Introduction

Ligand-protected metal nanoclusters (NCs) have attracted significant attention as new nanomaterials with unique, tunable properties.^[1-8] Advances in atomically precise synthesis, single-crystal X-ray diffraction analysis, and theoretical calculations have revealed how key structural parameters, such as the size, atomic arrangement, and surface modification, affect NC properties. It was found that electronic structures, which can be tuned by these parameters, govern the photophysical and catalytic properties of NCs.^{[9, 10]}

Relativistic effects play a crucial role in NCs composed of heavy elements such as Au.^[11] In particular, spin-orbit coupling (SOC) significantly affects their optical, photophysical, and magnetic properties.^[12-18] This phenomenon is exemplified by the benchmark NC [Au₂₅(SR)₁₈]⁻ (RS = thiolate), which has an icosahedral Au₁₃ core passivated by Au₂(SR)₃ units (Figure 1a)^{[19, 20]} and adopts a closed electron configuration (1S)²(1P)^[6] with delocalized superatomic 1P orbitals as its highest occupied molecular orbital (HOMO) (Figure 1b).^[21] Previous two-component density functional theory (2c-DFT) calculations^[22] showed that its 1P orbitals split into low-lying 1P_1/2 and high-lying 1P_3/2 by SOC (Figure 1b), yielding a gap of 0.20 eV.^{[13, 17]} Doublet features in the onset region of the UV–vis absorption spectrum of [Au₂₅(SR)₁₈]^{− [23]} are assigned to 1P_1/2→1D and 1P_3/2→1D transitions.^{[13, 17]} Optical spectroscopy and 2c-DFT calculations revealed that SOC is less influential than the Jahn–Teller effect on the electronic structures of the neutral and cationic Au₂₅(SR)₁₈.^[17] The importance of SOC has also been theoretically demonstrated in E@Au₁₂ (E = Si, Ge, Sn, and Pb) superatoms^[14] and in the superatomic molecule Au₃₈(SR)₂₄.^[15] In alloy system, doping a single heavy atom (Au or Pt) at the center of the Ag₁₃ superatomic core of [Ag₂₅(SR)₁₈]⁻ or [Ag₂₉(S₂R)₁₂]³⁻ enhances their photoluminescence,^[24-27] presumably by promoting intersystem crossing from S₁ to T₁. Although these studies underscore the importance of SOC in rationalizing the electronic structure of Au/Ag NCs, the fundamental relationship between the SO splitting of the 1P orbitals and structural factors, such as elemental composition, ligand type, and atomic arrangement, remains unclear.

Here, we clarify which structural factors govern the SO splitting of the 1P orbitals in ligand-protected Au₁₃ superatoms. First, we employed cryogenic anion photoelectron spectroscopy (PES)^[28-30] to quantify the SO splitting of the 1P orbitals of a series of vacuum-isolated superatoms [Au₂₅(SC8)₁₈]⁻ (SC8 = SC₈H₁₇; denoted Au₂₅⁻),^{[20, 21]} [Ag₂₅(DMBT)₁₈]⁻ (DMBT = 2,4-(CH₃)₂C₆H₃S; Ag₂₅⁻),^[31] and [AuAg₂₄(DMBT)₁₈]⁻ (AuAg₂₄⁻)^[32] (Figure 1a). PES can directly reveal the degree of SOC from the peak splitting of the 1P orbitals (Figure 1c), whereas photoabsorption energies include SOC effects in both 1P and 1D orbitals. Second, we investigated how elemental compositions, atomic arrangement, and surface modification affect the SO splitting by performing 2c-DFT calculations.

Results and Discussion

Au₂₅⁻, Ag₂₅⁻, and AuAg₂₄⁻ were synthesized according to the reported methods (Figure S1).^{[20, 21, 31, 32]} PES of these NCs was performed using a home-built apparatus consisting of an electrospray ionization (ESI) source, a linear ion trap, a time-of-flight mass spectrometer (TOF-MS), and a magnetic-bottle photoelectron spectrometer (MB-PES) (Figures 2a and S2).^[33-37] To minimize thermal broadening of PE spectra, we installed a liquid nitrogen (LN2)-cooled ion trap immediately upstream of the TOF-MS analyzer (Figure S3). The ESI mass spectra of Au₂₅⁻, Ag₂₅⁻, and AuAg₂₄⁻ showed the adducts of solvent molecules when the ion trap was cooled with LN2 (Figure S4), indicating efficient cooling of the NCs. The PE spectra of the mass-selected NC anions were recorded by irradiating a pulsed laser at the wavelength of 213 nm. Figure 2b compares the PE spectra of Au₂₅⁻ with and without LN2 cooling, while Figure S5 compares those of all NCs used in this study. Cooling of the ions sharpened the peak and steepened the onset, so the LN2-cooled ion trap significantly improved spectral resolution and accuracy.

