TDDFT Analysis of Optical Properties of Thiol Monolayer-Protected

Article pubs.acs.org/JPCC

TDDFT Analysis of Optical Properties of Thiol Monolayer-Protected Gold and Intermetallic Silver−Gold Au144(SR)60 and Au84Ag60(SR)60 Clusters Sami Malola,† Lauri Lehtovaara,‡ and Hannu Hak̈ kinen*,†,‡ †

Department of Physics, Nanoscience Center, and ‡Department of Chemistry, Nanoscience Center, University of Jyväskylä, FI-40014 Jyväskylä, Finland S Supporting Information *

ABSTRACT: The optical absorption spectra of atomistic model structures for experimentally isolated all-gold Au144(SR)60 and intermetallic Au84Ag60(SR)60 clusters are systematically analyzed from linear-response time-dependent density functional theory (LR-TDDFT) and time-dependent density functional perturbation theory (TD-DFPT) calculations. The computed spectra, utilizing the atomistic model for Au144(SR)60 published by us in 2009, reproduce closely the experimental observations for corresponding isolated compounds, reported previously by Kumara and Dass in 2011. A collective dipole oscillation within the metal cores of the all-gold and intermetallic clusters is formed as response to light in the visible range. The weight of the oscillation and especially the screening by Au(5d) electrons are shifted gradually closer to the metal/ligand interface as the excitation energy is increased, but none of these clusters supports formation of a localized surface plasmon resonance. Based on the comparison of calculated spectra for two isomers of the intermetallic Au84Ag60(SR)60 cluster and the previously published experimental data, one can conclude that silver preferentially occupies the core surface and induces strong radial reorganization of the electron density in the metal core. This arrangement magnifies the collective intraband (sp-electrons) dipolar response and brings up more distinct features in the absorption spectrum as compared to the all-gold case. The intrinsically chiral gold−thiolate interface of these clusters is predicted to induce strong circular dichroism (CD) signals for higher-energy excitations, below the wavelength of 500 nm.

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INTRODUCTION Nanometer-scale, ligand-stabilized noble metal clusters have emerged in recent years as a novel form of nanoscale matter with potential applications in molecular electronics, optics, sensing, drug delivery, and biolabeling. Tremendous advances have been achieved in understanding their stability and structure due to contributions from synthetic work, X-ray crystallography, and density functional theory computations.1−5 Their electronic structure can be understood surprisingly well from the simple concepts that have been used in the related field of bare gas-phase metal clusters since 1980s, particularly from the so-called “superatom model” that accounts for the delocalized sp-electrons in the metal core.6−10 Forming in most cases the frontier orbitals of the nanoparticle, these electrons are responsible for low-energy optical transitions and much of the chemistry. While a large body of work has concentrated on exploration of stabilizing gold in the nanoscale by using various thiols as ligand as inspired by the landmark synthesis work of Brust, Schiffrin, and collaborators in the mid-1990s,11,12 more recent work has shown exciting possibilities to synthesize intermetallic clusters made of a combination of gold, silver, and/or copper.5,13−18 The use of gold and thiols is not only beneficial to protect the easier-oxidized silver and copper in the © XXXX American Chemical Society

intermetallic compounds, but the presence of the other metals has been shown to modify the electronic structure of the gold as manifested by clear changes in the optical absorption. Understanding how inclusion of the other noble metals in gold clusters affects the electronic structure and optical properties can be beneficial for a better engineering of these novel nanomaterials for various applications. In this study we have concentrated on a systematic theoretical study of Au144(SR)60 and Au144−xAgx(SR)60 clusters that were reported by Kumara and Dass in 2011.14 We calculate the optical absorption and circular dichroism (CD) spectra from the time-dependent density functional theory in the linear-response formulation and analyze several excitations by using the time-dependent density functional perturbation theory. We are able to shed light on the question why silver enhances the UV−vis absorption by gold nanoclusters. We predict strong CD signals below 500 nm where the metal−thiolate interface contributes strongly to the transitions. Received: June 3, 2014 Revised: August 5, 2014

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dx.doi.org/10.1021/jp505462m | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Model structures used in the calculations. (a) Layer-by-layer decomposition of cluster 1 Au144(SH)60, showing the Mackay inner core layers M1 and M2, the anti-Mackay (AM) core surface, and the ligand layer L composed of HSAuSH units. The composition can be written as Au114@(HSAuSH)30. In the bottom, cluster 1 in (b) is compared to two intermetallic clusters of composition Au84Ag60(SH)60, where cluster 2 in (c) has all the 60 Ag atoms in the AM core surface while cluster 3 in (d) has 60 Ag atoms randomly distributed in M1 and M2. Left-handed enantiomers are shown for each cluster in (b)−(d). Part (a) reproduced from ref 23, copyright 2013 ACS publications.

