Configuration of the Surface Atoms in AlN - American Chemical Society

Nov 19, 2010 - Configuration of the Surface Atoms in AlN (270 e N e 500) Clusters. Xueguang Shao,* Xia Wu, and Wensheng Cai. Research Center for ...
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J. Phys. Chem. A 2010, 114, 12813–12818

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Configuration of the Surface Atoms in AlN (270 e N e 500) Clusters Xueguang Shao,* Xia Wu, and Wensheng Cai Research Center for Analytical Sciences, College of Chemistry, Nankai UniVersity, Tianjin 300071, P. R. China ReceiVed: July 8, 2010; ReVised Manuscript ReceiVed: NoVember 3, 2010

Configuration of the surface atoms in aluminum clusters was investigated based on the structures with global minimum potential energy of some Al clusters in the size range of 270-500. The structures were optimized by the dynamic lattice searching with constructed cores (DLSc) method with the NP-B potential. In the optimized structures, all clusters are identified as truncated octahedra (TO) including three complete TO at Al260, Al314, and Al405. With the model of TO260 and TO405, the configurations of the surface atoms in the structures of the clusters from 261 to 314 and from 406 to 459 were investigated. The sites on (100) faces are found to be preferable to those on (111) faces for locating the new atoms with the increase of the cluster size, but for the clusters larger than 405 atoms, the sites on the (111) face are favored when the number of atoms exceeds the site number of a (100) face. Furthermore, the sites on the edge adjoining a (100) face and a (111) face are found to be very important to make a cluster more stable. 1. Introduction Aluminum clusters have attracted much attention because of their unique electronic, optical, magnetic, catalytic, and structural properties.1-4 Extensive experimental and theoretical studies have been devoted to the studies of aluminum cluster structures, because they exhibit a wide range of size- and shape-dependent chemical properties that differ from their bulk systems.5,6 Moreover, melting point, reactivity, and surface adsorption are found to be closely dependent on geometric and surface structures.7-9 Therefore, the knowledge of cluster formation and growth mechanism with cluster size is critical for understanding the property evolution from aluminum clusters to face-centeredcubic (fcc) aluminum crystal. Because the growth of cluster structure with size, especially for the clusters in the same motif, occurs only on the surface, the atomic distribution on the surface of cluster is greatly concerned. In the theoretical calculations, density functional theory (DFT) was often employed to analyze the geometry and electronic structures of small and medium size AlN clusters.10-14 For instance, the lowest energy structures were found to change from planar to three-dimensional when the cluster contains 6 atoms, and only when N g 11, the interior of clusters may be occupied with atoms.10 For Al13, icosahedral structure was much more stable than face-centered-cubic structure.11 The lowest energy structures might undergo a transition to an aluminum bulk fcc motif above Al23.12 Further studies found that the aluminum clusters from Al31 to Al40 exhibit a bulklike stacking pattern.13 For larger clusters, empirical potential functions have played an important role for understanding the possible transition. For example, for N e 190, glue potential15 favors polytetrahedral structures. By a pair-potential and many-atom interaction, Al38, Al75, Al79, Al86, and Al102 were calculated as fcc.16 Another study on Gupta potential showed that truncated octahedra (TO) are the preferred fcc-like structures until complete transition to the bulk fcc lattice.17 For locating the stable structures of clusters, many optimization algorithm, such as genetic algorithm (GA),18-20 basin * To whom correspondence should be addressed. Phone: +86-2223503430. Fax: +86-22-23502458. E-mail: [email protected].

