Photoluminescence of ligand-protected gold nanoclusters: progress in experimental and theoretical studies

Abstract

Ligand-protected gold nanoclusters, with their small sizes and atomically precise structures, exhibit unique photophysical properties that position them as promising candidates for applications in bioimaging, sensing, and optoelectronics. However, except for a few ligand-protected gold nanoclusters, their photoluminescence quantum yield (PLQY) is still relatively low, and the underlying emission mechanisms are not yet fully elucidated. This review highlights recent experimental and theoretical advances aimed at enhancing and elucidating the photoluminescence (PL) mechanisms of ligand-protected gold nanoclusters. Experimentally, strategies such as heterometallic doping, ligand engineering, and structural rigidification have been employed to promote radiative transitions and suppress nonradiative decay, resulting in substantial improvements in PLQY. Theoretically, methods including density functional theory (DFT), time-dependent density functional theory (TDDFT), and nonadiabatic molecular dynamics (NA-MD) have provided important insights into the PL origin, emission pathways, and excited-state dynamics of ligand-protected gold nanoclusters. These advances will deepen our understanding of structure–property relationships in ligand-protected gold nanoclusters and pave the way for the rational design of highly emissive gold nanoclusters.

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Kang Li

Kang Li is a PhD candidate at Xiangtan University under the supervision of Prof. Yong Pei. His current research interest is focused on the photoluminescence properties of ligand-protected gold nanoclusters.

Pu Wang

Pu Wang received her PhD from Xiangtan University under the supervision of Prof. Yong Pei, and she joined the chemistry faculty of Xiangtan University in 2018. Her current research interests are focused on the structure, properties, and catalytic applications of gold nanoclusters.

Yong Pei

Yong Pei received his bachelor's degree from Xiangtan University in 2001 and his PhD from Nanjing University in 2006. He pursued postdoctoral research at the University of Nebraska-Lincoln from 2006 to 2010. He is now a Professor at Xiangtan University and Hunan Normal University, and his research interests focus on theoretical studies of the structure and optical, catalytic, and electronic properties of coinage metal nanoclusters.

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1. Introduction

Owing to their ultrasmall size (1–3 nm) and atomically precise structures, ligand-protected gold nanoclusters exhibit unique physical and chemical properties that distinguish them from traditional gold nanoparticles (>3 nm, characterized primarily by surface plasmon resonance). In particular, they display rich photoluminescence (PL) behaviors across the visible and near-infrared (NIR) regions, which has established them as a research focus in the field of advanced functional nanomaterials. This atomic-level precision is specifically reflected in the well-defined “metal core—ligand shell” configuration of ligand-protected gold nanoclusters, which not only provides a structural basis for regulating PL performance but also renders them an ideal model for elucidating the correlation between structure and PL properties. Notably, the PL properties of ligand-protected gold nanoclusters are highly aligned with the demands of biological applications. Their excellent biocompatibility, relatively low toxicity, and persistent NIR emission capable of penetrating biological tissues render them ideal fluorescent probes for bioimaging, disease diagnostics, and therapeutic applications.^1–7

However, research on the PL of ligand-protected gold nanoclusters still faces two major challenges. First, from an experimental perspective, although systems with high photoluminescence quantum yield (PLQY) have been synthesized in recent years (e.g., Ir@Au₁₂ (PLQY = 87%) and Au₁₆Cu₆ (PLQY ≈ 100%)),^8–13 the PLQY of most gold nanoclusters is still relatively low, particularly in the NIR-II region, which fails to meet the signal intensity requirements for practical applications. Second, from a mechanistic perspective, the complex electronic dynamics induced by core–ligand interactions in these gold nanoclusters make it challenging to experimentally determine the origin of PL (core-dominated vs. surface-ligand-involved). Furthermore, the strong intrinsic spin–orbit coupling (SOC) of Au atoms efficiently promotes intersystem crossing (ISC) and reverse intersystem crossing (RISC) between singlet and triplet states,^14–16 leading to fluorescence, phosphorescence, thermally activated delayed fluorescence (TADF), and the coexistence of multiple emission phenomena.^17–23 The overlapping emission peaks arising from the small singlet–triplet state energy gap (ΔE_ST) further hinder the differentiation of emission types (phosphorescence or TADF).

Recently, experimental studies have made substantial progress in exploring the PL mechanism of ligand-protected gold nanoclusters via various characterization techniques, such as steady-state and time-resolved spectroscopy.^18,24,25 These efforts have provided clues to the origin of PL but cannot fully reveal the microscopic mechanisms underlying excited-state dynamics and nonradiative relaxation. First-principles theoretical calculations have become a key tool to address these bottlenecks. Specifically, they can directly overcome the limitations of experimental characterization and provide atomic-level insights for the direct exploration of electronic structures, excited-state relaxation dynamics, and energy/charge transfer processes. With the ongoing advancement of computational methods and the increasing computational efficiency and computing resources, theoretical calculations have become an indispensable partner in experiments, offering theoretical references for the modulation of PL properties in these gold nanoclusters.

In this review, we summarize the latest experimental advances in enhancing the PL intensity of ligand-protected gold nanoclusters, as well as theoretical studies focused on exploring their excited-state properties. First, we summarize the experimental strategies employed to boost PL efficiency in recent years, including enhancing radiative decay (e.g., heterometal doping) and suppressing nonradiative pathways (e.g., ligand rigidification). Subsequently, we introduce the key computational methods utilized to study the excited-state properties of these gold nanoclusters, including time-dependent density functional theory (TDDFT) and nonadiabatic molecular dynamics (NA-MD), and analyze the applicability and accuracy boundaries of each method. Finally, we discuss theoretical investigations into the excited-state properties of these gold nanoclusters, including the origins of photoluminescence, SOC-driven emission pathways, and excited-state nonradiative relaxation dynamics, aiming to provide theoretical references for the precise design of ligand-protected gold nanoclusters featuring high PL performance.

2. Experimental advances in photoluminescence enhancement

Research on the photoluminescence of ligand-protected gold nanoclusters faces two primary challenges, including low PLQY and unclear photoluminescence mechanisms, which severely constrain the rational design of high-performance gold nanoclusters. Over the past decade, substantial experimental efforts have been devoted to addressing these issues, resulting in a range of effective strategies for PLQY enhancement, including size control,^26–28 heterometallic doping,^8,29–31 tailored ligand engineering,^9,32–34 and aggregation-induced emission (AIE).^35–37 The availability of ligand-protected gold nanoclusters with atomically precise structures and systematic spectroscopic data has also provided an essential experimental foundation for theoretical studies. Such well-defined cluster systems serve as benchmark models for validating computational approaches. For example, in TDDFT calculations, the assessment and selection of exchange–correlation functionals still rely largely on comparisons with experimental optical spectra (see Section 3).

Nevertheless, most existing reviews emphasize synthetic strategies and potential applications of gold nanoclusters with high PLQY, while discussions on how different experimental strategies enhance PLQY via photophysical modulation are fragmented across the literature. A unified photophysical framework linking experimental strategies to the key factors that determine PLQY is still lacking. In this context, the present section provides a systematic overview of recent experimental advances in improving the PLQY of ligand-protected gold nanoclusters from a photophysical perspective. By focusing on the key physical parameters governing PLQY, this section highlights major experimental breakthroughs, outlines unresolved challenges, and underscores the indispensable role of computational methods in elucidating PLQY enhancement mechanisms and guiding rational experimental design.

2.1 Photophysical basis for PLQY enhancement

According to the PLQY expression, Φ = k_r/(k_r + k_nr), the decay of the excited states in ligand-protected gold clusters proceeds primarily through two competing pathways, i.e., radiative and nonradiative transitions (as illustrated in Fig. 1). The relative magnitudes of the corresponding rate constants ultimately determine the PLQY of the system. Upon photon absorption, an electron is promoted from an occupied orbital to an unoccupied orbital with higher energy, driving the system from the ground state to an excited state. In accordance with Kasha's rule, excitation to higher-lying excited states is typically followed by rapid nonradiative relaxation processes, including internal conversion (IC), ISC, and vibrational relaxation, leading to population of the lowest excited state (S₁ or T₁), from which radiative decay to the ground state mainly occurs. In the radiative process, an excited-state molecule releases energy and returns to the ground state through photon emission. The efficiency of this process is quantified using Einstein's spontaneous emission rate formula:where ω = E_em/ℏ is the angular frequency of the emitted photon, e is the elementary charge, ε₀ is the vacuum permittivity, ℏ is the reduced Planck constant, c is the speed of light in vacuum, and µ is the transition dipole moment.