Figure 2c shows the PE spectra of LN2-cooled Au₂₅⁻, Ag₂₅⁻, and AuAg₂₄⁻. All spectra exhibited a distinct band X by electron detachment from the 1P orbitals (HOMO), followed by a broad, intense band A assigned to the Au 5d or Ag 4d band.^[34] From the onset of band X, the adiabatic electron affinities (AEA_exp) of Au₂₅⁰, Ag₂₅⁰, and AuAg₂₄⁰ were determined to be 3.53 ± 0.01, 3.98 ± 0.01, and 4.03 ± 0.01 eV, respectively (Table 1). Notably, these AEA_exp values match or exceed those of halogen atoms (e.g., 3.61 eV for Cl), supporting their classification as superhalogens.^[38] A closer look at band X (Figure 2d) shows that band X of Au₂₅⁻ and AuAg₂₄⁻ splits into two peaks (X1 and X2), while that of Ag₂₅⁻ does not. However, quantitative analysis of band X in terms of the peak position and intensity ratio X1/X2 is not straightforward due to the weak featureless PE signals between band X and band A for Au₂₅⁻ and the contribution of band A for AuAg₂₄⁻. To minimize arbitrariness in the analysis, limited regions of the spectra of Au₂₅⁻ (3.3–4.0 eV) and AuAg₂₄⁻ (3.8–4.5 eV) were fitted with a superposition of two Gaussian functions of equal width, while that of Ag₂₅⁻ (3.7–4.4 eV) was fitted with a single Gaussian function (Figure S6). The vertical detachment energies (VDE_exp) of Au₂₅⁻ and AuAg₂₄⁻ were determined to be 3.70 and 4.22 eV, respectively, from the peak position of band X1, while that of Ag₂₅⁻ was 4.25 eV (Table 1). The splitting energies of bands X1 and X2 (SOE_exp) in Au₂₅⁻ and AuAg₂₄⁻ were 0.24 and 0.22 eV, respectively (Table 1). The area ratios X1/X2 for Au₂₅⁻ and AuAg₂₄⁻ were 1.14 and 0.96, respectively. The full width at half maximum (FWHM) of band X of Ag₂₅⁻ (0.32 eV) was larger than those of bands X1 and X2 of Au₂₅⁻ (0.19 eV) and AuAg₂₄⁻ (0.21 eV). The FWHM values of the split bands X1 and X2 were significantly larger than the energy resolution of our PE spectrometer (0.06–0.07 eV, Figure S1c), suggesting that the PE bands are broadened by the associated Franck–Condon factor. These features of the fitted results will be discussed later on the basis of DFT calculations (Figure 3).

To interpret the PE spectra while considering SOC, we performed 2c-DFT calculations using the program TURBOMOLE on the model structures: [Au₂₅(SCH₃)₁₈]⁻, [Ag₂₅(SCH₃)₁₈]⁻, and [AuAg₂₄(SCH₃)₁₈]⁻ (denoted Au₂₅(m)⁻, Ag₂₅(m)⁻, and AuAg₂₄(m)⁻, respectively). First, we optimized three clusters at the scalar relativistic one-component DFT (1c-DFT) level with the CAM-B3LYP functional, including dispersion corrections and the dhf-SVP basis set. The optimized structures retained the crystal motifs (Figure S7). Then, electronic structures were computed by a single-point 2c-DFT calculations using the dhf-SVP-2c basis set. The calculated AEA values of the corresponding neutrals at the 1c-DFT level (AEA_calc,1c) and VDE values at the 1c- and 2c-DFT levels (VDE_calc,1c and VDE_calc,2c) appear in Table 1. The experimental and calculated values for Au₂₅(m)⁻ are in close agreement, whereas the calculated values for silver-based Ag₂₅(m)⁻ and AuAg₂₄(m)⁻ underestimate the experimental values by ∼0.3 eV, probably due to the simplification of the electron-withdrawing DMBT to CH₃S. The noticeable difference between VDE_calc,1c and AEA_calc,1c (∼0.15 eV) supports the Franck–Condon broadening of the experimental PE spectra.

