Electronic Structure and Photochemical Properties of a Monolayer

11904

J. Phys. Chem. B 2004, 108, 11904-11908

Electronic Structure and Photochemical Properties of a Monolayer-Protected Gold Cluster Katsuyuki Nobusada*,† DiVision of Chemistry, Graduate School of Science, Hokkaido UniVersity, Sapporo, 060-0810 Japan ReceiVed: January 9, 2004; In Final Form: April 9, 2004

The electronic structure of a monolayer-protected gold cluster, [Au13(SCH3)8]3+, has been investigated by performing density functional calculations. The cluster has a characteristic structure with Oh molecular symmetry, and eight (111) facets of a centered cuboctahedral Au13 core cluster are fully passivated by eight methanethiolates. The bond distance between two neighboring gold atoms (3.673 Å) is much larger than that of the bare Au13 cluster (2.929 Å), whereas the Au-S bond distance is 2.403 Å. This atomic rearrangement means that the methanethiolates stabilize the enlarged bare Au13 cluster by bonding to the (111) hollow sites of the bare cluster. The absorption spectrum of the [Au13(SCH3)8]3+ cluster is simulated within time-dependent density functional theory. The spectrum shows clear absorption peaks and each peak is assigned to specific excitation processes.

Introduction Nanometer-sized metal clusters protected by a monolayer of molecules such as thiolates have attracted much attention in various areas of science and technology.1-3 This is, in part, due to the fact that monolayer-protected metal clusters (MPCs) provide significantly different physicochemical properties such as optical response, catalysis, and reactivity from corresponding bare metal clusters or bulk metals. Furthermore, in the rapidly growing area of molecular electronics, a single molecule coupled to a noble metal electrode through, for example, thiolate groups has been as a promising candidate of molecular wire junctions conducting electrical current.4-10 Outstanding features of metalthiolate compounds are attributed to specific metal-thiolate interactions that thiolate groups have a strong affinity to a number of metals and have an ability to bridge two or more metal atoms. Accordingly, nanometer-sized metal-thiolate clusters show characteristic electronic structures and properties, which are strongly related to the nature of the clusters. Therefore, such metal-thiolate clusters have high potentialities for creating a new class of nanoparticle science and technology. Although their experimental and theoretical studies are still in a juvenile stage, recent remarkable experimental progress in preparing sizeselected and structurally characterized nanometer-sized particles allows us to tackle essential properties of such clusters. From a viewpoint of theoretical study, it is necessary to fully understand electronic structures and properties of those clusters with a special emphasis on describing metal-molecule interactions. Recently, density functional calculations have been extensively carried out to reveal electronic properties of various types of molecules.11 The density functional method is one of the reasonable theoretical approaches to physicochemical understanding of metal-molecule compounds such as MPCs and polynuclear complexes.12-15 The present theoretical study was partly motivated by the recent experiment of Negishi and Tsukuda.16 They prepared gold clusters composed of ∼10-13 atoms protected by meso-2,3* To whom correspondence should be addressed. E-mail: nobusada@ ims.ac.jp. † Present address: Department of Theoretical Studies, Institute for Molecular Science, Myodaiji, Okazaki 444-8585, Japan.

