Au 12 M (M=Na, Mg, Al, Si, P, S, Cl) 团簇的结构 稳定性和电子性质

Transcription

1 June 物理化学学报 (Wuli Huaxue Xuebao) Acta Phys. -Chim. Sin. 2012, 28 (6), [Article] doi: /PKU.WHXB Au 12 M (M=Na, Mg, Al, Si, P, S, Cl) 团簇的结构 稳定性和电子性质 * 赵高峰 王银亮孙建敏王渊旭 ( 河南大学计算材料科学研究所, 河南开封 ) 摘要 : 采用基于密度泛函理论的第一性原理方法系统地研究了 Au 12M (M=Na, Mg, Al, Si, P, S, Cl) 团簇的结构 稳定性和电子性质. 对团簇的平均结合能 镶嵌能 垂直离化势 最高占据分子轨道 (HOMO) 和最低未占据分子轨道 (LUMO) 的能级差 电荷布居分析 自然键轨道 (NBO) 进行了计算和讨论. 对于 Au 12M (M=Na, Mg, Al) 团簇, 它们形成了内含 M 原子的最稳定的笼状结构. 然而对于 Au 12M (M=Si, P, S, Cl) 团簇, 它们却形成了以 M 元素为顶点的稳定锥形结构. 在这些团簇中发现 Au 12S 团簇相对是最稳定的, 这是由于 Au 12S 团簇形成了稳定的满壳层的电子结构. 自然电荷布居分析表明 : 对于所有的 Au 12M (M=Na, Mg, Al, Si, P, S, Cl) 团簇电荷总是从 Au 原子转向 M 原子. 自然键轨道和 HOMO 分析表明 Au 12M 团簇中发生了 Au 原子的 s-d 轨道和 M 原子的 p 轨道间的杂化现象. 关键词 : 密度泛函理论 ; 团簇 ; 自然电荷布居分析 ; 稳定性 ; 自然键轨道分析 中图分类号 : O641 Geometries, Stabilities and Electronic Properties of Au 12 M (M=Na, Mg, Al, Si, P, S, Cl) Clusters ZHAO Gao-Feng * WANG Yin-Liang SUN Jian-Min WANG Yuan-Xu (Institute of Computational Materials Science, Henan University, Kaifeng , Henan Province, P. R. China) Abstract: The geometries, stabilities, and electronic properties of Au 12M (M=Na, Mg, Al, Si, P, S, Cl) clusters were systematically investigated by using first-principles calculations based on density functional theory (DFT). For each cluster, the average binding energy, the embedding energy, the vertical ionization potential, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the natural charge population analysis, and the natural bond orbital analysis (NBO) were calculated. The lowest-energy structures of Au 12M (M=Na, Mg, Al) clusters are cages with M encapsulated in the center, while structures of Au 12M (M=Si, P, S, Cl) clusters are pyramidal with M at the apex. The Au 12S cluster, having the full closed-shells, is the most stable. Furthermore, from the natural population analysis, it follows that charges transfer from Au to M in all the clusters. The NBO and HOMO analyses reveal that hybridization occurs between the Au s-d orbitals and the M p orbitals. Key Words: Density functional theory; Cluster; Natural charge population analysis; Stability; Natural bond orbital analysis Received: February 14, 2012; Revised: April 5, 2012; Published on Web: April 6, Corresponding author. zgf@henu.edu.cn; Tel: The project was supported by the National Natural Science Foundation of China ( , ) and Natural Science Foundation of Education Department of Henan Province, China (2011A140003). 国家自然科学基金 ( , ) 和河南省教育厅自然科学基金 (2011A140003) 资助项目 C Editorial office of Acta Physico-Chimica Sinica

2 1356 Acta Phys. -Chim. Sin Vol.28 1 Introduction During the past two decades, coinage metal clusters have been intensively studied by both experimental and theoretical methods. Clustering occurs due to the facile hybridization of core d-electrons with outer s-electrons. Gold clusters have been of particular interest. Recently, Bulusu et al. 1 reported evidence of hollow cages of pure metal atoms. A novel Au 20 tetrahedral structure identified by photoelectron spectroscopy correlates with relativistic density functional theory (DFT) calculations. 2 Fa and Dong 3 identified a stable tube-like Au n (n= 26-28) cluster with scalar, relativistic, all-electron DFT. Highly stable golden fullerene Au 32 and Au 42 clusters have been reported, 4,5 and core-shell structures have been verified by recent studies on Au 34 and Au 58 clusters. 6-8 The existence of these high-symmetry clusters is attributed to the manifestation of aurophilicity, which can further enhance strong gold-gold interactions. 9 In addition, relativistic-effect-enhanced s-d hybridization and s- electron delocalization may also reflect the preference for high-symmetry structures Doping of gold clusters with impurity atoms is expected to open up new channels in which one can tailor properties by varying the nature of the dopant atom Since Pykko 16 and Li 17 et al. first reported the existence of highly stable Au 12W via photoelectron spectroscopy, a considerable amount of experimental and theoretical work has been carried out on Au clusters doped with other impurity atoms. 