Revisiting ultrasmall phosphine-stabilized rhodium-doped gold clusters Au_nRh (n = 5, 6, 7, 8): geometric, electronic, and vibrational properties

Abstract

Incorporation of other transition metals in Au nanoclusters has been thriving recently due to its effect on their electronic and photophysical properties. Here, the ultrasmall phosphine-stabilized Rh-doped gold clusters Au_nRh (n = 5, 6, 7, 8), with metal core structures represented as fragments of a rhodium-centered icosahedron, are considered. The geometric and electronic properties of these nanoclusters are revisited and analyzed using density functional theory (DFT). Moreover, infrared spectra are simulated to identify the effects of Rh doping on the clusters through vibrational properties. Peaks are assigned to breathing-like normal modes for all AuRh clusters except for Au₈Rh, likely due to the presence of bound Cl ligands. Unlike their pure gold core counterparts, the % motions of both Au and Rh atoms are lower in the mixed metal clusters, suggesting more restrained metal cores by rhodium, which could result in other novel physical and chemical properties not hitherto discovered.

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1 Introduction

Ligand-stabilized atomically-precise metal nanoclusters have generated tremendous interest over the recent years because of their distinct physicochemical properties and potential applications.¹ A large number of structurally determined nanoclusters with defined elemental compositions have been prepared in the past decade, with various ligands used for stabilization. In ultrasmall gold nanoparticles, there has been an increasing interest in the understanding of transition bimetallic clusters. Doping a different transition metal atom into a metal cluster dramatically changes the electronic properties and catalytic behaviour of the host cluster.^2–5 There have been extensive theoretical and experimental studies on noble metal clusters such as Au and Ag, most especially due to their distinctive chemical properties. In early work on gas phase cationic Au_nX_m⁺ clusters (X = Cu, Al, Y, and In), the cluster geometries and electronic shell were shown to depend on the nature of dopant atoms.⁶ Heinebrodt et al. described the binding patterns of Au with Al, In, and Cs, wherein charge transfer takes place between Au and In while ionic interaction prevails between Au and Cs.⁷ Additionally, anionic binary Au_nM⁻ clusters (M = Pd, Ni, Zn, Cu, and Mg) were explored by Koyasu et al. using anion photoelectron spectroscopy.⁸ Density functional theory (DFT) studies of neutral bimetallic gold clusters have also been reported for Ni, Pd and Pt,⁹ Fe,¹⁰ Ag and Cu,¹¹ Ti,¹² Sc,¹³ and Rh.¹⁴ Buendia et al. reported the experimental and theoretical photoelectron (PES) and IR spectra of neutral and anionic non-ligated Au_nRh_m (n = 1–7 and m = 1–2) clusters in vacuum.¹⁵ Additionally, mechanistic insight into the catalyzed hydrogenation reaction revealed that the activation barrier of monorhodium-doped gold clusters is reduced compared to pure gold clusters.³ Notably, transition metal-doped gold clusters have been comprehensively studied due to their synergistic effects on catalysis.^1,16 Tsukuda and co-workers reported the use of Pd- and Rh-doped Au₃₄ superatom for hydrogenation catalysis wherein Rh-doped Au:PVP cluster proved to be superior.^4,5 Recently, doping metals onto Au₁₃ nanoclusters has been observed to enhance quantum yield with an increased HOMO–LUMO gap and was reported to act as more efficient and stable photocatalysts.¹⁷

Decades ago, Bott et al. reported a series of ultrasmall gold-rhodium clusters Au_nRh clusters (n = 5–8) with triphenylphosphine groups as their main ligands: [Au₅Rh(PPh₃)₅(C₉H₉N)₃]²⁺, [Au₆Rh(PPh₃)₆(CO)₂]⁺, [Au₇Rh(PPh₃)₇(CO)₂]²⁺, and [Au₈Cl₂(PPh₃)₆Rh(C₉H₉N)₂]⁺ (hereafter referred to as Au₅Rh, Au₆Rh, Au₇Rh, and Au₈Rh, respectively).¹⁸ Their gold-rhodium cores were all found to be structurally represented as fragments of the rhodium-centered icosahedron in Fig. 1. Based on the structures of the Au_nRh core alone, the lower-numbered gold-rhodium clusters could be obtained from the sequential removal of Au(PPh₃) moieties of the Au₈Rh cluster. In this study, we analyze the geometric and electronic structures of this series of Au_nRh clusters using density functional theory based on their experimental crystal structures.