dimercaptosuccinic acids (DMSAs) and predicted a structure of the Au13(DMSA)8 cluster with Oh molecular symmetry. The purpose of the present study is to theoretically determine a possible structure of such a nanometer-sized metal cluster with high molecular symmetry and also to elucidate photochemical properties of the cluster by performing density functional calculations. In the actual calculations, we choose a model system of [Au13(SCH3)8]3+ with constrained Oh molecular symmetry. Thus, all the discussions in the remainder of this article are based on the results for the cluster system with Oh molecular symmetry.17 This paper is organized as follows. In the next section, we define a theoretical model of a gold-thiolate cluster. The method of calculations is also described in this section. In section 3, the optimized geometry and the electronic properties of the cluster are reported. The absorption spectrum for the gold cluster is elucidated. Finally, the concluding remarks are given in section 4. Method of Calculation We calculated the electronic structure of a gold cluster passivated by methanethiolate molecules [Au13(SCH3)8]3+ within Oh molecular symmetry at the level of Kohn-Sham density functional theory (KS-DFT). The calculations employed the Becke three-parameter hybrid exchange functional with the Lee-Yang-Parr correlation functional (B3LYP).18,19 A 60electron relativistic effective core potential (ECP)20 was utilized for the gold atom, and the remaining 19 valence electrons were treated explicitly. A set of contracted Gaussian-type orbitals Au(7s6p5d)/[6s3p2d] optimized for the ECP by Ahlrichs21 was chosen. We used valence double-ζ polarized basis sets22 for S, C, and H atoms. An absorption spectrum for the cluster was simulated by calculating oscillator strength within time-dependent density functional theory (TDDFT). The present TDDFT is based on time-dependent Kohn-Sham response theory.23-25 Excited-state properties are obtained from a pole analysis of frequency-dependent linear response functions. All the calculations have been performed with the program package Turbomole.21 Before ending this section, we refer to the reason for choosing the triply charged metal cluster. We carried out a preliminary

10.1021/jp049879l CCC: $27.50 © 2004 American Chemical Society Published on Web 07/17/2004

Monolayer-Protected Gold Cluster

J. Phys. Chem. B, Vol. 108, No. 32, 2004 11905

Figure 1. Optimized geometry of the methanethiolate-protected gold cluster, [Au13(SCH3)8]3+: Au (magenta), S (yellow), CH3 (gray).

TABLE 1: Structural Parameters of the [Au13(SCH3)8]3+, [Ag13(SCH3)8]3+, and [Cu13(SCH3)8]3+ Clusters parameter

[Au13(SCH3)8]3+ [Ag13(SCH3)8]3+ [Cu13(SCH3)8]3+

-M ) (Å) r(Ma-S) (Å) r(S-C) (Å) r(C-H) (Å) ∠S-Ma-S (deg) ∠Ma-S-C (deg) r(Ma

a

a

3.673 2.403 1.845 1.096 165.6 118.0

3.786 2.467 1.851 1.096 164.7 117.6

3.160 2.215 1.851 1.095 178.6 124.5

M: Au, Ag, Cu.

calculation of geometry optimization for the neutral MPC Au13(SCH3)8 within Oh molecular symmetry. Although the cluster has a similar optimized structure, the details of the electronic structure are rather different from those of [Au13(SCH3)8]3+. The highest-occupied molecular orbital (HOMO) of Au13(SCH3)8 is triply degenerate because of high molecular symmetry, and each of the orbitals is occupied by R spin, that is, the quartet state. MPCs are usually synthesized in solvents, and there are counterpart negative ions such as halogens in such an environment. Actually compounds in ionic forms such as [Aum(SCH3)n]k+Clk- are also present in solvents together with neutral compounds. In the present calculations, to avoid carrying out DFT calculations explicitly including spin and also to take account of spin multiplicity of the neutral Au13(SCH3)8 (i.e., the quartet state), the triply charged MPC [Au13(SCH3)8]3+ was chosen. We make a comment further on the stability of the singly charged MPC [Au13(SCH3)8]+. We also carried out geometry optimization for [Au13(SCH3)8]+ within Oh molecular symmetry. However, the calculation implied that [Au13(SCH3)8]+ is not stable within Oh molecular symmetry. As mentioned above, because we focus on describing electronic properties of a nanometer-sized metal cluster with high molecular symmetry, the singly charged MPC is not considered. Results and Discussion Optimized Geometry and Electronic Properties of [Au13(SCH3)8]3+. The optimized geometry of [Au13(SCH3)8]3+ within Oh molecular symmetry is shown in Figure 1, and its structural parameters are summarized in Table 1. The figure shows that eight (111) facets of a centered cuboctahedral Au13 cluster15,26,27 are passivated by eight methanethiolates. This structure is very similar to the gold-thiolate cluster predicted experimentally by

Figure 2. KS orbital energy levels of the [Au13(SCH3)8]3+, [Ag13(SCH3)8]3+, and [Cu13(SCH3)8]3+ clusters. The energies are indicated in the unit of eV relative to the HOMO energies. cAu, cAg, and cCu denote the central metals. For details of the orbital classification, see text.