11,18-34 Most of these studies have focused on Au 12 doped with transition-metal (TM) atoms. The high I h or O h symmetry of the lowest-energy Au 12TM clusters is attributed to the strong relativistic effect, aurophilic attraction, and 18-electron bonding to the 4s, 5s, and 6s shells of the central heteroatom. 16,35 Furthermore, Au 12TM clusters are more stable relative to icosahedral Au 12 and Au 13 cages, as verified by previous experimental 17 and theoretical 11 results. It is thus clear that the ground-state geometries of Au 12TM clusters are icosahedral or octahedral, the reason being that TM atoms possess outer s electron shells. Although a number of studies have focused on the geometric structures and electronic properties of Au 12TM clusters, there have been relatively few studies on gold clusters doped with non-transition elements. 24,25,36-42 In this paper, we perform first-principles studies of single atom impurities with 3s and 3p electrons in Au 12 clusters. These impurity atoms come from the same row of the Periodic Table, thus their principle quantum numbers remain the same while having an increasing number of valence electrons. When these atoms are embedded in Au 12 clusters, however, there are clear differences in their lowest-energy Au 12M structures. 2 Computational details All computations were performed by DFT with the unrestricted B3LYP exchange-correlation potential and the effective core potential standard LanL2DZ basis sets The standard LanL2DZ basis sets are effective in calculating noble metals because they reduce difficulties in two-electron integral calculations caused by the heavy atoms. Calculations were performed with the Gaussian 03 program package. 52 For each stationary point of a cluster, the stability was examined by calculating the harmonic vibrational frequencies. If an imaginary frequency was found, a relaxation along the coordinates of the imaginary vibrational mode was carried out until a true local minimum was obtained. Therefore, all isomers for each cluster are guaranteed to be the local minimum. In addition, for the geometry optimization of each isomer, the spin multiplicity (SM) was at least 1, 3, and 5 for even-electron clusters (Mg, Si, S,) and 2, 4, and 6 for odd-electron clusters (Al, P, Cl). If the total energy decreases with increasing SM, we would use a higher spin state until the energy minimum was found. In order to test the validity of the computational method, we performed calculations on Au 2 and AuAl dimers. As illustrated in Table 1, our results are in good agreement with previous experimental and theoretical data. 25, Results and discussion 3.1 Structures of clusters We examined a considerable number of low-lying isomers and determined the lowest-energy structures for Au 12M (M= Na, Mg, Al, Si, P, Cl) clusters that are illustrated in Fig.1. For comparison, the icosahedral and octahedra cages for pure Au 13 clusters are also in Fig.1. In order to explain the structural features of these lowest-energy structures, we list the point group symmetry, the smallest bond length for Au-Au and Au-M, and the spin multiplicity in Table 2. Previous studies indicate that the ground-state structures of Au 12TM clusters have TM encapsulated in the center of Au 12 icosahedral or octahedral cages with high I h or O h symmetry. 11,16,17,26,27 In our work, the lowest-energy structures of Au 12M (M=Na, Mg) clusters are similar to the octahedral structures of Au 12TM clusters. However, the other Au 12M (M=Al, Si, P, S, Cl) structures differ from the Au 12TM structures. The ground state of the Au 12Na cluster is an octahedral structure with the Na atom at its center, with D 3d symmetry, and a spin multiplicity of 2. The icosahedral structure also has the Na atom in the Au 12 cage center; however, its energy is 1.36 ev Table 1 Bond lengths (R), lowest harmonic vibrational frequencies (Freq), average binding energies (Eb), and vertical ionization potentials (VIPs) for the ground states of Au2 and AuAl dimers Dimer Au2 AuAl Method B3LYP/LanL2DZ a GGA/PW91 53 PBE/SDD 25 expt B3LYP/LanL2DZ a PBE/SDD 25 expt R/nm a our calculation Eb /ev VIP/eV ± Freq/cm