Figure 1. Structure of the complete TO Al260 (lines) and its surface sites (spheres).

hopping method (BH) and its variants,21,22 simulated annealing (SA),23,24 dynamic lattice searching (DLS) method,25-27 and heuristic algorithm combined with the surface and interior operators28 have been developed. A variation of DLS named as the DLS with constructed core (DLSc)26 method has been successfully applied to the optimization of large clusters, for example, Lennard-Jones (LJ) clusters up to 670 atoms, silver and aluminum clusters up to 310 atoms.29-31 In our previous work, putative global minimum structures of Al2-10 clusters29 were obtained by NP-B potential4,32 based on an embeddedatom model (EAM),33 and all clusters were identified as TO except for five decahedral structures at Al64, Al72, Al74, Al76, and Al101, four stacking fault fcc structures at Al91, Al99, Al129, and Al135, and one icosahedron at Al147. It means that the possible structural transition may occur around Al65. Moreover, with the increasing sizes, the structural growth was found to be on (100) and (111) facets of six complete TO structures at Al38, Al79, Al116, Al140, Al201, and Al260.29 Similar atomic distribution on both facets was also found to be favored in a recent study by Daw’s EAM potential.34 Figure 1 shows the structure with global minimum potential energy of Al260 with complete TO motif, in which each of the six (100) or eight (111) facets has the same number of atoms, and on the surface of Al260, one-shell growth of the TO configuration generates 230 lattice sites as shown with small spheres. Among the 230 sites, 6 × 9 sites are located above the (100) faces, 8 × 10 sites are located above the (111) faces, and other sites are located at the edges adjoining the two faces. For example, among the 15 sites above a (100) face, only 9

10.1021/jp106339f  2010 American Chemical Society Published on Web 11/19/2010

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TABLE 1: Potential Energies (E) of the Optimized Structures of AlN (N ) 314-500) Clusters N

E (eV)

N

E (eV)

N

E (eV)

314 316 320 330 338 340 344 345 350 360

-971.3151 -977.5031 -990.4781 -1022.4893 -1048.1062 -1054.6619 -1067.6200 -1070.9807 -1086.4761 -1118.5084

370 380 390 400 405 410 420 426 430 440

-1151.0290 -1183.4731 -1215.6240 -1248.2827 -1264.8608 -1280.4637 -1312.6482 -1331.8442 -1344.9099 -1376.9234

450 459 460 470 480 483 489 490 500

-1409.2859 -1438.7115 -1441.5367 -1474.3458 -1506.6076 -1516.4515 -1535.6096 -1538.9709 -1571.1338

sites are above the area of the face, but the other 6 sites are located at the edge adjoining the (100) face and a (111) face. Therefore, the site numbers for a (100) face and a (111) face are 9 and 10, respectively. In this work, the growth rule of the surface atoms, that is, the occupying sequence of the surface sites along with the increase of the cluster size, was discussed. For the discussions, stable structures of Al clusters up to 500 atoms are optimized with the DLSc method by the NP-B function. Clusters with complete TO structure are determined, and a detailed observation of the growth pattern on (100) or (111) facets is performed. 2. Method The DLSc method is used to obtain the stable structures. It is a development of our previous DLS method.25,26 The essential idea of DLS is based on the fact that just specific positions would be located after local minimization (LM) when atoms are added to a fixed cluster. Therefore, a DLS run starts from a randomly generated and locally minimized structure of a cluster. Then, the repetition of “lattice construction” and “lattice search” is performed until no lower energy structure could be found. The function of lattice construction is to construct vacant dynamic lattice (DL) sites around the starting structure, and lattice searching operation finds a solution with lower energy by iteratively moving the atoms with higher energy to the vacant DL sites with lower energies. DLS has been proven to be high speed and unbiased.25-27,30 For optimization of large clusters, however, DLSc was proposed to improve the searching ability and reduce the searching space.26,31 In the DLSc method, an

inner core is used to generate the starting structure, and only atoms in outer shells are optimized. In this study, for optimization of the clusters containing above 310 atoms, the inner cores with decahedral (Dh), icosahedral (Ih), and fcc configurations are used in DLSc method based on the knowledge of the possible structural motifs in aluminum clusters.29 The final structure was determined by selecting the structure with the lowest energy from the results of the independent runs of DLSc with different cores. A NP-B potential energy function is used for describing the interaction between atoms of aluminum clusters. The total energy of a system with N atoms is given by the following: N

U)