Negishi and Tsukuda except that methanethiolates were replaced by DMSAs in their experiment.16 It is reasonable to assume that the difference between DMSA and methyl groups has a little influence on the main structure composed of the gold and sulfur atoms. To determine the stability of the optimized structure, we carried out a second derivative calculation and made a Mulliken population analysis for the [Au13(SCH3)8]3+ cluster. We found only one imaginary frequency corresponding to a triply (t1u) degenerate vibrational mode, but the frequency is small enough to be neglected within a numerical error of the present calculations. The Mulliken population analysis revealed that charge on the gold atoms (except the central gold atom) significantly transfers to the sulfur atoms, i.e., Au (0.29) and S (-0.31). As a result, the Au-S bond distance (2.403 Å) becomes rather small indicating the Au-S bond formation, whereas the bond distance between two neighboring gold atoms (3.673 Å) is much larger than that of a bare Au13 cluster (2.929 Å)15 because of Coulomb repulsion. These findings are very similar to those obtained by Larsson et al. in the study of Au13SCH3.15 For these reasons, it is reasonable to think that the methanethiolates significantly stabilize the bare Au13 cluster by forming the Au-S bonds and thus the optimized structure of [Au13(SCH3)8]3+ is stable even within Oh molecular symmetry. To analyze electronic properties of [Au13(SCH3)8]3+, we show KS orbital energy levels of the cluster in Figure 2. The energies are indicated in the unit of eV relative to the energy of the HOMO. Main components of atomic orbitals contributing to each KS orbital are compiled in Table 2. The HOMO is constructed mainly from the central Au 6s orbital and the HOMO-1 and the HOMO-2 from the central Au 5d orbitals. HOMO-3 through HOMO-8 are characterized as the Au-S bonding orbitals constructed from the surrounding Au sd hybrid orbitals (or the surrounding Au 5d orbitals) and the S 3p orbitals. (The HOMO-1 and the HOMO-2 have the same Au-S bonding orbital character although their main component is the central Au 5d orbitals as mentioned above.) The central Au 5d orbitals

11906 J. Phys. Chem. B, Vol. 108, No. 32, 2004 TABLE 2: Main Atomic Orbitals Contributing to Each KS Orbital for the [Au13(SCH3)8]3+, [Ag13(SCH3)8]3+, and [Cu13(SCH3)8]3+ Clusters MO

energy (eV)

LUMO+3 (19t2g) LUMO+2 (21t1u) LUMO+1 (20t1u) LUMO (14a1g) HOMO (13a1g) HOMO-1 (18t2g) HOMO-2 (10eg) HOMO-3 (10t2u) HOMO-4 (17t2g) HOMO-5 (6eu) HOMO-6 (9eg) HOMO-7 (8t1g) HOMO-8 (19t1u)

3.827 3.656 2.871 2.518 0.000 -1.692 -1.771 -2.161 -2.444 -2.467 -2.606 -2.958 -3.054

[Ag13(SCH3)8]3+ LUMO+3 (19t2g) LUMO+2 (21t1u) LUMO+1 (14a1g) LUMO (20t1u) HOMO (13a1g) HOMO-1 (10t2u) HOMO-2 (18t2g) HOMO-3 (6eu) HOMO-4 (10eg) HOMO-5 (8t1g) HOMO-6( 19t1u) HOMO-7 (17t2g) HOMO-8 (9eg)

4.042 3.699 2.854 2.837 0.000 -2.113 -2.124 -2.376 -2.406 -2.720 -2.832 -3.343 -3.364

