Supporting Information

A Density Functional Theory Study of Gold Clusters

Supported on Layered Double Hydroxide

Yue Zhu, Xin Liu, Min Pu,and Fazhi Zhang*

State Key Laboratory of Chemical Resource Engineering

BeijingUniversity of Chemical Technology

Beijing 100029 (China)

Fax: (+86) 10-6442-5385

E-mail:

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1. Isolated AuN clusters

The initial structures of AuN(N=1-8) clusters in the presentwork were chosen from the bulk Au structure and alsobased on thereferences of building novel structures [1,2].The possible geometries of neutral clusters are shown in Figure S1, which are investigated atthelevel of BPW91/LanL2DZ by using DFT method.The average bond lengths of clusters increase from 2.546 Å to 2.833 Å, close to but less than the bulk gold, 2.88 Å.In bulk gold, the electrons are mainly distributed in the bulk space, while the electron distributions of clusters are in between the adjacent Au atoms due to boundary effects. Therefore, the average bond length of bulk gold is more expandable than that of AuN clusters.Figure 1 also displays the calculated Mulliken atomic charge of AuN clusters.For all the cluster structures with high symmetry, their Mulliken atomic charges also have correspondingsymmetry.The electronic state,symmetry, average bond length, and the energycorrected byZPE of AuN (N=1-8) are listed in Table S1.

Figure S1. The optimized structures(A) and Mulliken atomic charges(B) of the AuN (N=2-8) clusters, (A: the geometric parameters for interatomic bond lengths in Å and bond angles in degree; B: Mulliken atomic charge are given in parentheses)

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Table S1.Symmetry, electronic state, average bond length, and the systemenergyof neutralAuN (N=1-8)

Symmetry / Electronic state / Average bond length (Å) / E / EH-L
(a.u.) / (eV)
Au / - / 2A1G / - / -135.484243 / 6.17
Au2 / D∞h / 1SGG / 2.546 / -271.038078 / 3.41
Au3 / C2v / 2B2 / 2.611 / -406.555912 / 3.27
Au4 / (YD) / C2v / 1A1 / 2.671 / -542.117917 / 1.06
(RD) / D2h / 1AG / 2.719 / -542.117176 / 2.06
Au5 / (2D) / C2v / 2A' / 2.708 / -677.669909 / 2.57
(3D) / C2v / 2B2 / 2.793 / -677.637139 / 1.31
Au6 / (2D) / D3h / 1A1' / 2.675 / -813.254887 / 3.55
(3D) / C2v / 1A' / 2.702 / -813.221372 / 3.04
Au7 / (2D) / D2h / 2B3G / 2.761 / -948.769752 / 1.03
(3D) / D5h / 2A2'' / 2.833 / -948.764337 / 1.99
Au8 / (2D) / C2v / 1A1 / 2.745 / -1084.341718 / 1.81
(3D) / C2v / 1A1 / 2.778 / -1084.339623 / 2.55
Au9 / (2D) / C2v / 2A1 / 2.748 / -1219.890552 / 1.85
(3D) / C3v / 2A1 / 2.782 / -1219.879373 / 1.25
Au10 / (2D) / D2h / 1AG / 2.765 / -1355.460808 / 2.35
(3D) / C2v / 1A1 / 2.797 / -1355.440263 / 1.77
Au∞ / 2.88 (Exp.)[3]

Based on the optimized structures of AuN cluster, per-atom bindingenergies (EB,N) of the ground state neutral clusters are calculatedusing the equation: EB,N=E(Au)-n-1E(AuN) (N=2-8), where E(Au)and E(AuN) are the energies of Au atom and AuNclusters, respective. Obviously,theaveragebinding energies for clusters (see Figure 2(a)) increasesubstantiallyascomparedtothe cluster size,exceptthat the valueof Au7 is lower than that of Au6.Thehighest averagebinding energyis 1.59 forAu8,correspondingitshigheststability. Theaveragebinding energies of Au6 is 1.53 eV, which is slight lower than Au8.It is worth noting that the2D Au clusters are morestable than their 3D isomers at N=5-8. The calculated results are in very good agreement with the Ref. 1, where the trend of the 2D clustersbeing more stable than their corresponding 3D isomersreverses in the clusters consisting of more than 15 Auatoms.This property is different from that predicted inthe previous work[2], where the 2D-3D structuraltransition occurs at the cluster consisting of 7 Au atoms.

Figure S2.(a) Binding energy per atom, EB, for neutral clusters; (b) The second difference Δ2E in the bindingenergy with respect to the particle number N; (c) HOMO-LUMOgap, EH-L,; (d) Size dependenceofthecalculatedIPandEAforAuN clusters with planar structure.

The second difference in the binding energy, Δ2EB,N=EB,N+1-2EB,N+EB,N-1 (N=2-8), are obtained and displayed in Figure 2 (b). For boththeplanar clusters and their corresponding 3D structures, Δ2EB,N exhibits periodicalodd-even oscillation. The odd-even effect at smallercluster sizes was also explained [2,4]. Au atom target the electronic configuration of the outer shells 5d106s1 forfree atoms may be separated into a conduction or free-electron band of mixed s, p characterand a nearly free band formed by the localized d electrons[5]. It may induce the even-numbered AuNclusters with electron pairing and odd-numbered clusters with an unpaired electron, so we conclude that the spinpairingeffect stabilizes the clusterswith an even number of electrons.

