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J. Phys. Chem. C 2008, 112, 12646–12652
Stable Geometric and Electronic Structures of Gold-Coated Nanoparticles M@Au12 (M ) 5d Transition Metals, from Hf to Hg): Ih or Oh? Juan Long, Yi-Xiang Qiu, Xian-Yang Chen, and Shu-Guang Wang* School of Chemistry and Chemical Technology, Shanghai Jiao Tong UniVersity, Shanghai 200240, China ReceiVed: April 16, 2008; ReVised Manuscript ReceiVed: June 4, 2008
The geometric and electronic structures of 5d transition metal “impurities” Hf to Hg encapsulated in icosahedral and cuboctahedral Au12 cages have been investigated theoretically. The best density functional results of the small molecules Au2, AuH, AuCl, and AuCu were obtained for the geometric structures with XR, and for the electronic energies of those frozen structures with VBP. The same procedure was then applied to the clusters. At the zeroth order regular relativistic approximation ZORA, both at the spin-averaged scalar and at the spin-orbit-split spinor levels, the cuboctahedral clusters tend to be more stable than their icosahedral isomers, except for W@Au12. The neutral clusters have electronic closed shells only for Ih and Oh W@Au12 and for Oh Hg@Au12. The embedding energy of M into Au12 is less attractive for the later transition metal atoms M. 1. Introduction In recent years, clusters have attracted much attention in science and technology, forming the bridge from small molecules via nanoparticles to the bulk, and providing an understanding of the variation of the physical and chemical properties. The quantum states in nanoclusters are size-dependent, leading to fascinating optical and magnetic properties, catalytic activity, and so on. For instance, while bulk gold is rather inert, there is ample experimental as well as theoretical evidence for the catalytic activity of gold nanoclusters for, for example, CO oxidation at low temperatures.1,2 Clusters with particular “magic” numbers of atoms can be particularly stable. For example, clusters with 13, 55, or 147 atoms tend to form geometrically rather stable “Mackay icosahedra”. The 13-atom case is the most studied one among these clusters. It meets the first geometric closed shell for both the icosahedral (Ih) and the cuboctahedral (Oh) structures. The most stable structures of M13 (M ) Cu, Ag, or Au) were theoretically predicted somewhat flexible and asymmetric, so to say amorphous.3 However, Ih and Oh structures are geometrically and electronically not much different; they occur in surface covered compounds (e.g., [Au13(PMe2Ph)10Cl2](PF6)3),4 and they are much easier to investigate. Also, clusters with certain numbers of valence electrons become particularly stable. They are called “electronically magic clusters”, typically with closed electronic shells. If a cluster of pure composition is not electronically closed, we can dope it with a suitable heteroatom.5,6 Therefore, “impurities” in clusters become more and more popular. 3d and 4d transition metal (TM) impurities in Cu12, Ag12, and Au12 clusters have already been investigated,7–9 while 5d TM impurities in coinage-metal clusters are more rare. We mention studies of W@Au12, Ta@Au12-, and Au13.10–15 Reviews about the peculiar properties of gold nanoparticles were given by Pyykko¨16,17 and by Schwerdtfeger.18 Pyykko¨ and Runeberg10 theoretically predicted icosahedral W@Au12 as particularly stable, with a comparatively wide HOMO-LUMO * To whom correspondence should be addressed. E-mail: sgwang@ sjtu.edu.cn.