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COMPUTATIONAL METHODS We used density functional theory with projector augmented waves (PAW) as implemented in the real-space grid codepackage GPAW19,20 to study the ground-state electronic structure, optical absorption, and chiral optical response of the Au144(SR)60 and Au84Ag60(SR)60 clusters. A simple SH ligand was used in place for the thiolates (SR = SH). For the PAW setup, the atomic valence was defined as Au(5d106s1), Ag(4d105s1), S(3s23p2), and H(1s1), with scalar-relativistic effects included for Au and Ag. Optimization of the clusters were done symmetry-free with grid spacing of 0.2 Å until the residual forces were below 0.05 eV/Å. Local density approximation (LDA) was used for the structural optimizations, based on the previous experience that LDA reproduces the experimental metal−metal distances better than the GGAbased functionals. Angular momentum resolved projected density of states analysis of the ground state was performed by projection to the center of mass of the structures in a sphere with a radius of 11 Å, which includes all the atoms.6 Optical spectra were calculated through the linear response form of the time-dependent density functional theory (LR-TDDFT), as implemented in the GPAW package,21 by using the PBE-GGA functional22 for the exchange-correlation kernel, and a grid spacing of 0.25 Å. The nature of the optical transitions was analyzed at selected excitation energies by examining contributions of particle−hole excitations to a given peak (the so-called transition contribution map, TCM) and visualizing induced densities using our recently published method15,23 that is based on the time-dependent density functional perturbation theory (TD-DFPT). Oscillator and rotatory strengths were calculated with an updated code of the recent implementation of circular dichroism (CD) spectra into GPAW.24 All the optical and CD spectra were folded for

plotting with a Gaussian broadening of 0.1 eV of single transitions.

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RESULTS AND DISCUSSION Atomistic Models. We considered three model clusters with the same overall geometry, shown in Figure 1. Cluster 1 is an all-gold Au144(SH)60 representing a widely used model25 for experimentally characterized Au144−146(SR)59−60 compounds. Though the precise X-ray single crystal structures of these compounds are still not known at the present, our previous work has shown that the computed X-ray powder diffraction function, optical absorption, and electrochemical properties of cluster 1 are in a very good agreement with experimental data.14,26−34 The cluster has an icosahedral 114-atom core built out of two Mackay layers (M1, M2) and one anti-Mackay (AM) layer (Figure 1a,b). The core is protected by 30 RS− Au−SR units. This “divide and protect” geometrical motif35 is frequently found in the structurally defined thiolate-protected gold nanoclusters as well as in thiolate monolayers on gold surfaces.4 Placement of the 30 RS−Au−SR units on the core is chiral which also induces a slight chiral distortion to the 60atom AM surface layer of the core. The cluster is highly symmetric in line with experimental evidence of highly symmetric ligand layer of water-soluble Au144 clusters from NMR studies.36 In addition we have considered two models (clusters 2 and 3) for intermetallic gold−silver clusters that are based on the overall geometry of 1. Both clusters have a composition Au84Ag60(SH)60 corresponding to the estimate for the highest Ag/Au ratio in the experimental samples.14 In 2, all the silver atoms are placed in the 60-atom AM surface layer of the core while in 3 30 Ag atoms are randomly placed in the two innermost M layers and another 30 Ag atoms randomly in the AM core surface (Figure 1c,d). B



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Analysis of Optical Spectra. Figure 2 shows the computed optical absorption spectra of 1, 2, and 3 as compared

Figure 2. Experimental optical absorption spectra of Au144−xAgx(SR)60 clusters from Dass group (ref 14), compared to computed ones for clusters 1, 2, and 3. For the experimental curves, the ratio of Ag/Au increases from red to black.