[Cu13(SCH3)8]3+ LUMO+3 (27t1u) LUMO+2 (15eg) LUMO+1 (19a1g) LUMO (26t1u) HOMO (18a1g) HOMO-1 (22t2g) HOMO-2 (7eu) HOMO-3 (14t2u) HOMO-4 (14eg) HOMO-5 (10t1g) HOMO-6 (21t2g) HOMO-7 (13eeg) HOMO-8 (25t1u)

4.787 4.704 4.044 2.619 0.000 -1.394 -1.481 -1.482 -1.765 -1.909 -2.041 -2.192 -2.245

3+

[Au13(SCH3)8]

ac

AO Au(6s), S(3s, 3p) Au(6s, 6p), S(3p) C(2s) Au(6s), S(3s) Au(6s), S(3s) c Au(6s), S(3s)a c Au(5d)a c Au(5d)a Au(5d, 6s), S(3p) c Au(5d), Au(5d, 6s), S(3p)a Au(5d), S(3p) c Au(5d), Au(5d, 6s), S(3p)a Au(5d), S(3p) Au(5d, 6s), S(3p) Ag(5s, 5p), S(3s, 3p) Ag(5p), Ag(5s), S(3p), C(2s)a c Ag(5s), Ag(5s), S(3s)a Ag(5s), S(3s) c Ag(5s), S(3s)a Ag(4d, 5s), S(3p) Ag(4d, 5s), S(3p) Ag(4d), S(3p) Ag(4d, 5s), S(3p) Ag(4d), S(3p) Ag(4d, 5s), S(3p) c Ag(4d)a c Ag(4d)a c

Cu(4s), S(3s, 3p), C(2s) Cu(4s, 4p), S(3p) c Cu(4s), Cu(4s), S(3s)a Cu (3d, 4s, 4p), S(3s) c Cu(4s), Cu(3d), S(3s)a Cu(3d, 4s), S(3p) Cu(3d), S(3p) Cu(3d, 4s), S(3p) c Cu(3d), Cu(3d, 4s), S(3p)a Cu(3d), S(3p) c Cu(3d), Cu(3d)a c Cu(3d), Cu(3d)a Cu(3d, 4s), S(3p)

Au, cAg, and cCu are central metals.

also contribute to the HOMO-4 and the HOMO-6. Figure 2 shows that d band structure constructed almost from the surrounding Au 5d orbitals appears below the HOMO-8. Therefore, the KS orbital energy levels are classified into four as shown in Figure 2: (i) the central Au 6s orbital, (ii) the central Au 5d orbitals, (iii) the Au-S band constructed mainly from the surrounding Au sd hybrid orbitals (or the surrounding Au 5d orbitals) and the S 3p orbitals, and (iv) the surrounding Au 5d band. Since the central Au 5d orbitals are somewhat involved in the Au-S band as mentioned above, the classification between (ii) and (iii) is not necessarily clear. The lowest-unoccupied molecular orbitals (LUMOs) approximately form the Au sp band constructed from the surrounding Au unoccupied 6s and 6p orbitals. Although the S 3s and 3p orbitals also contribute to these low-lying LUMOs, they do not form the Au-S bonding or antibonding orbitals (i.e., the Au-S nonbonding orbitals). The S-C band localizes in the energy range from ∼-6.7 eV to -7.8 eV below the surrounding Au 5d band. Thus, laserinduced cleavage of the S-C bond needs much more photons than that of the Au-S bond. To analyze these electronic properties much more clearly, it is useful to introduce silver and copper thiolate clusters in the same Oh structure, i.e., [Ag13(SCH3)8]3+ and [Cu13(SCH3)8]3+,