3 No.6 ZHAO Gao-Feng et al.: Geometries, Stabilities and Electronic Properties of Au12M Clusters 1357 Fig.1 Equilibrium geometries of the lowest-energy structures and low-lying isomers for pure Au13 and Au12M (M=Na, Mg, Al, Si, P, S, Cl) clusters All the atoms without labels are Au atoms. higher than the ground state. In the octahedral structure, the shortest bond lengths of Au Au and Au Na are and nm, respectively, while the shortest bond lengths of Au Au and Au Na are and nm, respectively, for the icosahedral structure. When an Mg atom imbeds in the Au12 cluster, it also forms an octahedral structure with the Mg in the center. However, the symmetry (Oh) of Au12Mg is higher than that (D3d) of Au12Na because all the Au Au and Au Mg bond lengths are the same (0.288 nm). The next higher energy isomer Au12Mg (b) in Fig.1 has S4 point group symmetry with an energy very close to the ground-state structure (ΔE=0.59 ev). Recently, the geometric and electronic structures of clusters with a central 3d, 4d, and 5d transition-metal atom encapsulated in an Au12 cage have been investigated.11,26 For encapsulated 3d and 4d transition-metals, the icosahedral clusters tend to be more stable than their octahedral isomers. But for 5d transitionmetals, the octahedral clusters tend to be more stable than their Table 2 Geometries of the lowest-energy isomers of Au12M (M= Na, Mg, Al, Si, P, S, Cl) and Au13 clusters Cluster Sym RAu Au/nm Au13 Ih RAu M/nm SM Au12Na D3d Au12Mg Oh Au12Al D2h Au12Si Cs Au12P C4v Au12S C Au12Cl C Sym is the point-group symmetry, SM denotes spin multiplicity, and RAu M and RAu Au represent the shortest Au M and Au Au bond lengths, respectively. icosahedral isomers (except for Au12W). The octahedral structures of Au12Na and Au12Mg are more stable than their icosahedral isomers. Thus their ground state structures are similar to the clusters with a central 5d transition-metal (except for Au12W), but they differ from those with 3d, 4d transition-metal impurities. In the case of Au12Al, the ground-state structure can be seen as a deformed octahedron with D2h symmetry. Although the Al atom remains at the center, the outer Au12 octahedral cage undergoes severe deformation. The first important change occurs in the lowest-energy structure of Au12Si, where the Si atom is now located at the top of a pyramid formed by the Au atoms. The pyramidal structure possesses Cs symmetry and a spin multiplicity of 1. The fact that the Si atom is not encapsulated in the Au12 cage as for Au12Na and Au12Mg may be due to the bonding properties and the orbital hybridization between M and Au atoms. The octahedral Au12Si cluster has an energy that is 1.45 ev higher than the pyramidal isomer. The ground-state structure of Au12P is also a pyramid, however it has higher symmetry (C4v) compared to Au12Si. The shortest bond lengths of Au P and Au Au are and nm. As shown in Fig.1, the Au12P cluster is more compact than Au12Si, which may be attributed to different Au Si and Au P bondings. The lowest-energy structure for Au12S is an irregular flat pyramid with low symmetry (C1), with the S atom at the bottom (Fig.1). It is thus more flat and extended than Au12P and Au12Si. It can be argued that the structure of Au12S results from electron delocalization over all the atoms. Surprisingly, a planar rhombic structure of Au12S is also observed, where the S atom

