Electronic Structure and Optical Properties of the Intrinsically Chiral 16

Article pubs.acs.org/JPCA

Electronic Structure and Optical Properties of the Intrinsically Chiral 16-Electron Superatom Complex [Au20(PP3)4]4+ Stefan Knoppe,*,† Lauri Lehtovaara,‡ and Hannu Hak̈ kinen‡,§ †

Molecular Imaging and Photonics, Department of Chemistry, KU Leuven, Celestijnenlaan 200D, 3001 Heverlee, Belgium Department of Chemistry, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland § Department of Physics, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland ‡

S Supporting Information *

ABSTRACT: The recently solved crystal structure of the [Au20(PP3)4]Cl4 cluster (PP3: tris(2-(diphenylphophino)ethyl)phosphine) is examined using density functional theory (DFT). The Au20 core of the cluster is intrinsically chiral by the arrangement of the Au atoms. This is in contrast to the chirality of thiolate-protected gold clusters, in which the protecting Au-thiolate units are arranged in chiral patterns on achiral cores. We interpret the electronic structure of the [Au20(PP3)4]Cl4 cluster in terms of the superatom complex model. The 16-electron cluster cannot be interpreted as a dimer of 8electron clusters (which are magic). Instead, a superatomic electron configuration of 1S2 1P6 1D6 2S2 is found. The 2S band is strongly stabilized, and the 1D states are nondegenerate with a large gap. Ligand protection of the (Au20)4+ core leads to a significant increase of the HL-gap and thus stabilization. We also tested a charge of +II, which would give rise to an 18-electron superatom complex. Our results indicate that the 16-electron cluster is indeed more stable. We also investigate the optical properties of the cluster. The experimental absorption spectrum is well-reproduced by time-dependent DFT. Prominent transitions are analyzed by time-dependent density-functional perturbation theory. The intrinsic chirality of the cluster is compared to that of Au38(SR)24. We observe that the chiral arrangement of the protecting Au-SR units in Au38(SR)24 has very strong influence on the strength of the CD spectra, whereas phosphine protection in the title compound does not.

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INTRODUCTION Monolayer-protected noble-metal clusters have gained significant interest in recent years. This is because of advances in synthesis1−6 and the successful determination of X-ray crystal structures as well as their prospective uses in catalysis,7 sensing,8,9 and bioimaging.10−14 Gold and, more recently, silver clusters protected with thiolates15−23 and phosphines24−29 have been successfully crystallized in recent years. Of note, the structures can be explained in terms of the superatom complex model (SACM),30 which is derived from jellium models of bare gas-phase clusters.31,32 The understanding of the electronic structure of noble-metal clusters touches fundamental questions of metallurgy, for example, how many atoms are needed to induce the collective electronic behavior of a metal? In addition, the understanding of cluster structures may allow for directed synthesis and tailored properties for use in various applications. Chirality has been identified as an intrinsic structural property of a number of gold−thiolate clusters, most prominently in the cases of Au102(SR)44 and Au38(SR)2415,17,33,34 but also in the recently determined structure of Au28(SR)2019,35 as well as in the predicted structure of Au40(SR)24.36−38 The optical activity of monolayer-protected gold clusters has been studied for more than a decade.39−42 Chirality has also been studied both experimentally43,44 and theoretically45 in Au−phosphine systems using chiral ligands. In the case of gold−thiolate clusters, the chirality is determined by © 2014 American Chemical Society

the arrangement of the protecting SR(AuSR)n motifs (n = 1, 2, 3) on the surface of the clusters. Very recently, Wang and coworkers reported the structure of the intrinsically chiral [Au20(PP3)4]Cl4 cluster (PP3: tris(2-(diphenylphosphino)ethyl)phosphine).29 The structure was confirmed in independent work.46 In this all-phosphine-protected gold cluster, the Au20 core is intrinsically chiral. A Au13 icosahedron is capped by a Au7 unit, as shown in Figure 1. The 3-fold Au7 unit is chiral and occurs in its left- and right-handed forms in the unit cell of the cluster, thus forming a racemate. Of note, the Au20− phosphine system represents one of a very few cases in which a gold cluster adopts a different geometry under the influence of different ligands. A rod-shaped [Au20(PPhpy2)10Cl4]Cl2 cluster was characterized in 2012.28 Such constitutional isomerism has also been observed in Au25 clusters, in which the all-thiolate structure is a spherical 8-electron superatom16 and the other one, protected by a mixed thiolate−phosphine layer, is a rodshaped 8 + 8-electron superatom dimer.26 The two clusters, [Au20(PP3)4]4+ and [Au20(PPhpy2)10Cl4]2+, not only differ in the arrangement of the Au atoms but also in their superatomic electron count (16 and 14). Although the rod-shaped cluster has been interpreted as a dimer of 7-electron superatoms Received: April 7, 2014 Revised: May 21, 2014 Published: May 23, 2014 4214