Fig. 1 The structural relationship among the AuRh clusters synthesized by Bott et al.¹⁸ The idealized metal core geometries are shown as fragments of a centered icosahedron with rhodium atom (turquoise) at the center.

Takano et al. have reported the importance of core rigidification by the ligands in the effective photoluminescence of Ru-doped Au₁₂ clusters.¹⁹ Metal core motion and ligand suppression can be analyzed using infrared spectroscopy by detecting the vibrational modes of key functional groups. Several studies have reported the IR spectra of ligand-stabilized gold clusters,^20–23 but we are not aware of any involving the Au_nRh clusters. This present work extends our previous far-IR and computational studies of atomically precise gold-based clusters^20,21 and ruthenium-based clusters²⁴ to ligand-protected bimetallic Au_nRh clusters (n = 5–8) focused on low frequency vibrational modes (λ = 50–450 cm⁻¹).

2 Computational details

Geometry optimization and harmonic vibrational frequency calculations (including force constant, k) of the fully-ligated Au₅Rh, Au₆Rh Au₇Rh, and Au₈Rh clusters were performed using M06 density functional²⁵ with all atoms treated with the LANL2DZ basis set and related effective core potentials (ECP)²⁶ using the Gaussian 09 suite of programs.²⁷ This level of theory has been used for similar metal cluster systems previously, and has shown good agreement to experimental far IR spectra.^20,24 Initial geometries of Au₅Rh (CSD Refcode KOFTOO), Au₇Rh (CSD Refcode KOFVAC), Au₈Rh (CSD Refcode JAPWOM) were taken from previously reported X-ray crystal structures of the synthesized clusters deposited in the Cambridge Crystallographic Database.²⁸ The initial structure of Au₆Rh was based on the description of Bott et al. wherein one AuPPh₃ unit in an equatorial position of Au₇Rh is removed.¹⁸ Counter ions were removed, with the appropriate number of electrons removed from the calculations to balance the charge and no symmetry constraints were used in the calculations. After optimization, a frequency calculation was performed to confirm that the optimized geometry is a true minimum without any imaginary frequencies. To obtain the simulated IR spectra, all peaks were convoluted with a Gaussian line shape function with 8 cm⁻¹ full width at half-maximum (FWHM). The Cartesian coordinates of the optimized structures for these four clusters are also provided in the ESI.†

3 Results and discussion

3.1 Geometric parameters and ligand binding energies

The optimized structures of the Au_nRh clusters are shown in Fig. 2. Both Au₆Rh and Au₇Rh have 2 carbonyl ligands attached to the Rh atom while Au₅Rh and Au₈Rh have 3 and 2 isocyanide-based xylyl ligands attached on their central Rh atom, respectively. The Au₈Rh also has additional Cl atoms attached to two Au atoms. For all Au_nRh clusters in this study, the ligands attached to the Rh atom are known to be easily removed. Moreover, the PPh₃ ligands attached on the Au atoms also require lower temperature to be removed than their thiolate counterparts.²⁹ The DFT-optimized structures have longer bond lengths when compared to the crystal structures because the experimental geometries are tightly-packed in condensed phase rather than in “gas-phase” of the calculations. Even so, a close match between the optimized geometries and experimental crystal structures is observed for the gold-rhodium clusters (Fig. S1, ESI†).

Fig. 2 Optimized structures of the fully ligated (a) Au₅Rh, (b) Au₆Rh, (c) Au₇Rh, and (d) Au₈Rh clusters. Au, Rh, N, O, and P atoms are represented by yellow, turquoise, blue, red, and orange spheres, respectively. C and H atoms are represented by transparent gray and white spheres, respectively.