Fig. 1 Schematic illustration of PL processes in ligand-protected gold nanoclusters (left) and the key factors influencing PLQY of ligand-protected gold nanoclusters (right).

Within the framework of Einstein's theory of spontaneous emission, both a larger emission energy E_em and a larger transition dipole moment µ favor an increased radiative decay rate. Meanwhile, excited states can also return to the ground state through nonradiative pathways. The corresponding nonradiative rate constant k_nr is commonly governed by the energy gap law and decreases exponentially with increasing excited–ground state energy gap, which is often correlated with a higher emission energy E_em. Consequently, increasing E_em not only enhances the radiative transition rate but also suppresses nonradiative decay. Because the equilibrium geometries of the ground and excited states differ, photoexcitation is followed by structural relaxation on the excited-state potential energy surface. This relaxation involves an energetic cost associated with geometric reorganization, which is commonly described by the reorganization energy λ. This relaxation leads to an emission energy E_em that is lower than the vertical excitation energy E_ex defined at the ground-state equilibrium geometry. Therefore, for a given electronic level structure, suppressing excited-state structural relaxation can reduce energy loss and increase E_em. Beyond indirect modulation via emission energy, direct control of nonradiative decay channels is also critical. In particular, weakening nonadiabatic coupling between electronic states and reducing electron–vibrational coupling strength can effectively suppress nonradiative processes, thereby lowering k_nr.

In summary, enhancing the PLQY of ligand-protected gold nanoclusters can be achieved by engineering their electronic structures to increase the emission energy and transition dipole moment, while simultaneously suppressing excited-state structural relaxation and nonradiative decay through ligand engineering or structural rigidification. Such strategies enable larger radiative rates and smaller nonradiative rates, ultimately leading to improved photoluminescence efficiency. On this basis, the following sections will systematically review recent experimental efforts aimed at enhancing the PLQY of ligand-protected gold nanoclusters, with particular emphasis on strategies that promote radiative transitions and suppress nonradiative processes.

2.2 Promoting the efficiency of the radiative process

In the radiative process, an excited-state molecule releases energy and returns to the ground state through photon emission. According to Einstein's theory of spontaneous emission, the radiative rate is mainly governed by two key factors: the emission energy E_em and the transition dipole moment µ. Accordingly, strategies for enhancing the radiative rate can be broadly classified into two aspects: (i) increasing the emission energy of the lowest excited state through electronic structure modulation, and (ii) enhancing the transition dipole moment to accelerate radiative decay.

2.2.1 Increasing the emission energy. Relative to the ground state, the excitation energy E_ex, defined as the energy difference between the excited state and ground state, is determined by the energy gap between occupied and unoccupied orbitals and the electron–hole interaction following excitation. When the lowest excited state (S₁ or T₁) is dominated by a single HOMO → LUMO electronic transition, the excitation energy E_ex shows a strong correlation with the HOMO–LUMO gap E_g. In such cases, enlarging E_g through electronic structure modulation is expected to increase the excitation energy of the lowest excited state and increase the emission energy E_em. Recently, Buschmann et al. summarized the correlations among the HOMO–LUMO gap E_g, the emission energy E_em, and the PLQY for a series of Au₁₃ core clusters protected by different ligands.³⁸ Their results revealed that Au₁₃ clusters with larger E_g simultaneously exhibit higher emission energies and higher PLQY. These observations provide empirical support for the design strategy of enhancing the emission energy via E_g engineering, thereby promoting radiative decay while suppressing nonradiative relaxation.

Previous studies have demonstrated that the HOMO–LUMO gap E_g in ligand-protected gold nanoclusters can be effectively tuned through various experimental strategies, including cluster size control,^39–41 ligand modification,^33,42–44 and metal doping.^8,45,46 Among these strategies, metal doping is an effective strategy to enhance the luminescence efficiency by enlarging the E_g, and it has been widely applied in experiments. Takano and co-workers showed that replacing the central atom of the Au₁₃ core with elements lighter than Au (in the order of Au > Pt > Ir in atomic weight) can widen the E_g (Fig. 2A and B).⁴⁷ Using this principle, they successfully synthesized a series of heterometal-doped clusters, including [RuAu₁₂(dppm)₆]²⁺, [RhAu₁₂(dppm)₆]³⁺, and [IrAu₁₂(dppm)₆]³⁺ (dppm = 1,2-bis(diphenylphosphino)methane). Notably, [RuAu₁₂(dppm)₆]²⁺ exhibits intense room-temperature phosphorescence in degassed CH₂Cl₂ solution, with a PLQY of 37%.⁸ Using a similar doping strategy, a series of clusters with the general formula [MAu₁₂(dppe)₅Cl₂] (M = Au, Pd, Pt, Rh, Ir; dppe = Ph₂PCH₂CH₂PPh₂) were also successfully prepared.³⁰ Experimental results showed that heterometal doping substantially enlarges the E_g of the clusters (Fig. 2B), thereby accelerating radiative transitions while suppressing nonradiative decay pathways. As a result, the PLQY of these systems is significantly enhanced (Fig. 2C). Importantly, such doped cluster systems with well-defined atomic structures and systematic spectroscopic data not only validate the physical mechanism of enhancing radiative efficiency through HOMO–LUMO gap engineering, but also provide ideal experimental models and reliable benchmarks for subsequent excited-state electronic-structure calculations using TDDFT and methodological assessment.

Fig. 2 (A) Two-step jellium potentials for doping lower (left) and higher (right) valent atoms into Au₁₃. Reproduced with permission.⁴⁷ Copyright 2021, American Chemical Society. (B) Plot of the HOMO–LUMO gaps of M@Au₁₂(dppe)₅Cl₂ (M = Ir, Pt, Au, Rh, Pd). (C) Plot of the PLQYs of M@Au₁₂(dppe)₅Cl₂ (MAu₁₂) and M@Au₁₂(dppm)₆ (MAu₁₂-m) versus the energy of their PL peaks. Reproduced with permission.³⁰ Copyright 2022, Wiley-VCH.

2.2.2 Increasing the transition dipole moment. In addition to the emission energy E_em, the transition dipole moment µ represents another key parameter governing the radiative transition rate. For a given emission energy, excited states with larger transition dipole moments generally exhibit a higher radiative transition rate. Recent studies on the Au₃₈S₂(S-Adm)₂₀ cluster (S-Adm = adamantanethiolate) have shown that this system displays a relatively high PLQY of 15%.⁴⁸ The enhanced radiative efficiency was attributed to symmetry-allowed transitions between frontier orbitals (Fig. 3A), which lead to an increase in the transition dipole moment.^48,49 Beyond orbital symmetry, the cluster's overall geometry, specifically its aspect ratio, exerts notable influence on the transition dipole moment. Luo and co-workers reported that a series of rod-shaped Au clusters (Au₄₂, Au₆₀, Au₇₈, Au₉₆, and Au₁₁₄) with hexagonal close-packed (HCP) cores exhibit unusually intense absorption peaks in their UV-vis spectra⁴⁰ (Fig. 3B). Theoretical calculations revealed that these absorption features originate from electronic transitions with large transition dipole moments (Fig. 3C). Among them, the Au₄₂(PET)₃₂ cluster (PET = 2-phenylethanethiolate) shows a relatively high PLQY (11.9%),⁵⁰ and subsequent theoretical studies by Xie et al. confirmed that its large transition dipole moment significantly enhances the radiative decay channel.⁵¹ Similar conclusions have also been supported by computational investigations of Au₆₀ clusters.⁵² Similarly, in a theoretical study on the optical absorption properties of the Au₇₆(SR)₄₄ cluster with a face-centered cubic (FCC) core, Ma et al. found that its larger aspect ratio leads to a stronger longitudinal transition dipole moment⁵³ (Fig. 3D). Although existing studies across different cluster systems have revealed several empirical correlations between geometric structure, orbital symmetry, and transition dipole moments, a comprehensive understanding of the relationship between the structure of a specific cluster and its transition dipole moment remains to be established.

Fig. 3 (A) Isosurface and irreducible representation of the frontier orbitals of Au₃₈S₂(S-Adm)₂₀ and Au₃₀(S-Adm)₁₈. Reproduced with permission.⁴⁹ Copyright 2024, American Chemical Society. (B) Optical absorption spectra of Au₄₂, Au₆₀, Au₇₈, Au₉₆, and Au₁₁₄; (C) the HOMO and LUMO orbitals and electric transition dipole moment for transitions from the ground state to the excited states of Au₄₂(SCH₃)₃₂, Au₆₀(SH)₄₄, Au₇₈(SH)₅₆, and Au₉₆(SH)₆₈. Reproduced with permission.⁴⁰ Copyright 2024, National Academy of Sciences. (D) Transversal and longitudinal dipole moment transitions of Au₇₆(SR)₄₄. Reproduced with permission.⁵³ Copyright 2016, American Chemical Society.