Nobusada and to compare their electronic properties with each other. It should be here remarked that the [Ag13(SCH3)8]3+ and [Cu13(SCH3)8]3+ clusters have not been structurally characterized experimentally. Thus, we introduce such silver and copper clusters as model systems to be compared with the [Au13(SCH3)8]3+ cluster in order to analyze the electronic properties of the gold cluster in detail. The geometry optimization for the [Ag13(SCH3)8]3+ and [Cu13(SCH3)8]3+ clusters was carried out in the same way as for the gold cluster. (For the copper atom, we did not use an effective core potential but treated all 29 electrons.) The calculations were successfully completed, and both clusters have similar optimized geometries. Their structural parameters and KS orbital energy levels are compared with those of [Au13(SCH3)8]3+ in Table 1 and Figure 2, respectively. The structural parameters of [Ag13(SCH3)8]3+ do not change largely from those of [Au13(SCH3)8]3+. Although the optimized geometry of [Cu13(SCH3)8]3+ shrinks compared with [Au13(SCH3)8]3+ and [Ag13(SCH3)8]3+ owing to smaller size of a copper atom, the main structure qualitatively remains unchanged. The main components of the atomic orbitals contributing to each KS orbital of the [Ag13(SCH3)8]3+ cluster are compared with those of the gold cluster in Table 2. The most different feature is that the central Ag 4d orbitals are localized and lowered in energy. Unlike the case of [Au13(SCH3)8]3+, these central 4d orbitals make a less contribution to the occupied KS orbitals other than the HOMO-7 and the HOMO-8. Thus, the central Ag 4d orbitals are well separated from the Ag-S band. We classify the KS orbital energy levels of [Ag13(SCH3)8]3+ as shown in Figure 2: (i) the central Ag 5s orbital, (ii) the Ag-S band constructed mainly from the surrounding Ag sd hybrid orbitals (or the surrounding Ag 4d orbitals) and the S 3p orbitals, (iii) the central Ag 4d orbitals, and (iv) the surrounding Ag 4d band. As a result, the Ag-S band becomes narrower than the Au-S band implying that the Ag sd hybrid orbital band is narrower than that of Au. This is, in part, due to a relativistic effect of the gold atom.28-30 The KS orbitals of [Cu13(SCH3)8]3+ become more complicated in the sense that the Cu 3d and 4s and S 3p electrons much more correlate with each other and thus we cannot classify the KS orbitals clearly as distinct from the case of the gold and silver clusters. As will be described latter, the difference in the electronic properties of three metal clusters has an influence on their absorption spectra. Absorption Spectra. Figure 3 shows absorption spectra (i.e., oscillator strength) for [Au13(SCH3)8]3+, [Ag13(SCH3)8]3+, and [Cu13(SCH3)8]3+. (For the sake of convenience, we plot the spectra as a function of wavelength.) The solid lines were obtained by convoluting each peak of the oscillator strength with the Lorentz function. Representative absorption peaks are assigned to single excitation processes from the ground state in Table 3. Figure 3 illustrates that the global features of the absorption spectra of [Au13(SCH3)8]3+ and [Ag13(SCH3)8]3+ are similar to each other as follows. The first and second peaks at longer wavelengths (532 and 395 nm for [Au13(SCH3)8]3+; 500 and 391 nm for [Ag13(SCH3)8]3+) correspond to the excitation from the HOMO to the unoccupied lowest two t1u orbitals. As was described above, the HOMO is constructed mainly from the s orbital of the central metal, whereas the low-lying two t1u orbitals predominantly form the metal sp band. Thus, these excitations induce electric charge transfer from the central metal to the surrounding metals. The absorption spectra of [Au13(SCH3)8]3+ and [Ag13(SCH3)8]3+ have onsets at ∼300 nm and have similar shoulder structures at 224-268 nm for [Au13(SCH3)8]3+ and at 231-

Monolayer-Protected Gold Cluster

J. Phys. Chem. B, Vol. 108, No. 32, 2004 11907 involved in the Au-S band. These electronic properties make the absorption spectrum of [Au13(SCH3)8]3+ broader than that of [Ag13(SCH3)8]3+. The absorption spectrum of [Cu13(SCH3)8]3+ also shows similar features to the gold and silver clusters except that it becomes much broader. This is due to the fact that the Cu 3d electrons correlate with the Cu 4s electrons much more significantly. Concluding Remarks

Figure 3. Absorption spectra for the [Au13(SCH3)8]3+, [Ag13(SCH3)8]3+, and [Cu13(SCH3)8]3+ clusters.

