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Ligand-Protected Gold Alloy Clusters: Doping the Superatom Michael Walter*,†,‡ and Michael Moseler†,§ Modelling of functional Nanosystems, Physics Deptartment, Hermann-Herder-Strasse 3, UniVersity of Freiburg, 79106 Freiburg, Germany, Freiburg Materials Research Center, Stefan-Meier-Strasse 21, 79104 Freiburg, Germany, and Fraunhofer Institute for Mechanics of Materials, Wo¨hlerstrasse 11, 79108 Freiburg, Germany ReceiVed: March 16, 2009; ReVised Manuscript ReceiVed: June 29, 2009
A density functional study of the experimentally observed ligand-protected gold alloy clusters PdAu12(PR3)8Cl4 and PtAu6Ag6(AgI3)2(PR3)6 reveal the same stabilization mechanism as in ligand protected pure AuN: the delocalized s-electron subsystem of a high symmetry metal core exhibits a shell closing. On the basis of this observation it is predicted that the substitution of a single Au atom in the well-known Au25(SR)18 compound with Pd, Ag, and Cd will produce stable clusters resulting in a method to tune redox properties in such a nanoscale building block. 1. Introduction The considerable scientific and technological interest in ligand-protected (LP) metal clusters is driven by the fact that these clusters can be synthesized in macroscopic quantities as well as by their pronounced stability in different environments and over a broad temperature range.1 Currently, only few wellcharacterized nanoscopic building blocks exist that possess these important prerequisites for a future use in large-scale application such as sensors, markers, or catalysts.2 Prominent representatives of the LP metal clusters are the thiol and phosphine protected gold clusters. Interestingly, the wet chemical production of these systems results in monodisperse samples with specific cluster sizessso-called magic numbers, whose origin was unclear until recently. Fortunately, there has been remarkable progress in the last two years in this field both experimentally as well as theoretically. Experimentally the crystal structure of two thiol-protected species that waited structural characterization for a long time was determined.3-5 Theoretically it was demonstrated that the traditionally separated fields of thiol- and phosphine-protected gold clusters can be joined under a unified view and that the magic stability of these clusters can be explained by delocalized electron shell closings (DESC) suggesting a superatom picture for the clusters.6 All the magic clusters fulfill the simple counting rule
Ndel - M - q ) ns
that LP gold alloy clusters obey the same stabilization mechanism as pure Au clusters. There is even strong evidence that this viewpoint is appropriate for some nickel-gold LP clusters, while it is unfounded for others.11 In this article, we report an explorative density functional theory (DFT) study of LP gold alloy clusters. First, the stability of experimentally known alloyed Au clusters (containing Pd, Pt, and Ag) is explained in terms of their electronic and nuclear structure. Second, other LP Au alloy clusters in different charge states are considered and particularly stable candidates are identified. All the stable clusters studied in this letter exhibit (a) a strong DESC at ns ) 8 (i.e., closing of the free electron P shell) and (b) the occurrence of an icosahedral core in the center of the LP gold alloy system. This suggests that the superatom rules found for pure LP gold clusters apply equally well for alloyed Au clusters, i.e., the stability of these clusters can be understood by the simple rule (1). 1.1. Methods. Our DFT calculations were performed with the real-space grid code GPAW12 using a generalized gradient approximation.13 The Kohn-Sham states were represented via the projector-augmented wave method.14 The smooth wave functions are represented on a real space grid with 0.2 Å spacing. A frozen core approximation was used for the core electron states. Spin polarization is considered if there are unpaired electrons in the calculation. Structures were considered to be relaxed15 when the atomic forces were below 0.05 eV/Å.
(1) 2. Results and Discussion
where Ndel is the number of delocalized electrons, M is the number of electron localizing ligands, q is the cluster charge, and ns is the DESC number (2, 8, 18, 34, ...).7 On the basis of this concept the structure of a cluster was predicted8 and independently found in the experiment.4,5 Recently, it was suggested to substitute some of the atoms in the LP gold cluster by more reactive transition metal atoms.9,10 This could be a versatile route to tailor the functionality (e.g., catalytic, magnetic, electronic, or optical properties) of LP gold clusters. However, for the time being it is not evident at all * To whom correspondence should be addressed. † Physics Deptartment. ‡ Freiburg Materials Research Center. § Fraunhofer Institute.