The HOMO–LUMO gap E_g can be indirectly obtained from experimental techniques such as optical absorption spectroscopy and can be effectively tuned through modulation of cluster size, choice of heterometal dopants, or ligand electronic effects. In contrast, the intensity of an apparent absorption peak in the experimental spectrum may arise from the superposition of multiple excited-state transitions. As a result, it is experimentally challenging to directly correlate the intensity of the longest-wavelength absorption peak with the transition dipole moment of the lowest excited state. Fundamentally, the transition dipole moment is determined by the spatial distribution and symmetry characteristics of the orbitals involved in the electronic transition, which generally require excited-state electronic structure calculations for detailed analysis. This issue becomes particularly important in the context of applications such as bioimaging, where NIR emission is desired and blue-shifting the emission (i.e., increasing the emission energy) is no longer an option. Under such conditions, enhancing the transition dipole moment represents a more viable approach for improving radiative efficiency. Therefore, establishing more general and design-oriented relationships between the cluster structure and transition dipole moment through theoretical calculations is essential for guiding the rational design of highly emissive gold clusters.

2.3 Suppressing nonradiative processes

In addition to radiative transitions, excited-state ligand-protected gold nanoclusters can also undergo nonradiative deactivation pathways, which diminish the PLQY. Consequently, beyond enhancing radiative efficiency, suppressing nonradiative decay channels is another critical strategy for improving the PL performance of gold clusters. In fact, most reported ligand-protected gold nanoclusters still exhibit relatively low PLQY, indicating that nonradiative channels generally dominate the excited-state decay processes.

Structurally, ligand-protected gold nanoclusters adopt a core–shell structure consisting of a metallic core surrounded by an organic ligand shell.⁵⁴ In such systems, various vibrational modes introduced by both the metal core and the ligands can couple with electronic excited states, providing efficient pathways for nonradiative energy dissipation. Recent studies have emphasized strategies like ligand shell rigidification and suppression of surface vibrations to mitigate nonradiative relaxation pathways and consequently enhance PLQY.

2.3.1 Ligand rigidification. In ligand-protected gold nanoclusters, increasing the overall rigidity of the ligand shell represents an important strategy for suppressing nonradiative decay. To date, gold clusters protected by various types of ligands have been reported, including thiolates,^55–57 phosphines,⁵⁸ alkynyls,⁵⁹ and N-heterocyclic carbenes (NHCs).^60,61 By comparing Au₁₃ clusters protected by different ligand types, Buschmann et al. showed that Au₁₃ clusters protected by X-type ligands (i.e., thiolates and alkynyls) typically undergo larger structural relaxation in the excited state, whereas Au₁₃ clusters protected by L-type ligands (i.e., phosphines and NHCs) exhibit much smaller excited-state geometric changes.³⁸

In recent years, a series of NHC-protected gold clusters with exceptionally high PLQY have been reported. Luo et al. synthesized chiral NHC-protected Au₁₃ clusters with PLQY as high as 61% (ref. 62) (Fig. 4A). By combining ligand-exchange experiments with theoretical simulations, they revealed that noncovalent inter-ligand interactions, including C–H⋯N, C–H⋯π, and π⋯π interactions, play a crucial role in enhancing the overall rigidity of the ligand shell and suppressing excited-state structural relaxation. Subsequently, Kulkarni et al. reported bidentate NHC-protected Au₁₃ clusters with PLQY reaching 62% (ref. 10) (Fig. 4B), attributing the enhanced performance to increased ligand rigidity and strong interligand interactions. For diphosphine-protected gold nanoclusters, Mutoh and co-workers combined Ir doping with tailor-made diphosphine ligands to synthesize [IrAu₁₂(bbpe)₆]³⁺ (bbpe = bis[benzo[b]phosphindole]ethane), which exhibits an exceptionally high PLQY of 87%.⁹ Similar ligand-engineering strategies have also been successfully applied to thiolate-protected gold nanoclusters. Enhancing the π⋯π interactions by reducing the methyl group at the end of the thiol ligand, Wang et al. improved the PLQY of the Au₅₂(SR)₃₂ cluster from 3.8% to 18.3% (ref. 34) (Fig. 4C). And this approach was subsequently applied to the Au₃₆(SR)₂₄ cluster, achieving a similar PLQY enhancement⁶³ (Fig. 4D).

Fig. 4 (A) The chiral NHC-stabilized Au₁₃ cluster with high PLQY (61%). Reproduced with permission.⁶² Copyright 2023, Wiley-VCH. (B) The bis-NHC-protected Au₁₃ clusters with π-extended aromatic systems and high PLQY. Reproduced with permission.¹⁰ Copyright 2025, American Chemical Society. (C) The PLQY of Au₅₂(SR)₃₂ with four different aromatic thiolate ligands. Reproduced with permission.³⁴ Copyright 2023, American Chemical Society. (D) Emission spectra of Au₃₆(SR)₂₄ with four different aromatic thiolate ligands. Reproduced with permission.⁶³ Copyright 2024, American Chemical Society.

Collectively, these studies indicate that enhancing interligand interactions to rigidify the ligand shell is an effective strategy for suppressing excited-state structural relaxation and thereby reducing nonradiative decay. However, most ligand-modification approaches reported to date have focused on hydrophobic ligands. Meanwhile, hydrophilic ligands are essential for ligand-protected gold nanoclusters aimed at biological applications,^4,18,64,65 and the surrounding aqueous environment plays a decisive role in governing their PL properties. From a theoretical perspective, a faithful description of these aqueous environment effects requires going beyond implicit-solvent treatments of bulk polarity and instead adopting explicit, dynamic multiscale simulations (e.g., QM/MM), coupled with nonadiabatic excited-state dynamics to capture solvent-coupled structural relaxation as well as charge- and energy-transfer processes.^66–72 Notably, such multiscale and nonadiabatic approaches have been less frequently applied to ligand-protected gold nanoclusters and merit further development.

2.3.2 Suppression of staple motions. Unlike phosphine and NHC ligands, which bind directly to the metallic core through anchoring atoms (P or C), thiolate ligands in thiolate-protected gold nanoclusters can form characteristic Au–S staple motifs involving a portion of surface gold atoms. The vibrational modes associated with these staple motifs can couple with electronic excited states, thereby facilitating nonradiative energy dissipation. Modulating the Au–S staple structures to restrict their vibrational relaxation has therefore been demonstrated as an effective strategy for enhancing the PLQY of thiolate-protected gold nanoclusters.⁷³ In 2021, Li et al. reported that the Au₃₈S₂(S-Adm)₂₀ cluster exhibited a relatively high PLQY of 15%.⁴⁸ They attributed this PL enhancement to the rigidifying effect of surface µ₃-S atoms and eight bridging SR ligands (Fig. 5A), which significantly suppresses energy dissipation caused by Au–S vibration. Similar effects have been further validated in isomeric systems. Chen and Xia et al. identified two isomers of Au₂₈(SR)₂₀ (Au_28i and Au_28ii) with identical gold cores but different surface Au–S staple motif structures, leading to significant differences in the PL intensity.^74,75 In particular, the long-lived emission component of Au_28ii is significantly enhanced, indicating that the interlocked short motifs effectively inhibit nonradiative decay. Subsequently, Dong et al. synthesized the Au₂₈(SCH₂Ph-^tBu)₂₂ cluster, whose compact and rigid shell layer effectively reduced nonradiative energy loss and enhanced the fluorescence intensity.⁷⁶

Fig. 5 (A) Atomic structure of Au₃₈S₂(S-Adm)₂₀ determined from single-crystal diffraction. Reproduced with permission.⁴⁸ Copyright 2021, American Chemical Society. (B) PLQY of Au₄₂ dissolved in deaerated 2-MeTHF containing DMBA (N,N-dimethylbenzamide) with different concentrations. (C) PL spectra of Au₄₂ dissolved in C₂Cl₄ and embedded in a polystyrene (PS) film. Reproduced with permission.¹² Copyright 2024, American Chemical Society. (D) Schematic diagram of intramolecular cross-linking of ligands by the formation of bis-Schiff linkages on the Au₂₂(SG)₁₈ surface. (E) PL spectra of Au₂₂(SG)₁₈ and PDA-Au₂₂(SG)₁₈ NCs. Reproduced with permission.⁷⁷ Copyright 2022, Springer Nature. (F) Comparison of the emission spectra of Au₁₆Cu₆ and Au₂₂ in CH₂Cl₂. Reproduced with permission.¹¹ Copyright 2024, American Association for the Advancement of Science.

