Energy Gap Law for Exciton Dynamics in Gold ... - ACS Publications

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Energy Gap Law for Exciton Dynamics in Gold Cluster Molecules Kyuju Kwak,† Viraj Dhanushka Thanthirige,‡ Kyunglim Pyo,† Dongil Lee,*,† and Guda Ramakrishna*,‡ †

Department of Chemistry, Yonsei University, Seoul 03722, Korea Department of Chemistry, Western Michigan University, Kalamazoo Michigan 49008, United States

‡

S Supporting Information *

ABSTRACT: The energy gap law relates the nonradiative decay rate to the energy gap separating the ground and excited states. Here we report that the energy gap law can be applied to exciton dynamics in gold cluster molecules. Size-dependent electrochemical and optical properties were investigated for a series of n-hexanethiolate-protected gold clusters ranging from Au25 to Au333. Voltammetric studies reveal that the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO−LUMO) gaps of these clusters decrease with increasing cluster size. Combined femtosecond and nanosecond time-resolved transient absorption measurements show that the exciton lifetimes decrease with increasing cluster size. Comparison of the size-dependent exciton lifetimes with the HOMO−LUMO gaps shows that they are linearly correlated, demonstrating the energy gap law for excitons in these gold cluster molecules.

O

consequence of single-electron excitations, excitons, between discrete states, and thus the relaxation dynamics in these clusters can be described by exciton relaxation. There are ample examples of excitonic transitions in gold cluster molecules. For example, rich quantum information was found to prevail until the size of Au144 and strong electronic transitions were realized at lower temperatures for Au25, Au38, and Au144.4,29 For the last two decades, excitons in nanoscale systems have been the focus of research in both fundamental science and technological applications.30−33 It has been widely accepted that organic/inorganic molecules show Frenkel excitons that are strongly bound with greater binding energies.30 In contrast, semiconductor nanostructures show Wannier excitons with low binding energies.33 Additionally, the quantum confinement alters exciton binding energies at nanoscale.30 Strongly bound excitons typically found applications in light emitting diodes while loosely bound excitons dissociate easily to form free charge carriers and found applications in solar cells.32 Exciton dynamics in molecules often referred to as excited state relaxation dynamics was also studied extensively. In particular, the energy gap law that relates the nonradiative decay rate to the HOMO−LUMO gap of a transition was able to satisfactorily describe the excited state dynamics in organic/ inorganic molecules.34−41 The main take away from the energy gap law is the decrease of excited state lifetime with decrease in energy gap. Although excitons have been recognized in gold clusters, their nature and dynamics remain largely unaddressed. Understanding the structural factors that control the exciton

wing to unique quantum size effects, gold clusters have emerged as a new class of promising nanomaterials during the past decade.1−7 The advent of novel synthetic methods, precise characterization, and structural elucidation has opened the avenue to control their size-dependent properties with atomic precision. In particular, metal-to-molecule transitions in gold clusters have been the focus of recent studies.8−15 Size-dependent electrochemical6,16−18 and catalytic properties,19 chirality,20 magnetism,21,22 and nonlinear optical properties8,12,23 of these gold clusters were studied. Notably, systematic investigations of atomically precise gold clusters protected with the same ligand have revealed that the metal-tomolecule transitions are indeed observed in these gold clusters.8,10,11,13,14 For example, in the study of electronic and geometric structures of gold clusters ranging from Au25 to Au∼520, Negishi et al. reported10 that the metal-to-molecule transition occurs between Au144 and Au187 clusters. The metal-to-molecule transitions have also been disclosed in a number of size-dependent optical studies of gold clusters. Using ultrafast transient absorption measurements, Jin and coworkers have shown that gold nanoparticles containing more than 333 gold atoms are plasmonic metallic-state.14 In this plasmonic regime, electrons in the conduction band are heated up to a high electronic temperature upon light excitation and the relaxation is dictated by electron dynamics.24−26 In the molecular regime, gold clusters display discrete electronic transitions that can be correlated with their structure and symmetry.4 In addition, decent photoluminescence,6,8,27,28 large two-photon absorption cross sections,8 coherent oscillations,11 chirality19 and unusual temperature dependence29 have been reported for the molecule-like gold clusters. The discrete absorption peaks observed for gold cluster molecules are the © XXXX American Chemical Society