The orbital energy diagrams of Au₂₅(m)⁻, Ag₂₅(m)⁻, and AuAg₂₄(m)⁻ at the 1c- and 2c-DFT levels appear as black and red bars in Figure 3a, respectively. The 1P orbitals of Au₂₅(m)⁻, nearly triple degenerate at the 1c-DFT level, are split into two subsets (2:1 ratio) at the 2c-DFT level by SOC. In contrast, the 1P orbitals of Ag₂₅(m)⁻ and AuAg₂₄(m)⁻ are not degenerate even at the 1c-DFT level. This nondegeneracy may be due to deformed ligation of the Ag₂(SCH₃)₃ units rather than core deformation, since the continuous shape measure (CSM) analysis (Table S1)^[39] showed the higher symmetry of the cores of Ag₂₅(m)⁻ and AuAg₂₄(m)⁻ than that of Au₂₅(m)⁻. At the 2c-DFT level, the 1P orbitals of Ag₂₅(m)⁻ remain unchanged, while those of AuAg₂₄(m)⁻ are split into two with a 2:1 ratio. We simulated the PE spectra by isotropic broadening of each orbital energy level^[40] (Figure 3b), which qualitatively reproduce the splitting of band X for Au₂₅⁻ and AuAg₂₄⁻ and an unsplit broadened band X for Ag₂₅⁻ (Figure 2c). The theoretical SO splitting energies (SOE_calc) of Au₂₅(m)⁻ calculated at various theory levels (0.17–0.21 eV) (Figure S8) and AuAg₂₄(m)⁻ (0.25 eV) agree with the experimental values (SOE_exp) of Au₂₅^– and AuAg₂₄^– (0.24 and 0.22 eV, Table 1). Notably, these SOE_exp values of Au₂₅^– and AuAg₂₄^– are comparable to that of Cl (0.11 eV) yet smaller than that of I (0.94 eV).^[41] However, the intensity ratios of X1/X2 for Au₂₅⁻ and AuAg₂₄⁻ estimated by the fitting shown in Figure S6 were 1.14 and 0.96, respectively, and significantly smaller than 2 predicted theoretically based on the density of states. The underestimation of the X1/X2 ratio for AuAg₂₄⁻ is attributed to the overestimation of the intensity of band X2 by ignoring the contribution of the tail of band A. On the other hand, the deviation of the X1/X2 ratio for Au₂₅⁻ can be understood as follows, based on the weak PE signals between bands X and A, where no PE signals are predicted by the DFT calculation (Figure 3b). These PE signals suggest an asymmetric Franck–Condon factor for the electron detachment^[42] of band X2. Assuming a similar asymmetric Franck–Condon factor of band X1, the intensity of band X2 is overestimated, leading to an underestimation of the X1/X2 ratio for Au₂₅⁻. Thus, although an unambiguous determination of the X1/X2 ratio is currently impossible, the above interpretation qualitatively supports the assignment of bands X1 and X2 for Au₂₅⁻ and AuAg₂₄⁻ (Figure 2d) to electron detachment from the SO-split 1P_3/2 and 1P_1/2 orbitals (Figure 1c).

The sharp difference in splitting between AuAg₂₄⁻ and Ag₂₅⁻ may be attributable to the doped Au atom at the center. To verify this hypothesis, we examined two putative regioisomers of [AuAg₂₄(SCH₃)₁₈]⁻: Au^shAg₂₄(m)⁻ and Au^olAg₂₄(m)⁻, where the Au atom resides on the icosahedral shell or within the Ag₂(SCH₃)₃ oligomer, respectively. Au^shAg₂₄(m)⁻ and Au^olAg₂₄(m)⁻ were less stable than AuAg₂₄(m)⁻ by 0.70 and 0.73 eV, respectively, at the 2c-DFT level. Although the 1P orbitals of Au^shAg₂₄(m)⁻ and Au^olAg₂₄(m)⁻ lack degeneracy at the 1c-DFT level due to the asymmetric Au placement, their orbital energies remained unchanged even after the including SOC (Figure 3a). Hence, we conclude that the “central” Au atom drives the SO splitting of the 1P orbitals of AuAg₂₄⁻.