Au–S staple motion can also be constrained through external molecular environments. By introducing amide molecules to further restrict staple vibrations in Au₄₂(PET)₃₂ clusters, the room-temperature PLQY was increased to 50% and even reached 75% when embedded in a polymer matrix containing amide molecules¹² (Fig. 5B and C). In addition to environmental confinement, surface modification engineering can achieve similar effects. Deng et al. employed bis-Schiff base cross-links to restrict the movement of Au–S staples in individual Au₂₂(SG)₁₈ clusters (SG = glutathione), achieving a PLQY of 48% (ref. 77) (Fig. 5D and E). Similar to thiolate-protected systems, alkynyl-protected gold nanoclusters also feature Au–C≡CR staple motifs. Recently, metal doping within staple motifs provides another effective means of suppressing nonradiative decay in alkynyl-protected gold nanoclusters. Shi et al. doped six Cu atoms into the surface staple units of Au₂₂(^tBuPhC≡C)₁₈, yielding a more compact Au₁₆Cu₆(^tBuPhC≡C)₁₈ cluster with a near-unity PLQY approaching 100% (ref. 11) (Fig. 5F). From a theoretical perspective, suppressing staple vibrations can be viewed as mitigating excited-state structural relaxation and vibronic coupling at the surface, thereby reducing nonradiative decay.

In summary, experimental studies on the photoluminescence of ligand-protected gold nanoclusters in recent years have established a clear and reproducible set of structure–property relationships. Although the specific experimental strategies differ in their practical implementations, their underlying mechanisms can be consistently rationalized in terms of effective modulation of key parameters governing excited-state decay processes. On the one hand, radiative decay rates are enhanced by increasing the emission energy and the transition dipole moment. On the other hand, nonradiative decay is efficiently suppressed by strengthening the rigidity of ligands and surface motifs and by reducing the coupling between vibrational modes and electronic excited states.

It should be emphasized that these experimental observations cannot be fully understood solely on the basis of static structural parameters or ground-state electronic structures. Instead, they critically depend on excited-state electronic structure characteristics, including energy levels, coupling parameters, and the dynamical evolution of excited-state decay processes. Therefore, to achieve a systematic mechanistic understanding and predictive capability for the PLQY of ligand-protected gold nanoclusters, it is essential to introduce theoretical and computational frameworks centered on excited states. Beyond identifying the key factors governing PLQY, theoretical methods are also indispensable for determining emission types, elucidating emission origins, and describing the dynamics of nonradiative relaxation processes. This includes not only calculations of excited-state energies and transition properties based on TDDFT, but also quantitative descriptions of SOC effects, ISC, and vibrational coupling accompanied by structural relaxation. On this basis, the following section will focus on the crucial role of excited-state theoretical approaches in addressing these issues.

3. Theoretical tools for understanding photoluminescence

Although extensive experimental efforts have been devoted to enhancing the PLQY of ligand-protected gold nanoclusters and to elucidating their excited-state properties and emission pathways,^{18,19,24,31,41} there is still a lack of a comprehensive understanding of their PL mechanisms, which hinders the rational design of clusters with specific emission wavelengths and lifetimes. Specifically, experimental characterization faces three limitations. Firstly, the origin of photoluminescence remains ambiguous due to the inherent core–shell structure of ligand-protected gold nanoclusters. Experimental researchers have proposed several competing explanations, including core-dominated emission, ligand participation, ligand-to-metal charge transfer (LMCT), and metal-to-ligand charge transfer (MLCT). These hypotheses remain under debate because the electronic distribution and transfer processes in the excited states of the clusters cannot be directly observed. Secondly, the strong SOC in gold atoms often results in the coexistence of multiple emission types, including fluorescence, phosphorescence, and TADF. However, the experimentally observed fluorescence and phosphorescence emission bands usually overlap owing to their broad bandwidths and small energy separations, making it challenging to unambiguously distinguish and assign the emission types. Finally, although ultrafast spectroscopy provides powerful means to probe the timescales of excited-state relaxation in these clusters, capturing the atomic-scale details of processes such as structural relaxation (e.g., core distortion and ligand vibration) and charge or energy transfer remains highly challenging.

Theoretical calculations can complement these experimental limitations and serve as indispensable tools for elucidating PL mechanisms. In light of the challenges mentioned above, this section systematically reviews two major computational approaches employed to investigate the PL mechanisms of ligand-protected gold nanoclusters and clarifies their relevance to the unresolved experimental issues (as illustrated in Fig. 6). The first category involves electronic structure methods, including density functional theory (DFT), TDDFT, and multiconfigurational methods. By selecting an appropriate theoretical methods, theoretical calculations can reproduce experimental absorption and emission spectra, thereby providing a reliable foundation for subsequent rate-constant evaluations and excited-state property analyses. In particular, analytical tools such as natural transition orbital (NTO) and electron–hole analysis⁷⁸ enable direct visualization of charge distribution and transfer characteristics in excited states, helping to elucidate the origin of photoluminescence. The second category focuses on the simulation of nonradiative processes, encompassing static rate-constant calculations based on Fermi's golden rule and NA-MD methods that explicitly account for electron–nuclear coupling. By computing and comparing rate constants associated with different decay pathways, one can distinguish emission types, estimate PLQY, and unravel the underlying mechanisms. Moreover, NA-MD simulations provide time-resolved insights into electronic relaxation dynamics, revealing transition times and pathways among excited states. Together, these computational strategies establish a robust methodological framework for in-depth mechanistic analysis of photoluminescence and for the rational design of ligand-protected gold nanoclusters with enhanced PL performance.

Fig. 6 Computational approaches for investigating PL mechanisms in ligand-protected gold nanoclusters.

3.1 Electronic structure methods

The selection of electronic structure methods is pivotal for accurately modeling the electronic configuration and deriving dependable photophysical characteristics, serving as a fundamental prerequisite for valid theoretical interpretations. DFT and TDDFT are widely used to analyze the electronic structure and excited-state properties of ligand-protected gold nanoclusters, owing to their favorable balance between computational efficiency and accuracy.^43,55,79,80 However, the reliability of theoretical predictions, such as UV-vis absorption spectra, emission energies, and excited-state lifetimes, strongly depends on the choice of the exchange–correlation functional.^80–83

Generalized gradient approximation (GGA) functionals, such as BP86 (ref. 84) and PBE,⁸⁵ are frequently selected in computational studies of ligand-protected gold nanoclusters due to their computational efficiency and acceptable accuracy. However, they tend to underestimate excitation energies, thus limiting their applicability in excited-state properties. Recently, in the computational investigation of X@Cu₁₄ (X = Au, Cl) clusters, Luo et al. assessed the performance of three GGA/meta-GGA functionals (BP86, PBE, and TPSS^86,87) and nine hybrid functionals (PBE0,⁸⁸ B3LYP,^89,90 revPBE38,⁹¹ TPSSh,⁹² TPSS0,⁹³ M06, M06-2X,⁹⁴ CAM-B3LYP,⁹⁵ and ωB97X-D4 (ref. 96)) for the calculation of fluorescence and phosphorescence emission energies.⁹⁷ For Au@Cu₁₄, hybrid functionals with high Hartree–Fock exchange (e.g., revPBE38) most accurately replicate the experimental T₁ → S₀ phosphorescence emission energy (Fig. 7), while for Cl@Cu₁₄, GGA/meta-GGA functionals (BP86, PBE, and TPSS) align more closely with the experiment. Notably, the calculated ΔE(S₁–T₁) increased with higher HF exchange fractions, resulting in a growing deviation between the calculated fluorescence and phosphorescence emission properties and experimental data. Additionally, the oscillator strengths of fluorescence radiation show an increasing trend with rising HF exchange percentage in the functional. For phosphorescence radiation, except for M06-2X, other functionals showed minimal influence on the oscillator strengths. Qian and co-workers evaluated the performance of various functionals for ligand-protected noble-metal clusters, finding that the proportion of HF exchange predominantly influences simulated spectral features, regardless of the hybrid functional type.⁹⁸ Benchmarking against experimental spectra indicates that functionals incorporating approximately 10–20% HF exchange yield the most accurate spectral predictions. Furthermore, She et al. examined the fluorescence mechanisms and doping effects in heteroatom-doped M@Au₁₂(dppe)₆^x−2 clusters, with M representing a 4d or 5d transition metal, and x denoting the nominal charge. They benchmarked several exchange–correlation functionals by comparing the calculated optical absorption and fluorescence spectra of [Au₁₃(dppe)₅Cl₂]³⁺ with experimental data.⁷⁹ They found that the PBE functional markedly underestimates emission energies, while HSE06 (ref. 99) offers the best consistency with experimental observations. Taken together, these studies indicate that no universal exchange–correlation functional has yet been established for ligand-protected gold nanoclusters. The optimal choice remains system-dependent and typically requires benchmarking against experimental spectra or higher-level calculations.

