Raman modes, dipole moment and chirality in periodically positioned Au₈ clusters

Abstract

This study reports the solution-based assembly of hexagonal + 1 shaped Au₈ clusters surrounded by six ligands into a local periodic structure (LPS) of periodicity 1.47 nm, which was confirmed by experimental and theoretical Raman scattering analyses as well as transmission electron microscopy, X-ray diffraction and small angle X-ray scattering measurements. The enhancement of the net electric dipole moment to 21.17 Debye is due to the rearrangement of the charge distribution in the electronic states of the LPS. This results in exciton–exciton coupling through dipole interactions, which was evidenced by the splitting of the excitonic states in the circular dichroism (CD) spectra. The strong negativity of the CD index at the longer wavelength confirms the negative chirality of the LPS-Au₈.

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The synthesis and characterization of free standing micro-clusters (MCs) consisting of ten or a fewer atoms is of great interest to many researchers in the field of cluster science because of their unique electrical and optical properties, which can be applied to next-generation sensors and electro/optical devices.^1–6 Up to now, many theoretical and experimental studies have been carried out to synthesize the smallest possible MCs and characterize their structure and physical properties.^7,8 For example, in the case of metallic gold clusters, the Au₈ (eight atoms gold cluster) is one of the smallest possible MCs (atomicity < 10) that maintains a stable solid phase.⁹ There are only a few studies on such small Au clusters.¹⁰ Recent studies have revealed that the structures are significantly influenced by the medium/substrate.^11,12 Although a theoretical study showed that the most likely structure of the Au₈ is a two dimensional (2D) planar star in free space, which has the lowest energy,^13,14 the 2D planar hexagonal + 1 is experimentally found the most likely⁹ in the case of bottom-up growth. A three-dimensional (3D) Au₈ was also grown on an MgO substrate by vapor phase deposition,⁴ but is less interesting from an application point of view because of its “ordinary” properties.

In addition to the structural studies, experimental and theoretical attempts were made to understand the origin of the electronic chirality in the Au MCs, which is associated with their optical and magnetic properties.^15–18 However, the synthesis of monodispersed and stable 2D Au MCs with a well-defined structure is required to physically and accurately understand the optical properties. Note that the high-resolution transmission imaging of the 2D Au MCs requires the periodic assembly of the clusters in the vertical direction. Nevertheless, noncommensurate packing of a small clusters into the local periodic structure (LPS) is an intriguing but difficult attempt,¹⁹ because the MCs with low atomicities hardly show any periodic arrangement of atoms in the pristine state. We now report the synthesis of the stable Au₈ MCs and their structural characterization. Both theoretical and experimental analyses confirm the formation of the LPS-Au₈ MCs. Their chiroptical properties are also addressed within the dipole approximation.

The LPS-Au clusters were synthesized by controlling the interactions of the functionalized molecules. First, the Au ions in gold chloride tetrahydrate were allowed to interact with L-cysteine methyl ester (LCME) hydrochloride for complex formation in an aqueous solution, and then reduced in the presence of an ice-cold solution of sodium borohydride (NaBH₄). Details of the sample preparation and identification of the Au₈ MCs are described elsewhere.⁹ Because the cysteine derivative forms a bilayer with metal ions at low pH,^20,21 the sample was aged at a pH of 2.33 and temperature of 343 K with continuous stirring. The sample was dispensed on a substrate appropriate for each characterization.

The structures of the Au clusters collected on a carbon (C)-coated copper (Cu) mesh were studied using a JEM-2100F transmission electron microscope (TEM) with a resolution as 0.1 nm. The ZrO/W (100) Schottky-type field emission electron gun with an acceleration voltage of 200 kV was used for the TEM analysis. Fig. 1(a) shows the high resolution TEM (HRTEM) image of the fresh Au₈ MCs, which indicates the presence of clusters (highlighted by colored atoms in the cluster) though identification is not trivial. However, the HRTEM images of the LPS-Au₈ MC sample at two different positions shown in Fig. 1(b) and (c) evidence the presence of hexagonal + 1 shaped Au₈ (h-Au₈) MC with an in-plane lattice spacing of 0.26 nm (marked by dotted-line boxes), which is consistent with the theoretical spacing (0.28 nm).²² The schematic representation of the dotted regions are shown as the insets of Fig. 1(b) and (c) and marked by the arrows for the visualization. The observed h-Au₈ structure is also in accordance with the structure estimated from the experimentally and theoretically obtained optical properties.⁹ Since, in general, the HRTEM lattice fringes imprint the interference of scattered electrons from a periodic structure, imaging of the Au₈ planar structure provides evidence of a periodic structure along the c-axis of the hexagon. Although the assembly was not described in detail, the TEM image of the Au_n (n = 2–7) clusters grown on carbon nanotubes showed the 2D Au clusters with a given atomicity.¹⁰ Further, according to the Bragg's rule, the X-ray diffraction at low angle (LXRD), 2θ ∼ 0–10 degrees and wide angle (WXRD), 2θ > 10 degrees, provides information on periodicity in inter-layer structure on a nanoscopic scale (e.g. repeat distance between two consecutive layers) and within the layer structure on an atomic scale (e.g. lattice spacing) respectively.²³ Since X-ray diffraction (XRD) is useful to study the ligand-mediated arrangement of metal clusters,²⁴ the ordering of our sample was also studied by the XRD using a Philips X'pert X-ray diffractometer. A thick layer (thickness ∼ 20 micrometers) of the sample was prepared by the dip coating method on a Si (100 plane) substrate for the XRD measurements. The LXRD and WXRD patterns are shown in Fig. 2(a) and its inset, respectively. Note that the WXRD has a featureless characteristics indicating the absence of periodicity within the cluster. In contrast to the WXRD, a distinct LXRD peak is observed at an angle, 2θ ∼ 6 degrees, which is attributed to the inter layer periodic structure in the sample with the spacing of 1.47 nm.