Received: July 23, 2017 Accepted: September 21, 2017 Published: September 21, 2017 4898

DOI: 10.1021/acs.jpclett.7b01892 J. Phys. Chem. Lett. 2017, 8, 4898−4905

Letter

The Journal of Physical Chemistry Letters

Figure 1. (A) MALDI mass spectra and (B) UV−vis−NIR absorption spectra of Au25, Au38, Au67, Au102, Au144, and Au333 clusters. The absorption spectra of clusters were obtained in tetrachloroethylene and were offset for clarity. The wavelength-scale absorption spectrum, Abs(λ), was converted to the energy-scale, Abs(E), according to the relation Abs(E) = Abs(λ) × λ2.

Figure 2. SWVs of (A) Au25, Au38, and Au67 clusters and (B) Au102, Au144, and Au333 clusters in CH2Cl2 containing 0.1 M Bu4NPF6.

molecules. Well-defined gold clusters ranging from Au25 to Au333 were synthesized, and their electrochemical and excited state dynamics were systematically studied. Voltammetry of these gold clusters revealed that the HOMO−LUMO gap decreases as the size increases. Combined femtosecond and microsecond time-domain transient absorption measurements were carried out to address the size-dependent exciton dynamics in these gold cluster molecules. Syntheses of gold clusters were conducted following literature procedures with some modifications.16,53−56 Figure 1A shows positive-mode MALDI mass spectra of the isolated clusters. As can be seen in the figure, there is only a sharp peak observed for each cluster, indicating that the isolated clusters are highly pure. The observed peaks at around m/z 7034, 10298, 17300, 25249, 35397, and 74852 Da, correspond respectively to the intact cluster ions with chemical compositions of Au 2 5 (SC 6 H 1 3 ) 1 8 , Au 3 8 (SC 6 H 1 3 ) 2 4 , Au 67 (SC 6 H 13 ) 35 , Au 102 (SC 6 H 13 ) 44 , Au 144 (SC 6 H 13 ) 60 and Au333(SC6H13)79. It is worth noting that these clusters are protected by the same ligand, n-hexanethiolate (SC6H13), allowing us to compare the size effect in the same ligand system. These clusters will be abbreviated as Au25, Au38, Au67, Au102, Au144, and Au333, respectively. The gold clusters also exhibit size-dependent optical characteristics as can be seen in Figure 1B. The absorbance appears to be extinguished as an absorbance edge in the nearinfrared region; for example, 1.3, 0.9, and 0.7 eV for Au25, Au38,

dynamics in gold clusters are crucial for their applications. A special point of interest is whether the energy gap law can predict the exciton lifetimes in the gold cluster molecules. Among various techniques, time-resolved laser spectroscopic measurements have been successfully used to probe the excited state dynamics in nanoscale materials.9,13−15,42−50 Transient absorption measurements were used to monitor the electron dynamics of metallic gold nanoparticles.24−26 Ultrafast transient absorption has also been the preferred technique to probe the excited state dynamics in gold cluster molecules, as their photoluminescence quantum yields are usually low. Earlier time-resolved studies on gold clusters have shown subpicoseconds to picoseconds core-gold state relaxation, followed by long-lived excited states for Au25 and bi-icosahedral Au25 clusters.43,48 Recent theoretical calculations correlate ultrafast decay components to relaxation within core-gold states.51,52 Ultrafast dynamics in metal-doped gold clusters was also studied, and the metal dopant was found to have strong influence on the intra core-gold relaxation as well as long-lived dynamics.45,47,49 In a recent study, we have shown that exciton relaxation is much faster in a Pt-doped PtAu24 cluster exhibiting a smaller HOMO−LUMO gap.49 Although various aspects of excited state dynamics were addressed for gold clusters, the relationship between the size of the cluster and the exciton relaxation was not understood, especially within the molecule-like regime. This motivated us to investigate the size-dependent exciton dynamics in gold cluster 4899