Fig. 7 Calculated T₁ → S₀ emission energies of Au@Cu₁₄ using functionals with different fractions of Hartree–Fock exchange.

In theoretical calculations, electronic excitation properties (such as local and charge-transfer excitations) can be characterized using NTO or hole–electron analysis. Specifically, such analyses are performed to calculate the excited-state properties of clusters via DFT and TDDFT methods combined with optimal exchange–correlation functionals, to further obtain the orbital compositions and transition contributions of the excited-state electronic structure, and ultimately to quantitatively determine the respective contributions of the metal core and ligand shell in the excited-state transitions, thereby elucidating the origin of photoluminescence. For instance, Weerawardene et al. utilized TDDFT to study Au₂₅(SR)₁₈⁻ clusters and revealed that the emission primarily originates from core-based transitions (i.e., excitations out of superatom P orbitals into the lowest two superatom D orbitals).¹⁰⁰

While DFT and TDDFT provide an advantageous compromise between computational efficiency and accuracy, their computational cost escalates rapidly as the size of gold nanoclusters (e.g., beyond Au₅₀) increases, limiting the feasibility of simulating larger systems. Concurrently, the electronic and steric influences of protecting ligands markedly affect the photophysical characteristics of gold nanoclusters.^9,34,79 This presents a methodological challenge: simplifying ligand structures to reduce computational demand introduces systematic discrepancies, whereas employing realistic ligand models substantially elevates computational resource requirements. In their study of the dual-emission mechanism of the Au₁₄Cd(S-Adm)₁₂ cluster,¹⁰¹ Havenridge and co-workers observed that the absorption spectra are highly sensitive to ligands. Simplifying ligands, such as substituting Adm groups with hydrogen or methyl groups, may lead to deviations from the authentic photophysical responses of the actual system. They thus applied a combined approach of TDDFT and tight-binding approximation (TDDFT + TB)¹⁰² to simulate absorption spectra of Au₁₄Cd(S-Adm)₁₂ protected by full ligands. This approach yielded computational efficiency comparable to that of TDDFT while significantly reducing computational effort. Subsequently, they developed an innovative approximation method, termed TDDFT-aas (time-dependent density functional theory approximate auxiliary s-function), which does not depend on tight-binding parameters.¹⁰³ Within higher computational efficiency, the calculated absorption spectra of silver and gold nanoparticles using the TDDFT-aas method are in good agreement with the results of TDDFT and TDDFT + TB. Furthermore, the implementation of analytical excited-state gradients within the TDDFT-aas framework facilitates efficient calculation of emission energies for larger nanoclusters.

It is worth noting that TDDFT may struggle to accurately describe potential energy surfaces near conical intersections or state crossings, where multi-configurational methods (e.g., CASSCF) become essential. In 2016, Wu et al. investigated the photoluminescence mechanisms of ultrasmall ligand-protected gold nanoclusters using the CASPT2//CASSCF approach, which enabled highly accurate predictions of absorption and emission wavelengths in excellent agreement with experimental data.¹⁰⁴ For example, when applied to the cluster [Au₇(dppp)₄]³⁺ (dppp = 1,3-bis(diphenylphosphino)propane), the calculated phosphorescence emission energy was 644 nm, matching the experimental value (642 nm) with a deviation of only 2 nm. However, the high computational cost and the need for careful active-space selection limit the applicability of multi-configurational methods to larger or more complex systems.¹⁰⁵

3.2 Simulation of nonradiative processes

The PLQY of ligand-protected gold nanoclusters is determined by the competition between radiative and nonradiative decay pathways, serving as a critical parameter for evaluating their photoluminescence efficiency. However, experimental approaches often face challenges in directly resolving the microscopic mechanisms of nonradiative relaxation processes (such as excited-state structural relaxation and electron-nuclear coupling interactions) and in quantitatively assessing their influence on PLQY. Consequently, theoretical calculations become essential for providing deeper mechanistic insight. To theoretically determine the PLQY value, the primary goal is to calculate the radiative rate constant k_r and the nonradiative rate constant k_nr,^106–108 which in turn allows for a clear determination of the reasons behind low PLQY. Notably, early theoretical studies of ligand-protected gold nanoclusters focused primarily on their absorption and emission spectra, oscillator strengths, emission energies, and radiative rate constants.

The radiative rate constant k_r is predominantly determined using Einstein's spontaneous emission rate expression (eqn (1)), which requires prior calculation of the emission energy and transition dipole moment through methods such as TDDFT. In contrast, modeling nonradiative processes remains a significant challenge in theoretical chemistry and is critical for accurately predicting the PLQY of ligand-protected gold nanoclusters. According to the energy gap law,¹⁰⁹ the IC rate constant k_IC increases exponentially as the emission energy E_em decreases, which can be expressed as k_IC = Ae^−αE_em. However, since vibronic coupling phenomena between electronic states are not explicitly incorporated, this empirical expression provides only a rough estimate and has limited applicability. Additionally, the strong relativistic effect in gold atoms induces significant SOC, which facilitates ISC from singlet to triplet states. Consequently, ligand-protected gold nanoclusters can exhibit phosphorescence, TADF, or dual emission^17–23,50 involving triplet states and the associated ISC and RISC processes. Therefore, a thorough analysis of both ISC and RISC pathways is essential for understanding the luminescence properties and mechanisms of these nanoclusters. Typically, ΔE_ST and spin–orbit coupling matrix elements (SOCMEs) are utilized to estimate the competition between ISC and RISC via Fermi's golden rule, thereby helping to identify the emission type of ligand-protected gold nanoclusters. Furthermore, direct evaluation of ISC rate constant k_ISC and RISC rate constant k_RISC, and their comparison with k_r and IC rate constant k_IC, enables comprehensive mapping of excited-state decay pathways and facilitates quantitative prediction of excited-state lifetimes and PLQY.¹⁰⁶

However, nonradiative processes, such as IC, ISC, and RISC, involve intricate couplings among electronic and nuclear degrees of freedom,^110,111 making accurate theoretical treatment particularly challenging. According to Fermi's golden rule, the nonradiative transition rate constant k_nr governing transitions between two electronic states can be expressed as follows:

where 〈Ψ_f|Ĥ′|Ψ_i〉 represents the nonadiabatic coupling (NAC) Hamiltonian (for IC) or the SOC Hamiltonian (for ISC) between the initial state i and the final state f, ℏ is the reduced Planck constant, and ρ(ΔE) is the vibrational density of states at the energy gap ΔE.

Recent advances by Shuai,^107,112 Marian,^113,114 Santoro,¹¹⁵ Valiev¹¹⁶ and others have established general rate-constant formulations that incorporate vibrational overlap and the Duschinsky rotation effect, which have been implemented in computational packages for evaluating nonradiative rate constants. For instance, Xie et al.⁵¹ applied Lin's formalism^117,118 to compute the ISC and RISC rate constants (6.87 × 10⁷ s⁻¹ and 2.87 × 10² s⁻¹, respectively). By combining these with the fluorescence and phosphorescence radiative rate constants (1.53 × 10⁸ s⁻¹ and 8.52 × 10³ s⁻¹, respectively), they provided a theoretical explanation of the dual-emission behavior observed in the Au₄₂(PET)₃₂ cluster. Recently, Li et al. computed nonradiative rate constants for Au₃₈S₂(SR)₂₀ and Au₃₀(SR)₁₈ with the FCclasses3 program.⁴⁹ Based on the computed rate constants and the law of mass action, exciton population evolution diagrams were subsequently constructed to analyze the excited-state decay pathways and emission characteristics of these clusters. In addition to rate-constant calculations, analyses of the Huang–Rhys factors and reorganization energies, which were decomposed into contributions from individual vibrational normal modes, provided further insight into how cluster structure influences nonradiative decay processes. However, the excited-state lifetimes and PLQYs predicted by the current methods tend to be significantly lower than experimental values, primarily due to the neglect of anharmonic vibrational effects.^{108,116,119,120} Moreover, these Fermi's golden rule-based approaches require the computation of excited-state vibrational frequencies, which becomes computationally prohibitive for larger clusters. As a practical alternative to Fermi's golden rule-based approaches, Marcus theory has been employed to estimate the ISC and RISC rate constants:^121–124

where ΔE_ST is the adiabatic energy difference between the S₁ and T_n states. k_B is the Boltzmann constant and T is the thermodynamic temperature. V_SOC is the spin–orbit coupling matrix element (SOCME), and λ is the reorganization energy.