to the experimental data of Au144−xAgx(SR)60 clusters.14 The highest ratio in the experiment, marked as Au91Ag53 in Figure 2, was assigned to the maximum of a binomial distribution of Ag/ Au compositions in a sample that results from a synthesis with maximum silver-to-gold feed ratio.14 That distribution extended up to a composition of Au84Ag60 that was taken for cluster models 2 and 3 as explained above. Figure 2 shows that the absorption spectra are quite sensitive to the silver/gold ratio. The all-gold Au144 spectrum is quite featureless both in the experiment and in the calculation (see also Supporting Information Figure S1 for a comparison of the peak at 380 nm in the calculated spectrum to another experiment). The intermetallic clusters develop two clear peaks/shoulders around 560 and 430 nm in the experiment that are fairly well reproduced by the calculation at around 550 and 480 nm for cluster 2. On the other hand, the computed spectrum of cluster 3 is not in a qualitative agreement with the experimental spectrum. We also note that an additional peak develops at around 310 nm in the experimental data as the silver content increases. The computed spectrum of 2 has additional peaks at around 340 and 400 nm. Previously37 we investigated possible structures and energetics of a series of intermetallic Au144−xAgx(SH)60 (x up to 60) clusters that were based on our proposed25 geometrical structure of the Au144(SR)60. Those calculations showed clearly that (i) the formation energy of the clusters, calculated with respect to bulk Au and Ag metals and intact SH2 molecules, is optimal for a cluster that has 60 Ag atoms at the core surface (corresponding to cluster 2 in the present work), (ii) mixing silver into gold in this ordered fashion creates alternating negatively and positively charged atom layers throughout the cluster, and (iii) different locations of Ag(4d) and Au(5d) bands may affect collective intraband (d → sp) optical transitions. In what follows, we analyze systematically the nature of optical transitions for several selected transition energies in energy space and real space for clusters 1 and 2 by building the transition contribution maps (TCMs)23 in correlation to the electronic DOS for occupied and unoccupied states (Figure 3). The general electronic structure of both clusters is expected to be similar with 84 electrons in the superatomic shells as

Figure 3. TCM analysis of optical transitions of (a) cluster 1 and (b) cluster 2. The analysis is done between 1.5 and 3.5 eV with increments of 0.1 eV, and the two-dimensional correlation plots on the upper left parts show a sum of the results. Five selected energies corresponding to 0.5 eV increments are marked by vertical dotted lines on the bottom right spectrum of each subfigure. In the correlation plots these energies are shown by the diagonal dotted lines as marked. The electronic state contributions to absorption arising from the Au(5d)-band and ligand/ Au(6sp)-band parts are divided by the vertical dotted lines. Angular momentum projected electronic density of states is shown for occupied states (horizontal) and unoccupied states (vertical) in each subfigure. The brighter yellow is the area in the correlation plot; the stronger is the contribution from this region of occupied to unoccupied single-electron contribution in the transition. The Fermi energy is at zero.

deduced from the widely used counting rule.6 In the electron shell model this implies that the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital C