First, let us consider PdAu12(PR3)8Cl4sa cluster synthesized and characterized by Laupp and Stra¨hle (LS).16 In this work the entire LS cluster is investigated (the experimental PR3 groups where replaced by PH3 groups for computational convenience) in contrast to earlier calculations that disregarded the influence of the ligands completely.17 The fully relaxed structure of PdAu12(PH3)8Cl4 is shown in Figure 1a. The icosahedral metal core has a central Pd atom and each of the 12 gold vertex atoms bind to exactly one ligand. The electronic density of states (DOS) of PdAu12(PR3)8Cl4 exhibits a remarkably large gap of 1.77 eV between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) in agreement with the observed high stability of this cluster. An inspection of the local DOS (LDOS)
10.1021/jp9023298 CCC: $40.75 2009 American Chemical Society Published on Web 08/17/2009
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Figure 1. The relaxed structures of (a) PdAu12Cl4(PH3)8, (b) PtAu6Ag6(AgI3)2(PH3)6 and (c) Au25(SR)18. In panel c, the R groups are omitted for clarity. The purple atoms in panel c indicate the replacement positions for the substitutional metal atoms (X ) Pd, Ag, and Cd) resulting in the three different XAu24(SR)18 isomers C, V, and U. Pd and Pt atoms are shown in black, Au in orange or purple, Ag in gray, Cl or I in green, S in yellow, P in blue, and H in white.
Figure 2. Electronic properties of Au12Pd(PH3)8Cl4 (panels a and c) and PtAu6Ag6(AgI3)2(PH3)6 (panels b and d). Panels a and b show the DOS projected on the metal atoms while panels c and d exhibit the DOS projected on global spherical harmonics (see text for further details). The energy is given relative to Fermi energy and all density of states are broadened by Gaussians of 0.1 eV width.
in Figure 2a on the metal atoms reveals that the states around the Fermi energy (εF) are dominated by the metal s and p contributions (note that the DOS is folded for better visibility, which hinders the direct determination of the HOMO-LUMO gap from the plot). Pd contributes to the HOMO while the LUMO is located on gold atoms mainly. Similar as in pure ligand-protected Au clusters, also the LS cluster’s orbitals around εF are a delocalized combination of metal s and p orbitals. These states are further analyzed as follows. The Kohn-Sham orbitals φn(r) are expanded in spherical harmonics Ylm(rˆ) centered at the central atom of the icosahedral cage (here the Pd atom) to obtain the radial weights φnlm(r) ) ∫ drˆ Y*lm(rˆ) φn(r). The orbitals weight for a particular global angular momentum l is then calculated as cnl(R0) ) Σm ∫0R0 dr r2|φnlm(r)|2, where R0 ) 4 Å was used representing a cutoff roughly half way between the 12 Au atom shell and the ligands. In the following the global angular momenta will be denoted by capital letters (l ) S, P, D, ...) to distinguish them from the local angular momenta in the LDOS. The global angular momentum analysis for the LS cluster is presented in Figure 2b. Three states with P symmetry are located below εF and five states with D symmetry above. The appearance of these symmetries is a confirmation of the simple DESC model. The cluster closes the P shell, hence having 8 valence electrons effectively. Therefore formula 1 works perfectly for this structure. There are 12 delocalized Au(s) electrons, from which 4 electrons are localized by the Cl atoms and the cluster
is neutral. The phosphine ligands play the role of a Lewis base, not contributing to the delocalized electron countsas in the case of pure Au clusters. Interestingly, a slight broadening in both the P and D shell states is observed. This effect can be explained by a slight splitting of the two global angular momentum shells due to the symmetry breaking by the Chlorine atoms that are on nonequivalent positions. Note that the icosahedral symmetry itself does not split either the P or the D levels. Another experimentally completely characterized gold alloy cluster is the trimetallic PtAu6Ag6(AgI3)2(PR3)6 synthesized by Teo and Zhang (TZ).18 The relaxed structure of the TZ cluster is shown in Figure 1b. This cluster contains a central icosahedral core, which now consists of a Pt atom in the center and a 12 metal atom cage that is formed by a Au6 ring sandwiched between two Ag3 caps. Each silver cap is decorated with a AgI3 unit while the gold ring is terminated with 6 phosphines. Also this compound has a large HOMO-LUMO gap of 1.82 eV as can be seen in the LDOS shown in Figure 2b. Similar to the LS cluster the HOMOs are located at the metal atoms with a major contribution of Au and Ag s + p. Applying the simple counting rule in eq 1, the icosahedral cage has 12 delocalized electrons originating from the Ag and Au atoms. The Platinum atom does not contribute to the delocalized electron count as its 6s electron is transferred to the 5d shell upon binding to the other metal atomssa tendency that is also observed in the Pt bulk phase.19 (Opening the Pt 5d shell by forcing a spin splitting of the PtAu6Ag6(AgI3)2(PH3)6 cluster
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Walter and Moseler
TABLE 1: Relative Energy (in eV) of XAu24(SCH3)18 Depending on the Position of Xa isomer
X ) Pd
X ) Ag
X ) Cd
C V U
(0, 0, 0) (0.27, 0.31, 0.40) (0.71, 0.70, 0.71)
(0.30, 0.37, 0.42) (0, 0, 0) (0.28, 0.28, 0.26)
(0.50, 0.55, 0.28) (0, 0, 0) (0.4, 0.48, 0.45)
a The relative energies are given for the total cluster charge of q ) (1, 0, 1-)|e|, respectively.