To calculate the binding energies of the ligands in Table 1, we use the following equation:

where E_total is the total energy of the fully ligated clusters, N is the number of ligands under consideration, E_ligand is the energy of free PPh₃, xylyl, or CO ligand under consideration and E_complex is the rest of the cluster without the ligand(s) under study. For example, the average binding energy of the xylyl ligands on Au₅Rh is calculated with N = 2 and E_complex as the energy of [Au₅(PPh₃)₅]²⁺, whereas the average binding energy of PPh₃ on Au₅Rh is calculated with N = 5 and E_complex as the energy of [Au₅(C₉H₉N)₃]²⁺. The calculated average binding energies of PPh₃ in all gold-rhodium clusters are 44–59 kcal mol⁻¹, consistent with previous studies.^29–33 These values are consistent with a temperature range of 150–200 °C required to fully remove the triphenylphosphine ligands.^34,35 Both xylyl and C=O ligands of Rh atom have similar average binding energies to PPh₃.

Table 1 Summary of the average binding energies in kcal mol⁻¹ of the ligands on Au₅Rh, Au₆Rh, Au₇Rh, and Au₈Rh clusters based on eqn (1) using M06/LANL2DZ level of theory

Cluster	BEave of Rh-bound ligands	BEave of PPh3
Au5Rh	51.2 (xylyl)	56.9
Au6Rh	51.3 (CO)	43.6
Au7Rh	49.7 (CO)	59.1
Au8Rh	56.8 (xylyl)	48.5

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3.2 Electronic structure

The Au_nRh clusters offer a specific perspective into the contribution of Rh to the electronic structure. Tsukuda and co-workers summarized the effect of doping on the spherical superatoms of gold clusters using the jellium model.³⁶ When dopants are more electronegative (such as Pt, Pd, and Rh) than gold, the superatomic orbitals are destabilized due to reductions of the effective positive charge of the core, resulting in an upshift to their energy levels. This is only observed when icosahedral Au cores are considered. However, the Au_nRh clusters presented here are fragments of a centered icosahedron, Au₁₃, as shown in Fig. 1. Therefore, we can also consider z-axis compression based on the closed-shell electron count of Hakkinen's superatom concept (SAC) equation.³⁷ If Rh is considered as another Au atom, we expect the following electron count for the Au_nRh clusters: 4e (Au₅Rh) and 6e (Au₆Rh, Au₇Rh, Au₈Rh). Thus, the Au₅Rh cluster is expected to adopt a prolate shape with z-axis expansion while the others have an oblate shape with z-axis compression. This in turn results in an orbital with 1p_z character for the Au₅Rh HOMO and 1p_x and 1p_y character for the LUMO and LUMO+1, respectively. On the other hand, 6e clusters should exhibit 1p_x and 1p_y characteristics for HOMO and HOMO–1, and 1p_z and 1d character for the LUMO and LUMO+1 orbitals.

The topological plots of the frontier molecular orbitals (FMO) of the Au_nRh clusters are shown in Fig. 3. All FMO plots reveal that the HOMO−1, HOMO, LUMO, and LUMO+1 are mainly localized on the AuRh core (Tables S1 and S2, ESI†). The contribution of Rh in the HOMO of Au₅Rh is significantly higher than the other clusters, with approximately 1 : 1 ratio of Au and Rh contributions to the orbital based on the results of three different partition methods. Interestingly, the shapes of the frontier MOs of Au₅Rh deviate from the expected trend based on SAC electron count and z-axis expansion discussed above. The HOMO−1, HOMO, and LUMO all have 1p characteristics while the LUMO+1 displays 1d character in Au₅Rh, similar to Au₆Rh and Au₇Rh. This suggests an effect from the heteroatom on the electronic properties of the Au₅Rh cluster, wherein the Rh contribution on the HOMO is evident by the presence of its δ orbitals. The Au₈Rh cluster has similar FMO characteristics as the butterfly structure of [Au₉(PPh₃)₈]³⁺,³⁸ wherein the LUMO has 1d character while the LUMO+1 has 1p character, evidently similar to the previous MO calculations presented by Mingos and co-workers.³⁹ Both the structures of Au₈Rh and the butterfly isomer of Au₉ are toroidal rather than spherical in shape such as in the case of the crown isomer of Au₉ and Au₈Pd.^38–40 This difference in the bonding pattern causes the 1p_z orbital to be higher in energy, making it unavailable for skeletal bonding and subsequently deviating from the expected MO trend based on electron count. Additionally, the contribution of δ orbitals from Rh stabilizes the LUMO+1 (1p_z) orbital of Au₈Rh. The trend of the HOMO–LUMO energy gaps of the AuRh clusters is also consistent with the colors of the synthesized crystals. The Au₇Rh and Au₈Rh clusters both have a relatively low calculated energy gap of ∼3.20 eV and both exhibit a red color. On the other hand, Au₆Rh has an orange-like color while Au₅Rh has a distinct yellow color, and with both having larger HOMO–LUMO energy gaps calculated to be 3.42 and 3.82 eV, respectively.