∑ F(Fi) + ∑ φ(rij) i

(1)

i>j

where F(Fi) is a many-body interaction that depends on the local electron density at atom i, and φ(rij) is an effective two-body interaction. Parameters were described in detail in ref 32. 3. Results and Discussion 3.1. Structural Growth of Al Clusters up to 500 Atoms. Due to the computational complexity, only 29 clusters were optimized in this work. Nineteen clusters with tens of atoms in the size range of 320-500 were selected at first, and then, 10 clusters that can possibly take a complete TO motif within the sizes from 310 to 500 were optimized. For all the studied clusters, it was found that the energy of the structure in TO motif is lower than those in Dh, Ih, or stacking fault (SF) fcc motifs. In the following analysis, however, six clusters, that is, Al270, Al280, Al290, Al300, Al309, and Al310 reported in our previous work29 were also included. Table 1 summarizes the potential energy of the 29 clusters from 314 to 500, and Figure 2 shows some of the optimized structures within the size range from 270 to 500. For clarity, atoms in the inner cores are shown with dark spheres, and the surface atoms are represented with light spheres in the figure. The Cartesian coordinates of the structures for Al314-500 are provided as Supporting Information. Furthermore, various low-energy structures above the lowest one have been found in the calculations, which may be valuable and important for understanding the actual behavior and observable

Figure 2. Putative global minimal structures of the studied clusters. Inner core atoms and surface atoms are shown with dark and light spheres, respectively.

Surface Atom Configuration in Al Clusters

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TABLE 2: Number of (100) and (111) Faces, N(100) and N(111), in Al270-500 Clusters N

N(100) a

270 280a 290a 300a 309a 310a 314a 316a 320a 330a 338a 340a 344a 345a 350a 360a 370a 380a

2 3 2 3 4 4 6 3 3 4 3 5 5 5 5 6 6 4

N(111) 0 0 1 1 1 1 0 2 2 2 3 2 2 2 2 2 3 4

N a

390 400a 405a 410b 420b 426b 430b 440b 450b 459b 460b 470b 480b 483b 489b 490b 500b

N(100)

N(111)

5 5 5 1 0 1 1 2 1 3 2 2 3 3 2 2 3

4 4 4 0 1 1 1 1 2 1 2 2 2 2 3 3 3

a Clusters grow on the basis of Al260. b Clusters grow on the basis of Al405.

forms of aluminum clusters. Therefore, Cartesian coordinates for some local minima of the Al314-500 clusters with Dh, Ih, or SF fcc motifs are supplied as Supporting Information. From Figure 2, two complete TOs can be found at Al314 and Al405 in the size range of 270-500. This result gives proof of the possible complete TOs predicted in our previous work.29 However, it should be noted that, compared with the complete TO at Al260 as shown in Figure 1, the 54 extra atoms in Al314 are all located on the six 16-atom (100) faces, WITH 9 atoms on each face. Thus, Al314 clusters can be known as a complete TO owning the same vacant center (there is no atom at the center of the cluster)29 and considered as the same sequence. On the other hand, the extra atoms in Al405 over Al260 are located on the five (100) faces and four (111) faces. Two layers are added on one (100) face, but no atom is added on its opposite face. Therefore, the symmetry is different from Al260, and the center of Al405 is occupied by an atom. Further investigation shows that Al270-405 clusters adopt a growth on the surface of complete TO, Al260. For quantitative