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(LUMO) lie inside a manifold of states with 1H−2D−3S symmetries (after 58, the next major shell closing is at 92 electrons where 1H−2D−3S shells are full). Figure 3 shows that this is indeed true: the 2D and 3S shells are fully occupied in 2 and 3, but the 1H shell is split into subshells over an energy range of almost 1 eV and the highest subshell is unoccupied containing also the LUMO level. This analysis agrees well with earlier theoretical and experimental studies.25 While clusters 1 and 2 are “close to being metallic” in the sense that the HOMO−LUMO and optical gaps are very small (ca. 0.1−0.2 eV), confinement effects are still clearly visible in the calculated electronic structure in the sp-band in the form of the well-defined superatom shells of given angular momenta within about 1 eV on both sides from the Fermi level. Since the lowest-energy optical transitions (below 1 eV) have been analyzed experimentally and theoretically in detail before,32,34 we focus here on a comparative analysis of optical absorption of clusters 1 and 2 mainly in the UV−vis region. Figure 3 shows the TCM analysis of clusters 1 and 2 between transition energies of 1.5 and 3.5 eV, respectively, along with the calculated electronic density of states (DOS) for occupied and unoccupied single-particle states. Comparison of the spectra in the low-VIS range shows that while the superatom → ligand and ligand → superatom transitions generally dominate for energies below 2.5 eV (wavelengths beyond 500 nm), cluster 2 has a concentrated edge around 600 nm where ligand → superatom transitions become significant causing the steep increase of the absorption (Figure 3b). At and above 2.5 eV, transitions originating from the Au(5d) band start to contribute. Collectivity of the transitions in the energy space also increases as the transition energy increases. TCM analysis of selected absorption peaks are additionally analyzed for cluster 1 in Supporting Information Figure S2 and for cluster 2 in Supporting Information Figure S3. Further information on the nature of the corresponding transitions can be gained from the real-space induced density in Figures 4 (density contours) and 5 (radial profiles), respectively, and from the radial profile of the hole/electron densities in Figure 6. Figures 4 and 5 show that both clusters 1 and 2 develop a dipolelike response to the excitation by light at all of the analyzed excitation energies. As the excitation energy increases, the weight of the dipole response moves gradually to outer layers in the clusters and at the same time the d-band screening effects become more distinct. Previously we analyzed the distribution of atomic charge in the ground-state electronic structure of 1 and 2.37 It was found that 2 has a very prominent layer-by-layer distribution of charges, with the M1, M2, AM and ligand layers having total charges of −0.4, −5.3, +15.0, and −9.4 |e|, respectively. As comparison, the corresponding layers of cluster 1 have charges of −0.4, −0.3, +4.1, and −3.5 |e|. The strongly positively charged layer of 60 Ag atoms of cluster 2 is seen to enhance the sp/ligand contributions in the absorption in the range of 2−2.5 eV which contributes to the enhanced features in the calculated spectrum. The highest energy peak in the computed spectrum at 340 nm/3.63 eV (Figure 2) of 2 arises from a strong contribution from the Ag(4d) band (Supporting Information Figure S3). This peak also develops in the measured spectra around 310 nm as the silver content increases (Figure 2) but is naturally absent in the all-gold cluster 1 and in the corresponding experimental data. Prediction of Chiroptical Response. Circular dichroism is a striking feature of most known thiolate-stabilized gold nanoclusters.38,39 The pioneering contributions by Whetten’s

Figure 4. Induced densities in (a) cluster 1 and (b) cluster 2 at the marked selected excitation energies. The sp/ligand- and d-contributions are visualized separately, and the classification is based on the location of the hole states (initially occupied single-electron states) as marked in Figure 3. Note the opposite phase in density oscillations of d-electrons to that of the sp/ligand visualizing a screening effect.

group for more than a decade showed that by passivating Au clusters with a chiral glutathione ligand, clear CD signals could be detected even at rather low excitation energies where the transitions are metal-based (the glutathione ligand itself produces a CD signal at near-UV/UV energies).40 In principle, the chiroptical response can arise from various different sources: from a geometrically chiral metal core, from a geometrically chiral core−ligand interface, from the ligand itself, or from a combined effects in the electronic structure of the whole nanocluster. Later on the many successful crystallographic total structure determinations, in combination with theory, of molecularly precise Au:SR clusters have revealed the origins of the chiroptical response. Two prevalent effects in most structurally known clusters are (i) the chiral arrangements of the protecting RS(AuISR)x (x = 1, 2, 3) units on the core surface and (ii) the sulfur itself as the chiral center when it is bridging the gold atoms in two oxidation states at the interface (AuI in the unit and Au0 in the core surface).4,39 Both these effects induce strong CD signals for the known clusters stabilized by achiral ligands such as Au28(SR)20,41,42 Au30S(SR)18,43 Au38(SR)24,44,45 and Au102(SR)44;46,47 these same effects are predicted also for the case of Au40(SR)24.24,48 In the case of Au28 and Au30 the chiral interface influences the metal core as well. Interestingly for Au25(SR)18, both the core and the arrangement of the RS(AuSR)2 units are achiral but a weak CD signal of metal-based optical transitions is induced by two of the three sulfurs in each RS(AuSR)2 unit.49−51 We turn now the attention to the Au144(SR)60 clusters for which the widely used geometric model predicts a chiral response due to the geometric chirality of the core−ligand interface. The circular dichroism (CD) spectra of clusters 1 and 2 are shown in Figure 7. Aside from slight differences at long wavelengths, it is interesting to note that the two spectra are almost identical up to about 450 nm (2.75 eV), signaling a very D



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Figure 5. Radial analysis of the induced density of clusters 1 (a) and 2 (b) at the marked selected excitation energies. The analyzed energies and spand d-contributions correspond to those shown in Figure 4. The atomic shells are shown on top of both panels.