dx.doi.org/10.1021/jp5033959 | J. Phys. Chem. A 2014, 118, 4214−4221

The Journal of Physical Chemistry A

Article

Figure 1. (Left) Structure of the bare Au20 core of the cluster. The triblade adatom motif is highlighted in blue. (Center) Structure of the full ligandprotected cluster. Hydrogen atoms are not shown for clarity. Yellow, Au; violet, phosphorus; and gray, carbon. The right-handed enantiomer is shown. (Right) Structure of the tris(2-(diphenylphosphino)ethyl)phosphine (PP3) ligand.

protected cluster. The computed HL gap for [Au20(PP3)4]4+ is in very good agreement with the experimentally determined optical gap. The Au20 core of the cluster is inherently chiral, and as such, an asymmetric distribution of the charge is assumed. We calculated the Bader charges for each of the atoms in the (Au20)4+ core. In the related (Au13)5+ core of the [Au25(SR)18]− cluster, only two types of Au atoms are found (12 symmetryinvariant atoms on the surface of the icosahedron and one atom in its center). In contrast, we identify eight different symmetry environments in the (Au20)4+ cluster. This is due to the capping of the Au13 icosahedron with a Au7 moiety. Within the Au13 unit, five different symmetry environments are found. Each atom in a distinct symmetry environment has its distinct Bader charge (Figure 2). Except for the two atoms that fall on the C3 axis (the central atom of the icosahedron and the central atom in the Au7 unit), the Bader charges are triply degenerate according to the 3-fold symmetry of the cluster. Angular-momentum resolved projected density-of-states (PDOS) for the two computed structures shows a HOMO with S-symmetry and a D-symmetric LUMO for the bare core and both HOMO and LUMO of D-symmetry for the ligandprotected cluster (Figure 3). The Kohn−Sham (KS) wave functions of the two structures were visualized in order to assign the individual electronic states to superatomic electron configurations. We first focus on the bare core, (Au20)4+. A series of delocalized bands (formed from the 6s and 6p states of the Au atoms) is found for (Au20)4+ (Figure 4). For a 16-electron cluster, a superatomic electronic configuration of 1S2 1P6 1D8 is expected in a spherical geometry. Note that 16 is not a magic number (indicating electronic shell closing) for spherical clusters. However, for strongly nonspherical geometries, 16 was identified as being a semimagic number.31 We identify the following superatomic configuration: 1S2 1P6 1D6 1S2. The 2S band is stabilized (under the influence of the high positive charge of the cluster), and the D-states are split into two sets, of which the occupied states are nearly degenerate and the unoccupied ones are doubly degenerate (these two states are the LUMO). The three occupied D-states are not perfectly degenerate, but they are very close in energy. Two states are degenerate, and the third state is slightly higher in energy (0.05 eV). The degeneracy of the D-states in the (Au20)4+ cluster is in agreement with the expected splitting of d-orbitals in C3 point group. Two superatomic gaps are identified, the HL-gap (2S− 1D) at 0.54 eV and the 1D−1F gap (20 electrons) at 0.94 eV.

(forming a supermolecule; for prolate clusters, 14 is a semimagic number31),47 the newly reported cluster has not yet been interpreted in terms of the SACM.

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METHODS All calculations were carried out using the real-space gridprojected augmented wave method as implemented in GPAW.48 The electronic structures were calculated using the PBE functional49,50 with a grid-spacing of 0.2 Å. Timedependent DFT (TD-DFT) was performed using the recently implemented38 code into the GPAW package, and timedependent density-functional perturbation theory (TD-DFPT) was done according to a recently developed protocol.23,51 All spectra were folded with a Gaussian broadening of 0.125 eV. The Kohn−Sham (KS) wave functions were visualized with an isosurface cutoff of 0.05. Bader charges were computed using the software provided by the Henkelman group.52 The coordinates of the discussed structures were extracted from the X-ray structures published in refs 29 and 17 (the coordinates from ref 46 gave virtually the same results). The [Au20(PP3)4]4+ cluster was analyzed using the crystal structure directly, whereas a DFT-optimized structure of Au38(SMe)24 (Me = methyl) was used in place of the original crystal structure of Au38(SCH2CH2Ph)24. This was done because some atoms in the ligands are missing in the crystal structure. The Au38(SMe)24 structure was optimized until the remaining forces on all atoms were below 0.05 eV/Å.