Fig. 1 (a) Transmission electron micrograph (TEM) of the as-grown Au₈ MCs. Some of the possible clusters are highlighted by reconstruction as a visual guide. (b) and (c) are the HRTEM images of the sample aged at 343 K and ph of 2.33. The dotted region shows the most likely planar hexagon + 1 shaped Au₈ structures which are demonstrated schematically for better visualization.

Fig. 2 (a) The X-ray diffraction pattern of the LPS-Au₈ MCs. The inset is the diffraction pattern in the angle range from 20 to 60 degrees. The low angle diffraction pattern reveals the presence of a periodic structure (periodicity ∼ 1.47 nm) in the sample. (b) The desmeared small angle X-ray scattering spectrum of the sample. The grey line shows the fitted curve. (c) The electron density distribution profile extracted by fitting the experimental result to the theoretical one.

To understand the intricate structure of the samples, a small angle X-ray scattering (SAXS) measurement was carried out using Anton Paar SAXSess-mc² instrument calibrated with silver behenate as the standard sample. The specimen for the SAXS analysis was prepared by keeping the samples on krypton foils. For the measurement, the line-focused Cu K_α X-ray operated at 3 kW power was used as the incident light source. Fig. 2(b) shows the background-corrected desmeared SAXS spectrum of the LPS-Au₈. In order to understand the structure, the radial electron density (RED) was estimated from the SAXS results using the expression²⁵ where the de-smeared intensity  the pair distance distribution function (PDDF), p(r) = γ(r)·r², area, A, the normalized 1D autocorrelation function, r is the coordination along which the electron density distribution, q is the scattering vector and Generalized inversion Fourier transformation (GIFT) technique is used to extract the PDDF profile from the scattering data by fitting with theory.²⁵ Then, the RED has been estimated by spectral fitting of the PDDF profile using DECON software as per the above theory.²⁵ Note that, in case of layer structures, the SAXS measures the relative scattering contrast between the electron-rich (positive) and -deficit (negative) densities for the molecular species present in the sample with respect to the background set as zero and the width of the RED provides the thickness of the different layers.^26,27 The RED profile of the sample in the inset of Fig. 2(b) exhibits distinct steps of positive- and negative-distributions of relative electron densities confirming the stacking structure.²⁷ As the electron density of the Au cluster is higher than the LCME, the positive and negative RED profile may be assigned to the Au₈ MC structures and the LCME layers, with the thickness as 0.43 nm and 0.72 nm respectively. Considering two LCME molecules in between the Au₈ MCs and allowing the Au–S and amine–amine interaction through optimization by the density functional theory (DFT) level calculation using the Gaussian-9 package, the distance between the two Au₈ clusters was observed to be 1.41 nm, which is comparable to the periodic spacing between the clusters layers estimated from the XRD as 1.47 nm. Interestingly, the distance of the amine–amine bond mediated LCME bilayer obtained from the theory and SAXS measurement are 0.67 nm and 0.72 nm respectively. This suggests the formation of the LCME bilayer mediated LPS-Au₈ MC structures complementing the TEM, XRD and SAXS measurements. More experimental evidences are required to establish the formation mechanism of the above structures.