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Figure 3. Transient absorption spectra of Au25 (A) at picosecond time delays and (B) nanosecond time delays obtained from femtosecond and nanosecond transient absorption, respectively. Insets show the kinetic decay traces at 730 nm. (C) Comparison of decay traces of Au25, Au38, Au67, Au102, and Au144 obtained from combined femtosecond and nanosecond transient absorption measurements. Solid lines are the fits to multiexponential decay function.

capacitors exhibiting quantized double layer (QDL) charging properties.57,58 That is, the double layer capacitance of these clusters is sufficiently small to cause the potential interval between successive single-electron changes in the electronic charge on the cluster core to become experimentally observable. The capacitance (CCLU) of these clusters can be estimated by

and Au67, respectively. The absorption edge corresponds to the optical gap of a cluster for electronic transition and decrease with increasing cluster size. The absorption edge becomes less clear for larger clusters such as Au102, Au144, and Au333 that all show that the optical energy gap is less than 0.5 eV. In addition, Au333 exhibits a noticeable surface plasmon resonance band at around 2.3 eV as can be seen in Figure 1B. These gold clusters also exhibit size-dependent electrochemical properties and their voltammograms have been effectively used to study the electronic structures of clusters near the HOMO−LUMO levels. As can be seen in Figure 2, SWVs of Au25, Au38, Au67, Au102, Au144, and Au333 exhibit wellresolved current peaks that lie at the formal potentials of the cluster charge-state couples. For example, the SWV of Au25 in Figure 2A shows that there are two oxidation peaks observed at 0.45 (O2) and 0.11 (O1) and one reduction peak at −1.55 V (R1) in the potential range investigated. The electrochemical gap determined from the difference between the first oxidation (O1) and reduction (R1) potentials is found to be 1.66 V. Subtracting the charging energy that is typically estimated using the gap between O1 and O2 (0.34 V) from the O1-R1 gap gives an energy gap of 1.32 eV, which corresponds to the electrochemically determined HOMO−LUMO gap for Au25 cluster.6,57 The electrochemical HOMO−LUMO gaps for Au38, Au67, Au102, and Au144 were similarly determined as 0.99, 0.61, 0.18, and 0.15 eV, respectively, from their SWVs. These are in reasonable agreement with those reported in the literature (SI Table S1). The O1-R1, HOMO−LUMO gaps and optical energy gaps are given in SI Table S1. Whereas size-dependent O1−R1 gaps were observed for smaller gold clusters, the O1−R1 gaps for Au102, Au144, Au333 are rather small, respectively 0.49, 0.39, and 0.22 V, and the O1 and R1 peaks are observed along with other evenly spaced current peaks as can be seen in Figure 2B. These voltammograms suggest that Au102, Au144, and Au333 behave as quantum

Ezo, z − 1

= E PZC

1 z − 2 )e ( +

CCLU

(1)