TABLE 3: Representative Excitation Processes Contributing to the Absorption Spectra energy (nm) 3+

[Au13(SCH3)8]

532 395 268 263 235 224 212 207

[Ag13(SCH3)8]3+

500 391 246 242 232 231 203

[Cu13(SCH3)8]3+

550 375 359 220 216

transition 13 a1g f 20t1u 13 a1g f 21t1u 17 t2g f 20t1u 10 eg f 21t1u 10 eg f 21t1u 18 t2g f 21t1u 8 t1g f 20t1u 17 t2g f 21t1u 8 eg f 20t1u 15 t2g f 20t1u 13 a1g f 20t1u 13 a1g f 21t1u 8 t1g f 20t1u 19 t1u f 14a1g 18 t2g f 21t1u 17 t2g f 20t1u 9 eg f 20t1u 6 eu f 19t2g 10 t2u f 11eg 18 a1g f 26t1u 22 t2g f 26t1u 14 eg f 26t1u 14 t2u f 15eg 7 t1g f 26t1u 16 a1g f 26t1u

246 nm for [Ag13(SCH3)8]3+. As is clearly seen from Tables 2 and 3, these shoulder structures are caused by the excitations both from the Au-S (or Ag-S) band and from Au (or Ag) d band to the Au (or Ag) sp band. Therefore, the origin of the shoulder structure is attributed to the combination of ligandmetal charge transfer (LMCT) and metal-centered (MC) transition. The absorption spectra rise up further because excitations occur from the surrounding Au (or Ag) d band below HOMO-8 to the Au (or Ag) sp band. These structural features of the absorption spectrum for [Au13(SCH3)8]3+ at shorter wavelengths (200-300 nm) are qualitatively similar to typical absorption spectra of gold-thiolate clusters.16,31 As mentioned above, the Au-S band is wider than the Ag-S band because of the relativistic effect and the central Au 5d orbitals are somewhat