The vibrational properties of the LPS-Au₈ samples dispensed on a quartz substrate were analyzed using a T64000 Horiba Scientific Raman system with an excitation wavelength of 488 nm from an Argon ion laser source operated at 20 mW. Before the measurement, the instrument was optimized with a single-crystal Si for a high signal-to-noise ratio. The Raman spectra of the sample on quartz and quartz substrate alone are shown in Fig. 3 in red (a₁) and gray (a₂), respectively. The spectrum of the sample contains a series of sharp Raman modes listed in Table 1. The Raman analyses have been carried out at different positions of the sample showing the reproducibility of the studies. Similar sharp Raman modes were observed in the metal (Au and Ag) atomic clusters by other researchers.^28,29 According to J. Paul et al.³⁰ the h-Au₈ shows its stability in presence of six ligands. Therefore, to assign the above modes, the geometry optimization of the bare star shape, the h-Au₈ and six-ligand passivated h-Au₈ (Au₈-(SR)₆) cluster^9,30 were carried out using the B3LYP (Becke three parameter Lee–Yang–Parr) functional with LANL2DZ (Los Alamos National Laboratory 2-double Zeta) basis set for the singlet state. The corresponding Raman modes were calculated using the DFT-B3LYP/LANL2DZ level of theory utilizing Gaussian-9 package. The inset in Fig. 3 shows the calculated Raman modes at different frequencies (listed in Table 1) for the optimized geometries. Note that the contribution from the ligands was included by using the next nearest neighbour interaction in the calculation to optimize the computational time. Comparing the theoretical results with experiment, the Raman modes at 81.24 cm⁻¹ and 86.48 cm⁻¹ correspond to the symmetric Raman vibration of the surrounded ligands shell and h-Au₈ core respectively in the Au₈-(SR)₆. This suggests the stability of hexagonal + 1 structure in presence of ligands in the LPS. The other Raman modes are weak. These may be assigned to the restricted degrees of vibrational modes due to the LPS-Au₈ MC structure. The experimental results were also compared to the theoretical Raman modes for the planar star shape Au₈ (shown in Table 1), suggesting absence of the star shape in the LPS-Au₈ samples.

Fig. 3 Room-temperature Raman spectra of the LPS-Au₈ MCs (a₁) deposit on quartz substrate and quartz background (a₂), shown in red and gray, respectively. The insets (i)–(iii) show the calculated Raman vibrational modes of a star shape, hexagonal + 1 shape and six ligands surrounding hexagonal + 1 shape Au₈ MCs, respectively. The shape optimization and Raman frequency calculation have been made using the DFT-B3LYP/LANL2DZ level of theory in a singlet state. The symbol star (*) and plus (+) indicates the Raman modes of the h-Au₈ and Au₈-(SR)₆ in comparison to the theory.

Table 1 Calculated and experimentally obtained Raman vibrational modes (cm⁻¹) of Au₈ (star shape), h-Au₈ and six-ligand protected h-Au₈ [h-Au₈-(SR)₆]. A comparison of theory with the experimentally observed Raman modes

Sample	Theory	Experiment
Au8 (star shape)	74.92, 111.92, 182.92	81.24^+, 86.48*^+, 91.80^+, 100.71*, 106.35^+, 114.60*, 121.69^+, 135.17^+, 141.87*, 149.41^+, 153.90*, 165.40, 171.14^+
*h-Au8 (hexagon + 1)	85.03, 99.36, 113.80, 140.82, 153.44, 161.48
^+h-Au8-(SR)6	81.93, 85.46, 91.05, 105.48, 108.35, 120.82, 134.95, 149.34, 169.95, 175.91