Beyond the static excited-state decay models based on Fermi's golden rule discussed above, nonadiabatic molecular dynamics (NA-MD) has emerged as a powerful tool for elucidating the ultrafast excited-state relaxation pathways of ligand-protected gold nanoclusters.^125,126 NA-MD simulations can provide detailed information on the electronic relaxation dynamics, including state-to-state transition times and mechanisms. For instance, NA-MD simulations of the Au₂₅(SR)₁₈⁻ cluster revealed that the experimentally observed picosecond-scale processes likely originate from core-to-core transitions rather than the previously proposed core-to-half-ring transitions.¹⁰² However, most current NA-MD studies of ligand-protected gold nanoclusters neglect SOC effects, thereby omitting ISC between singlet and triplet states. For ligand-protected gold nanoclusters, reproducing ISC processes that accompany dynamical structural transformations within NA-MD remains highly challenging. This difficulty primarily arises from the need to compute triplet-state energy levels and SOCMEs along nuclear trajectories. Additionally, earlier nonadiabatic simulations of nanoclusters primarily relied on the independent-particle approximation, in which excited states are represented as single-particle excitations constructed from Kohn–Sham orbitals. Within this framework, the state energies and nonadiabatic couplings (NACs) are evaluated using single Slater determinants, thereby neglecting critical carrier–carrier interactions. Recently, Xie and co-workers¹²⁷ compared simulation results obtained from both single-particle and many-body (MB) treatments in their NA-MD study of Au₂₅(SR)₁₈⁻. Their findings demonstrated that the inclusion of MB effects significantly enhanced the NAC between excited states, resulting in ultrafast IC from higher excited states on a sub-picosecond timescale, which is consistent with previous experimental observations. Future developments of NA-MD simulation methods in ligand-protected gold nanoclusters need to incorporate relativistic effects, ISC processes, and carrier–carrier interactions to more accurately reproduce the excited-state dynamics of ligand-protected gold nanoclusters.^{71,72,127–129}

4. Mechanistic insights into photoluminescence and excited‐state dynamics

Section 3 has already systematically introduced the applicability logic of core methods such as DFT, TDDFT, and NA-MD in the study of ligand-protected gold nanoclusters. Therefore, this section will adopt a “Computational Method → Mechanism Elucidation” framework to systematically summarize the current theoretical research status concerning the photoluminescence origin, excited-state relaxation dynamics, and emission mechanisms, using case studies from typical cluster systems. This summary will explicitly define the core role of different computational methods in elucidating these mechanisms, thereby providing a valuable reference for subsequent theoretical studies and rational structure design.

4.1 Origin of photoluminescence

The core–shell structure of ligand-protected gold nanoclusters, consisting of a metal core and a ligand shell (as illustrated in Fig. 8), gives rise to diverse PL origins, including core-dominated emission, ligand-involved emission, and charge-transfer processes such as LMCT and MLCT. In some systems, structural relaxation and nonradiative processes (IC or ISC) can reshape the character of the excited state, enabling conversion between initially populated charge-transfer states and a core-dominated excitation state before emission. Furthermore, the intricate interactions between the metal core and ligand shell lead to complex excited-state properties and electronic dynamics, which make experimental identification of the PL origin highly challenging. TDDFT, combined with NTO analysis or electron–hole analysis, has thus emerged as a powerful tool for clarifying excited-state electronic behavior. This method serves as an important tool for elucidating the dominant PL origin and understanding the structural factors that modulate emission by enabling direct comparison among different cluster systems. At present, research on the PL origin in ligand-protected gold nanoclusters can be broadly classified into two major categories.

Fig. 8 The photoluminescence origin diagram of ligand-protected gold nanoclusters.

(1) Core-dominated excitation: for the majority of ligand-protected gold nanoclusters, PL originates primarily from core-localized electronic excitation. In this case, the emission is governed by electronic transitions within the metal core, whereas the ligands mainly modulate the orbital energy levels through electron-donating or -withdrawing effects and influence core structural relaxation via steric hindrance. This conclusion has been consistently validated across multiple systems using TDDFT calculations. For example, early transient absorption spectroscopy (TAS) studies on the Au₂₅(SR)₁₈⁻ cluster suggested that its PL might arise from ligand–metal, charge-transfer, or semi-ring states.¹³⁰ To resolve this controversy, Weerawardene et al. employed TDDFT to calculate the excited-state electronic structures of Au₂₅(SR)₁₈⁻ clusters clearly modified with different R groups (R = H, CH₃, C₂H₅, C₃H₇).¹⁰⁰ Their results clearly demonstrated that the emission originates predominantly from core-based transitions rather than charge-transfer or semi-ring states (Fig. 9A), thereby providing a theoretical resolution to the long-standing debate over this system's emission origin. Subsequent TDDFT calculations on systems such as Au₃₈(SR)₂₄,¹³¹ Au@Cu₁₄,⁹⁷ Au₂₂(C≡CR)₁₈,¹³² Au₄₂(PET)₃₂ (Fig. 9B),⁵² and Au₃₈S₂(S-Adm)₂₀ (ref. 49) further confirmed the dominance of core-localized excitation. Furthermore, Weerawardene et al.¹⁰⁰ illustrated the ligand-dependent modulation of emission energy for Au₂₅(SH)₁₈⁻, Au₂₅(SCH₃)₁₈⁻, and Au₂₅(SCH₂CH₂CH₃)₁₈⁻, and the fluorescence emission energies were calculated to be 0.829 eV, 0.655 eV, and 0.512 eV, respectively.

Fig. 9 (A) Kohn–Sham orbitals and orbital energies for the S₁ state of Au₂₅(SH)₁₈⁻. Reproduced with permission.⁹⁴ Copyright 2016, American Chemical Society. (B) Distributions of hole and electron pairs during the electronic transitions of Au₄₂ and Au₆₀ (blue regions represent holes and green regions represent electrons). Reproduced with permission.⁵³ Copyright 2025, American Chemical Society. (C) Distribution of hole and electron pairs during the T₁ → S₀ transition at the optimized T₁ geometry of Au@Cu₁₄ and Cl@Cu₁₄. Reproduced with permission.⁹¹ Copyright 2025, American Chemical Society.

(2) Charge transfer: in contrast, for certain Au(I) clusters and specific ligand-protected systems, the ligands participate directly in electronic transitions, giving rise to LMCT. For instance, studies on the PL properties of Au(I) and Cu(I) clusters protected by NHC ligands,¹³³ which exhibit highly efficient TADF, revealed through NTO analysis that the S₁ state in all clusters displayed LMCT characteristics. Similarly, in the Cl-doped Cl@Cu₁₄ cluster, the T₁ state exhibits charge-transfer features (Fig. 9C),⁹⁷ whereas the PL origin in the Au@Cu₁₄ system remains core-localized excitation. Furthermore, He et al. demonstrated that Au doping in AuAg₁₂ and Au₃Ag₁₀ induces significant charge-transfer characteristics.¹³⁴

4.2 SOC and emission pathways

Ligand-protected gold nanoclusters, which comprise several tens of gold atoms or more, exhibit pronounced SOC owing to the heavy-atom effect of gold. Serving as a pivotal mediato, SOC accelerates ISC between singlet and triplet states and, by regulating the RISC rate, directly dictates the emission pathway, namely fluorescence, phosphorescence, or TADF (Fig. 10 left). Early studies often overlooked SOC and the associated ISC/RISC processes, which obscured the interpretation of complex photoluminescence behaviors. Here, we summarize advances in elucidating emission types of ligand-protected gold nanoclusters based on quantitative rate-constant calculations and analyses, with particular emphasis on how SOC is incorporated into the models. By computing ISC and RISC rate constants, we clarify the determinative roles of SOC and the ΔE_ST in selecting the final emission channel, thereby establishing a “Structural Factors → SOC Effects → Emission Type” regulatory framework (Fig. 10 right).

Fig. 10 Jablonski diagram of fluorescence, TADF, and phosphorescence emission processes (left), and factors influencing ISC and RISC processes (right).