destroys the large HOMO-LUMO gap and results in an overall energy cost of 1.77 eV.) The AgI3 units localize 2 electrons each and again the PH3 groups act as Lewis base ligands. Consequently, also the TZ cluster exhibits a DESC with ns ) 8. This finding is again confirmed by a global angular momentum analysis (Figure 2d). We now turn to the well-studied thiol protected gold cluster (Au25(SR)18)-. This compound was shown to be exceptionally stable and even survived an excess thiol environment.20 Only last year the structure of this cluster was elucidated.4,5,8 There is experimental evidence that a similar cluster also might be stable if one Au atom is substituted by a Pd atom.9 In the following the stability of XAu24(SCH3)18 with X ) Pd, Ag, and Cd will be investigated. The idea behind this study is that the substitutional atoms Pd, Ag, and Cd contribute with 0, 1, and 2 delocalized electrons, respectively, hence modifying the superatom nature of the cluster substantially. The structure of the Au25(SR)18 cluster is shown in Figure 1c. It comprises a 13 Au atom core and 6 SR-Au-SR-Au-SR units. The Au13 core itself consists of a 12 atom cage around a central atom, where the cage atoms are all in nearly equivalent icosahedral positions, each of them connecting to a sulfur atom from the six units. The units are placed in nearly octahedral symmetry only slightly distorted by the asymmetric direction of the CH3 ligand molecules (not shown). The strong asymmetry reported in ref 21 is not present in the theoretical structure and is probably related to the presence of the bulky counterion in the experimental crystal structure. There are three distinct positions for a replacement of a single Au by another metal atom resulting in three different isomers (C, V, and U). In C the central atom is replaced, in V one of the 12 vertex atoms, and in U one of the Au atoms from the thiol-gold units. According to this scheme, we have replaced one gold atom of the icosahedral Au25(SCH3)18 and relaxed the (XAu24(SCH3)18)(q) (X ) Pd, Ag, Cd, q ) 1,0, 1-) to the next local minimum. The relative energies in each charge state q are presented in Table 1. The lowest energy isomer (ground state, GS) is found to be independent of q in all cases and is well separated from the higher lying isomers. In the case of Cd and Ag, the GS is V whereas the Pd atom prefers isomer C as GS. This finding is in line with the C position of the Pd or Pt atoms found experimentally in the LS and TZ clusters. Further support of our calculations comes from the analysis of Mingos et al.22 and from the experimental compounds characterized by Gould and Pignolet.23 Significant HOMO-LUMO gaps of 1.23, 1.18, and 1.18 eV are found for X ) Pd, Ag, and Cd in the cluster charge states q ) 2-, 1-, 0 respectively. These values compare very well to the 1.2 eV gap of Au25(SCH3)18-.8 To study the electronic properties, we will concentrate on the GS and the charge states with the largest HOMO-LUMO gap, i.e., isomers C, V, and V and charge states q ) 2-, 1-, and 0 for X ) Pd, Ag, and Cd respectively, in the following. Figure 3 shows the atom projected DOS. In the energy region important for the stability (around εF) only Pd shows a significant contribution to the
Figure 3. The atom projected DOS of Au24Cd(SCH3)18, Au24Ag(SCH3)18-, and Au24Pd(SCH3)182-. The energy axis is defined relative to Fermi energy and the density of states is broadened by Gaussians of 0.1 eV width.