Eoz,z−1

where z is the charge state of a cluster core, is the formal potential of z/z − 1 charge state change, EPZC is the potential of zero charge for the cluster core, and e is the electric charge. The capacitances of Au102, Au144, Au333 clusters are estimated to be 0.49, 0.57, and 0.88 aF from the slopes of the z-plots (Eoz,z−1 vs z) shown in SI Figure S1. These results indicate that CCLU increases with cluster size as predicted for a concentric sphere capacitor displaying QDL charging behavior.57−59 Comparing with the charging behavior of Au25, Au38, and Au67, one can conclude that the cluster molecules with the prominent emergence of the HOMO−LUMO gap behave as molecular capacitors60 and become QDL charging capacitors as the gap decreases. We next probe the size effect on the electronic excitation and relaxation dynamics using transient absorption measurements. It has been found that metallic nanoparticles display vastly different relaxation dynamics depending on their size. For photoexcited plasmonic metal nanoparticles of 10−100 nm diameter, electrons in the conduction band undergo fast relaxation via electron−electron scattering, followed by electron−phonon coupling.24−26 The electron dynamics of metal nanoparticles can be described by the two-temperature model, in which the energy exchange between electron and phonon is dependent on the fluence of pump pulse.26 By 4900


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same transient is monitored even in nanosecond time delays. The decay at 730 nm (inset of Figure 3B) shows the complete recombination of exciton within 800 ns. The long-time decay trace was fitted with a two-exponential function and decay times of 24 ± 3 ns (35.5%) and 150 ± 12 ns (64.5%) were obtained from the analysis. Average lifetime was obtained by τavg = Σiaiτi/Σiai and it was used to determine the exciton lifetime of the cluster. As the exciton recombination did not follow single exponential decay, the average lifetime can be used as a measure of the exciton lifetime of the cluster. Similar femtosecond and nanosecond transient absorption analyses were carried out for Au38 (SI Figure S4) and Au67 (SI Figure S5). Both core-state relaxation and the ESA of excitons were observed and the excitons of Au38 and Au67 did not recombine in the shorter time window of 400 ps and the nanosecond time-resolved absorption measurements were carried out to monitor the complete recombination of excitons. On the other hand, only femtosecond transient absorption measurements were carried out for Au102 as no transient was observed in nanosecond transient absorption measurements. (SI Figure S6) In contrast to Au102, the transient absorption spectra of Au144 have shown interesting growth and decay of transient spectra (SI Figure S7), and the observed transient spectral features matched quite well with the reported data.14,46 From the analysis and fitting of the transient decay traces, three main decay components were observed with time constants of 650 fs and 1, 5, and 3.2 ps. (SI Figure S7C) The 3.2 ps decay constant is assigned to the exciton lifetime and the shorter time constants to intra core-state relaxation. As noted above, the decay kinetics of Au144 is pump-power independent and the use of exciton dynamics to describe the relaxation is justified. Also, the decay kinetics of Au67, Au102, and Au144 has shown little pump wavelength dependence, suggesting that the exciton recombination is the main decay pathway for these clusters. Thus far, most transient absorption studies of gold clusters have relied only on time windows until 1 ns, where the exciton recombination is not complete.9,12,14,15,43−50 To acquire complete exciton recombination dynamics, transient decay traces were obtained from combined femtosecond and nanosecond transient absorption measurements and shown in Figure 3C for Au25, Au38, Au67, Au102, and Au144 clusters. To obtain the decay traces shown in Figure 3C, the changes in absorption signal at 400 ps time delay for both femtosecond and nanosecond transient absorption were matched. The lifetimes were obtained by fitting these decay traces to a multiexponential function and average lifetimes were obtained from the decay constants. The corresponding lifetimes are provided in Table S2. Note from Table S2 and Figure 3C that Au25 decays slowly with an average lifetime of 109 ns compared to Au144 that decays fast with a decay lifetime of 3.2 ps. A closer inspection of decay traces presented in Figure 3C and lifetimes in Table S2 reveals the size dependence of exciton lifetimes, where the exciton lifetime decreases with increasing cluster size. The average exciton lifetime (τavg) from the combined transient absorption analysis of the clusters is related to a combination of radiative and nonradiative decay rates via

