(0.1),60(0.0),63(0.2),67(0.6),72(0.1), 82(0.0),85(0.5),94(0.2),110(0.0),133(0.3),141(0.8), 189(0.9),196(0.5),219(2.8) 38(0.0),39(0.0),51(0.0),51(0.1),61(0.0),68(0.5), 74(0.0),79(0.0),82(0.1),87(0.2),94(0.3),104(0.8), 114(0.0),137(0.6),144(1.3),200(1.1),213(0.1), 287(0.2)
Ag5Al+ Ag6Al+
Ag7Al+
15
Ag5Al Ag6Al
Ag7Al
16
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17
Ag2+
AgAl+
Ag2Al+
Ag3Al+
Ag4Al+
Ag5Al+
Ag6Al+
Ag7Al+
AgAl
Ag2Al
Ag3Al
Ag4Al
Ag5Al
Ag6Al
Ag7Al
LUMO
HOMO
LUMO
HOMO
Fig. 5. HOMOs and LUMOs of Ag2+, AgnAl and AgnAl clusters.
Fig. 6. Second difference of energy (a) AgnAl+, and (b) AgnAl vs. cluster size for the ground state structures.
Table 4 Calculated HOMO, LUMO energies (in hartrees) and HOMO–LUMO gap (Eg) energies (in eV) of the ground state structures for AgnAl(0,+1) (n = 1–7). Clusters
HOMO (a)
LUMO (a)
Eg (a)
HOMO (b)
HUMO (b)
Eg(b)
AgAl+ Ag2Al+ Ag3Al+ Ag4Al+ Ag5Al+ Ag6Al+ Ag7Al+ AgAl Ag2Al Ag3Al Ag4Al Ag5Al Ag6Al Ag7Al
0.3962 0.3885 0.3405 0.3537 0.3281 0.3527 0.2929 0.1766 0.1673 0.1970 0.1787 0.2001 0.1576 0.1762
0.2767 0.2657 0.2629 0.2541 0.2409 0.2349 0.2291 0.0862 0.0880 0.0868 0.0979 0.0881 0.0966 0.1003
3.2518 3.3394 2.1124 2.7113 2.3726 3.2071 1.7366 2.4602 2.1568 3.0000 2.1990 3.0477 1.6580 2.0678
0.5071 0.3885 0.3840 0.3537 0.3691 0.3527 0.3605 0.1766 0.2037 0.1970 0.1963 0.2001 0.2026 0.1762
0.3284 0.2657 0.2824 0.2541 0.2700 0.2349 0.2457 0.0862 0.1111 0.0868 0.1258 0.0881 0.1101 0.1003
4.8619 3.3394 2.7639 2.7113 2.6964 3.2071 3.1233 2.4602 2.5190 3.0000 1.9198 3.0477 2.5179 2.0678
AIP is defined as the energy difference between the cationic and þ neutral clusters: AIP ¼ Eþ n En , where En is the total energy of the lowest-energy structures of the cationic cluster and En is of neutral one.
Fig. 7. Adiabatic ionization potentials vs. cluster size for the ground state structures of the neutral AgnAl clusters.