4 1358 Acta Phys. -Chim. Sin Vol.28 Fig.2 Average binding energies (Eb) of ground-state Au12M (M=Na, Mg, Al, Si, P, S, Cl) and Au13 clusters Fig.4 HOMO-LUMO energy gaps in ground-state Au12M (M=Na, Mg, Al, Si, P, S, Cl) and Au13 clusters occupies the center of the plane. However, its energy is 1.38 ev higher than the ground-state structure. Finally, we note that the Au 12Cl cluster has a lowest-energy structure that is basketlike with the Cl atom at the apex. 3.2 Stabilities of clusters The average binding energy (E b) of a given cluster is a measure of its thermodynamic stability, which is defined as the difference between the energy sum of all the free atoms constituting the cluster and the total energy of the cluster, as given by: E b(au 12M)=[E T(M)+12E T(Au)-E T(Au 12M)]/13 (1) where E T(M), E T(Au), and E T(Au 12M) represent the total energies of the lowest-energy M, Au, and Au 12M, respectively. As seen from Fig.2, the E b for the ground states of Au 12M (M=Na, Mg, Al, Si, P, S, Cl) clusters are higher than that of the pure Au 13 cluster. The Au 12S cluster, possessing the largest E b, is also found to be the most stable under study. This is attributed to the closed-shell (18-electron shell-filling) rule, with one electron from each Au atom and six electrons from the S atom. To further understand the stabilities of Au 12M clusters, we will discuss the embedding energy (E d) of the ground-state structure, which is defined as: E d(au 12M)=E T(M)+E T(Au 12)-E T(Au 12M) (2) where E T(M), E T(Au 12), and E T(Au 12M) represent the total energies of the lowest-energy M, Au 12, and Au 12M clusters, respectively. As shown in Fig.3, Au 12S possesses the highest embedding energy among Au 12M (M=Na, Mg, Al, Si, P, S, Cl) clusters. Hence, Au 12S should be the most stable. The energy gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO- LUMO) is a useful quantity when examining the chemical stability of clusters. A large energy gap correlates with a high barrier required to perturb the electronic structure. HOMO- LUMO energy gaps for ground-state Au 12M (M=Na, Mg, Al, Si, P, S, Cl) and Au 13 clusters are displayed in Fig.4. The largest energy gap (1.73 ev) is for Au 12Mg, which indicates that it is the most chemically stable of these clusters. Meanwhile, Au 12S has the second highest energy gap, and since it has the largest average binding energy among these clusters, it is both chemically and thermodynamically stable. The vertical ionization potential (VIP) is yet another parameter used to assess the chemical stability of small clusters, and is given by: VIP=E T(Au 12M + )-E T(Au 12M) (3) where E T(Au 12M + ) is the total energy of the ionic clusters at the optimized neutral geometry. Large VIPs indicate high chemical stability. As shown in Fig.5, the VIPs of Au 12Mg, Au 12Si, and Fig.3 Embedding energies of ground-state Au12M (M=Na, Mg, Al, Si, P, S, Cl) and Au13 clusters Fig.5 VIP of ground-state Au12M (M=Na, Mg, Al, Si, P, S, Cl) clusters

5 No.6 ZHAO Gao-Feng et al.: Geometries, Stabilities and Electronic Properties of Au 12M Clusters 1359 Au 12S clusters are surprisingly higher than those for Au 12Na, Au 12Al, Au 12P, and Au 12Cl. This trend may be attributed to the number of electrons; recall that Au 12Mg, Au 12Si, and Au 12S possess electrons in closed-shells, while the other four have electrons in open-shells. It indicates that Au 12M (M=Mg, Si, S) clusters are chemically more stable than the other Au 12M (M= Na, Al, P, Cl) clusters. Additionally, the VIP of Au 12S is the largest in this series, which can be explained on the basis of its full closed-shells (18-electron rule) Electronic properties Charge-transfer phenomena in the Au 12M clusters can be obtained by natural population analysis. The atomic charges of the M atoms in the ground-state Au 12M (M=Na, Mg, Al, Si, P, S, Cl) clusters are listed in Table 3, where we see that charges always transfer from the Au atoms to the electron-accepting M atoms. This clearly differs from that observed for Au 5M and Au 6M (M=Na, Mg, Al, Si, P, S, Cl) clusters. 