Figure 6. Electron−hole densities of clusters 1 (a) and 2 (b) at the same excitation energies as shown in Figures 4 and 5. The atomic shells are shown on top of both panels.

similar electronic structure of both clusters. This is the range where the increasing silver content enhances features in the linear absorption spectra (Figure 2). For higher energies the ± oscillations in the CD signal are in different phases (noted by the arrows in Figure 7). The above discussion has shown that the outer atom shells of the core and the core−ligand interface contribute successively more intensively as the transitions approach higher energies. Since the overall geometric structure of the metal core−ligand interface of clusters 1 and 2 is similar, the differences in the CD signal thus reflect the different details of the electronic structure of the interface since the core surface of 1 is of gold while in 2 it is of silver. Our predicted spectra, containing signature features of the geometry and chemical composition of that interface, may prove valuable for further experimental work in case the enantiomeric separation of Au144(SR)60 and intermetallic Au144−xAgx(SR)60 clusters succeeds.

Figure 7. Computed CD spectra of clusters 1 and 2 (for the lefthanded enantiomers shown in Figure 1). Although the spectra are otherwise remarkably similar, the arrows indicate a range of transitions where the CD signals are of opposite sign.

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(6) Walter, M.; Akola, J.; Lopez-Acevedo, O.; Jadzinsky, P. D.; Calero, G.; Ackerson, C. J.; Whetten, R. L.; Grönbeck, H.; Häkkinen, H. A Unified View of Ligand-Protected Gold Clusters as Superatom Complexes. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 9157−9162. (7) Häkkinen, H. Atomic and Electronic Structure of Gold Clusters: Understanding Flakes, Cages, and Superatoms From Simple Concepts. Chem. Soc. Rev. 2008, 37, 1847−1859. (8) Aikens, C. M. Electronic Structure of Ligand-Passivated Gold and Silver Nanoclusters. J. Phys. Chem. Lett. 2011, 2, 99−104. (9) Khanna, S. N.; Jena, P. Assembling Crystals from Clusters. Phys. Rev. Lett. 1992, 69, 1664−1667. (10) Jena, P. Beyond the Periodic Table of Elements: The Role of Superatoms. J. Phys. Chem. Lett. 2013, 4, 1432−1442. (11) Brust, M.; Walker, M.; Bethell, D.; Schiffrin, D. J.; Whyman, R. Synthesis of Thiol-Derivatized Gold Nanoparticles in a Two-Phase Liquid−Liquid System. J. Chem. Soc., Chem. Commun. 1994, 801−802. (12) Brust, M.; Fink, J.; Bethell, D.; Schiffrin, D. J.; Kiely, C. Synthesis and Reactions of Functionalised Gold Nanoparticles. J. Chem. Soc., Chem. Commun. 1995, 1655−1656. (13) Negishi, Y.; Iwai, T.; Ide, M. Continuous Modulation of Electronic Structure of Stable Thiolate-Protected Au25 Cluster by Ag Doping. Chem. Commun. 2010, 46, 4713−4715. (14) Kumara, C.; Dass, A. (AuAg)144(SR)60 Alloy Nanomolecules. Nanoscale 2011, 3, 3064−3067. (15) Yang, H.; Wang, Y.; Huang, H.; Gell, L.; Lehtovaara, L.; Malola, S.; Häkkinen, H.; Zheng, N. All-Thiol-Stabilized Ag44 and Au12Ag32 Nanoparticles with Single-Crystal Structures. Nat. Commun. 2013, 4, 2422. (16) Yang, H.; Wang, Y.; Lei, J.; Shi, L.; Wu, X.; Mäkinen, V.; Lin, S.; Tang, Z.; He, J.; Häkkinen, H.; et al. Ligand-Stabilized Au13Cu(x) (x = 2, 4, 8) Bimetallic Nanoclusters: Ligand Engineering To Control the Exposure of Metal Sites. J. Am. Chem. Soc. 2013, 135, 9568−9571. (17) Yang, H.; Wang, Y.; Yan, J.; Chen, X.; Zhang, X.; Häkkinen, H.; Zheng, N. Structural Evolution of Atomically Precise Thiolated Bimetallic [Au12+ nCu32(SR)30+N)4− (N = 0, 2, 4, 6) Nanoclusters. J. Am. Chem. Soc. 2014, 136, 7197−7200. (18) Kumara, C.; Aikens, C. M.; Dass, A. X-ray Crystal Structure and Theoretical Analysis of Au25−xAgx(SCH2CH2Ph)18− Alloy. J. Phys. Chem. Lett. 2014, 5, 461−466. (19) Mortensen, J.; Hansen, L.; Jacobsen, K. Real-Space Grid Implementation of the Projector Augmented Wave Method. Phys. Rev. B 2005, 71, 035109. (20) Enkovaara, J.; Rostgaard, C.; Mortensen, J. J.; Chen, J.; Dulak, M.; Ferrighi, L.; Gavnholt, J.; Glinsvad, C.; Haikola, V.; Hansen, H. A.; et al. Electronic Structure Calculations with GPAW: A Real-Space Implementation of the Projector Augmented-Wave Method. J. Phys.: Condens. Matter 2010, 22, 253202. (21) Walter, M.; Häkkinen, H.; Lehtovaara, L.; Puska, M.; Enkovaara, J.; Rostgaard, C.; Mortensen, J. J. Time-Dependent Density-Functional Theory in the Projector Augmented-Wave Method. J. Chem. Phys. 2008, 128, 244101. (22) Perdew, J.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (23) Malola, S.; Lehtovaara, L.; Enkovaara, J.; Häkkinen, H. Birth of the Localized Surface Plasmon Resonance in Monolayer-Protected Gold Nanoclusters. ACS Nano 2013, 7, 10263−10270. (24) Malola, S.; Lehtovaara, L.; Knoppe, S.; Hu, K.-J.; Palmer, R. E.; Bürgi, T.; Häkkinen, H. Au40(SR)24 Cluster as a Chiral Dimer of 8Electron Superatoms: Structure and Optical Properties. J. Am. Chem. Soc. 2012, 134, 19560−19563. (25) Lopez-Acevedo, O.; Akola, J.; Whetten, R. L.; Grönbeck, H.; Häkkinen, H. Structure and Bonding in the Ubiquitous Icosahedral Metallic Gold Cluster Au144(SR)60. J. Phys. Chem. C 2009, 113, 5035− 5038. (26) Schaaff, T. G.; Shafigullin, M. N.; Khoury, J. T.; Vezmar, I.; Whetten, R. L. Properties of a Ubiquitous 29 kDa Au:SR Cluster Compound. J. Phys. Chem. B 2001, 105, 8785−8796.