Density functional calculations have been carried out to investigate electronic structures and photochemical properties of the gold-thiolate cluster [Au13(SCH3)8]3+ within constrained Oh molecular symmetry. It has been found that the cluster has a structure that eight (111) facets of a centered cuboctahedral Au13 cluster are passivated by eight methanethiolates. To determine the stability of the optimized structure, we carried out a second derivative calculation and made a Mulliken population analysis for [Au13(SCH3)8]3+. These calculations showed that the Au-S bond are formed to stabilize the goldthiolate cluster and that the neighboring Au-Au distance becomes much larger than that of the bare Au13 cluster because of the Au-Au Coulomb repulsion. The electronic properties and the absorption spectrum of [Au13(SCH3)8]3+ were analyzed in detail in comparison with the same structural silver and copper thiolate clusters. The absorption spectra of these clusters showed some features depending on the difference in the electronic properties of three types of metals. Acknowledgment. The present work was partly supported by the Matsuo foundation “theoretical study of electron-ion dynamics in noble metal clusters”. The author thanks T. Tsukuda and R. L. Whetten for their valuable comments. References and Notes (1) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. J. Chem. Soc., Chem. Commun. 1994, 801. (2) (a) Whetten, R. L.; Khoury, J. T.; Alvarez, M. M.; Murthy, S.; Vezmar, I.; Wang, Z. L.; Stephens, P. W.: Cleveland, C. L.; Luedtke, W. D.; Landman, U. AdV. Mater. 1996, 8, 428. (b) Whetten, R. L.; Shafigullin, M. N.; Khoury, J. T.; Schaaff, T. G.; Vezmar, I.; Alvarez, M. M.; Wilkinson. A. Acc. Chem. Res. 1999, 32, 397. (3) Templeton, A. C.; Wuelfing, W. P.; Murray, R. W. Acc. Chem. Res. 2000, 33, 27. (4) Simon, U. AdV. Mater. 1998, 10, 1487. (5) Emberly, E. G.; Kirczenow, G. Phys. ReV. B 1998, 58, 10911. (6) Ha¨kkinen, H.; Barnett, R. N.; Scherbakov, A. G.; Landman, U. J. Phys. Chem. B 2000, 104, 9063. (7) Seminario, J. M.; De La Cruz, C. E.; Derosa, P. A. J. Am. Chem. Soc. 2001, 123, 5616. (8) Cui, X. D.; Primak, A.; Zarate, X.; Tomfohr, J.; Sankey, O. F.; Moore, A. L.; Moore, T. A.; Gust, D.; Harris, G.; Lindsay, S. M. Science 2001, 294, 571. (9) Park, J.; Pasupathy, A. N.; Goldsmith, J. I.; Chang, C.; Yaish, Y.; Petta, J. R.; Rinkoski, M.; Sethna, J. P.; Abrun˜a, H. D.; McEuen, P. L.; Ralph, D. C. Nature 2002, 417, 722. (10) Nitzan, A.; Ratner, M. A. Science 2003, 300, 1384. (11) Modern density functional theory: A tool for chemistry; Seminario, J. M.; Politzer, P., Eds.; Elsevier: Amsterdam, 1995. (12) Ha¨kkinen, H.; Barnett, R. N.; Landman, U. Phys. ReV. Lett. 1999, 82, 3264. (13) (a) Garzo´n, I. L.; Rovira, C.; Michaelian, K.; Beltra´n, M. R.; Ordejo´n, P.; Junquera, J.; Sa´nchez-Portal, D.; Artacho, E.; Soler, J. M. Phys. ReV. Lett. 2000, 85, 5250. (b) Garzo´n, I. L.; Artacho, E.; Beltra´n, M. R.; Garcı´a, A.; Junquera, J.; Michaelian, K.; Ordejo´n, P.; Rovira, C.; Sa´nchezPortal, D.; Soler, J. M. Nanotechnology 2001, 12, 126. (c) Roma´nVela´zquez, C. E.; Noguez, C.; Garzo´n, I. L. J. Phys. Chem. B 2003, 107, 12035. (14) (a) Reiss, P.; Weigend, F.; Ahlrichs, R.; Fenske, D. Angew. Chem., Int. Ed. 2000, 39, 3925. (b) Ahlrichs, R.; Besinger, J.; Eichho¨fer, A.; Fenske, D.; Gbureck, A. Angew. Chem., Int. Ed. 2000, 39, 3929.

11908 J. Phys. Chem. B, Vol. 108, No. 32, 2004 (15) Larsson, J. A.; Nolan, M.; Greer, J. C. J. Phys. Chem. B 2002, 106, 5931. (16) (a) Negishi, Y.; Tsukuda, T. J. Am. Chem. Soc. 2003, 125, 4046. (b) Negishi, Y.; Tsukuda, T. Chem. Phys. Lett. 2004, 383, 161. (17) Garzo´n et al. reported that the global minimum structures of similar gold-thiolate clusters do not have high molecular symmetry but that the clusters are considerably distorted.13 Thus, it is necessary to carry out geometry optimization without assuming molecular symmetry if we precisely analyze electronic properties of the global minimum structure of such clusters. (18) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (19) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (20) Andrae, D.; Ha¨ussermann, U.; Dolg, M.; Stoll, H.; Preuss, H. Theor. Chim. Acta 1990, 77, 123. (21) Turbomole Version 5.6, Quantum Chemistry Group, University of Karlsruhe, Germany. (22) Scha¨fer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97, 2571.

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