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ARTICLE IN PRESS Journal of Physics and Chemistry of Solids 71 (2010) 770–775 Contents lists available at ScienceDirect Journal of Physics and Chemistry of Solids journal homepage: www.elsevier.com/locate/jpcs Density functional theory study of AunMn(n =1–8) clusters Die Dong a,b,n, Kuang Xiao-Yu b,c,nn, Guo Jian-Jun a, Zheng Ben-Xia a a b c School of Physics and Chemistry, Xihua University, Chengdu 610039, China Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China International Centre for Materials Physics, Academia Sinica, Shengyang 110016, China a r t i c l e in f o a b s t r a c t Article history: Received 19 November 2009 Received in revised form 31 December 2009 Accepted 27 January 2010 Equilibrium geometries, relative stabilities, and magnetic properties of small AunMn (n = 1–8) clusters have been investigated using density functional theory at the PW91P86 level. It is found that Mn atoms in the ground state AunMn isomers tend to occupy the most highly coordinated position and the lowest energy structure of AunMn clusters with even n is similar to that of pure Aun + 1 clusters, except for n =2. The substitution of Au atom in Aun + 1 cluster by a Mn atom improves the stability of the host clusters. Maximum peaks are observed for AunMn clusters at n =2, 4 on the size dependence of second-order energy differences and fragmentation energies, implying that the two clusters possess relatively higher stability. The HOMO–LUMO energy gaps of the ground state AunMn clusters show a pronounced odd– even oscillation with the number of Au atoms, and the energy gap of Au2Mn cluster is the biggest among all the clusters. The magnetism calculations indicate that the total magnetic moment of AunMn cluster, which has a very large magnetic moment in comparison to the pure Aun + 1 cluster, is mainly localized on Mn atom. & 2010 Elsevier Ltd. All rights reserved. Keywords: A. Nanostructures C. Ab initio calculations D. Magnetic properties 1. Introduction Previous experimental and theoretical work has demonstrated that the introduction of a dopant atom in a small cluster can significantly change the properties of the host cluster [1–4]. Gold clusters doped with transition metal atoms (V, Cr, Fe, Co, Ni, etc.) have been actively sought to tailor the desired structural, electronic, optical, magnetic, and catalytic properties for potential applications in solid state chemistry, materials science, microelectronics, biology, and nanotechnology [5–11]. For instance, Yuan et al. [6] investigated the structure of AunM (n =1–7, M= Ni, Pd, Pt) clusters and found that the dopant atoms can considerably alter the geometric and electronic properties of the gold cluster. Zhang et al. [7] reported that M@Au6 clusters (M =Sc–Ni), where the transition metal atoms are located in the center of Au6 ring, could be used as a new nanomaterials with tunable magnetic moment. Graciani et al. [8] proved that the isolated V-doped Au12 cluster can bind a high number of oxygen molecules above pure gold cluster and is an improved novel catalyst for CO oxidation. Recently, the pure gold materials doped with manganese have also been studied widely owing to their unique physical and n Corresponding author at: School of Physics and Chemistry, Xihua University, Chengdu 610039, China. nn Corresponding author at: Institute of Atomic and Molecular Physics, Sichuan University, Chengdu 610065, China E-mail addresses: [email protected] (D. Dong), [email protected] (K. Xiao-Yu). 