24,25 Thus an important finding is that the direction of charge-transfer in M-doped gold clusters depends on cluster size. Table 3 Natural charge population and the electron configurations for M atoms in Au12M (M=Na, Mg, Al, Si, P, S, Cl) clusters through natural bond orbital (NBO) analysis Cluster Au12Na Au12Mg Au12Al Au12Si Au12P Au12S Au12Cl Charge/e Electron configuration Na[core]3s p s p 0.01 Mg[core]3s p s p 0.01 Al[core]3s p s p 0.04 Si[core]3s p p 0.01 P[core]3s p p 0.01 S[core]3s p p 0.01 Cl[core]3s p 5.52 To examine hybridization between M (M=Na, Mg, Al, Si, P, S, Cl) atoms and Au in Au 12M clusters, we present in Table 3 the natural electron configurations obtained from natural bond orbital (NBO) analysis. The valence electron configurations of the free atoms Na, Mg, Al, Si, P, S, and Cl are 3s 1, 3s 2, 3s 2 3p 1, 3s 2 3p 2, 3s 2 3p 3, 3s 2 3p 4, and 3s 2 3p 5, respectively. The NBO analysis in Table 3 reflects this s-p hybridization, where electrons transfer mainly from 3s to 3p orbitals in the M atoms. We also note that electrons transfer from 6s and 5d orbitals to 6p orbitals in the Au atoms, indicating sd-p hybridization. Since the 3p orbital gains more than the 3s orbital loses in the M atoms, it follows that the 6s and 5d orbitals in the Au atoms transfer electrons to the M 3p orbital. Thus hybridization does occur between the p orbital of the M atom and the s-d orbitals of the Au atoms. In order to further understand the chemical bonds in these systems, we plot in Fig.6 the spatial orientation of the HOMO energy levels for the Au 12M clusters. The HOMOs show hybridization phenomena between p orbitals of the M atoms and the s-d orbitals of the Au atoms. These pictures are in good agreement with the NBO analysis. However, the hybridization of Au 12M clusters differs from that in Au 12TM, 11 which is attributed to the electronic properties of the dopant atoms. 4 Summary We have carried out a first-principles investigation using DFT to systematically study the geometries and electronic properties of Au 12M (M=Na, Mg, Al, Si, P, S, Cl) clusters. The Au 12M (M=Na, Mg, Al) clusters form the lowest-energy cage structures with the M atom encapsulated in the center, while Au 12M (M=Si, P, S, Cl) clusters form pyramids with the M atom at the apex. The lowest-energy geometries of Au 12M (except Au 12Na and Au 12Mg clusters) are different from the high symmetry structure of 3d, 4d, and 5d transition-metals in Au 12TM clusters. This indicates that impurity atoms play a critical role in determining the structures and properties of Au 12M clusters. The Au 12S cluster, having full closed-shell orbitals, not only possesses a relatively high average binding energy and doping energy, but also a high VIP and HOMO-LUMO energy gap. Thus it is more stable than the other Au 12M clusters. Finally, we note that an NBO analysis reveals that hybridization between the s-d orbitals in Au atoms and the p orbitals of the M impurities occurs in Au 12M clusters. References (1) Bulusu, S.; Li, X.; Wang, L. S.; Zeng, X. C. Proc. Natl. Acad. Sci. U. S. A. 2006, 103, (2) Li, J.; Li, X.; Zhai, H. J.; Wang, L. S. Science 2003, 299, 864. (3) Fa, W.; Dong, J. M. J. Chem. Phys. 2006, 124, (4) Johansson, M. P.; Sundholm, D.; Vaara, J. Angew. Chem. Int. Edit. 2004, 43, Fig.6 Spatial orientation of the highest occupied molecular orbitals of the ground-state Au12M (M=Na, Mg, Al, Si, P, S, Cl) clusters (5) Gao, Y.; Zeng, X. C. J. Am. Chem. Soc. 2005, 127, (6) Gu, X.; Bulusu, S.; Li, X.; Zeng, X. C.; Li, J.; Gong, X. G.; Wang, L. S. J. Phys. Chem. C 2007, 111, 8228.