Fig. 3 The plots of frontier molecular orbital (HOMO−1, HOMO, LUMO, LUMO+1) of Au₅Rh, Au₆Rh, Au₇Rh, and Au₈Rh clusters as calculated by M06/LANL2DZ with an isosurface value of 0.02 a.u.

3.3 Far IR spectroscopy

The DFT-simulated far IR spectra of the four Au_nRh clusters are presented in Fig. 4. A summary of the peak assignments for each cluster is shown in Tables S3 to S6, ESI.† The normal coordinate motions that involve significant motion of Au, Rh, P, and Cl (for Au₈Rh) are identified and shown as percentages of total non-mass-weighted atomic motion. The simulated spectra were scaled from the DFT-calculated numbers by a functional-independent correction factor (eqn (2)) used previously for low-frequency vibrations.⁴¹

[small nu, Greek, tilde]_corr = 22 cm⁻¹ + [small nu, Greek, tilde]_calc × 0.94 (2)

Fig. 4 Calculated normal mode displacements associated with the cluster core vibrations for (a) Au₅Rh at 164.3 cm⁻¹, (b) Au₆Rh at 182.5 cm⁻¹, (c) Au₇Rh at 175.4 cm⁻¹, and (d) Au₈Rh at 246.7 cm⁻¹. The simulated (bottom) far-IR spectra of the Au_nRh clusters are also shown and numbered based on their peak assignments in the ESI.† The IR peaks denoted with asterisks are those assigned to the calculated normal mode displacements presented.

Generally, all four clusters exhibit large peaks between 430–450 cm⁻¹ which were previously assigned to distortion of the triphenylphosphine ligands (PPh₃), while peaks <250 cm⁻¹ are transitions involving the Au core distortions.^20,24

3.3.1 Au₅Rh cluster. The first broad peak is assigned to AuRh core distortions, one of which is the breathing mode shown in Fig. 4a. The breathing modes are a distinguishing feature for large metal nanoparticles and their linear dependence on the nanoparticle diameter has been investigated using time-resolved pump–probe spectroscopy and continuum mechanics.⁴² Low-frequency symmetric breathing modes have been experimentally detected as Raman active in several ligand-stabilized atomically-precise Au nanoclusters^23,43 and the nature of bonding with the ligands affect the confinement of these gold vibrational modes.⁴⁴

The % Au motions of Au₅Rh are significantly lower than previously found for Au₆; 14–16% Au motion in the previous study²⁰ but only 1.2% Au and 0.3% Rh motion in Au₅Rh. The vibrations arising from the xylyl ligands appear from 220 cm⁻¹ onwards and the Rh–C wagging and twisting motions are assigned to the large peaks at 300 and 330 cm⁻¹, respectively. The normal modes of vibration due to PPh₃ ligands are visible at 260 and 430 cm⁻¹ as has been previously reported.²⁰