analysis of the growth rule of the surface atoms, the number of (100) and (111) faces on which extra atoms grow with the increase of cluster size, denoted by N(100) and N(111), is given in Table 2. For example, N(100) ) 6 and N(111) ) 0 for Al314 cluster because there are six (100) faces on which atoms are located and no atom grows on THE (111) face compared with the 260atom complete TO. From the table, it can be seen that, in Al270-405 clusters, N(100) is larger than or equal to N(111). Therefore, atoms prefer to grow on the (100) faces in this size range. For instance, in the structure of Al270 shown in Figure 2, the 10 extra atoms and 8 atoms originally located on the edges of 260-atom TO are combined to form two 9-atom (100) faces. Its N(100) is thus two bigger than N(111), but the inner TO core becomes incomplete. The phenomenon has been found in Dh and Ih sequences.35 Moreover, except for Al370, two-layer atoms are added on one (100) face from Al350 to Al405, but there is still (111) faces on which no atom grows. For clusters of Al410-500, the growth is based on the complete TO Al405, and except for Al459, the difference between N(100) and N(111) alternatively changes from +1 to -1 then to 0. The reason is that, in this size range, the extra atoms prefer to grow on (100) faces but all the extra atoms prefer to be located on one face regardless of (100) or (111). When the number of extra atoms exceeds the site number of a (100) face but is less than the site number of a (111) face, the latter will be occupied. For instance, compared with Al405, the five extra atoms in Al410 are located on a (100) face, but three atoms originally located on the edges of Al405 are also moved onto the (100) face to fill all the eight sites. In this case, N(100) is one bigger than N(111). Then, in the structure of Al420, the number of extra atoms is 15, bigger than the site number (9) of a (100) face but less than the site number (18) of a (111) face. Therefore, the 18 sites on a (111) face are occupied by the 15 atoms and the 3 atoms from the edges of Al405. In this case, N(100) is one smaller than N(111). However, in the structure of Al426, the 21 extra atoms are located on one 9-atom (100) face and one 12-atom (111) face, respectively. Thus, both N(100) and N(111) equal to 1, and the difference becomes zero. Therefore, in the size range of 270-500, the structures of Al270-405 and Al410-500 can be known as a growth sequence from the complete TO, Al260 and Al405, respectively. With the increase of cluster size, atoms prefer to occupy the sites on (100) faces,

Figure 3. Isomers of Al261 cluster (a) and Al262 cluster (b). The spheres represent the possible sites for the 261st atom in (a) and the 261st and 262nd atoms in (b) on the (100) or (111) faces. The number labeled near a site means the isomer with the site(s) occupied, and the energies of these isomers are listed on the right-hand.

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Figure 4. Growth pattern of the extra atoms on TO260. Inner core atoms and surface atoms are shown with dark and light spheres, respectively.

but they are more favored to grow together on one face. For the clusters larger than 410, the sites on (111) faces will be occupied when the number of extra atoms is bigger than the site number of a (100) face. 3.2. Surface Growth on TO260 and TO405. As discussed above, the structures of Al270-405 and Al410-500 are based on complete TO Al260 and Al405, respectively. In order to further investigate the growth rule of the atoms on the surface, the locations of the extra atoms on the surface of complete TO Al260 and Al405 were analyzed in detail. In the calculations, the inner core of 260 or 405 atoms is fixed; only the location of the extra atoms is optimized. Due to the fixation of the core, the optimized structures are not real cases of the clusters. Therefore, structures are denoted as T, instead of Al as above. When one extra atom is added to Al260, seven possible isomers for the Al261 cluster are found after LM as displayed in Figure 3(a) because of the geometrical symmetry. In the figure, the 261st atom on (100) or (111) faces is represented by a sphere, and the energies of these isomers are listed. Apparently, the isomers with the 261st atom on the (100) faces have 0.2 eV lower energies than those on the (111) faces. Therefore, as discussed above, the extra atoms prefer to grow on (100) faces. This is also consistent with the fact that, for fcc crystals, (100) faces generally have higher surface energy than (111) faces;36 the extra atoms added on the (100) faces thus can decrease the surface energies. Furthermore, the isomer 1 owns the lowest energy because the 261st atom is located in the central site of the (100) face. When two extra atoms are added to Al260, numerous isomers for the Al262 cluster can be generated. Ten of them with relatively low energies are shown in Figure 3(b). At first, it was found that the isomers with the two extra atoms on one face always have lower energy than those with the two extra atoms on different faces. Furthermore, a closer distance between the two extra atoms makes the isomer lower in energy, for example, the energy difference between isomers 1 and 3 is 0.23 eV. Therefore, extra atoms prefer to grow together on one face and around the central site. T263-314 and T406-459 are optimized for understanding the locations of the extra atoms on the surface of T260 and T405.