0022-3697/$ - see front matter & 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2010.01.015 chemical properties [12–15]. It was shown that the magnetocrystalline anisotropy energy of Mn@Au nanotube is dramatically enhanced by one order of magnitude and this hybrid structure can be used in ultrahigh density magnetic storage [12]. The icosahedral Au12 cage filled with single Mn atom, which has a large local spin magnetic moment, shows unexpected large binding energy compared with icosahedral Au13 cluster [13]. The positive charge of cationic AunMn + clusters is mostly localized in Mn atom and decreases when the size of the cluster increases [14]. Moreover, these studies primarily focus on the ionic or special-size clusters. To the best of our knowledge, there have been no reports regarding small neutral Mn-doped gold clusters so far. On the other hand, it is well-known that small metal clusters usually exhibit extraordinary size-dependent properties, which should be extremely different from those of the bulk, due to a large fraction of surface atoms and a distinct electronic structure. Therefore, in this paper, the geometric structures, relative stabilities, and magnetic properties of AunMn (n= 1–8) clusters will be investigated systematically on the basis of density functional theory (DFT). It is hoped that this work would be useful to understand the influence of material structure on its properties and could provide powerful guidelines for future experimental studies. 2. Computational method DFT methods and an effective core potential LanL2DZ basis set, as implemented in GAUSSIAN03 program package [16–18], have ARTICLE IN PRESS D. Dong et al. / Journal of Physics and Chemistry of Solids 71 (2010) 770–775 Table 1 The bond lengths (r) and dissociation energies (De) of ground state Au2 dimer obtained by using different density functional methods. Methods r(Å) De (eV) LSDA PW91P86 PW91PW91 PBEPBE BLYP Experimental (ref.25) 2.49 2.54 2.55 2.55 2.59 2.47 2.83 2.30 2.20 2.17 1.99 2.30 been employed for the calculations of structures and vibrational frequencies. The exchange–correlation energies were treated using PW91P86 functional of the generalized gradient approximation (GGA) [19,20]. The convergence thresholds were set to 1.5 10 5 Hartree/Bohr for the forces, 6.0 10 5 Å for the displacement, and 10 6 Hartree for the energy change. To search the lowest energy structures, lots of possible initial isomers, which include one-, two- and three-dimensional configurations, had been considered in geometry optimizations. Furthermore, the number of possible initial isomers increases rapidly with the increase in size of clusters. Due to the spin polarization, every initial configuration was optimized at various possible spin multiplicities. Each geometry optimization was followed by an analysis of harmonic vibrational freqencies to confirm that the optimized geometry corresponds to a local minimum. The reliability of current computational method has been tested by comparative calculations on gold dimer. The results are listed in Table 1. It can be seen from Table 1 that the calculated bond length and dissociation energy based on PW91P86 method are in good agreement with experimental values. These indicate the suitability of current computational method to describe small AunMn (n = 1–8) clusters. 3. Results and discussion 3.1. Geometrical structures For AunMn (n = 2–8) clusters, more than 300 initial configurations were optimized and many isomers have been obtained. The ground state structure and three low-lying isomers for each AunMn cluster are displayed in Fig. 1. According to the energies from low to high, these isomers are designated by na, nb, nc, and nd, where n represents the number of Au atoms in the AunMn clusters. Their symmetry, spin multiplicity and energy difference compared to each of ground state structures are also indicated in the figure. Meanwhile, in order to examine the effects of dopant Mn on gold clusters, geometry optimizations of Aun (n = 2–9) clusters have been carried out using identical method and basis set. The lowest energy structures of Aun clusters, as shown in Fig. 1, were found. These structures are also in accord with the results of Idrobo et al [21–25]. The calculated results for AuMn manifest that the total energy of septet spin state is the