contrast, for gold cluster molecules such as Au25, raising the pump power can only generate more excited clusters, and the excited state dynamics will not be altered. The powerinsensitive electron dynamics is a unique feature of moleculelike gold clusters that set them apart from the plasmonics metallic nanoparticles. In other words, an attractive Coulombic interaction between electron and hole binds them into an exciton in ultrasmall gold clusters, and thus the relaxation dynamics in such materials is best described by exciton relaxation. Recently, Jin and co-workers clearly mapped out three distinct states: metallic, transition regime, and nonmetallic (or excitonic state) based on the pump-power-dependent electron dynamics of gold nanoparticles.14 However, experimental evidence that delineates the structural factors controlling the exciton dynamics has never been found. In this work, we focus on the exciton dynamics of gold cluster molecules; i.e., n-hexanethiolate protected Au25, Au38, Au67, Au102, and Au144. We first carried out pump-powerdependent transient absorption measurements for Au144 and Au333 to set the cluster size limit where the excitonic features are observed. All the transient absorption results present in this study are carried out with 370 nm as the excitation wavelength. As can be seen in SI Figure S2, there was no power dependence observed for Au144, while small power dependence was observed for Au333. We note that earlier studies46,47 have shown power dependence for transient decay traces of Au144 clusters, although the transient spectra are quite similar to the results obtained here. The power independence for Au144 observed in the present study matches well with the recent work reported by Jin and co-workers.14 These results suggest that Au144 is a molecule-like cluster that can be described by exciton dynamics, while Au333 shows plasmonic character and is best described by electron dynamics. Transient absorption spectra of Au333 shown in SI Figure S3 indeed resemble the spectra of plasmonic gold nanoparticles.25 Among the clusters investigated, Au144 appears to be the upper limit where the dynamics is described via the excitons, so transient absorption measurements were carried out for clusters from Au25 to Au144 and the exciton lifetimes were determined. For the determination of exciton lifetime, it is important to monitor the complete recombination of electrons and holes in a wider time window. Thus, transient absorption measurements were carried out for all clusters after excitation at 370 nm at a wider time window starting from 100 fs to 1 μs. Shown in Figure 3A are the transient absorption spectra of Au25 at different time delays monitored in picosecond time delays. The transient absorption spectra of Au25 at initial time delays show a positive absorption with a maximum around 600 nm and a bleach at 670 nm that are assigned to the excited state absorption (ESA) of the exciton and ground-state bleach, respectively. However, the bleach grew with time delay, suggesting ultrafast intra core-state relaxation from the higher excitonic states to the lower excitonic states. The inset of Figure 3A shows the decay trace at 730 nm, and it can be observed that the decay is not complete even after 200 ps, suggesting that the exciton is long-lived. Similar transient absorption results were reported for Au25 in other studies.43,48 As the transients did not decay in the monitored time window, nanosecond transient absorption measurements in a larger time window of 1 μs were carried out for Au25 after excitation at 370 nm and corresponding transient absorption at a time delay of 20 ns is shown in Figure 3B. The ESA spectrum observed at 20 ns matched well with the 200 ps spectrum, suggesting that the

τavg = 1/(k r + k nr)

(2)

where kr is the rate of radiative decay, and knr is the average rate of nonradiative decay. Factors that can influence the exciton dynamics are the type of electronic transitions involved, involvement of surface states, HOMO−LUMO gap, etc. In the case of n-hexanethiolate-protected gold clusters, τavg is 4901