The adiabatic ionization potentials show odd–even oscillations, and decrease with increasing of the cluster size. The variation of the AIPs is in the range of 5.165–6.935 eV. It was observed that the AIP of the neutral clusters with odd Ag atoms is the highest one among their neighboring clusters with even Ag atoms. The reason of variation of the calculated IP values with the cluster size is mainly due to the sum of valence electrons of all atoms. The AIPs with even electrons are higher than those with odd electrons, indicating that it is more difficult for even-electron clusters to lose electron than odd–electron neighbors. The AIP of Ag6Al with nine valence electrons is the lowest (5.165 eV). This means that Ag6Al cluster is easily to lose an electron and transform to Ag6Al+ with eight valence electrons. It proves again that Ag6Al+ cluster is more stable. 3.5. Dissociation channels Table 5 lists the lowest dissociation energies of cationic and neutral clusters AgnAl(0,+1) (n = 1–7). The dissociation energy is defined as XY = X + Y. In all cases, the energetically lowest fragmentation channel is monomer Ag ejection for odd-electron clusters and dimmer Ag ejection for even-electron clusters. The result is similar to the theoretical [43] and experimental results [44,45] for pure clusters Agn. A general odd–even behavior in the dissociation ener-
F. Liu, G. Jiang / Journal of Molecular Structure: THEOCHEM 953 (2010) 7–17 Table 5 Energetically preferred dissociation channels of the ground state structures for AgnAl+ and AgnAl, 1 6 n 6 7. Cations
E (eV)
Neutrals
E (eV)
AgAl+ ? Ag + Al+ Ag2Al+ ? Ag2+Al+ Ag3Al+ ? Ag + Ag2Al+ Ag4Al+ ? Ag2 + Ag2Al+ Ag5Al+ ? Ag + Ag4Al+ Ag6Al+ ? Ag2 + Ag4Al+ Ag7Al+ ? Ag + Ag6Al+
1.059 3.008 1.018 1.615 1.330 2.017 0.917
AgAl ? Ag + Al Ag2Al ? Ag + AgAl Ag3Al ? Ag2 + AgAl Ag4Al ? Ag + Ag3Al Ag5Al ? Ag2 + Ag3Al Ag6Al ? Ag + Ag5Al Ag7Al ? Ag2 + Ag5Al
1.971 1.139 1.577 1.100 1.639 0.895 1.172
gies indicates that even-electron clusters are usually more stable than their odd–electron neighbors. AgAl+ prefers to dissociate to Ag atom and Al+ ion. This proves again it is available that the BE for AgnAl+ is defined as Eb = (nE[Ag]+E[Al+] E[AgnAl+])/(n + 1). Additionally, we found that Ag7Al+ prefers to dissociate to Ag atom and Ag6Al+ cluster. And Ag6Al prefers to dissociate to Ag atom and Ag5Al. The dissociation energies for Ag6Al+ and Ag5Al are the largest of all cationic and neutral clusters, which are 2.017 and 1.639 eV, respectively. Ag7Al+ and Ag6Al have the lowest dissociation energies, which is 0.917 and 0.895 eV, respectively. These results suggest that Ag6Al+ and Ag5Al clusters are more stable which is consistent with the fact that Ag6Al+ and Ag5Al have larger calculated binding energies and the second difference of energies. It also consist with our conclusion that n = 6 and 5 are magic numbers for cationic clusters and neutral clusters, respectively. 4. Conclusion The equilibrium structures and electronic properties of AgnAl(0,+1) (n = 1–7) clusters have been studied using a density-functional method (B3LYP) with the relativistic PPs and corresponding basis sets. The ground state structures and their isomers are first predicted. The results show that binding energies (BE), second differences (SDE), HOMO–HUMO gaps, adiabatic ionization potentials (AIPs) of the ground state structures of AgnAl(0,+1) (n = 1–7) clusters show remarkable odd–even alternation behaviors, which reveal that even-electron clusters are more stable than odd-electron clusters. Moreover, the satiability of AgnAl (n = 1–7) are enhanced by doping the Al atom. Odd-electron clusters prefer to eject monomer Ag and even-electron clusters prefer to eject dimmer Ag. The n = 6 is the magic number of AgnAl+ (n = 1–7) and more stable. The n = 5 is predicted as the magic number of AgnAl (n = 1–7) and more stable. Acknowledgment The authors acknowledge to the support by Heilongjiang Education Department Foundation of China (Grant No. 11533046). References [1] M. Valden, X. Lai, D.W. Goodman, Science 281 (1998) 1647–1650. [2] M.B. Kinickelbein, Annu. Rev. Phys. Chem. 50 (1999) 79–115.
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