gap of 3.0 eV. Three reasons were given for the unusual stability: aurophilic dispersive attractions, relativistic stabilization effects, and the magic 18-electron rule. Soon after, Xi Li et al.11 experimentally verified icosahedral W@Au12 and Mo@Au12 in the gas phase. Theoretically, the Ih isomer of W@Au12 was found to be 9.8 kJ mol-1 more stable than the Oh one. In addition, Autschbach et al.12 explained the properties of W@Au12 in full detail. All of these results lead one to ask: which properties will emerge upon systematic variation of the central atom of M@Au12? Significant changes are expected, due to different angular momentum couplings in the differently filled 5d-6s shells, with various magnetic moments and formation energies. Another interesting prediction would be the stability of W@Au12 in comparison to the other hypothetical members of this class of compounds. Therefore, we will here discuss some basic properties of the M@Au12 series, where M means a 5d TM element from Hf to Hg, encapsulated in the center of an Ih and Oh Au12 cage. Neither impurity atoms in the Au12 surface nor Jahn-Teller distorted clusters will be investigated, which are expected to have additional stabilization energies of less than a few kJ/mol at room temperature. 2. Theoretical Calculations All calculations were carried out based on density functional theory (DFT), with the Amsterdam DFT package (ADF 2005) initially developed by Baerends et al.19,47 Several different DFT exchange-correlation potentials were applied: the local spin density approximations (LSDA) for the exchange functional of Slater and Schwarz (XR)20,21 and the correlation functional of Vosko, Wilk, and Nusair (VWN),22 and the nonlocal improvements by the generalized gradient approximations (GGA) of Perdew-Burke-Ernzerhof (PBE),23 Becke-Perdew (BP),24,25 and Perdew-Wang-1991 (PW91).26 For comparative purposes, the post-HF ab initio MP4 method was also applied, using the Gaussian 03 program.27 The important relativistic effects were accounted for by the scalar and spinor relativistic zero-order regular approximations (ZORA).28–31
10.1021/jp8033006 CCC: $40.75 2008 American Chemical Society Published on Web 07/29/2008
Structures of Gold-Coated Nanoparticles M@Au12
J. Phys. Chem. C, Vol. 112, No. 33, 2008 12647
TABLE 1: Spectroscopic Ground-State Parameters of AuH, AuCl, Au2, and AuCu from Different DFT Exchange-Correlation Functionals (A//B Means Energy from A for Structure Optimized with B)a VWN
XR
VBP VPBE VPW91 VBP//VWN VPBE//VWN VPW91//VWN VBP//XR VPBE//XR VPW91//XR MP4
exp.
AuH Re D0 ωh
153.3 153.8 154.4 154.4 3.60 2.78 3.16 3.03 2299 2264 2245 2248
154.3 3.05 2252
153.3 3.15 2295
153.3 3.03 2286
153.3 3.05 2288
153.8 3.16 2274
153.8 3.03 2272
153.8 3.05 2270
154.5 152.4 2.80 3.36 2260 2305
AuCl Re D0 ωh
218.5 219.1 223.3 223.1 3.65 3.34 3.02 3.10 395 387 362 364
223.0 3.11 363
218.5 3.00 407
218.5 3.08 406
218.5 3.09 406
219.1 3.00 401
219.1 3.09 400
219.1 3.10 400
229.4 219.9 2.30 3.54 367 383
Au2 Re D0 ωh
246.2 247.3 252.2 252.4 2.90 2.56 2.24 2.30 194 189 175 174
252.2 2.32 177
246.2 2.22 202
246.2 2.28 202
246.2 2.30 200
247.3 2.23 197
247.3 2.28 197
247.3 2.31 195
247.2 247.2 2.96 2.29 204 191
AuCu Re 230.9 232.0 236.5 236.9 D0 2.93 2.51 2.31 2.37 ωh 260 253 236 234 j| |∆R 1.4 0.8 3.5 3.6 j| |∆D 0.39 0.31 0.20 0.21 |∆ω j| 8 13 28 27
236.5 2.39 236 3.4 0.21 25
230.9 2.29 269 1.4 0.22 16
230.9 2.35 269 1.4 0.20 18
230.9 2.36 269 1.4 0.20 17
232.0 2.30 263 0.8 0.21 17
232.0 2.36 263 0.8 0.20 17
232.0 2.37 262 0.8 0.20 17
232.2 233 2.94 2.34 272 250 3.1 0.77 24
a Re: minimum energy bond length (in pm). D0: dissociation energy (in eV) for the harmonic vibrational ground state. ωh: harmonic j |: average absolute deviation from experimental values, X ) Re, D0, ωh. vibrational frequency (in cm-1). Exp: experimental values.35–37 |∆X