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was ascribed to the increased surface states in smaller quantum dots and also to confinement-induced relaxation.63 As mentioned earlier, the energy gap law has been successfully applied to explain the nonradiative transitions in various molecular systems such as metal complexes, aromatic molecules, and conjugated polymers. In these molecules, however, it was difficult to vary the energy gap significantly in a similar structural system, and thus the energy gap law was observed for relatively narrow energy gap windows (from 0.1 to 0.6 eV).37−39 By contrast, the present study offers an opportunity to examine materials with considerably larger energy gap window (from 0.15 to 1.32 eV) offered by gold clusters protected with the same ligand. Furthermore, the clusters display well-defined electronic and atomic structures with no surface states, and only exciton dynamics is observed from the lifetime measurements in contrast to semiconductor nanomaterials. The slope of the best fit straight line for data shown in Figure 4 was determined to be −8 ± 2 eV−1, which is higher than those observed for Pt, Ru, or Os-based organometallic systems,37,38 Pt-containing polymers (−6 eV−1), monomers (−3.8 eV−1),40 and conjugated polymers (−1.7 eV−1).41 According to eq 3, the slope of the plot is given by − γ/ℏωM and thus is controlled by the molecular parameter (γ) and the maximum vibrational frequency available for the system. While the γ term can vary from system to system, the ωM term has been the key factor controlling the rate of nonradiative decay, in which energy is released from the excited state to the surroundings through the vibration of bonds. In the case of organic molecules, the C−H stretching mode (2950 cm−1) is the dominant vibration while ring stretching vibrations of 1300 cm−1 are active for Pt-based diimine complexes,40 Ru and Osbased complexes.38 Higher ωM would lead to smaller gradient and faster nonradiative decay. In gold clusters, the dominant vibrational modes arise not from the peripheral vibrations of ligands but rather from the Au−S vibrations and − S−Au−S− based stretching or bending modes.64,65 Raman and far-infrared measurements have shown that the Au−S stretching and the vibrational frequencies of staple motifs arise around 200 to 400 cm−1.65 Our earlier temperature-dependent absorption measurements have shown that the phonon that couples the core-gold and shell-gold is around 350 cm−1.29 As the dominant vibration frequency is low in the case of gold clusters, a greater gradient would be expected as observed in this study. In addition, the linear correlation observed in Figure 4 indicates that γ/ℏωM is quite constant for all clusters, suggesting that their molecular parameters and vibrational modes do not differ significantly. Based on the fitting results shown in Figure 4, the energy gap law was able to explain the size-dependent exciton dynamics in gold cluster molecules. The energy gap dependent exciton dynamics appears to be applicable to other molecule-like metal cluster systems. A PtAu24 cluster exhibiting the HOMO− LUMO gap of 0.3 eV shows the exciton lifetime of 3.5 ps,49 which fits very well with the energy gap law predictions. In summary, these are the first results demonstrating the energy gap law for exciton dynamics in gold cluster molecules. Highly monodisperse n-hexanethiolate-protected gold clusters ranging from Au25 to Au333 were synthesized. These clusters exhibit size-dependent absorption and electrochemical properties. The voltammetry study showed that the electrochemical HOMO−LUMO gap decreases from 1.32 to 0.15 V as the cluster size increases from Au25 to Au144. In addition, the cluster

mostly dominated by the rate of nonradiative decay as the radiative decay rates, i.e., photoluminescence quantum yields for the clusters are usually low (quantum yields are much less than 0.1% for the clusters).8 The nonradiative decay involves internal conversion, intersystem crossing, electron transfer, and electron−hole recombination. The nonradiative decay in molecular systems has been explained by the energy gap law that relates the nonradiative decay rate to the energy gap separating the ground and excited states. The energy gap law34−36 was developed for weakly coupled electronic states and can be presented as k nr ∝ e−γ ΔE / ℏωM

(3)

where γ is a term describing molecular parameters and ωM is the highest energy vibrational mode involved in the nonradiative transition to ground state and ΔE is the energy difference between the potential minima of the states involved. The relationship is based on the vibrational overlap between the states and the nonradiative decay rate is controlled by the vibrationally induced electronic coupling term and the Franck− Condon overlap integral.34 The energy gap law has been successfully applied to describe the nonradiative decay transitions in a variety of systems such as aromatic molecules, heavy-atom complexes, conjugated polymer films and organometallics.37−41 The distinct size dependence observed for exciton lifetimes of gold clusters in Figure 3C have prompted us to relate them to their HOMO−LUMO gaps. Figure 4 shows a plot of ln(knr)