Figures 4 and 5 show the putative stable structure of TN for N ) 261-314 and N ) 406-459, respectively. In Figure 4, it is clear that the extra atom is added to the central site of a (100) face for T261, as shown in Figure 3(a), and the one more extra atom in T262 is added to the neighboring site in the center of a (100) face as illustrated in Figure 3(b). Then, with the increase of the size, from T263 to T269, the extra atoms are gradually added to the sites around the central site on the (100) face, until they fill all nine sites. In T270-314 clusters, the extra atoms prefer to grow on another (100) face, because N(100) is larger than or equal to N(111). For example, at T278, T287, T296, T305, and T314, two, three, four, five, and six 9-atom (100) faces are filled with the extra atoms. Furthermore, no atom is added on the (111) face in T282 and T291 clusters, with even two layers added on one (100) face. In Figure 5, however, except for T422, T437-439, and T459, the growth obeys the rule that the difference between N(100) and N(111) alternatively changes from +1 to -1 then to 0 as summarized in Al410-500 clusters. From T406 to T414, the extra 9 atoms take the same growth pattern on the 16-atom (100) face as in T261-269, but at T415, the 9 extra atoms originally located on one (100) face move to a (111) face with the new extra atom. In this case, N(100) is one smaller than N(111). With the increase of sizes, at T424, one extra atom is located on one (100) face, making N(100) equal to N(111), because the other 18 extra atoms have filled all the sites on a (111) face. Although the atoms on (100) and (111) faces have a dominant effect on the properties of clusters, few papers have discussed the problem for aluminum and other metal clusters. However, the mobility of the adatom from a (111) face to a (100) face of TO is reported to be much easier in gold clusters than in silver clusters due to the energy barriers for the diffusion,37 and in the experiment of shape-controlled synthesis of palladium nanostructures, the formed structure depends on the ratio of growth rates along the [100] and [111] directions of the truncated octahedral seed.38 Therefore, it is hard to find more information from the literature to support the above results, but (100) and (111) facets may play different role in the growth of clusters. 3.3. Quantitative Analysis of the Surface Atoms on Truncated Octahedra. Studies have shown that atoms on the (100) and (111) faces make the clusters different in chemical

Surface Atom Configuration in Al Clusters

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Figure 5. Growth pattern of the extra atoms on TO405. Inner core atoms and surface atoms are shown with dark and light spheres, respectively.

Figure 6. Locations of the occupied sites on (100) and (111) faces of TO260 and TO405 and their energies. (a), (b), (c), and (d) show the cluster of 279, 432, 282, and 435 atoms, respectively. The sites are represented by circles, and the energies of the atoms labeled in alphabetical order are listed on the right-hand. Atoms on (111) faces are labeled with A and B, atoms on (100) faces are labeled with C and D, and atoms on the adjoining edge are labeled with E and F, respectively.

and physical properties.39-41 It is of significant importance to investigate the atoms on (100) and (111) faces of TO structures. In order to quantitatively describe the surface atoms, the energy of an atom was calculated by the following: N

Ui ) F(Fi) +

∑

1 φ(rij) 2 j)0(j*i)

(2)

The symbols in the equation are the same as in eq 1. At first, the energy of each atom in Al260 and Al405 was calculated by eq 2. The results show that the energies of surface atoms are significantly higher than those of inner-shell atoms. It clearly indicates that surface atoms determine the stability and the properties of a cluster.

Second, the atoms on the edge of the (100) and (111) faces are more significant affecting the energy of a cluster. For example, by a comparison of the energies of T420, T430, T440, and T450 clusters in Figure 5 with those of Al420, Al430, Al440, and Al450 clusters in Figure 2, it can be found that the clusters with an incomplete 405-atom TO inner core have lower energies than those with a complete TO core. Quantitatively, the energies of atoms on (100) and (111) faces in Al405 are generally 0.2-0.4 eV lower than those of edge atoms. To further account for the growth of the surface atoms with the increase of cluster size, the possible configurations of 279-, 432-, 282-, and 435-atom Al clusters are displayed in Figure 6(a)-(d). In the figures, the extra atoms over TO260 and TO405 are presented by circles, and the energies of the labeled atoms are listed. In Figure 6(a) and (b), the sites of one (100) and