lowest in all possible spin states. Hence, the septet AuMn dimer with electronic state of 7Sg is the ground state structure, and the bond length of ground state AuMn dimer (2.45 Å) is shorter than that of Au2 (2.54 Å). This may be attributed to the fact that the radius of Mn atom is smaller than that of Au atom. The linear 2a isomer with DNh symmetry is found to be the most stable structure of Au2Mn cluster. The Au–Mn bond length is 2.43 Å and the corresponding electronic state is 6Sg. The 2b 771 isomer is a linear configuration with CNV symmetry and 1.33 eV higher in energy than the 2a isomer. The trigonal 2c isomer in octet spin state is another metastable isomer. The 2d isomer with an apex angle of 119.21 is similar to the ground state structure of Au3 cluster. The lowest energy structure of Au3Mn cluster is the 3a isomer, which is obtained by distorting the geometry starting from D3h to C2V symmetry. The electronic state for the 3a isomer is 5B2. The rhombus 3b and 3c isomers resemble the most stable structure of Au4 cluster and are less stable than 3a isomer by 0.20 and 1.02 eV, respectively. At the same time, the 3b isomer can be seen as intermediate between 3a and 3c isomers. The 3d isomer has the same spin multiplicity and structure as 3a isomer. But Mn atom in 3d isomer is located at a lowly coordinated position. Similar to the configuration of ground state Au5 cluster, the trapezoidal 4a isomer in electronic state of 6A1 is the most stable structure of Au4Mn clusters. The planar 4b isomer with an uncompact structure is energetically higher than the 4a isomer by 0.16 eV. The sextet 4c isomer is a square pyramid with Mn atom on the top and the first three-dimensional (3D) configuration. The 4d isomer, which is 0.32 eV higher in energy than the 3D 4c isomer, possesses a triangular bipyramid structure. Other planar and 3D isomers are less stable than the four isomers. Among the Au5Mn isomers, the lowest energy structure is the planar 5a isomer with electronic state of 5B2 and C2V symmetry. The Mn atom is surrounded by five Au atoms. But the isomer belonged to point group of D5h is not obtained in geometry optimizations. The 5b, which relates to the most stable structure of Au6 cluster, is found as a low-lying isomer, with 0.45 eV higher than the lowest energy structure. The 5c isomer in quintet spin state is energetically lower than the same structure with other spin states. The septet 5d isomer with C4V symmetry is an octahedral configuration, where the tetrahedrally coordinated Mn atom occupies the vertex position. In addition, several planar isomers, which are not displayed in Fig. 1, have a big energy difference relative to the forgoing four isomers. In the case of Au6Mn clusters, seven isomers, such as 6a in Fig. 1, show a similar structure to that of the ground state Au7 cluster and their energies decrease as the coordinated number of Mn atom increases. The 6a isomer with electronic state of 6A0 is the most stable structure in all isomers. Other six isomers, which are not plotted in Fig. 1, are significantly higher in energy than the 6a isomer. The 6b isomer with Mn atom at the center of Au6 ring is a high-symmetry planar structure, which was expected to be the lowest energy structure. But its energy is higher by 0.13 eV than that of the 6a isomer. The 6c and 6d isomers, whose energies are closed to the 6b isomer, are more stable than other 3D configurations. Due to the Jahn–Teller effect, Mn atom in the 6c isomer with C3V symmetry is shifted along the C3 axis of D3h symmetry. The quintet planar 7a isomer with electronic state of 5B2 is the lowest energy structure of Au7Mn cluster. However, our results show that this configuration corresponds to the metastable isomer of Au8 cluster. The 7b isomer with Au–Mn-Au bond angle of 161.31, which is the most stable 3D configuration, is still 0.33 eV less stable than the 7a isomer. The 7c and 7d isomers are two low-lying