Why does the SO splitting of the 1P orbitals occur only for of AuAg₂₄⁻ and Au₂₅⁻ and not for Ag₂₅⁻? Mulliken population analysis shows that the 6p orbital of the central Au atom or the 5p orbital of the central Ag atom contributes to the 1P orbitals of Au₂₅(m)⁻, Ag₂₅(m)⁻, and AuAg₂₄(m)⁻ (Figure S9). This suggests that the 1P orbitals of an icosahedral M“@M₁₂ (M”, M = Au, Ag) core are constructed by symmetry-dictated coupling^[43] between the 6p/5p orbitals of the central M' atom and the 1P orbitals formed by the M₁₂ shell. Accordingly, the SO splitting of the 1P orbitals of Au₂₅(m)⁻ and AuAg₂₄(m)⁻ reflects the splitting of both the central 6p/5p orbitals and the surrounding 1P orbitals (Scheme 1). Scheme 1 is tested by 2c-DFT calculations on naked, model superatoms (M“@M₁₂)⁵⁺. The structures of (M”@M₁₂)⁵⁺ and M₁₂⁴⁺ shell were extracted from Au₂₅(m)⁻, Ag₂₅(m)⁻, and AuAg₂₄(m)⁻, followed by single point calculations. The calculation was also performed on (Ag@Au₁₂)⁵⁺, although the corresponding thiolate-protected superatom has not yet been synthesized. The energy diagrams for the 1P orbitals of the (M“@M₁₂)⁵⁺ superatoms are shown in Figure S10. The large SO splitting of the 6p orbital of the Au⁺ (0.64 eV) is transferred to that of the 1P when it is surrounded not only by the Au₁₂⁴⁺ shell (SOE = 0.59 eV) but also by the Ag₁₂⁴⁺ shell (SOE = 0.06 eV). This result supports Scheme 1 and indicates that the SO splitting of the 6p orbital of the central Au atom is crucial for the SO splitting of the 1P orbitals of Au₂₅(m)⁻ and AuAg₂₄(m)⁻. In contrast, the small SO splitting of the 5p orbital of Ag⁺ (SOE = 0.18 eV) cannot be enhanced by the Ag₁₂⁴⁺ shell (SOE = 0.06 eV), but by the Au₁₂⁴⁺ shell (SOE = 0.59 eV). This result not only explains the absence of SO splitting in Ag₂₅⁻, but also predicts that NCs with the Ag@Au₁₂ superatomic core will exhibit a large SO splitting. Meanwhile, the 1D orbitals of the (M”@M₁₂)⁵⁺ core, corresponding to the lowest unoccupied molecular orbitals, are composed mainly from the 1D orbitals of the M₁₂⁴⁺ shell with a small contribution from the 4d/5d orbitals of the central M' atom (Scheme 1). The model calculations on the naked (M'@M₁₂)⁵⁺ predict the large SO splitting of the 1D orbitals of AuAg₂₄⁻ and Au₂₅⁻ (Figure S11).

Finally, we investigated how chemical modification affects the SO splitting in the Au₁₃ superatom. Representative Au₁₃ superatoms protected by different ligands – [Au₂₅(C≡CR)₁₈]⁻ (C≡CR = alkynyl),^[44] [Au₁₃(NHC)₉Cl₃]²⁺ (NHC = N-heterocyclic carbene),^[45] and [Au₁₃(P₂R)₅Cl₂]³⁺ (P₂R = diphosphine)^[46] – were modeled as [Au₂₅(C≡CMe)₁₈]⁻, [Au₁₃(NHC^Me)₉Cl₃]²⁺ (NHC^Me = benzimidazole with two CH₃ wing tips), and [Au₁₃(Me₂PC₂H₄PMe₂)₅Cl₂]³⁺, respectively, using simplified ligands. The optimized structures and their Kohn–Sham energy diagrams from the PBE functional are shown in Figure 4, confirming the intactness of Au₁₃ cores. [Au₂₅(C≡CMe)₁₈]⁻ and [Au₁₃(NHC^Me)₉Cl₃]²⁺ already display two-fold splitting in the 1P orbitals at the 1c-DFT level due to the asymmetric ligation. Nevertheless, in all cases, the three 1P orbitals split into one lower-energy and two higher-energy orbitals under SOC. This result indicates that SOC is an inherent property of Au₁₃ superatoms, regardless of the protecting ligands.

Conclusion

In summary, cryogenic anion PES revealed that 1P orbitals of Au₂₅⁻ and AuAg₂₄⁻ undergo SO splitting, whereas those of Ag₂₅⁻ do not. Two-component (2c-) DFT calculations identified that the central Au atom as the principal structural factor driving the SO splitting of 1P orbitals of AuAg₂₄⁻. 2c-DFT calculations on naked, model superatoms (M“@M₁₂)⁵⁺ revealed that the splitting of both the p orbitals of the central M” atom and the 1P orbitals in the surrounding M₁₂ shell are responsible for the large SO splitting of 1P superatoms of M'@M₁₂. These insights will pave the way for the rational design of superatoms with spin-related properties, such as magnetic circular dichroism^[47] and magneto-optical responses.^[48]

Supporting Information

The authors have cited additional references within the Supporting Information.^[49-52]

Conflict of Interests

The authors declare no conflict of interest.