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RESULTS AND DISCUSSION Electronic Structure. The electronic structure of the (Au 20 ) 4+ core and the full ligand-protected cluster, [Au20(PP3)4]4+, was calculated using the coordinates of the X-ray structure.29 The HOMO−LUMO gaps (HL) of the computed structures and the experimentally reported optical gap are listed in Table 1. Of note, a significantly smaller gap is found for (Au20)4+ when compared to that of the ligandTable 1. HL (Simulated) and Optical Gap (Experiment) of [Au20(PP3)4]4+ and (Au20)4+ gap (eV) [Au20(PP3)4]4+, exp29 [Au20(PP3)4]4+, sim (Au20)4+, sim

1.33 1.30 0.54 4215



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Figure 2. (Left) Bader charges of the Au atoms in (Au20)4+. (Right) Au20 core; the atoms are colored according to their Bader charge (positive values indicate oxidation). Color scheme is according to the plot on the left.

Figure 3. PDOS of (Au20)4+ (left) and [Au20(PP3)4]4+ (right). The Fermi level is marked with ε. Note the opening of the HL-gap when moving from the bare core to the ligand-protected cluster.

Figure 4. (Left) Energies of the frontier orbitals in (Au20)4+. The dashed line denotes the Fermi level. The 2S orbital (HOMO) is shown in red, the 1D states, in green, and the 1F orbitals, in cyan. Marked with arrows are the superatomic gaps, gap 1 (HL-gap) at 0.54 eV and gap 2 (1D−1F) at 0.94 eV. (Right) Visualized KS wave functions of the 1D and 2S (HOMO) states. The unoccupied 1D states have a different color coding than the occupied states.

1D0 1F0. We ascribe this unusual occupation with the deviation of the core from a spherical geometry. We also calculated the electronic structure of both the bare core and the full ligand-protected cluster for a charge state of +II instead of +IV. In this case, the cluster would represent a closed-shell (18-electron) system with an expected configuration of 1S2 1P6 1D10. Without optimization, however, we find that the former LUMO in (Au20)4+, which are doubly degenerate, are singly occupied now, giving rise to a paramagnetic triplet species. The HL gap opens up to ca.

The situation is similar in the phosphine-protected [Au20(PP3)4]4+ cluster, but the 2S state is stabilized even further and its energy is now below the 1D state, which forms the HOMO (Figure 5). The 2S2−1D0 gap increases to 1.72 eV (from 0.54 eV), and the 1D−1F gap essentially vanishes (0.13 eV, the 1F orbital is below the 1D orbital). The LUMO is of Fsymmetry now, followed by the remaining two empty Dorbitals. Overall, the HL gap is increased (1.30 eV). The occupation in the superatomic orbitals is 1S2 1P6 1D4 2S2 1D2 | 4216



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Table 2. Transition Energies in Au20 Clusters [Au20(PP3)4]Cl4, exp