Slater-type-orbital (STO) basis sets of triple-ζ plus double polarization quality (TZ2P)32 were chosen for the valence electrons of all of the atoms. The inner core shells up to 4d were calculated by the atomic Dirac method and kept frozen.33 The ground state of atoms was chosen as: dns2, n ) 2-7 for Hf, Ta, W, Re, Os, Ir, and d9s1 for Pt, d10s1 for Au, d10s2 for Hg, respectively. For the MP4 calculations, somewhat restricted Gaussian bases were applied, SDD+2f for Au and 6-31G for the coordinated atom. To improve the numerical precision, the geometries of all molecules were optimized by converging the energies to 10-4 hartree, the energy gradients to 10-3 hartree Å-1, and the atomic displacements to 10-3 Å. The parameter for the number of point of the numerical integration was set to 6.0. Frequency analyses were performed to confirm the stability of the obtained structures. The atomic formation (binding) energies of the title clusters are of the order of 20-30 eV. The total zero-point vibrational energies (ZPVE) are less than 0.2 eV, and their variations are negligible. Most of the M@Au12 molecules are electronic open-shell structures. The ground states were found with highest-spin states. Fore example, the total energy of Pt@Au12 with t2gRRRβ is lower by 0.13 eV than are t2gRRββ configurations in Oh symmetry. Unrestricted DFT calculations were performed. Partial occupied electrons are average distributed on the HOMOs, for example, one R-electron and 1/3 β-electron occupied on each t2g orbital in Pt@Au12 of Oh symmetry. 3. Results and Discussion 3.1. Test Calculations of Diatomics Au2, AuH, AuCl, and AuCu. In the past decades, DFT has been significantly developed and widely applied also in TM cluster investigations. Average configuration DFT calculations are rather accurate,34 while specific correlations of individual states are still a problem at both the DFT and the post-HF ab initio levels. DFT has the unique advantage of useful calculational accuracies at affordable computational efforts. Different DFT approaches have been reported to yield quite different reliabilities for TM compounds,14 where relativistic effects and correlation effects both
Figure 1. Ih and Oh structure models of M@Au12 clusters.
influence the properties. Very few experimental data on TM cluster compounds are available for validation. Therefore, we have at first performed some test calculations of diatomic Aucontaining molecules to determine the best selection of DFT potentials. Four gold-containing diatomic molecules were chosen for this test: AuH, AuCl, Au2, and AuCu. The results are summarized in Table 1. Concerning the average absolute deviations, the LSDA, especially XR, give less error for the bond lengths. The GGA usually overestimate the bond lengths in heavy atomic systems, here by about 3 1/2 pm. The LSDA usually overestimate the bond energies, here too. Therefore, we will choose LSDA to determine the geometric structures, and then calculate the energies with GGA. The most satisfying results were here obtained for VBP energies at XR structures, denoted as VBP// XR. This approach had also been recommended by Ro¨sch et al.,38 and we will use it here for the clusters. For test purposes, also ab initio single-reference-MP4 results are given in Table 1. The results are not satisfactory at that level. 3.2. Geometric Structures of M@Au12. Ih and Oh models of the M@Au12 clusters are shown in Figure 1. In both cases, the central atom has 12 “radial bonds” to the surface atoms. The Ih and Oh clusters differ only in the Au “surface bonding”. The Oh cluster has 24 equivalent nearest-neighbor bonds in the surface, of the same length as the 12 radial bonds. The Ih cluster has 30 equivalent surface bonds, which are approximately 5.1% longer than its radial bonds.
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TABLE 2: Optimized Geometric Structures and Binding Energies of M@Au12 Clusters (M ) 5d TM, from Hf to Hg) in Ih Symmetrya Ih
RM-Au
RAu-Au
Hf@Au12 Ta@Au12 W@Au12 Re@Au12 Os@Au12 Ir@Au12 Pt@Au12 Au@Au12 Hg@Au12 Au12 cage
270.2 268.2 267.1 267.2 267.6 268.1 268.9 270.1 271.5
284.1 282.0 280.9 281.0 281.4 281.9 282.8 284.0 285.4 272.2
∆E
∆E
b
-32.67 -33.30 -32.46 -29.27 -28.95 -28.41 -26.45 -23.63 -20.39 -21.97
emb
-10.48 -11.02 -10.16 -6.97 -6.66 -6.13 -4.20 -1.44 1.73
IPa
EAa
HOMO
n
RM
7.14 7.18 7.20 5.74 6.08 6.37 6.62 6.90 6.74
3.69 3.71 2.03 2.49 2.85 3.10 3.32 3.19 3.43
hg hg hg hg* hg* hg* hg* hg* hg*
8 9 10 1 2 3 4 5 6
156.4 143.0 137.0 137.1 133.8 135.7 137.3 144.2 150.3
a
RM-Au: radial bond lengths between central M and surface Au atoms (in pm). RAu-Au(∼1.051RM-Au): bond lengths between the surface Au atoms (in pm). ∆Eb: binding (atomization) energy of M@Au12 (in eV). ∆Eemb: embedding energy of M into the Au12 cage (in eV). IPa: adiabatic ionization energy (in eV). EAa: adiabatic electron affinity (in eV). HOMO: symmetry species of the highest (partially) occupied MO (hg and hg* mean slightly bonding and slightly anti-bonding orbitals). n: respective occupation numbers. RM: effective radius of M in the bulk at rt (in pm).