Figure 4. Plot of ln(knr) versus HOMO−LUMO gap for gold clusters. The solid line is the best fit straight line for data (Au25−Au144).

versus HOMO−LUMO gap of the clusters obtained from transient absorption and voltammetry measurements (Figure 2), respectively. As can be seen in the figure, the ln(knr) versus HOMO−LUMO gap plot was satisfactorily fitted to a linear function indicating that the exciton dynamics of the gold clusters can be explained by the energy gap law. In Figure 4, the decay rate of Au144 appears to be faster than other clusters and thus it is slightly off the trend line. This is probably because Au144 is the transition region above which the metallic nature is observed.14 It is interesting to note that the size-dependent exciton dynamics observed for the gold clusters is fundamentally different from that observed for semiconductor quantum dots. Size-dependence of exciton dynamics was previously studied for semiconductor nanoparticles.61,62 As opposed to the case of gold clusters, excitons in smaller quantum dots were found to decay faster than the larger ones that possess smaller band gaps.61,63 The observed size-dependence of exciton dynamics 4902


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the Ubiquitous Au144(SR)60 Gold Nanocluster. Nat. Commun. 2014, 5, 3785. (5) Maity, P.; Xie, S.; Yamauchi, M.; Tsukuda, T. Stabilized Gold Clusters: From Isolation toward Controlled Synthesis. Nanoscale 2012, 4, 4027−4037. (6) Lee, D.; Donkers, R. L.; Wang, G.; Harper, A. S.; Murray, R. W. Electrochemistry and Optical Absorbance and Luminescence of Molecule-like Au38 Nanoparticles. J. Am. Chem. Soc. 2004, 126, 6193−6199. (7) 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. (8) Varnavski, O.; Ramakrishna, G.; Kim, J.; Lee, D.; Goodson, T. Critical Size for the Observation of Quantum Confinement in Optically Excited Gold Clusters. J. Am. Chem. Soc. 2010, 132, 16−17. (9) Link, S.; El-Sayed, M. A.; Gregory Schaaff, T.; Whetten, R. L. Transition from Nanoparticle to Molecular Behavior: A Femtosecond Transient Absorption Study of a Size-selected 28 Atom Gold Cluster. Chem. Phys. Lett. 2002, 356, 240−246. (10) Negishi, Y.; Nakazaki, T.; Malola, S.; Takano, S.; Niihori, Y.; Kurashige, W.; Yamazoe, S.; Tsukuda, T.; Häkkinen, H. A Critical Size for Emergence of Nonbulk Electronic and Geometric Structures in Dodecanethiolate-Protected Au Clusters. J. Am. Chem. Soc. 2015, 137, 1206−1212. (11) Varnavski, O.; Ramakrishna, G.; Kim, J.; Lee, D.; Goodson, T. Optically Excited Acoustic Vibrations in Quantum-Sized MonolayerProtected Gold Clusters. ACS Nano 2010, 4, 3406−3412. (12) Philip, R.; Chantharasupawong, P.; Qian, H.; Jin, R.; Thomas, J. Evolution of Nonlinear Optical Properties: From Gold Atomic Clusters to Plasmonic Nanocrystals. Nano Lett. 2012, 12, 4661−4667. (13) Ramakrishna, G.; Varnavski, O.; Kim, J.; Lee, D.; Goodson, T. Quantum-Sized Gold Clusters as Efficient Two-Photon Absorbers. J. Am. Chem. Soc. 2008, 130, 5032−5033. (14) Zhou, M.; Zeng, C.; Chen, Y.; Zhao, S.; Sfeir, M. Y.; Zhu, M.; Jin, R. Evolution from the Plasmon to Exciton State in LigandProtected Precise Gold Nanoparticles. Nat. Commun. 2016, 7, 13240. (15) Zeng, C.; Chen, Y.; Kirschbaum, K.; Appavoo, K.; Sfeir, M. Y.; Jin, R. Structural Patterns at All Scales in a Nonmetallic Chiral Au133(SR)52 Nanoparticle. Sci. Adv. 2015, 1, e1500045. (16) Kwak, K.; Tang, Q.; Kim, M.; Jiang, D.-e.; Lee, D. Interconversion between Superatomic 6-Electron and 8-Electron Configurations of M@Au24(SR)18 Clusters (M = Pd, Pt). J. Am. Chem. Soc. 2015, 137, 10833−10840. (17) Kwak, K.; Choi, W.; Tang, Q.; Kim, M.; Lee, Y.; Jiang, D.-e.; Lee, D. A Molecule-like PtAu24(SC6H13)18 Nanocluster as an Electrocatalyst for Hydrogen Production. Nat. Commun. 2017, 8, 14723. (18) Antonello, S.; Maran, F. Molecular Electrochemistry of Monolayer-Protected Clusters. Curr. Opin. Electrochem. 2017, 2, 18− 25. (19) Li, G.; Jin, R. Atomically Precise Gold Nanoclusters as New Model Catalysts. Acc. Chem. Res. 2013, 46, 1749−1758. (20) Knoppe, S.; Bürgi, T. Chirality in Thiolate-Protected Gold Clusters. Acc. Chem. Res. 2014, 47, 1318−1326. (21) McCoy, R. S.; Choi, S.; Collins, G.; Ackerson, B. J.; Ackerson, C. J. Superatom Paramagnetism Enables Gold Nanocluster Heating in Applied Radiofrequency Fields. ACS Nano 2013, 7, 2610−2616. (22) Crespo, P.; Litrán, R.; Rojas, T. C.; Multigner, M.; de la Fuente, J. M.; Sánchez-López, J. C.; García, M. A.; Hernando, A.; Penadés, S.; Fernández, A. Permanent Magnetism, Magnetic Anisotropy, and Hysteresis of Thiol-Capped Gold Nanoparticles. Phys. Rev. Lett. 2004, 93, 087204. (23) Olesiak-Banska, J.; Waszkielewicz, M.; Matczyszyn, K.; Samoc, M. A Closer Look at Two-Photon Absorption, Absorption Saturation and Nonlinear Refraction in Gold Nanoclusters. RSC Adv. 2016, 6, 98748−98752.