3.3.2 Au₆Rh cluster. The description of the Au₆Rh core by Bott et al. allowed the simulation of the IR spectrum even without an experimental crystal structure. The DFT-optimized structure is shown in the ESI.† The first peak is assigned to metal core distortion, primarily from Au atoms, while the 2nd and 4th peaks account for Au–Rh–Au symmetric and asymmetric stretching, respectively. The breathing mode of the metal core (Fig. 4b) is assigned to the peak at 195 cm⁻¹. We can compare the % metal motions of this cluster with Au₆Pd from our previous study.²⁰ Interestingly, the % Au and % Rh motion for Au₆Rh are lower than its Pd-doped counterpart that has significant % Pd contributions ranging from 1–5%. The largest total metal motion (5.87%) for Au₆Rh is assigned to the Au–Rh–Au asymmetric stretching. The % Au motion of Au₆Rh is only 3.3% whereas it reaches ∼8% Au motion for the Au₆Pd cluster. Based on these observations, Rh-doping seems to stiffen the Au core more than the Pd-doping. Finally, the pronounced single peak at 340 cm⁻¹ is assigned to Rh–C–O rocking and the large peak at 425 cm⁻¹ comes from PPh₃ distortions.

3.3.3 Au₇Rh cluster. The small broad peak at 100 cm⁻¹ is assigned to a low-intensity Au core distortion. Next, there are three prominent peaks between 170–260 cm⁻¹. The peak at 175 cm⁻¹ is assigned to Au core distortion, with 3.46% Au motion (in Table S5, ESI†), which is also remarkably lower than previously reported for Au₈ that ranges from 16–20%.²⁰ There is a tiny shoulder at 185 cm⁻¹ which is assigned to the breathing mode of the Au₇Rh core (Fig. 4c). The peak at 210 cm⁻¹ is a convolution of different transitions displaying Au–Au stretches and the next peak at 260 cm⁻¹ is assigned to PPh₃ distortions. The wagging of the carbonyl group is assigned to the small peak at 335 cm⁻¹, similar to Au₆Rh, while the large peaks at 400–450 cm⁻¹ are assigned to PPh₃ distortions. Both Au₆Rh and Au₇Rh reveal stronger contributions from the heavy metals than Au₅Rh and Au₈Rh (vide infra) for the Au core distortion and AuRh breathing modes. This can be attributed to the lighter CO ligands attached to the Rh central atom that permit more motion of the heavy metals than the heavier xylyl ligands present in both Au₅Rh and Au₈Rh.

3.3.4 Au₈Rh cluster. No breathing mode is observed for the Au₈Rh core unlike the smaller AuRh clusters. This can be explained by the presence of heavy Cl ligands on two Au atoms which also reduces the symmetry of the cluster. Furthermore, the % Rh motions are noticeably lower for the IR peaks that are assigned to the metal core transitions between 70–230 cm⁻¹ while a Cl wagging motion with 2.26% motion is observed in the same region, as summarized in Table S6 (ESI†). The highest % metal core motion of Au₈Rh is 2.77% which is much lower than 8–17% for Au core distortion of Au₉.²⁰ The primary peak at 247 cm⁻¹ is assigned to the asymmetric Au–Cl stretch with only 1.61% Au but 7.66% Cl motion. In the case of Au₈Rh cluster, it is observed that not only the presence of Rh but also Cl inhibits the motion of the Au core. Peaks 5–7 are assigned to vibrations of the xylyl ligands attached to the Rh atom, similar to peaks 5 and 6 of the Au₅Rh cluster.

4 Conclusion

We report the geometric, electronic, and vibrational properties of ultrasmall bimetallic gold-rhodium nanoclusters Au_nRh (n = 5, 6, 7, and 8). The average ligand binding energies are calculated to be ∼50 kcal mol⁻¹, which is low enough to be removed at calcination temperatures of 150–200 °C. The calculated electronic properties indicate a stabilization effect of the Rh atom in the Au₅Rh and Au₈Rh clusters. Additionally, the calculated HOMO–LUMO energy gap trend corresponds to the observed colors of the respective crystals. The metal core transitions are significantly affected by the presence of the Rh atom which inhibits the motion of Au atoms as observed in the simulated IR spectra. Likewise, all clusters display the symmetric breathing mode of the AuRh core except for Au₈Rh due to the presence of Cl ligands.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

J. M. L. M. acknowledges previous financial support from Adelaide Scholarship International (ASI), Future Fuels Cooperative Research Center (FFCRC), and the Ministry of Education, Singapore, under its Academic Research Fund Tier 1 RG83/20. Supercomputing resources at the University of Adelaide and Nanyang Technological University were provided by the Phoenix and Gekko HPC services, respectively.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d3cp05976f

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