Figure 4. The global Ylm projected density of states (PDOS) for the core region of Au25(SCH3)18-, Au24Cd(SCH3)18, Au24Ag(SCH3)18-, and Au24Pd(SCH3)182-. The energy axis is defined relative to Fermi energy and the PLDOS is broadened by Gaussians of 0.03 eV width.
delocalized statessmainly to the HOMO as already observed for the LS and TZ clusters. The angular momentum projected DOS of all three compounds (Figure 4) is similar to panels b and d of Figure 2 and resembles the rare-gas superatom picture known from Au25(SCH3)18- also shown in the figure. The LUMO is of D and the HOMO of P symmetry showing again a DESC with ns ) 8 and explaining the large HOMO-LUMO gaps. The splitting seen in the D shell is a consequence of of the octahedral symmetry of the SR(AuSR)2 units around the cage. In the case of Au25(SCH3)18- or X ) Pd, where the Pd atom is located in the cluster center, the P-shell shows a single peak only. This is not the case anymore for X ) Ag and Cd since here the alloy atom is located on a vertex leading to symmetry breaking and hence to the small splitting of the P-shell. The DESC for the different charge states shown in Figure 4 can be understood by a simple s-electron counting as given in eq 1: Cd donates two, Ag one, and Pd no electron to the number of delocalized electrons in the cluster, hence Ndel ) 12, 13, 14 in the case of X ) Pd, Ag, Cd, respectively. All clusters contain
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TABLE 2: Energy Gain (in eV) Due to the Replacement of One Au Atom in (Au25(SCH3)18)(q) with the Given Element Xa charge q
X ) Pd
X ) Ag
X ) Cd
1 0 –1 –2
1.18 (1.2) 1.16 (1.2) 1.14 (1.2) 1.83 (1.9)
0 (0) 0.02 (0) 0.03 (0)
-0.06 (-0.1) -0.04 (-0.1) -0.81 (-0.8)
a Only the lowest energy isomer is considered. The values in parentheses are according to the simple model explained in the text.
M ) 6 electron localizing units and therefore a charge of q ) 2-, 1-, 0 is needed to fulfill the 8 electron shell closing for Pd, Ag, Cd, respectively. Finally we ask the question, is it energetically favorable to replace a gold atom in Au25(SCH3)18 by X ) Pd, Ag, or Cd? We therefore compare the total energy of (Au25(SCH3)18)(q) and an isolated X atom with the total energy of (XAu24(SCH3)18)(q) and an isolated Au atom. This substitutional energy gain ∆E(X,q) ) E[(Au25(SCH3)18)(q) + X] - E[(XAu24(SCH3)18)(q) + Au] is a direct measure of the internal energy released by the replacement of one gold atom in the cluster. The values for the ground state geometry and considering different cluster charges q are reported in Table 2. A general trend in the “solubility” of the X element in the Au host (exothermic for Pd, neutrothermic for Ag, and slightly endothermic for Cd) is intermixed with a peculiar charge dependence causing a stabilization of the q ) 2- state for X ) Pd and a destabilization of the q ) 1- state for X ) Cd. Interestingly, this variation in ∆E(X,q) obeys the simple model
∆E(X, q) ) Esub(X) + [nD(Au, q) - nD(X, q)]ED
(2) where Esub(X) ) 1.2, 0, and -0.1 eV is a general (q-independent) energy gained upon the substitution of a gold atom by Pd, Ag, and Cd, respectively, nD(X,q) is the number of electrons occupying the delocalized D-shell of XAu24(SCH3)18)(q), and ED ) 0.7 eV is the effective energy needed to occupy the D-shell. This model describes the corresponding DFT energies very well (see Table 2) confirming the relevance of the delocalized shell model even in the charge dependence of total energies. 3. Conclusions In conclusion we have shown for two experimentally characterized clusters that the superatom picture found for pure Au clusters applies equally well to protected Au alloy clusters. The stability of these clusters is a consequence of the 8-electron shell closing, where the elements Ag and Au donate one and the elements Pd and Pt donate no electron to the set of delocalized electrons. Moreover, we have proposed the stability of clusters similar to the exceptionally stable thiol protected Au25(SR3)18 via the