[Au20(PP3)4]4+, sim

(Au20)4+, sim

370 nm 495 nm 550 nm (shoulder) 833 nm not observed not observed

422 nm 519 nm 575 nm (shoulder) 805 nm not observed not observed

365 nm 495 nm 560 nm (shoulder) 780 nm 1100 nm 2030 nm

ligand-protected cluster). The spectra that were calculated for the clusters with a charge of +II are shown in Figure S1 (Supporting Information). The spectrum of the (Au20)2+ cluster is somewhat broadened and less defined than the spectrum of (Au20)4+. A significant deviation from the experimental spectrum is found for [Au20(PP3)4]2+, which displays a strong and broad absorption peak that is not found in the experiment. We assign the prominent transitions in the absorption spectra using TD-DFPT (Figure 7 and Table 3).23,51 Four features in the spectrum of [Au20(PP3)4]4+ were analyzed. The most prominent peak at 2.39 eV (519 nm) is ascribed to a transition from the degenerate 1D states (HOMO-2 and HOMO-3) into antibonding π-orbitals of the phenyl groups in the ligand. The transitions at 1.54 eV (weak broad band at 805 nm) and the shoulder at 2.16 eV are transitions within the superatomic core of the cluster (1D → 1F). The prior is the transition from the HOMO to LUMO+3, and the latter are HOMO-2/HOMO-3 to LUMO+6/LUMO+7 transitions. Of note, we could not identify the HOMO−LUMO transition, which would be a 1D → 1F transition also. We assume that it is hidden in the tail of the absorption spectrum and very weak in intensity. The peak at 422 nm (2.94 eV) originates mainly in transitions from the HOMO-2/HOMO-3 (1D) states to higher π* orbitals in the ligands. Overall, the electronic transitions at lower energy can be associated with transitions in the superatomic core of the cluster, whereas at higher energies, metal-to-ligand charge transfer (MLCT) bands are found. In the bare core, the two weak transitions at very low energy (0.61 and 1.13 eV) are associated with the HOMO−LUMO/LUMO +1 transition (2S → 1D) and HOMO-1/-2/-3 → LUMO/ LUMO/+1 transitions (1D → 1D). Both of the electronic transitions are dipole-forbidden (ΔL = 0, 2). CD Spectra. We also calculated the CD spectra of both the intrinsically chiral core of the cluster and the ligand-protected

Figure 5. Energies of the frontier orbitals in [Au20(PP3)4]4+. 2S, red; 1D, green; and 1F, cyan. The dashed line denotes the Fermi level. Note that the LUMO is a 1F state. The visualized KS wave functions are shown in the Supporting Information.

0.84 eV. This is the 1D−1F gap (which is 0.94 eV in the (Au20)4+ cluster). In the case of the ligand-protected cluster, the HL gap essentially vanishes (from 1.30 to ca. 0.02 eV), and a series of nominally unoccupied energy states is party occupied. A partial occupation is found up to LUMO+15. On the basis of this, we deem that a charge of +IV is indeed the correct one for the geometry considered here. We also find that the optical spectra of the clusters with a charge of +II are less realistic than those for a charge of +IV (see below and Supporting Information). Optical Properties. We computed the linear absorption and circular dichroism spectra of (Au20)4+ and [Au20(PP3)4]4+ (Figure 6). In comparison with the experiment, an overall good agreement is found (although this can be made only for the absorption spectra). The general features of the spectrum are reproduced for both the bare core and the ligand-protected cluster. However, because the HL gap is smaller for the bare cluster, it shows a peak in the absorption spectrum at 0.61 eV (2030 nm) that is not observed in the ligand-protected cluster, both in simulation and experiment. The nature of this transition is analyzed below, but it is close to the HL gap (0.54 eV) and should therefore be dipole-forbidden (2S → 1D). An overview of the absorption maxima is given in Table 2. The other features, especially the signature transitions at 370, 495, and 550 nm, are well-reproduced (and slightly red-shifted in the

Figure 6. (Left) Experimental (black) and simulated absorption spectra of (Au20)4+ (red) and [Au20(PP3)4]4+ (blue). The experimental data are reproduced with permission from ref 29. Copyright 2014 WILEY-VCH Verlag GmbH & Co. KGaA. The red trace shows weak bands at 1100 and 2030 nm (not shown here), which are not present in the spectra of the ligand-protected clusters, both experimental and simulated. (Right) Calculated CD spectra of (Au20)4+ (red) and [Au20(PP3)4]4+ (blue). 4217



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Figure 7. (Left) Transition contour plots (left) of the features at 1.54 eV (top) and 2.39 eV (bottom) in the absorbance spectra of [Au20(PP3)4]4+. The x axis shows the energies of the occupied states, and the y axis, the unoccupied states. Energies are relative to the Fermi level. (Right) Orbitals involved in the transitions, showing that the low-energy transition is a core−core transition and the peak at higher energy is a core−ligand chargetransfer band.