planar structures and have a large structural distortion relative to the most stable Au8 cluster. For the 7c isomer, the septet spin state is energetically lower than the quintet spin state by 0.09 eV. The 7d geometry in septet spin state turns into the 7c isomer. With regard to Au8Mn cluster, 30 odd isomers were found and the low-lying isomers evidently favor planar structures, as shown in Fig. 1. The 8a and 8b isomers, which exhibit a configuration ARTICLE IN PRESS 772 D. Dong et al. / Journal of Physics and Chemistry of Solids 71 (2010) 770–775 D∞h, 6 2a C∞V, 6, 1.33 eV 2b C2V, 8, 1.69eV 2c C2V, 2, 2.97eV 2d D2h, 1 Au4 C2V, 5 3a C2V, 5, 0.20eV 3b C2V, 5, 1.02eV 3c C2V, 5, 1.48eV 3d C2V, 2 Au5 C2V, 6 4a C2V, 6, 0.16eV, 4b C4V, 6, 0.53eV 4c C3V, 6, 0.85eV 4d D3h, 1 Au6 C2V, 5 5a C2V, 5, 0.45eV 5b CS, 5, 0.62eV 5c C4V, 7, 0.98eV 5d CS, 2 Au7 CS, 6 6a D6h, 4, 0.13eV 6b C3V, 6, 0.19eV 6c C2V, 6, 0.27eV 6d D4h, 1 Au8 C2V, 5 7a C2V, 5, 0.33eV 7b C2V, 7, 0.50eV 7c C2V, 5, 0.60eV 7d C2V, 2 Au9 C2V, 6 8a C2V, 6, 0.22eV 8b D2h, 6, 0.30eV 8c CS, 6, 0.37eV 8d C2V, 2 Au3 Fig. 1. The lowest energy structures of Aun + 1 and AunMn (n= 2–8) clusters, and three low-lying isomers for doped clusters. Bond lengths are in Å. Their symmetry, multiplicity, and energy difference compared to each of the ground state structures are given below them. The yellow and blue balls represent Au and Mn atoms, respectively. For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article. similar to the ground state structure of Au9 cluster, are more stable than other isomers. The former with electronic state of 6A1 is lower in energy than the latter and the lowest energy structure. The 8c isomer is a rhombus structure with D2h symmetry. Mn atom in the 8c isomer is at the center of this structure. The 8d isomer with CS symmetry is above the lowest energy structure by 0.37 eV. Nevertheless, the 8d-like configuration with Mn atom at the center was found to be an unstable structure. As for the 3D isomers of Au8Mn cluster, their energies are higher than the planar 8d isomer. ARTICLE IN PRESS D. Dong et al. / Journal of Physics and Chemistry of Solids 71 (2010) 770–775 Fig. 2. Size dependence of the averaged binding energies for the ground state structures of AunMn and Aun + 1 clusters. 773 Fig. 3. Size dependence of the second-order energy differences for the ground state structures of AunMn and Aun + 1 clusters. From the above discussions, it is obvious that the ground state structures of AunMn (n= 1–8) clusters favor the linear structures for n = 1–2 and planar structures for n =3–8. The Mn atom in the most stable AunMn clusters tend to occupy the most highly coordinated position. On the other hand, for n= 3–8, the ground state geometries of AunMn clusters with even n are similar to those of pure Aun + 1 clusters. 3.2. Relative stabilities In this part, compared with the pure Aun + 1 clusters, the relative stabilities of AunMn (n = 1–8) clusters for the most stable structures are analyzed based on the atomic averaged binding energies, second-order difference of energies, fragmentation energies, and energy gaps between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). The atomic averaged binding energies (Eb) of AunMn and Aun + 1 clusters are defined as [26] Eb ½Aun Mn ¼ ðnE½Au þ E½MnE½Aun MnÞ=ðn þ1Þ ð1Þ Eb ½Aun þ 1 ¼ fðn þ1ÞE½AuE½Aun þ 1 g=ðn þ 1Þ ð2Þ where E represents the energies of the corresponding systems. The calculated binding energies per atom for the most stable AunMn and Aun + 1 clusters are shown in Fig. 2. As seen from Fig. 2, the substitution of Au atom by an Mn atom enhances the stability of the host clusters. For AunMn clusters, the averaged binding energy of AuMn dimer is much smaller than those of other AunMn (n= 2–8) clusters. A local visible peak occurs at n = 2. This hints that the Au2Mn cluster is more stable than its neighboring clusters. From n4 3, the Eb of AunMn clusters increase