replacement of one of the Au atoms by X ) Pd, Ag, and Cd. Whereas the replacement by Cd or Ag is nearly neutral in energy, the replacement by Pd is found to be exothermic. We have shown that the underlying energetics even for different charge states of the clusters can be understood in a simple model that splits structural and electronic contributions. The replacement energetics and the differences between the elements are so clear that we do not expect substantial changes by using a different exchange-correlation functional. The shell closing rules and hence the rules for stability of mixed clusters involve the delocalized s electrons only and are therefore very clear and simple. Depending on the valence electron count, the proposed structures show large HOMOLUMO gaps for different charge states. Therefore controlled tuning of the redox properties should be possible via doping with metals of different valence electron counts. Acknowledgment. We thank FZ Ju¨lich, RZ Karlsruhe, and the Black-Forest Grid for providing computational resources and the Deutsche Forschungsgemeinschaft for funding within the priority program 1153. References and Notes (1) Burda, C.; Chen, X.; Narayanan, R.; El-Sayed, M. A. Chem. ReV. 2005, 105, 1025–1102. (2) Daniel, M.-C.; Astruc, D. Chem. ReV. 2004, 104, 293–346. (3) Jadzinsky, P. D.; Calero, G.; Ackerson, C. J.; Bushnell, D. A.; Kornberg, R. D. Science 2007, 318, 430–433. (4) Heaven, M.; Dass, A.; White, P.; Holt, K.; Murray, R. J. Am. Chem. Soc. 2008, 130, 3754–3755. (5) Zhu, M.; Aikens, C. M.; Hollander, F. J.; Schatz, G. C.; Jin, R. J. Am. Chem. Soc. 2008, 130, 5883–5885. (6) Walter, M.; Akola, J.; Lopez-Acevedo, O.; Jadzinsky, P. D.; Calero, G.; Ackerson, C. J.; Whetten, R. L.; Gro¨nbeck, H.; Ha¨kkinen, H. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 9157–9162. (7) de Heer, W. A. ReV. Mod. Phys. 1993, 65, 611–676. (8) Akola, J.; Walter, M.; Whetten, R.; Ha¨kkinen, H.; Gro¨nbeck, H. J. Am. Chem. Soc. 2008, 130, 3756–3757. (9) Fields-Zinna, C.; Crowe, M.; Dass, A.; Murray, R. W. Submitted for publication 11/2008. (10) Jiang, D.-e.; Dai, S. Inorg. Chem. 2009, 48, 2720–2722. (11) Walter, M.; Ha¨kkinen, H.; Whetten, R.; Moseler, M. Manuscript in preparation. (12) Mortensen, J. J.; Hansen, L. B.; Jacobsen, K. W. Phys. ReV. B 2005, 71, 035109. (13) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865–3868. (14) Blo¨chl, P. E. Phys. ReV. B 1994, 50, 17953–17979. (15) Bitzek, E.; Koskinen, P.; Ga¨hler, F.; Moseler, M.; Gumbsch, P. Phys. ReV. Lett. 2006, 97, 170201. (16) Laupp, M.; Stra¨hle, J. Angew. Chem., Int. Ed. 1994, 33, 207–209. (17) Arratia-Perez, R. H.-A. L Chem. Phys. Lett. 1999, 303, 641–648. (18) Teo, B. K.; Zhang, H. J. Organomet. Chem. 2000, 614-615, 66– 69. (19) Bond, G. C. Platinum Metals ReV. 2007, 51, 63–68. (20) Shichibu, Y.; Negishi, Y.; Tsunoyama, H.; Kanehara, M.; Teranishi, T.; Tsukuda, T. Small 2007, 3, 835–839. (21) Zhu, M.; Eckenhoff, W. T.; Pintauer, T.; Jin, R. J. Phys. Chem. C 2008, 112, 14221–14224. (22) Mingos, D. M. P.; Zhenyang, L. Comments Inorg. Chem. 1989, 9, 95–122. (23) Gould, R. A. T.; Pignolet, L. H. Inorg. Chem. 1994, 33, 40–46.
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