Table 3. Assignment of Electronic Transitions in [Au20(PP3)4]4+a eV 1.54 2.16 2.39 2.94 a

1D 1D 1D 1D

→ → → →

1F 1F π* π*

HOMO → LUMO+3 HOMO-2/-3 → LUMO+6/+7 HOMO-2/-3 → LUMO+8/+9 HOMO-2/-3 → LUMO+20−LUMO+28

core−core core−core MLCT MLCT

The energies in the table refer to simulated transition energies.

protecting SR-(AuSR)2 units on its surface.17,33,53 The Au23 core itself, however, can be regarded as a face-fused biicosahedron, which is achiral (note that this is idealized as the core is distorted in a “banana shape”). On the basis of this obviousness of the chirality, one would expect significantly stronger optical activity of the (Au20)4+ cluster than in the (Au23)9+ cluster (Figure 8). This is indeed found for both the rotatory strength (the CD spectrum) and the anisotropy factor, g = R/D (the CD spectrum divided by the absorption spectrum). However, when moving from the bare cluster cores to the ligand-protected clusters, [Au20(PP3)4]4+ and Au38(SR)24, the situation is reversed. In both the CD spectra and anisotropy factors, the thiolate-protected cluster exhibits stronger optical activity. Apparently, the chiral pattern of SR-(Au-SR)2 units in

cluster (Figure 6, right). Although the enantiomers of the cluster have not been separated and their experimental CD spectra remain unknown, we observe that the CD spectra resolve more electronic transitions than the absorption spectra. As in the absorption spectra, the spectrum of the bare cluster core shows at least two transitions at low energy that are not observed in the ligand-protected case (0.61 and 1.13 eV or 2030 and 1100 nm, respectively; not shown in Figure 6). The additional MLCT bands in the phosphine-protected cluster are also seen in the CD spectrum, which shows significantly more signals than the spectrum of (Au20)4+. Because the core of the cluster is intrinsically chiral, it may be enlightening to compare the strength of the optical activity to that of the Au38(SR)24 cluster. In the latter, the core is perturbed under the influence of a chiral arrangement of the 4218



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Figure 8. (Top left) CD spectra of (Au20)4+ (black) and (Au23)9+ (red). (Top right) CD spectra of [Au20(PP3)4]4+ (black) and Au38(SMe)24 (red). (Bottom left) Anisotropy factors of (Au20)4+ (black) and (Au23)9+ (red). (Bottom right) Anisotropy factors of [Au20(PP3)4]4+ (black) and Au38(SMe)24 (red). The low-energy region is cut for the anisotropy factors because the very low absorption creates unrealistically high values.

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the Au38 cluster is capable of inducing very strong optical activity and is the main cause for the observed33,39 strong CD spectra of the cluster. In addition, the sulfur atoms are rendered stereogenic centers because of the orientation of the organic groups relative to the SR-Au-units. This additional feature is not found in the phosphine clusters.

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ASSOCIATED CONTENT

S Supporting Information *

Visualized KS wave functions of the frontier orbitals in [Au 2 0 (PP 3 ) 4 ] 4 + and computed optical spectra of [Au20(PP3)4]2+ and (Au20)2+. This material is available free of charge via the Internet at http://pubs.acs.org.

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CONCLUSIONS AND OUTLOOK

AUTHOR INFORMATION

Corresponding Author

The recently reported X-ray structure of the [Au20(PP3)4]Cl4 cluster was investigated by means of density functional theory. The cluster can be explained as a 16-electron superatom complex with strong splitting in the 1D and 1F superatomic states. This results in the unusual electronic configuration of 1S2 1P6 1D4 2S2 1D2. The Au204+ core of the cluster bears intrinsic chirality because of the triblade shape of a 7-atom motif that sits on top of a regular 13-atom icosahedron. The optical properties in the visible spectral region are dominated by electronic transitions within the superatomic core of the cluster and strong MLCT bands. Comparison of the computed circular dichroism spectra of the bare cluster cores ((Au20)4+ and (Au23)9+) and the ligand-protected clusters, [Au20(PP3)4]4+ and Au38(SMe)24, shows that the extent of optical activity in the bare clusters is dictated by the asymmetry of the clusters, whereas in the latter case, the chiral arrangement of the protecting (SR-Au)2-SR units dominates the CD spectra and the phosphine protection has little influence.

*E-mail: [email protected]. Phone: +32 16 32 68 43. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS S.K. is grateful to the German Academic Exchange Service (DAAD) for a postdoctoral fellowship. L.L. and H.H. thank the Academy of Finland for financial support. All computations were performed at CSC − The Finnish IT Center for Science in Espoo. We thank Q.-M. Wang (Xiamen University) for providing the experimental absorption spectrum from ref 29. We thank Kirsi Salorinne for a discussion on the crystal structure data.

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