TABLE 3: Optimized Geometric Structures and Binding Energies of M@Au12 Clusters (M ) 5d TM, from Hf to Hg) in Oh Symmetrya Oh
RAt-Au
Hf@Au12 Ta@Au12 W@Au12 Re@Au12 Os@Au12 Ir@Au12 Pt@Au12 Au@Au12 Hg@Au12 Au12 cage
275.1 273.2 272.2 272.4 272.9 273.4 274.2 275.6 276.8 267.7
∆E
b
-33.69 -33.67 -32.43 -29.40 -29.36 -29.16 -27.19 -24.66 -22.15
δ∆E
b
δ∆E
-1.02 -0.37 +0.03 -0.13 -0.41 -0.75 -0.74 -1.03 -1.76 -0.19
dist
-0.28 -0.19 -0.14 -0.15 -0.17 -0.19 -0.22 -0.27 -0.32
δ∆E
emb
-0.74 -0.18 0.17 0.02 -0.24 -0.57 -0.52 -0.76 -1.45
IPa
EAa
HOMO
n
6.79 6.76 6.89 5.87 6.29 6.62 6.54 6.94 7.22
3.29 3.38 2.06 2.64 3.05 2.74 3.21 3.64 3.14
eg eg eg t2g* t2g* t2g* t2g* t2g* t2g*
2 3 4 1 2 3 4 5 6
a RAt-Au: bond lengths between adjacent atoms (At ) M or Au) (in pm). ∆Eb: binding (atomization) energy of M@Au12 (in eV). δ∆ means the difference between Oh and Ih symmetries, δ∆Eb, of the M@Au12 binding energies (in eV), δ∆Edist, of distortion energy due to change of interatomic distances (in eV), δ∆Eemb, of embedding energy of M into the Au12 cage (in eV). IPa: adiabatic ionization energy (in eV). EAa: adiabatic electron affinity (in eV). HOMO: symmetry species of the highest (partially) occupied MO (slightly bonding eg and slightly anti-bonding t2g* orbitals). n: respective occupation numbers.
Figure 2. Bond lengths of M-Au in M@Au12 clusters with Ih and Oh symmetries.
The results are summarized in Table 2 for Ih and in Table 3 for Oh. The radial M-Au bond lengths of the Ih clusters are ∼5 pm smaller than those of the Oh isomers, see Figure 4, while the Au-Au surface bond lengths of the Ih clusters are ∼9 pm larger than those for the Oh isomers. The RAu-Au expand from the empty to the M-encapsulated Au12 cages by 9-13 pm in Ih and by 4 1/2-9 pm in Oh. Accordingly, the Au12 cage distortion energies are larger for Ih than for Oh throughout, by 0.14-0.32 eV. The electronic interaction energies shall be explained below. According to the effective atomic radii RM of the M atoms in the bulk metals, the minimum M-Au bond length should sit on Os atom. Yet it can be easily observed the changing of the M-Au bond lengths from Figure 2. RM-Au decreases at first, due to the increasing nuclear charge, until W with d6, and then
Figure 3. Valence shell orbital energy diagrams of M@Au12 of Ih symmetry. The numbers indicate the electron occupancies of the HOMO.
increases again due to increasing d-d interelectronic repulsion. RM contributes approximately 1/6 to the M-Au12 distances. 3.3. Molecular Orbitals. Molecular orbital energy diagrams of Ih and Oh M@Au12 are shown in Figures 3 and 4. In Ih M@Au12 with M ) Hf to W, the highest filled MO (with 8-10 electrons, respectively) is of hg ds-ds bonding type. If the HOMO is partial filled, the system is with open shell. The closed-shell electronic configuration is formed when the HOMO is full filled. W@Au12 has a closed valence shell. From Re to Hg, the next higher hg* ds-ds weakly antibonding MO level becomes partially populated with 1-6 electrons. For Oh symmetry, the highest energy valence electrons populate the eg
Structures of Gold-Coated Nanoparticles M@Au12
J. Phys. Chem. C, Vol. 112, No. 33, 2008 12649
∆Eemb ) ∆Eele + ∆EPauli + ∆Eorb
Figure 4. Valence shell orbital energy diagrams of M@Au12 of Oh symmetry. The numbers indicate the electron occupancies of the HOMO.