molecules with the prominent emergence of HOMO−LUMO gap behave as molecular capacitors and become quantized double layer charging capacitors as the gap decreases. Transient absorption measurements were carried out to address the sizedependent exciton dynamics for clusters that had shown pumppower independent dynamics (from Au25 to Au144). Combined femtosecond and microsecond transient absorption measurements have shown that excitons decay completely, and their lifetime decreases with increasing cluster size. The sizedependent exciton lifetime is found to be strongly correlated with the HOMO−LUMO gap, suggesting the applicability of energy gap law for excitons in these gold cluster molecules. This work provides the groundwork that can advance our understanding of the nature and dynamics of excitons in gold clusters, which has practical implications in photovoltaics and photocatalysis.66−70

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.7b01892. Syntheses and characterizations of gold clusters, supporting tables and figures, and transient absorption results of Au38, Au67, Au102, Au144, and Au333 are provided (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Guda Ramakrishna: 0000-0002-5288-8780 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS D.L. acknowledges support by the Korea CCS R&D Center (KCRC) grant (NRF-2014M1A8A1074219), the NRF grant (NRF-2014R1A2A1A11051032 and 2009-0093823), and the Yonsei University Future-leading Research Initiative of 2014. G.R. acknowledges the support of ACS-PRF #53999-ND5 and Western Michigan University startup. G. R. also acknowledges Dr. Gary Wiederrecht, Argonne National Laboratory, for help with transient absorption measurements. Use of the Center for Nanoscale Materials, an Office of Science user facility, was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC0206CH11357.

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REFERENCES

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