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(111) face are occupied by 19 (9 + 10) and 27 (9 + 18) atoms, respectively, and in Figure 6(c) and (d), the three sites adjoining the (100) and (111) face are filled with atoms. In Figure 6(a), the energies of the atoms A and B on the (111) face are about 0.16 eV higher than those of the atoms C and D on the (100) face. Due to the large difference in energy, extra atoms in T261-314 are always preferable to occupy the (100) faces. However, in Figure 6(b), the energy difference between the atoms on (111) and (100) faces is only 0.011 or 0.021 eV. Therefore, for the clusters of T406-459, the sites on (100) faces will be occupied when the number of extra atoms are less than the site number of a (100) face, but when the number of extra atoms exceeds the site number of a (100) face, the sites of (111) face will be occupied, because more atoms located together make a lower total energy. When all the sites on a (111) face are filled, the extra atoms will prefer to take the sites on another (100) face. Furthermore, from Figure 6(c) and (d), it can be seen that, when a site on the adjoining edge of the (100) and (111) face is occupied, the energies of atoms B and D in Figure 6(a) and atoms E and D in Figure 6(b) are significantly reduced. Therefore, when there are fully filled (100) and (111) faces, the sites on the adjoining edge will be the favorite ones. For the clusters in the size range of 406-459, the sites on the adjoining edges of a (100) face and a (111) face will be preferably occupied when the number of extra atoms is larger than the site number of a (100) face and a (111) face. It may be worthy of noting that the structures found in this study are just the thermodynamically most favored structures at 0 K under the adopted potential. In real synthesis of the clusters experimentally, however, kinetic factors may affect the formed structure. On the other hand, the effect of entropy is not discussed in this study. In some cases, for example, the case shown in Figure 6(b), where the energy difference is very small, entropy would become the determining factor for the formed structure. 4. Conclusions Global minimal structures of some aluminum clusters from Al270 to Al500 were optimized with the DLSc method. The dominant structures were found to be truncated octahedra (TO), and the structures of Al270-405 and Al410-500 were found to be a growth sequence from the complete TO, Al260 and Al405, respectively. With an investigation of the growth rule of the atoms on the surface of TO260 and TO405 and a quantitative analysis of the surface atoms, it was found that, in the size range from 261 to 314, the surface atoms prefer to occupy the sites on (100) faces of TO260, in the size range from 406 to 459, however, the growth pattern depends upon the number of extra atoms above 405. When the number of extra atoms is less than the site number of a (100) face of TO405, the sites on a (100) face are favored, but when the number of extra atoms is larger than a (100) face, the sites on a (111) face are favored. Furthermore, when both the sites on (100) and (111) faces are filled, the sites on the edge adjoining the (100) and (111) faces become important to make a cluster energetically more stable. Acknowledgment. This study is supported by the National Natural Science Foundation of China (NNSFC) (Nos. 20835002 and 20873066).