with n, but finally tends to saturate. In cluster physics, the second-order difference of energies (D2E), which can be compared with the relative abundances determined in mass spectroscopy experiment, are a quite sensitive quantity that reflects the relative stability of clusters [27]. For the most stable AunMn and Aun + 1 clusters, it can be estimated as follows D2 E½Aun Mn ¼ E½Aun þ 1 Mn þE½Aun1 Mn2E½Aun Mn ð3Þ D2 E½Aun ¼ E½Aun þ 1 þ E½Aun1 2E½Aun ð4Þ where E is the energy of the ground state clusters. Fig. 3 illustrates the size dependence of the second-order energy differences for the most stable AunMn and Aun + 1 clusters. It is clear from this Fig. 4. The fragmentation energies of the ground state structures of AunMn and Aun + 1 clusters via loss of an Au atom. figure that the even-numbered gold clusters are more stable than the odd-numbered ones. However, the presence of Mn atom changes the stable pattern of the host clusters. For AunMn clusters, two conspicuous maxima are found at n =2 and 4. Accordingly, it can be deduced that Au2Mn and Au4Mn clusters possess relatively higher stability and are magic clusters. The relative stability of the most stable AunMn and Aun + 1 clusters can also be investigated by examining the fragmentation energy [27], which involves the energy that an Au atom is separated from these clusters. In this case, the fragmentation energy (DE) can be calculated as DE½Aun Mn ¼ E½Aun1 Mn þE½AuE½Aun Mn ð5Þ DE½Aun þ 1 ¼ E½Aun þE½AuE½Aun þ 1 ð6Þ where E is the energy of the lowest energy clusters or atom. For the most stable AunMn and Aun + 1 clusters, the fragmentation energy as a function of the cluster size is displayed in Fig. 4. Obviously, the results are also in accord with the above analysis based on the second-order difference of energies. The HOMO–LUMO energy gap (Eg), which relies on the eigenvalues of the HOMO and LUMO energy levels, is always considered to be a significant parameter that characterizes chemical stability of small clusters. A big energy gap usually relates to a high chemical stability. For the most stable AunMn and ARTICLE IN PRESS 774 D. Dong et al. / Journal of Physics and Chemistry of Solids 71 (2010) 770–775 Aun + 1 clusters, the energy gaps are plotted in Fig. 5. The AunMn and Aun + 1 clusters show a strong odd–even oscillations in their energy gap spectrum. The energy gap of AunMn clusters is smaller for odd n and larger for even n than that of the corresponding Aun + 1 clusters. Although the energy gaps do not correlate directly with the second-order difference of energies and fragmentation energy, it can be seen from Fig. 5 that the magic clusters, Au2Mn, has a particularly large energy gap. In other words, the Au2Mn cluster is less reactive and could be useful as building block for constructing the cluster-assembled materials. The AuMn dimer has a very small energy gap (0.01 eV) relative to other clusters. This means that AuMn dimer has lower chemical stability. Table 2 The charge and local magnetic moment of 3d, 4s, and 4p states for Mn atoms in AunMn clusters Cluster AuMn Au2Mn Au3Mn Au4Mn Au5Mn Au6Mn Au7Mn Au8Mn Mn—3d Mn—4s Mn—4p Q (e) m (mB) Q (e) m (mB) Q (e) m (mB) 5.23 5.32 5.43 5.44 5.54 5.47 5.53 5.47 4.77 4.62 4.49 4.51 4.30 4.47 4.37 4.47 1.20 0.80 0.76 0.70 0.58 0.69 0.65 0.67 0.70 0.18 0.14 0.14 0.08 0.09 0.09 0.10 0.16 0.31 0.06 0.08 0.89 0.08 0.10 0.09 0.10 0.01 0 0 0.03 0 0.01 0.01 3.3. Magnetic properties The total magnetic moment of the most stable AunMn (n = 1–8) clusters has been calculated and the results are presented in Fig. 6, where we have also plotted the total magnetic moment of the host clusters. The ground state Aun + 1 clusters show a pronounced odd–even alternations with the number of Au atoms in the total magnetic moment. When an Mn atom substitutes for an Au atom in Aun + 1 cluster, the AunMn clusters generate a very large magnetic moment. In particular, the AuMn dimer, which is