ds-ds bonding orbital, again yielding a closed shell for W@Au12. For M ) Re to Hg, the t2g* ds-ds weakly antibonding to more and more bonding HOMO is filled, this time becoming a closed shell for Hg@Au12. Electronic d6 shell closure does not always result in the smallest bond lengths of an M@A12 series. We had previously investigated also M@Au12 (M ) 4d TM, from Y to Cd), M@Ag12 (M ) 5d TM, from Hf to Hg), and M@Cu12 (M ) 5d TM, from Hf to Hg).39 For Ih symmetry, d6 W@Au12, but d7 Tc@Au12, Re@Ag12, and Re@Cu12 have the shortest radial bond lengths, the difference to the neighbor system being minor, however, see Figure 2. For Oh symmetry, d6 W@Au12 and Mo@Au12, but d7 Re@Ag12 and Re@Cu12 are the smallest ones. The singly occupied HOMOs of the d7 M clusters are indeed only very weakly antibonding. Summarizing, two factors influence the M-Au bond lengths. One is the metallic radius of the central M atom, which is smallest for Os with 8 valence electrons. The other factor is the electronic structure of the M@Au12 cluster, resulting from the varying number of valence electrons of M and the 12 of the surface atoms. This shifts the minimum of the radial bond length from Os to W. 3.4. Bonding in M@Au12. The bonding energy ∆Eb of M@Au12 is defined as the difference between the ground configuration energies of M@Au12 and separated atoms. Another parameter of interest is the energy ∆Eemb of embedding M into an empty “@Au12” cage with a geometric structure as in the filled M@Au12. The atomization energies of these @Au12 cages are denoted by ∆E12Au (in M@Au12):
∆Eb ) EM@Au12 - EM - 12EAu )∆Eemb + ∆E12Au(in M @ Au12) The energy of a relaxed empty Au12 cage is lower than that of @Au12 in M@Au12. We define the M-dependent distortion energy ∆Edist as
∆Edist ) ∆E12Au(in M @ Au12) - ∆Eb(Au12) These energies are displayed in Figure 5 and in Tables 2 and 3. Because ∆Edist is comparatively small, the general trends of ∆Eb and ∆Eemb are very similar. There are also only small differences between the Ih and Oh structures. The energy-decomposition scheme,19 first proposed by Morkuma40 and further developed by Ziegler and Rauk,41,42 was applied to analyze the bonding mechanism. The energies are partitioned into three physical contributions:
∆Eele is the quasiclassical electrostatic overlap attraction between the superimposed fragments (here M and @Au12, with unchanged electron densities). ∆EPauli is the exchange overlap repulsion between the fragments due to the fact that two electrons cannot occupy the same spin-orbital. These two terms partially cancel each other near the equilibrium geometries. Their comparatively small positive or negative sum is called the steric energy ∆Ester. ∆Eorb is the energy lowering due to the quantum mechanical interference of partially occupied fragment orbitals, and due to the orbital relaxation from the initial fragment states to the final molecular states. It includes charge transfer contributions (mixing of occupied orbitals on one fragment and virtual orbitals on the other fragment) and polarization contributions (mixing of occupied and virtual orbitals from the same fragment). Figure 6 shows the energies ∆Eemb and the contributions ∆EPauli, ∆Eele, and ∆Eorb for the Ih and the Oh clusters. All energy terms become weaker for increasing atomic number of M. The main difference between the Ih and Oh systems is caused by ∆EPauli: The Pauli overlap repulsion between the central metal atom M and the (already expanded) @Au12 cage is 5.6-9.7 eV larger for an Ih than for an Oh structure. The larger overlap repulsion is only partially compensated by the slightly larger electrostatic, quantum mechanical, and relaxation attractions. Therefore, these results show some general trend toward a greater stability of the Oh clusters (except for W@Au12; see next section). Remarkably, neither the Ih nor the Oh W@Au12 clusters with filled bonding and empty antibonding orbitals have the biggest atomization energy among these clusters. For the Ih clusters, Ta@Au12 has the strongest binding energy (0.84 eV lower than for W@Au12), and for the Oh clusters, Hf@Au12 does (1.26 eV lower than for W@Au12). The M-Au bonds are mainly composed of 5d-6s-6p of Au and 5d of M. For example, in Ih W@Au12, the HOMO bonding orbital hg is composed of 18% 5d of W and 36% 5d, 27% 6s, 17% 6p of Au. 3.5. Stability of Ih and Oh Structures. 