6 1360 Acta Phys. -Chim. Sin Vol.28 (7) Huang, W.; Ji, M.; Dong, C. D.; Gu, X.; Wang, L. M.; Gong, X. G.; Wang, L. S. ACS Nano 2008, 2, 897. (8) Dong, C. D.; Gong, X. G. J. Chem. Phys. 2010, 132, (9) Scherbaum, F.; Grohmann, A.; Huber, B.; Krueger, C.; Schmidbaur, H. Angew. Chem. 1988, 100, (10) Pyykko, P. Chem. Rev. 1988, 88, 563. (11) Wang, S. Y.; Yu, J. Z.; Mizuseki, H.; Sun, Q.; Wang, C. Y.; Kawazoe, Y. Phys. Rev. B 2004, 70, (12) Hakkinen, H.; Moseler, M.; Kostko, O.; Morgner, N.; Hoffmann, M. A.; Issendorff, B. V. Phys. Rev. Lett 2004, 93, (13) Yu, Y. J.; Wang, H. Y.; Yang, C. L.; Chen, J. N. Acta Phys. -Chim. Sin. 2011, 27, 808. 学学报, 2011, 27, 808.] [ 于永江, 王华阳, 杨传路, 陈建农. 物理化 (14) Qian, H. F.; Barry, E.; Zhu, Y.; Jin, R. C. Acta Phys. -Chim. Sin. 2011, 27, 513. (15) Liang, W. H.; Wang, X. L.; Ding, X. C.; Chu, L. Z.; Deng, Z. C.; Fu, G. S.; Wang, Y. L. Acta Phys. -Chim. Sin. 2011, 27, [ 梁伟华, 王秀丽, 丁学成, 禇立志, 邓泽超, 傅广生, 王英龙. 物理化学学报, 2011, 27, 1615.] (16) Pykko, P.; Runeberg, N. Angew. Chem. 2002, 41, (17) Li, X.; Kiran, B.; Li, H.; Zhai, H. J.; Wang, L. S. Angew. Chem. Int. Edit. 2002, 41, (18) Chen, M. X.; Yan, X. H. J. Chem. Phys. 2008, 128, (19) Heinebrodt, M.; Malinowski, N.; Tast, F.; Branz, W.; Billas, I. M. L.; Martin, T. P. J. Chem. Phys. 1996, 110, (20) Huang, W.; Wang, L. S. Phys. Rev. Lett. 2009, 102, (21) Wang, L. M.; Pal, R.; Huang, W.; Zeng, X. C.; Wang, L. S. J. Chem. Phys. 2010, 132, (22) Ferrighi, L.; Hammer, B.; Madsen, G. K. H. J. Am. Chem. Soc. 2009, 131, (23) Zhang, M.; He, L. M.; Zhao, L. X.; Feng, X. J.; Luo, Y. H. J. Phys. Chem. C 2009, 113, (24) Majumder, C. K.; Kandalam, A. K.; Jena, P. Phys. Rev. B 2006, 74, (25) Zhang, M.; Chen, S.; Deng, Q. M.; He, L. M.; Zhao, L. N.; Luo, Y. H. Eur. Phys. J. D 2010, 58, 117. (26) Long, J.; Qiu, Y. X.; Chen, X. Y.; Wang, S. G. J. Phys. Chem. C 2008, 112, (27) Zhai, H. J.; Li, J.; Wang, L. S. J. Chem. Phys. 2004, 121, (28) Gao, Y.; Bulusu, S.; Zeng, X. C. ChemPhysChem 2006, 7, (29) Li, X.; Kiran, B.; Cui, L. F.; Wang, L. S. Phys. Rev. Lett. 2005, 95, (30) Yang, A. P.; Fa, W.; Dong, J. M. J. Phys. Chem. A 2010, 114, (31) Sun, Q.; Wang, Q.; Jena, P.; Kawazoe, Y. ACS Nano 2008, 2, 