The energygap (EH-L) betweenthehighestoccupiedmolecularorbital (HOMO)andthelowestunoccupiedmolecularorbital(LUMO) isconsideredtobeanimportantparameterintermsof theelectronicstabilityofsmallclusters.Alargegapsignifieshigh chemicalstabilitybecauseitisenergeticallyunfavorabletoadd electronstoahigh-lyingLUMOortoextractelectronsfromalow-lyingHOMO.TheHOMO-LUMOgapasafunctionofclustersize isplottedin Figure 2(c).Thereisnoobviousrelationshipbetweenthe sizenumberandthegap for AuN planar structures.However, we also note that HOMO-LUMOgap for single Au atom is a local maximum, and it is larger than the other clusters. The Au6 cluster has largerHOMO-LUMOgapsandrelativelymorechemicallystablethantheirneighboringclusters. For planar cluster size N≥5,EH-Lexhibits odd-even oscillations, andthe observation is that thereisobviousodd-even oscillation for AuN 3D structures.This odd-even alternation is consistentwith electron pairing. Even-numbered clusters have theirorbitals fully occupied giving them more stability than theodd-numberedclusters that have the HOMO singlyoccupied.The values and theoscillations of the HOMO-LUMO gaps that are seen todecrease suggest a transition towards a metallicbehavior as the cluster size increases.

The ionization potentials(IP) and Electron affinities (EA) arealsoimportantpropertiesfordescribingthe size-dependentevolutionofclusterelectronicstructures.ThelargertheIP,thehigheristhechemicalstability.Inthiswork,theIP ofAuN clustersarecalculatedandshownin Figure 2(d).The IP value of Au atom from the DFT/B3PW91 calculations with the LanL2DZ basis set is 9.34 eV, which agrees well with the experimental value, 9.23 eV. For the EA of Au atom, theexperimental value (2.31 eV) and the calculated result (2.10 eV) are in very good agreement.For both the IP and EA of the planar clusters, there exists a reverse trend of odd-even oscillation. According to Koopmans' theorem, the IP and EA associate with the frontier molecular orbital (HOMO and LUMO). It is noted that both the Au single atom and Au2 dimer have the larger IP and lower EA, because of their larger HOMO-LUMOgap. Therefore, the chemicalstability of the Au and Au2 is much higher than the other cluster.

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2. AuN clusters adsorbed on MgAl-LDH lamella

Table S2.The adsorption energies (Ead), cohesive energies (Eco),and energy gaps (EH-L) for the AuN clusters adsorbed on the topor at the edge of the MgAl-LDH.

Top Site / Edge Site
Ead (eV) / Eco (eV) / EH-L (eV) / Ead (eV) / Eco (eV) / EH-L (eV)
Au-lamella / 0.34 / - / 5.19 / 0.23 / - / 4.03
Au2-lamella / 0.81 / 2.35 / 3.76 / 1.07 / 2.73 / 3.8
Au3-lamella / (a) / 1.16 / 3.62 / 3.60 / 1.37 / 3.95 / 3.71
(b) / 1.06 / 3.52 / 3.76
Au4-lamella / (a) / 1.85 / 6.41 / 3.52 / 1.97 / 6.64 / 3.4
(b) / 1.51 / 6.07 / 2.64
Au5-lamella / (a) / 1.39 / 7.81 / 2.34 / 1.47 / 8.00 / 2.56
(b) / 1.35 / 7.77 / 2.68
(c) / 1.28 / 7.70 / 2.80
Au6-lamella / 1.47 / 10.63 / 3.36 / 1.57 / 10.85 / 3.43
Au7-lamella / (a) / 1.81 / 11.81 / 1.46 / 1.81 / 11.92 / 1.32
(b) / 1.78 / 11.78 / 1.48
Au8-lamella / (b) / 1.95 / 14.33 / 2.21 / 1.91 / 14.41 / 1.83
(a) / 1.81 / 14.19 / 1.74

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Table S3. Calculated Mulliken atomic charges of the AuN clusters on thetop and at the edge of MgAl-LDH lamella.

on the top / at the edge
Au / -0.004 / -0.007
Au2 / -0.050 / -0.512
Au3 / (a) / -0.022 / -0.484
(b) / -0.052
Au4 / (a) / -0.034 / -0.422
(b) / 0.000
Au5 / (a) / -0.153 / -0.398
(b) / -0.084
(c) / -0.117
Au6 / -0.115 / -0.368
Au7 / (a) / +0.022 / -0.317
(b) / -0.177
Au8 / (a) / -0.018 / -0.369
(b) / -0.093

* For the AuN clustersadsorbed on the topof LDH lamella with N = 3, 4, 5, 7, and 8, different stable configurationsare labeled separatelyasa, b, and c.

References

[1]Li Xiao, Lichang Wang. From planar to three-dimensional structural transition in goldclusters and the spin-orbit coupling effect. Chem. Phys. Lett. 392 (2004) 452–455

[2]Hannu Häkkinen, Uzi Landman. Gold clusters (AuN, 2≤N≤10) and their anions. Phys. Rev. B, 2000, 62(4): 2287-2290.

[3]Jun Li, Xi Li, Hua-Jin Zhai, Lai-Sheng Wang. Science. 2003, 299, 864-867

[4]Pekka Pyykkö. Theoretical Chemistry of Gold. Angew. Chem. Int. Ed. 2004, 43( 4), 4412–4456.

[5]E. A. Figueroa, E. D. Cantero, J. C. Eckardt, G. H. Lantschner, J. E. Valdés, and N. R. Arista. Threshold effect in the energy loss of slow protons and deuterons channeled in Au crystals. Phys. Rev. A, 2007, 75, 010901

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