13-Atom clusters are usually most stable for globular instead of near-planar structures. Often, the high-symmetry Ih and Oh structures are local minima, with some distorted geometries at slightly lower energies. The maximal degeneracy of irreducible representations of Ih and Oh symmetry is 5 and 3, respectively. Higher degeneracy allows for larger exchange splitting, that is, larger ground-state stabilization, and for larger spin magnetism. That is, an Ih cluster can have, for appropriate electron number, the greater magnetic moments. Large magnetic moment may stabilize the clusters. In a 13-atom cluster, the surface atoms have five nearestneighbor atoms for Ih, but only 4 for Oh. Indeed, it has been theoretically predicted that many 13-atom TM clusters are more stable for icosahedral than for cuboctahedral structures, such as Fe13,43 Pd13, Rh13, Ru13,44 and others. However, a few 13atom clusters, such as Pt1345 and Au13,3,46 are found with Oh being more stable than the Ih isomer. A compact structure with more nearest neighbor bonds should be more stable. Yet the strength of each bond also plays a significant role. Note even Ih has 42 ) 12 inner and 30 surface neighbor pairs, while Oh only has 36 ) 12 inner and 24 surface. Still Oh is usually lower in energy. The energies of the Oh isomers with reference to Ih are listed in Table 3. All open-shell M@Au12 and closed-shell Hg@Au12 are most stable for Oh symmetry, while for closedshell W@Au12 Oh and Ih are near-degenerate. It is interesting
12650 J. Phys. Chem. C, Vol. 112, No. 33, 2008
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Figure 5. Binding energy ∆Eb and embedding energy ∆Eemb of M@Au12 clusters.
Figure 6. Decomposition of the embedding energies ∆Eemb.
TABLE 4: Binding Energy ∆Eb (in eV) of M@Au12 on Relativistic Spin-Orbit Calculationsa M@Au12
Hf
Ta
W
Re
Os
Ir
Pt
Au
Hg
∆E b(Ih) ∆E b(Oh) δ∆E b(Oh-Ih)
-36.66 -37.52 -0.86
-37.67 -37.96 -0.29
-37.30 -37.21 0.09
-35.64 -35.65 -0.01
-34.30 -34.43 -0.13
-33.13 -33.38 -0.25
-31.19 -31.66 -0.47
-27.96 -28.93 -0.97
-24.42 -26.01 -1.59
a
δ∆Eb(Oh-Ih): difference of binding energy of M@Au12 between Oh and Ih symmetries.
to discover that, in our calculation, only the Ih is slightly more stable than its Oh isomer. The empty Au12 cage is only 0.2 eV more stable for Oh than for Ih. When a central atom is embedded, there are two opposite energy contributions: One is the stabilizing bond energy with 12 new M-Au interactions; the other is the structural deformation (relaxation) of the Au12 cage. When a 5d TM atom is encapsulated in an Au12 cage, the deformation energy of Au12Ih (which is already a little higher in energy) is by 0.14-0.32 eV bigger than that for Au12-Oh. The Oh Au12 cage has the advantage of less steric effect when a TM atom is encapsulated. So to say, the Ih cage is too compact. All of the distorted Oh Au12 cages are more stable than the Ih ones. Concerning the electronic interaction between M and Au12, they are small for W and Re, but for all other metals the interaction is stronger bonding for Oh than for Ih symmetry, by up to 1 1/2 eV (for Hg; see Table 3). The discussed results are without spin-orbit coupling. Spin-orbit coupling effects are significant for the 5d TM atoms, the Ih compounds being stabilized by 0.06-0.5 eV relative to Oh. Yet the general scalar nonrelativistic trend (Table 3) is similar to the more realistic relativistic trend (Table 4). 3.6. The HOMO-LUMO Energy Gap. The energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), that is, the chemical softness, plays an important role for the reactivity. For closed-shell systems with a wide HOMO-LUMO gap, it is difficult to create unpaired electrons for new bond formation. For open-shell systems, the HOMO is partially occupied and