4.2.1 Influence of SOC and ΔE_ST on emission types. The SOC effect operates chiefly by opening the phosphorescent radiative pathway and by setting the emission outcome through competition between ISC and RISC. This competition is governed by two key parameters: the ΔE_ST and the SOCMEs. A smaller ΔE_ST facilitates RISC and favors TADF, whereas a larger ΔE_ST suppresses RISC and favors phosphorescence. Larger SOCMEs enhance ISC efficiency and increase the phosphorescent radiative rate. The interplay between ΔE_ST and SOCMEs can therefore yield multiple emission types and even dual-emission behavior. This mechanism should be validated with multi-state model simulations and quantitative rate calculations.

(1) Differences of emission in isomers: in 2020, the groups of Jin and Wu independently reported two isomeric Au₂₈(SR)₂₀ clusters (i.e., Au_28i(SR)₂₀ and Au_28ii(SR)₂₀).^74,75 Although both possess an identical Au₁₄ core, differences in their ligand-staple motifs led to markedly different PLQYs. An earlier DFT/TDDFT study by Li et al.¹³⁵ proposed an anti-Kasha S₂ fluorescence mechanism but did not incorporate SOC effects or triplet states. More recently, Mazumder et al. combined temperature and oxygen quenching experiments with calculations of ISC and RISC rate constants,²⁰ revealing the emission type and PL mechanism of two Au₂₈(SR)₂₀ isomers (Fig. 11A). Au_28i(SR)₂₀ exhibited a small ΔE_ST (0.126 eV), resulting in comparable T₁ → S₁ RISC and S₁ → T₁ ISC rate constants (2.90 × 10¹⁰ s⁻¹ and 3.53 × 10¹⁰ s⁻¹, respectively), thus showing both phosphorescence and TADF. In contrast, Au_28ii(SR)₂₀ has a larger ΔE_ST (0.240 eV), which suppresses RISC (9.87 × 10³ s⁻¹) and leads exclusively to phosphorescence via the ISC pathway. Furthermore, rate constant calculations also indicated that the higher-lying T₂ state provides an indirect and efficient nonradiative channel from the excited singlet states to the triplet states, reinforcing the conclusion that SOC directly regulates the emission type.

Fig. 11 Simulated mechanism of photoluminescence for (A) Au_28i(SR)₂₀ and Au_28ii(SR)₂₀. Reproduced with permission.²⁰ Copyright 2024, American Chemical Society. (B) Au₂₄, Au₄₂, and Au₆₀ clusters. Reproduced with permission.⁵² Copyright 2025, American Chemical Society. (C) Au₅Ag₁₁ and Pt₁Ag₁₆. Reproduced with permission.¹³⁶ Copyright 2022, Wiley-VCH. (D) Au@Cu₁₄ and Cl@Cu₁₄. Reproduced with permission.⁹⁷ Copyright 2025, American Chemical Society.

(2) Three-state modeling of dual emission mechanism: to rationalize the dual emission of Au₄₂(PET)₃₂, Xie et al. established a three-state kinetic model (S₁, T_1, and S₀) and simulated the ISC and RISC processes.⁵¹ Because S₁ and T₁ share similar localized electronic character, the SOCME between S₁ and T₁ is relatively weak (46.49 cm⁻¹), consistent with the El-Sayed rule. In addition, the S₁ state has a large oscillator strength, yielding a high fluorescence radiative rate constant (1.53 × 10⁸ s⁻¹) that is comparable to the relatively modest S₁ → T₁ ISC rate constant (6.87 × 10⁷ s⁻¹). Consequently, a fraction of excitons return directly to S₀ via fluorescence, while the remainder populate T₁ through S₁ → T₁ ISC. From T₁, the subsequent phosphorescence rate (8.52 × 10³ s⁻¹) substantially exceeds the RISC rate (2.87 × 10² s⁻¹), producing phosphorescence. Overall, the competition among these sequential pathways accounts for the coexistence of fluorescence and phosphorescence in Au₄₂(PET)₃₂.

4.2.2 Modulation of SOC and ΔE_ST. Structural factors within a nanocluster, such as central-atom doping, ligand modification, and alloying, tune the spin–orbit landscape by modulating the SOCMEs and the ΔE_ST (Fig. 10 right). They shift the ISC/RISC balance and enable control over the emission channel, including fluorescence, phosphorescence, and TADF.

(1) Heavy-atom effect of core atom doping: a comparison of calculations between Au@Cu₁₄ and Cl@Cu₁₄ clearly illustrates the mechanism of heavy-atom regulation effect (Fig. 11D).⁹⁷ Owing to the incorporated Au, Au@Cu₁₄ shows a substantially larger SOCME value (2.17 cm⁻¹) compared to that of Cl@Cu₁₄ (0.77 cm⁻¹). This stronger SOC, together with a smaller ΔE_ST(S₁–T₂) of 0.03 eV, results in a faster S₁ → T₂ ISC rate (1.58 × 10¹⁰ s⁻¹). As a result, Au@Cu₁₄ exhibits strong phosphorescence (PLQY = 71.3%) via the S₁ → T₂ → T₁ → S₀ pathway. In contrast, the weaker SOC in Cl@Cu₁₄ leads to competition between ISC and RISC among S₁, T₁, and T₂, producing the coexistence of TADF and phosphorescence. This comparison clarifies the enhancing role of heavy-atom doping in strengthening SOC.

(2) Alloying effects: to investigate how doping concentration influences emission, He et al. performed theoretical calculations on Ag₁₃, Au₁₃, and the model alloy clusters AuAg₁₂ and Au₃Ag₁₀, all of which share the identical icosahedral core structure and superatom electronic configuration (1S²1P⁶).¹³⁴ For Au₁₃, which exhibits strong NIR emission, the large T₂–T₁ energy gap (0.55 eV) allows T₂ phosphorescence to compete effectively with the T₂ → T₁ IC process, indicating that its emission primarily originates from the T₂ → S₀ transition. In contrast to the localized S₁ and T₁ states found in Au₁₃ and Ag₁₃, the T₁ state in AuAg₁₂ and Au₃Ag₁₀ exhibits pronounced charge-transfer character induced by Au doping (Fig. 12). This modification enhances the SOCMEs (23.97 cm⁻¹ for AuAg₁₂ and 45.55 cm⁻¹ for Au₃Ag₁₀) and reduces the ΔE_ST relative to Ag₁₃ (about 0.01 eV for AuAg₁₂ and 0.03 eV for Au₃Ag₁₀). These effects accelerate ISC and increase the overall PLQY.

Fig. 12 Energy diagrams and images of the hole and electron pairs of (A) Ag₁₃, (B) Au₁Ag₁₂, (C) Au₃Ag₁₀ and (D) Au₁₃. The S_r index is defined as the full space integration of a function (S_r(r)) describing the overlap between electron and hole distributions, and the D index is the distance between a hole and an the electron center of mass. Reproduced with permission.¹³⁴ Copyright 2024, Oxford University Press on behalf of the Chinese Academy of Sciences.

Investigation into the analogous dopant effects of various metals on photoluminescence has also been conducted for Au₅Ag₁₁ (fluorescence) and Pt₁Ag₁₆ (phosphorescence).¹³⁶ The computational analysis revealed the photoluminescence mechanisms of Au₅Ag₁₁ and PtAg₁₆ (Fig. 11C). For Au₅Ag₁₁, only the T₁ state lies below the S₁ state, with a relatively larger ΔE_ST between S₁ and T₁ (0.034 eV) than that of Pt₁Ag₁₆ (the ΔE_ST between S₁ and T₂ is about 0.002 eV), resulting in a small ISC rate constant that favors radiative emission as fluorescence. In contrast, in Pt₁Ag₁₆, the S₁ and T₂ states are nearly degenerate (ΔE ≈ 0.002 eV), which promotes an efficient ISC from S₁ to T₂. This facilitates an efficient S₁ → T₂ → T₁ → S₀ decay pathway, ultimately leading to phosphorescence.¹³⁶

(3) Size effects: in a theoretical study of one-dimensional ultrathin rod-like ligand-protected gold nanoclusters (Au₂₄, Au₄₂, and Au₆₀), Luo and co-workers combined rate-constant calculations with multistate model analysis (Fig. 11B).⁵² They showed that the size indirectly controls the emission type by modulating the SOC effect. The smaller Au₂₄ cluster exhibits dual fluorescence, attributable to substantial excited-state structural distortion that creates two minima (S₁-MIN1 and S₁-MIN2) on the S₁ potential energy surface. These minima yield large ΔE_ST values (0.5 eV and 0.81 eV, respectively), which render ISC negligible. By contrast, for the longer rod-like clusters Au₄₂ and Au₆₀, the large transition dipole moments lead to fluorescence radiative rates (1.13 × 10⁸ s⁻¹ and 1.71 × 10⁸ s⁻¹, respectively) comparable to ISC rates (1.23 × 10⁸ s⁻¹ and 8.68 × 10⁸ s⁻¹, respectively). Together with larger ΔE_ST values (0.39 eV and 0.57 eV) that suppress RISC, the result is dual emission comprising fluorescence and phosphorescence.