CONCLUSIONS We have investigated systematically the optical properties of Au144(SR)60 and related Au144−xAgx(SR)60 nanoclusters by calculating the linear and chiroptical absorption by timedependent density functional theory and analyzing several excitations by using density functional perturbation theory. These compounds are at the interface between “molecular” and “metallic” systems, the former being characterized by distinct discrete absorption maxima as well as large HOMO−LUMO and optical energy gaps, while the latter show continuous absorption and vanishingly small energy gaps at the Fermi energy. We have shown that while these clusters respond to light in the UV−vis region by developing a collective dipole oscillation of the sp-electrons, screened by the d-electrons, they do not show a localized surface plasmon resonance. Enhancement of the absorption features induced by mixing silver into the clusters is due to reorganized charge distribution in the metal core. A cluster model that includes an organized 60-atom silver layer on the surface of the metal (gold) core gives an absorption spectrum that is in close agreement with the experimental data. Strong chiroptical absorption is predicted for excitation energies below 500 nm. We hope that this work helps in developing a better understanding of factors contributing to optical and chiroptical absorption of monometallic and intermetallic nanoclusters, which is crucial for developing these nanomaterials for applications.

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ASSOCIATED CONTENT

S Supporting Information *

Additional optical spectra for cluster 1 and TCM analysis of clusters 1 and 2 at selected transition energies (Figures S1− S3); full ref 20. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: hannu.hakkinen@jyu.fi. Tel: +358 400 247 973. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Academy of Finland. The computations were done at the CSCthe Finnish IT Center for Science in Espoo and as part of the PRACE project “Plasmonic ligand-stabilized gold nanoclusters” at the HLRSGAUSS Center in Stuttgart, Germany. We thank A. Dass and J. Enkovaara for discussions.

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TDDFT Analysis of Optical Properties of Thiol Monolayer-Protected

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