can easily accept or lose charge; the respective gap is zero by definition. A partially occupied degenerate orbital will often cause stabilizing Jahn-Teller distortions and a nonzero gap. The only closed-shell systems are W@Au12 (both for similarly stable Ih and Oh symmetry) and Hg@Au12 (for the more stable Oh symmetry). The calculated gap for Ih W@Au12 is 1.86 eV, which is close to the experimental gap11 (1.68 eV), and 0.37 eV larger than predicted for its Oh isomer. It indicates that Ih W@Au12 should be the less active isomer. The gap for Oh Hg@Au12 is only 0.81 eV. These trends are obvious from Figures 2 and 3. The other clusters, having a partially occupied HOMO, should tend to become stabilized by bond formation to ligands on the surface. The HOMO may act as a donor or acceptor or may form an ordinary covalence. Therefore, we studied the M@Au12q ions, which are isoelectronic with closed-shell W@Au12, for M ) Hf (q ) -2) to Hg (q ) +6). The respective gaps and their trends are displayed in Figure 7. The gaps of the Ih clusters are always larger than those of the Oh clusters, by 0.3-0.7 eV. 3.7. Adiabatic IPs and EAs. The energy differences between a neutral cluster and its positive or negative ions are also chemically interesting parameters. We have fully optimized the M@Au121+ and M@Au121- to determine the adiabatic ionization potentials IPa and electron affinities EAa. The effects of the zero-point vibrational energies (ZPVE) turned out to be negligible. The IPa values between 5.7 and 7.2 eV are large as compared to the HOMO energies (between 3.8 and 5.3 eV, see Figures 3 and 4), which approximate the vertical IPa values. The EAa
Structures of Gold-Coated Nanoparticles M@Au12
J. Phys. Chem. C, Vol. 112, No. 33, 2008 12651 (5) Comparatively large IPa and small EAa values are obtained for M ) W, and also M ) Hg and Ir (for Oh), small IPa for M ) Re, and large EAa for M ) Ta and Au. Acknowledgment. We acknowledge financial support by the National Nature Science Foundation of China (No. 2573074) and the SRFDP of China (No. 20040248017). References and Notes
M@Au12q
Figure 7. Energy gaps of the ions, isoelectronic with closedshell W@Au12, for M ) Hf (q ) -2) to Hg (q ) +6).
Figure 8. IPa and EAa of M@Au12 clusters with Ih and Oh symmetries.
values range from 2.0 to 3.7 eV, which is quite small as compared to the IPa’s. It indicates that it is relative easier for these clusters to obtain an electron than lose it. Figure 8 shows that the IPa’s and EAa’s of the Ih and Oh clusters are rather similar, differing by less than 1/2 eV. The variation of the IPa and EAa values can be rationalized with the help of the frontier orbital energies (Figures 3 and 4) and the effects of term splitting of open-shell configurations. That is, systems with half of the d completely filled shells tend to have large IPa’s and small EAa’s. Closed-shell W@Au12 has the largest IPa and smallest EAa of all investigated species. Similarly, Oh Hg@Au12 with t2g6 has a comparatively small EAa and large IPa, too. Relatively large IPa’s and small EAa’s are also found for Ih Au@Au12 with hg5 configuration, and for Oh Ir@Au12 with t2g3. Ta@Au12 with one electron hole has the largest EAa. 4. Conclusions Compact 13-atom clusters with a central 5d TM atom encapsulated in an Au12 cage have been investigated for the two highly symmetric Ih and Oh structures. We stress five points. (1) The M-Au distances are shorter for the more compact Ih symmetry than for Oh. Because of the influence of metallic radius of the central M atom and the cluster’s electronic structure, the shortest bond lengths are found for W@Au12. (2) The formation energy of M@Au12 varies with the binding energy of M in Au12 and with the deformation energy of the originally empty Au12 cage upon embedding the M atom. The overall trend is a decrease of stability with increase of atomic number. (3) In general, the Oh clusters are more stable. Only for W@Au12 is the Ih isomer slightly more stable. While (scalar) relativistic effects are important, the spin-orbit coupling does not change the qualitative trends. (4) Among the closed-shell M@Au12q ions with M/q ) Hf/ -2 to Hg/+6, the Ih clusters are less active than their Oh isomers.
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