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As the optical properties of the MCs are dominated by the symmetry of the atomic arrangement and their superstructures, different Au MCs exhibit a chirality in the optical and electronic properties due to a strong dipole moment in the presence of polarized light.^31–33 To study the structural and electronic properties of the LPS-Au₈ MCs, optical absorption measurements were carried out in the presence of unpolarized and circularly polarized light using a Perkin-Elmer ultraviolet-visible (UV-VIS) spectrometer and Applied Photophysics Circular Dichroic (CD) spectrometer. The spectra are shown in Fig. 4(i) and (ii) respectively. Fig. 4(i) depicts a strong excitonic absorption band at the wavelength 371.5 nm, which may be due to the excitonic transitions between the discretized highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO).⁹ The asymmetric broadening observed in the absorption band towards the lower wavelength is possibly due to the presence of transitions related to the higher order structures. Fig. 4(ii) shows a prominent band at 374.8 nm and a weak band at 348.9 nm with oppositely signed CD intensities, respectively. When the circularly polarized light with the electric vector, E = E₀(x̂ ± iŷ)e^ik·r−iωt, where E₀, k, t, x̂ and ŷ are the amplitude, wave vector, time, and unitary vector along the x and y directions, respectively, is directed on the MCs, it produces excitons with a dipole moment oriented either along the x (corresponding to left (+) circularly polarized (L)) or y (corresponding to right (−) circularly polarized (R)) direction with the extinction cross section and extinction efficiency where n, d, p_i and * are the number of dipoles, distance between two atoms in the clusters, dipole moment and complex conjugates, respectively. Thus for the equation CD = 〈Q^L_ext〉 − 〈Q^R_ext〉, where 〈…〉 then indicates the average of the extinction efficiency along the direction of the electric field.¹⁶ If 〈Q^L_ext〉 > 〈Q^R_ext〉, then the MCs have positive chirality properties. Similarly, if 〈Q^L_ext〉 < 〈Q^R_ext〉, then the MCs exhibit a negative chirality. In addition, when two different excitons are located very close to each other with a suitable orientation, there will be a dipole–dipole interaction³³ between them given by where μ₁ and μ₂ are the dipole moments of the exciton (bound state of the excited electron and hole separated by a distance), r₁₂ is the distance between two excitons, and e₁, e₂ and e₁₂ are the corresponding unit vectors. As a result, the excited state of the excitons-couplet is split into two distinct states centered around the main absorption band. A schematic diagram shown in inset of Fig. 4(i) illustrates the splitting of the excited states of the excitons-couplet. Therefore, considering the coupling of two identical excitons in LPS-Au₈ MCs, the origin of the doublet structure of the CD spectrum could be explained from the dipole–dipole interaction mediated splitting of the excitonic states. Based on the analysis of the CD spectra, the interaction potential, V₁₂ (equal to the half of the energy difference between doublet states at 374.8 nm and 348.9 nm) has been estimated to be 122 meV. A similar exciton couplet has been observed in many organic chromophores separated by a distance within the range of 1.3–1.4 nm.³⁴ Taking into account the interaction potential energy and distance between the excitons as the intercluster distance (1.47 nm), the net electric dipole moment (EDM) of the LPS-Au₈ MCs has been estimated to be 21.17 Debye (D). Note that during estimation of the EDM, the angle between the excitonic dipoles is assumed to be 20 degrees as the ligand (sulfur–gold angle) makes an angle of 80 degrees with the Au cluster.²² Furthermore, as observed in Fig. 5, the calculated HOMO and LUMO wave function reveals polarization of the electronic states in the presence of a ligand (EDM of Au₈-(SR)₆ ∼ 5.80 D) compared to the pristine one (EDM of h-Au₈ ∼ 0.90 D). Theoretical evaluation of the electric dipole moment corresponding to a closed-shell single-determinant wave function is given by³⁵ where the first summation is over atoms A, and the second pair of summations is over basic functions ϕ_μ and ϕ_ν. Z_A is the atomic number of atom A, r_A the position of atom A relative to the origin, P_μν is an element of the one-electron density matrix given by  The summation is over occupied molecular orbitals only. The factor of two indicates that two electrons occupy each molecular orbital, and the asterisk denotes complex conjugation (required if the molecular orbitals are not real functions). The r_μν is given by r_μν = ∫φ_μ(1)r(1)φ_ν(1)dτ where r is the position vector, and integration is carried out over the coordinates of a single electron. The difference in the EDM estimated from the CD spectra and EDM obtained from the theory may be due to (i) the LPS arrangement, which has not been taken into consideration in the theoretical calculation and (ii) the limitation of the approximation used in the theory. Such an enhanced EDM imparts a ferroelectric behavior in the sample. To confirm the ferroelectric nature, the electric polarization (PE) studies of the powder form of the sample had been carried out which shows a strong polarization loop with reminance polarization as 64.56 μC cm⁻² and coercive electric field as 1.55 kV cm⁻¹. The CD and PE results reveal the stability of the LPS in both dispersed state and powder form. Details of this work will be published elsewhere. A similar enhancement of the EDM leading to the ferroelectric property was observed by Lan-Sun Zheng et al.³⁶ in a supramolecular assembly of water molecules.

Fig. 4 (i) Optical absorption spectra and (ii) circular dichroic spectra of the LPS-Au₈ MC. Inset (i) shows the schematic diagram of splitting of the energy states due to the exciton–exciton coupling. The strong negative CD index predicts the negative chirality.

Fig. 5 Highest occupied molecular orbitals (a) and (c), and lowest unoccupied molecular orbitals (b) and (d) (green for positive and maroon for negative) wave functions of the Au₈ MC and Au₈-(SR)₆ calculated for the optimized structure using Gaussian-9 software. The isovalue was taken to be 0.02 for all the plots.

In conclusion, the ligand-mediated condensation of free standing Au₈ MCs into a local periodic structure has been well established. Distinct Raman modes corresponding to the in-plane symmetric vibration of each hexagonal + 1 structured Au₈ unit composed of six ligands have been observed in agreement with the DFT level calculations. The LPS-Au₈ structure causes a substantial rise in the electric dipole moment due to the exciton–exciton dipolar interactions, which was confirmed from the CD spectra. The intense negative CD index at a longer wavelength is evidence for the negative chirality of the sample. This study enhances the understanding of the local structure, and vibrational and electronic properties of the gold cluster-based compounds with atomic precision.

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