Shao et al. Supporting Information Available: Cartesian coordinates for the global minima of the Aln (n ) 314-500) clusters in Figure 2, and Cartesian coordinates for the local minima of the Al314-500 clusters with Dh, Ih, or SF fcc motifs. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Upton, T. H. Phys. ReV. Lett. 1986, 56, 2168. (2) Cox, D. M.; Trevor, D. J.; Whetten, R. L.; Rohifing, E. A.; Kaldor, A. J. Chem. Phys. 1986, 84, 4651. (3) Gates, B. C. Chem. ReV. 1995, 95, 511. (4) Li, Z. H.; Jasper, A. W.; Truhlar, D. G. J. Am. Chem. Soc. 2007, 129, 14899. (5) Leuchtner, R. E.; Harms, A. C.; Castleman, A. W., Jr. J. Chem. Phys. 1991, 94, 1093. (6) Bacic, Z.; Miller, R. E. J. Phys. Chem. 1996, 100, 12945. (7) Puri, P.; Yang, V. J. Phys. Chem. C 2007, 111, 11176. (8) Roach, P. J.; Woodward, W. H.; Castleman, A. W., Jr.; Reber, A. C.; Khanna, S. N. Science 2009, 323, 492. (9) Yacaman, M. J.; Ascencio, J. A.; Liu, H. B.; Gardea-Torresdey, J. J. Vac. Sci. Technol. B 2001, 19, 1091. (10) Pettersson, L. G. M.; Bauschlicher, C. W., Jr.; Halicioglu, T. J. Chem. Phys. 1987, 87, 2205. (11) Cheng, H. P.; Berry, R. S.; Whetten, R. L. Phys. ReV. B 1991, 43, 10647. (12) Sun, J.; Lu, W. C.; Li, Z. S.; Wang, C. Z.; Ho, K. M. J. Chem. Phys. 2008, 129, 014707. (13) Zhang, W.; Lu, W. C.; Zang, Q. J.; Wang, C. Z.; Ho, K. M. J. Chem. Phys. 2009, 130, 144701. (14) Goldberg, A.; Halls, M. D.; Kung, P.; Liang, J. J. J. Phys. B: At. Mol. Opt. Phys. 2009, 42, 125103. (15) Doye, J. P. K. J. Chem. Phys. 2003, 119, 1136. (16) Manninen, K.; Akola, J.; Manninen, M. Phys. ReV. B 2003, 68, 235412. (17) Turner, G. W.; Johnston, R. L.; Wilson, N. T. J. Chem. Phys. 2000, 112, 4773. (18) Deaven, D. M.; Tit, N.; Morris, J. R.; Ho, K. M. Chem. Phys. Lett. 1996, 256, 195. (19) Xiang, Y. H.; Jiang, H. Y.; Cai, W. S.; Shao, X. G. J. Phys. Chem. A 2004, 108, 3586. (20) Johnston, R. L. J. Chem. Soc., Dalton Trans. 2003, 22, 4193. (21) Wales, D. J.; Doye, J. P. K. J. Phys. Chem. A 1997, 101, 5111. (22) Leary, R. H.; Doye, J. P. K. Phys. ReV. E 1999, 60, 6320. (23) Wille, L. T. Chem. Phys. Lett. 1987, 133, 405. (24) Cai, W. S.; Shao, X. G. J. Comput. Chem. 2002, 23, 427. (25) Shao, X. G.; Cheng, L. J.; Cai, W. S. J. Comput. Chem. 2004, 25, 1693. (26) Yang, X. L.; Cai, W. S.; Shao, X. G. J. Comput. Chem. 2007, 28, 1427. (27) Shao, X. G.; Yang, X. L.; Cai, W. S. J. Comput. Chem. 2008, 29, 1772. (28) Takeuchi, H. J. Chem. Inf. Model. 2006, 46, 2066. (29) Shao, X. G.; Wu, X.; Cai, W. S. J. Phys. Chem. A 2010, 114, 29. (30) Yang, X. L.; Cai, W. S.; Shao, X. G. J. Phys. Chem. A 2007, 111, 5048. (31) Shao, X. G.; Yang, X. L.; Cai, W. S. Chem. Phys. Lett. 2008, 460, 315. (32) Bhatt, D.; Schultz, N. E.; Jasper, A. W.; Siepmann, J. I.; Truhlar, D. G. J. Phys. Chem. B 2006, 110, 26135. (33) Budi, A.; Henry, D. J.; Gale, J. D.; Yarovsky, I. J. Phys.: Condens. Matter 2009, 21, 144206. (34) Tang, F. L.; Che, X. X.; Lu, W. J.; Chen, G. B.; Xie, Y.; Yu, W. Y. Physica B: Condens. Matter 2009, 404, 2489. (35) Shao, X. G.; Xiang, Y. H.; Cai, W. S. Chem. Phys. 2004, 305, 69. (36) Wang, Z. L. J. Phys. Chem. B 2000, 104, 1153. (37) Baletto, F.; Mottet, C.; Ferrando, R. Surf. Sci. 2000, 446, 31. (38) Xiong, Y. J.; Xia, Y. N. AdV. Mater. 2007, 19, 3385. (39) Gartland, P. O. Surf. Sci. 1977, 62, 183. (40) Memmert, U.; Bushby, S. J.; Norton, P. R. Surf. Sci. 1989, 219, 327. (41) Netzer, F. P.; Madey, T. E. Surf. Sci. Lett. 1983, 127, L102.

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