341. (32) Wang, L. M.; Bai, J.; Lechtken, A.; Huang, W.; Schooss, D.; Kappes, M. M.; Zeng, X. C.; Wang, L. S. Phys. Rev. B 2009, 79, (33) Neukermans, S.; Janssens, E.; Tanaka, H.; Silverans, R. E.; Lievens, P. Phys. Rev. Lett. 2003, 90, (34) Walter, M.; Hakkinen, H. Phys. Chem. Chem. Phys. 2006, 8, (35) Autschbach, J.; Hess, B. A.; Johansson, M. P.; Neugebauer, J.; Patzschke, M.; Pyykko, P.; Reiher, M.; Sundholm, D. Phys. Chem. Chem. Phys. 2004, 6, 11. (36) Zhao, L. X.; Cao, T. T.; Feng, X. J.; Liang, X.; Lei, Y. M.; Luo, Y. H. J. Mol. Struct. -Theochem 2009, 895, 92. (37) Graciela, B. P.; Ignacio, L. G. J. Mol. Struct. -Theochem 2002, 619, 79. (38) Banerjee, A.; Ghanty, T. K.; Chakrabarti, A.; Kamal, C. J. Phys. Chem. C 2012, 116, 193. (39) Chen, D. D.; Kuang, X. Y.; Zhao, Y. R.; Shao, P.; Li, Y. F. Chin. Phys. B 2011, 20, (40) Li, Y. F.; Kuang, X. Y.; Wang, S. J. J. Phys. Chem. A 2010, 114, (41) Jayasekharan, T.; Ghanty, T. K. J. Phys. Chem. C 2010, 114, (42) Zhao, L. X.; Feng, X. J.; Cao, T. T.; Liang, X.; Luo, Y. H. Chin. Phys. B 2009, 18, (43) Becke, A. D. J. Chem. Phys. 1986, 84, (44) Becke, A. D. J. Chem. Phys. 1988, 88, (45) Becke, A. D. J. Chem. Phys. 1988, 88, (46) Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1988, 37, 785. (47) Becke, A. D. J. Chem. Phys. 1993, 98, (48) Kohn, W.; Sham, L. J. Phys. Rev. A 1965, 140, (49) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 270. (50) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299. (51) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985, 82, 284. (52) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; et al. Gaussian 03, Revision B.03; Gaussian Inc.: Pittsburgh, PA, (53) Zhao, G. F.; Zeng, Z. J. Chem. Phys. 2006, 125, (54) Morse, M. D. Chem. Rev. 1986, 86, (55) Negishi, Y.; Nakamura, Y.; Nakajima, A.; Kaya, K. J. Chem. Phys. 2001, 115, (56) Simard, B.; Hackett, P. A. J. Mol. Spectrosc. 1990, 142, 310. (57) Gingerich, K. A.; Blue, G. D. J. Chem. Phys. 1973, 59, 185. (58) Ho, J.; Ervin, K.; Lineberger, W. J. Chem. Phys. 1990, 93, (59) Taylor, K.; Pettitte-Hall, C.; Cheshnovsky, O.; Smalley, R. J. Chem. Phys. 1992, 96, (60) Tomlman, C. A. Chem. Soc. Rev. 1972, 1, 337.