more chemically active, has the biggest magnetic moment (6mB) among all the AunMn clusters. For n = 2–8, the total magnetic moments of AunMn clusters keep the same pattern of oscillation with the pure gold clusters and are 5mB for even n and 4mB for odd n. Simultaneously, it is also evident from the magnetic moment calculations that the doping by an Mn atom augments the magnetism of gold clusters. In order to understand the magnetic properties further, we have performed the natural bond orbital analysis for the most stable AunMn (n =1–8) clusters [28]. The local magnetic moments on Mn atoms are shown in Fig. 6. It can be seen from Fig. 6 that the total magnetic moment of the clusters is mainly localized in Mn atom. Small amount of magnetic moments are found in Au atoms. The Au atoms in AunMn clusters exhibit antiferromagetic alignment for n=3, 5, and 7 and ferromagetic alignment for even n and n=1 with respect to Mn atom’s magnetic moment. The charge and magnetic moment on 3d, 4s, and 4p states of Mn atom in AunMn clusters were listed in Table 2. It is found that the partially filled 3d orbital play an important role in determining the magnetism of Mn atom. The magnetic moment provided by 3d orbital is about 4.30–4.77mB. The 4s and 4p subshells, which are non-magnetic for a free Mn atom, contribute a little of magnetic moment. This may be ascribed to the internal charge transfer from 4s orbital to 3d and 4p states. Namely, the 4s orbital lose 0.80–1.42 electrons, while the 3d and 4p states obtain 0.23–0.54 and 0.06–0.89 electrons, respectively. At the same time, the magnetic moment of 4s and 3d orbitals decreases gradually with the increase in charge transfer. 4. Conclusions Fig. 5. Size dependence of the HOMO–LUMO energy gaps of ground state AunMn and Aun + 1 clusters. Equilibrium geometries, relative stabilities, and magnetic properties of AunMn (n=1–8) clusters have been studied by firstprincples density functional calculations. The geometric optimizations indicate that Mn atoms in ground state AunMn isomers tend to occupy the most highly coordinated position and the most stable structure of AunMn clusters with even n resembles that of pure Aun + 1 clusters, except for n=2. The substitution of Mn atom for an Au atom in Aun + 1 cluster enhances the stability of the host clusters. The analyses of the second-order energy differences and fragmentation energies indicate that Au2Mn and Au4Mn clusters are magic clusters. We also found from the HOMO–LUMO gaps that Au2Mn cluster have high chemical stability. The magnetism calculations show that the total magnetic moments of AunMn cluster are 4 or 6mB larger than those of pure Aun + 1 clusters. Mn atom in these clusters carries most of the magnetic moment. Acknowledgements Fig. 6. Total magnetic moment of the ground state AunMn and Aun + 1 clusters, and local magnetic moment on Mn atom. This project was supported by Xihua University (No. Zg0723304) and the Education Department of Sichuan Province (No. 2006B042). ARTICLE IN PRESS D. Dong et al. / Journal of Physics and Chemistry of Solids 71 (2010) 770–775 References [1] B. Chen, H. Zhang, B. Gilbert, J.F. Banfield, Mechanism of inhibition of nanoparticle growth and phase transformation by surface impurities, Phys. Rev. Lett. 98 (2007) 106103. [2] I.A. Paul, A.S. Steven, R.G. Daniel, Inorganic cluster syntheses of TM2 + -doped quantum dots (CdSe, CdS, CdSe/CdS): physical property dependence on dopant locale, J. Am. Chem. Soc. 129 (2007) 9808–9818. [3] C. Zeng, Z. Zhang, K.V. Benthem, M.F. Chisholm, H.H. Weitering, Optimal doping control of magnetic semiconductors via subsurfactant epitaxy, Phys. Rev. Lett. 100 (2008) 066101. [4] X. Li, B. Kiran, L.F. Cui, L.S. Wang, Magnetic properties in transition-metaldoped gold clusters: M@Au (M= Ti, V, Cr), Phys. Rev. Lett. 95 (2005) 253401. [5] R. Pal, L.M. Wang, W. Huang, L.S. Wang, X.C. Zeng, Structural evolution of doped gold clusters: MAux (M = Si, Ge, Sn; x = 5–8), J. Am. Chem. Soc. 131 (2009) 3396–3404. [6] D.W. Yuan, Y. Wang, Z. Zeng, Geometric, electronic, and bonding properties of AuNM (N = 1–7;M = Ni, Pd, Pt) clusters, J. Chem. Phys. 122 (2005) 114310. [7] M. Zhang, L.M. He, L.X. Zhao, X.J. Feng, Y.H. Luo, Tuning magnetic moments by 3d transition-metal-doped Au6 Clusters, J. Phys. Chem. C 113 (2009) 6491–6496. [8] J. Graciani, J. Oviedo, J.F. Sanz, V@Au12 : an improved novel catalyst for CO oxidation, J. Phys. Chem. B 110 (2006) 11600–11603. [9] L.M. Wang, J. Bai, A. Lechtken, W. Huang, D. Schooss, M.M. Kappes, X.C. Zeng, (M =Fe, Co, L.S. Wang, Magnetic doping of the golden cage cluster M@Au16 Ni), Phys. Rev. B 79 (2009) 033413. [10] M.B. Torres, E.M. Fernández, L. Balbás, Theoretical study of oxygen adsorption on pure Aun+ + 1 and doped MAun+ cationic gold clusters for M= Ti, Fe and n= 3– 7, J. Phys. Chem. A 112 (2008) 6678–6689. [11] P. Pyykkö, Theoretical chemistry of gold, Chem. Soc. Rev. 37 (2008) 1967–1997. [12] L. Zhu, J. Wang, F. Ding, Gold nanotube encapsulation enhanced magnetic properties of transition metal monoatomic chains: An ab initio study, J. Chem. Phys. 130 (2009) 064706. [13] S.Y. Wang, J.Z. Yu, H. Mizuseki, Q. Sun, C.Y. Wang, Y. Kawazoe, Energetics and local spin magnetic moment of single 3, 4d impurities encapsulated in an icosahedral Au12 cage, Phys. Rev. B 70 (2004) 165413. [14] M.B. Torres, E.M. Fernández, L.C. Balbás, Theoretical study of structural, electronic, and magnetic properties of AunM + clusters (M = Sc, Ti, V, Cr, Mn, Fe, Au; nr 9), Phys. Rev. B 71 (2005) 155412. 775 [15] L. Udvardi, S. Khmelevskyi, L. Szunyogh, P. Mohn, P. Weinberger, Helimagnetism and competition of exchange interactions in bulk giant magnetoresistance alloys based on MnAu2, Phys. Rev. B 73 (2006) 104446. [16] W.R. Wadt, P.J. Hay, Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi, J. Chem. Phys. 82 (1985) 284. [17] P.J. Hay, W.R. Wadt, Ab initio effective core potentials for molecular calculations. Potentials for K to Au including the outermost core orbitals, J. Chem. Phys. 82 (1985) 299. [18] M.J. Frisch, G.W. Trucks, H.B. Schlegel et al., GAUSSIAN 03 Revision E.01, Gaussian, Inc., Wallingford CT, 2004. [19] J.P. Perdew, K. Burke, Y. Wang, Generalized gradient approximation for the exchange- correlation hole of a many-electron system, Phys. Rev. B 54 (1996) 16533–16539. [20] J.P. Perdew, Density–functional approximation for the correlation energy of the inhomogeneous electron gas, Phys. Rev. B 33 (1986) 8822–8824. [21] J.C. Idrobo, W. Walkosz, S.F. Yip, S. Ögüt, J. Wang, J. Jellinek, Static ˘ polarizabilities and optical absorption spectra of gold clusters (Aun, n =2–14 and 20) from first principles, Phys. Rev. B 76 (2007) 205422. [22] C. Majumder, S.K. Kulshreshtha, Structural and electronic properties of Aun (n= 2–10) clusters and their interactions with single S atoms: Ab initio molecular dynamics simulations, Phys. Rev. B 73 (2006) 155427. [23] G. Philipp, R.M. David, R. Britta, F.G.M. Alexander, L.T. Jonathan, M. Gerard, F. André, Structures of neutral Au7, Au19, and Au20 clusters in the gas phase, Science 321 (2008) 674–676. [24] L. Xiao, B. Tollberg, X. Hu, L. Wang, Structural study of gold clusters, J. Chem. Phys. 124 (2006) 114309. [25] D. Ajanta, C.D. Ramesh, Structural and electronic properties of stable Aun (n= 2–13) clusters: a density functional study, J. Mol. Struc. THEOCHEM 870 (2008) 83–93. [26] M.D. Deshpande, S. Roy, D.G. Kanhere, Equilibrium geometries, electronic structure, and magnetic properties of NinSn clusters (n= 1–12 ), Phys. Rev. B 76 (2007) 195423. [27] C.C. Wang, R.N. Zhao, J.G. Han, Geometries and magnetisms of the Zrn (n= 2– 8) clusters: the density functional investigations, J. Chem. Phys. 124 (2006) 194301. [28] A.E. Reed, L.A. Curtiss, F. Weinhold, Intermolecular interactions from a natural bond orbital, donor-acceptor viewpoint, Chem. Rev. 88 (1988) 899–926.