(4) Ligand substituent effects: rate-constant calculations were performed on chiral Au(I)Cu(I) clusters protected by NHC ligands (R/S-py-X and R/S-ql-X, X = Cl, Br, I) to investigate the effect of the halide substituent (Fig. 13).¹³³ The results show that as the halogen atomic mass increases, the ΔE_ST(S₁–T₁) narrows systematically (Fig. 13A): the R-ql-Cl cluster (0.294 eV), R-ql-Br cluster (0.193 eV), and R-ql-I cluster (0.116 eV). This narrowing of the ΔE_ST(S₁–T₁) corresponds to an increase in the RISC rate constant: R-ql-I (7.05 × 10¹⁰ s⁻¹) > R-ql-Br (4.22 × 10⁹ s⁻¹) > R-ql-Cl (5.49 ×10⁸ s⁻¹). Consequently, the R-ql-I cluster exhibits the most efficient TADF owing to its minimal ΔE_ST(S₁–T₁).

Fig. 13 (A) Energy diagram of R-ql-Cl, R-ql-Br, and R-ql-I indicating TADF and phosphorescence emission processes. (B) The hole and electron pairs for S₁/S₀ and T₁/S₀ transitions were obtained by NTO analysis at the optimized S₁ and T₁ geometries of R-ql-Cl, R-ql-Br, and R-ql-I (isovalue of 0.02). Au, yellow; Cu, brown; N, dark blue; C, gray; Cl, blue; Br, green; I, light purple; H, white. Reproduced with permission.¹³³ Copyright 2023, Springer Nature.

In summary, recent studies establish that SOC, ISC, and RISC are pivotal in determining the photoluminescence of metal nanoclusters. The interaction between singlet and triplet states, which is quantified by SOCMEs and the ΔE_ST, governs the competition among fluorescence, phosphorescence, and TADF, thereby shaping the quantum yield and lifetime. Structural factors, including cluster architecture, heteroatom doping, ligand identity and rigidity, and heavy-atom contributions, tune SOCMEs and ΔE_ST and also modulate nonradiative channels, producing outcomes ranging from single-channel emission to dual emission. These insights underscore the need for multistate, rate-constant-based models that explicitly incorporate triplet states to explain and predict the diverse luminescent behaviors of metal nanoclusters.

4.3 Excited-state relaxation and nonradiative dynamics

Excited-state relaxation dynamics directly determine the cluster's excited-state lifetime and PLQY. These dynamics comprise IC and ISC among excited states, structural relaxation, charge transfer, and electron–hole recombination. Because such processes are not directly observable at the atomic scale, combining NA-MD with DFT/TDDFT enables atomistic elucidation of relaxation pathways, timescales, and nonradiative channels. Current research has successfully revealed how the ligand, metal core structure, and doping effects influence these excited-state relaxation dynamics.

By modifying the energy gap and orbital interactions, ligands regulate relaxation rates. TDDFT and NA-MD on Au₂₅(SR)₁₈⁻ showed that internal relaxation among high-lying singlets (S₆ → S₁) occurs on a sub-picosecond timescale, whereas the final S₁ → S₀ decay is about two orders of magnitude slower.¹²⁶ Comparing Au₂₅(SR)₁₈⁻ with different R groups (R = CH₃, C₂H₅, C₃H₇, MPA, PET) (MPA = mercaptopropionic acid) revealed S₁–S₆ relaxation times of 2–18 ps, with MPA producing distinctive dynamics due to a narrower LUMO+1–LUMO+2 gap.¹³⁷ For the phosphine-ligated Au₁₃(dppe)₅Cl₂³⁺, which shares the Au₁₃ core, NA-MD indicated a slower excited-state decay (0.5–20.3 ps) than in thiolate-protected Au₂₅(SR)₁₈⁻, consistent with its larger HOMO–LUMO gap.¹³⁸ TDDFT and NA-MD on Au₃₈(SR)₂₄ further identified low-frequency vibrations, such as the 24.2 cm⁻¹ bending mode, as key channels for electron–phonon coupling and nonradiative decay,¹³⁹ a behavior also observed in Au₁₈(SH)₁₄.¹⁴⁰ Notably, NA-MD simulations on Au₂₅(SR)₁₈⁻ by Xie et al. revealed that low-frequency modes, particularly the breathing and stretching modes of Au(core)–Au(core) and Au(core)–Au(ring), are strongly coupled to the electronic transitions.¹²⁷ More recent NA-MD work shows that ligands can also modulate carrier lifetimes by altering SOC.¹²⁹ For example, thiolate-protected Au₂₅(SR)₁₈⁻ relaxed in 99 fs, compared with 132 fs for the diphosphine-protected Au₁₃³⁺ cluster.¹³⁸

Studies of Au₃₀(SR)₁₈, Au₃₆(SR)₂₄, Au₃₈S₂(SR)₂₀, and Au₄₄(SR)₂₈ demonstrate that core stacking adjusts excited-state relaxation.¹⁴¹ Au₃₀(SR)₁₈ with a HCP core exhibits stronger electron–phonon coupling than Au₃₈S₂(SR)₂₀ with a body-centered cubic (BCC) core, resulting in a shorter lifetime. Additionally, nonadiabatic relaxation also depends on dopants.¹⁴² Yu et al. combined DFT with time-domain NA-MD to examine single-atom doping in MAu₂₄(SR)₁₈ (M = Pd, Pt, Cd, Hg), showing that dopants co-regulate relaxation through changes in the gap, phonon spectrum, and electron–phonon coupling strength.¹⁴³ In diphosphine-ligated M@Au₁₂ clusters, Ir doping enhances core–shell coupling and suppresses recombination, thereby extending the lifetime and confirming the dynamical impact of doping.¹⁴⁴

Overall, real-time NA-MD based on DFT and TDDFT has become indispensable for resolving the excited-state dynamics of ligand-protected gold nanoclusters. These simulations show that larger electronic gaps lengthen lifetimes, stronger electron–phonon coupling accelerates nonradiative decay, and low-frequency vibrations critically mediate energy dissipation. Moreover, subtle structural variations, including isomerism¹⁴⁵ and single-atom doping, can markedly reshape relaxation behavior and photophysical properties.

5. Conclusions and outlook

In this review, we summarize recent experimental advances in enhancing the PLQY of ligand-protected gold nanoclusters, with emphasis on strategies that promote radiative decay and suppress nonradiative pathways. Experimentally, increasing the radiative rate constant via HOMO–LUMO gap engineering, achieved through heterometal doping to widen the HOMO–LUMO gap and through enhancement of transition dipole moments, has proven highly effective. Suppressing nonradiative relaxation by rigidifying and constraining ligand motion in core–shell structures has likewise yielded substantial gains in quantum efficiency. Nevertheless, a deeper mechanistic understanding of how transition dipole moments are enhanced is still needed to further improve radiative efficiency. In addition, most ligand-protected gold nanoclusters are soluble only in organic solvents, limiting biomedical applications; consequently, simple and general strategies to convert organo-soluble clusters into water-soluble forms are highly desirable.⁶⁴

Theoretically, DFT/TDDFT methods and NA-MD have clarified photoluminescence origins, complex excited-state dynamics, and emission pathways—fluorescence, phosphorescence, TADF, and dual emission—governed by ΔE_ST, SOCMEs, and structural relaxation. Even so, improving the computational efficiency of excited-state optimizations and vibrational analyses remains essential, particularly for large clusters.^146,147 Computing radiative and nonradiative rate constants has deepened the understanding of competing decay channels, yet accurately predicting PLQYs is still challenging. Looking ahead, multiscale modeling that incorporates environmental effects such as solvent and matrix interactions will provide more realistic descriptions.^66–70 Moreover, machine-learning approaches trained on high-level quantum-chemical data promise to accelerate the discovery and screening of ligands, dopants, and structural motifs with desirable photophysical properties.^148–154

Author contributions

All authors contributed to writing and editing this article.

Conflicts of interest

There are no conflicts to declare.

Data availability

No primary research results, software or code have been included and no new data were generated or analysed as part of this review.

Acknowledgements

The authors acknowledge financial support from NSFC (22373082), the science and technology innovation program of Hunan Province (2023RC1055), the project of innovation team of the ministry of education (IRT_17R90), and the Scientific Research Fund of Hunan Provincial Education Department (22B0154).

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