Kernel–Surface Decoupling in 58-Electron ~100-Atom Thiolate-Protected Gold Nanoclusters: Mechanism of Surface-Controlled Relaxation from $Au_{103}S_2(S\text{-}Nap)_{41}$

The total structure of $Au_{103}S_2(S\text{-}Nap)_{41}$ (S-Nap = 2-naphthalenethiolate) showed that a bulky aromatic thiolate can rebuild the entire gold–thiolate surface — staple motifs and ligand supramolecular patterns — while leaving the $Au_{79}$ Marks-decahedral, 58-electron kernel of $Au_{102}(pMBA)_{44}$ untouched. With the kernel fixed, the HOMO–LUMO gap stayed near 0.45 eV but the excited-state lifetime dropped from >3 ns ($Au_{102}$) to 420 ps ($Au_{103}$), isolating the surface as the dominant control on relaxation. The open problem is to turn that single decoupling comparison into quantitative science: identify and quantify the microscopic channels by which specific Au–S interfacial arrangements and ligand–ligand interactions set excited-state relaxation pathways and lifetimes at fixed kernel, mapping out the respective roles of kernel and surface in determining the electronic and optical properties of these 58-electron clusters.

Background

Thiolate-protected gold nanoclusters $Au_n(SR)_m$ are molecules of precise formula and atomic structure, sitting between discrete gold complexes and plasmonic nanoparticles. They follow the 'divide and protect' architecture: a metallic kernel (a compact gold particle with decahedral, icosahedral, or face-centered-cubic packing) is coated not by bare facets but by oligomeric gold(I)–thiolate 'staple' motifs — curved units such as the monomeric $Au(SR)_2$, dimeric $Au_2(SR)_3$, and trimeric $Au_3(SR)_4$ — that bind to the kernel surface. In the superatom picture, the delocalized 6s electrons of the gold count as a shell filling (each thiolate withdraws one electron), so a cluster's stability correlates with closed shells; 58 electrons is one such closed-shell count. A 'Marks decahedron' is a decahedral nanoparticle shape truncated by reentrant {111} grooves, a common low-energy motif at this size. The landmark $Au_{102}(pMBA)_{44}$ structure (pMBA = p-mercaptobenzoic acid; Jadzinsky et al. 2007) revealed a $Au_{79}$ Marks-decahedral kernel with a 58-electron superatom configuration (Walter et al. 2008). For such clusters, femtosecond transient absorption (TA) spectroscopy — a pump–probe technique measuring excited-state populations — resolves successive relaxation steps: internal conversion (electronic relaxation to the lowest excited state), vibrational cooling, and final decay to the ground state. A long-standing question is which part of the cluster — kernel or surface — controls which observable. Higaki et al. (2017) synthesized $Au_{103}S_2(S\text{-}Nap)_{41}$, whose $Au_{79}$ Marks-decahedral kernel is the same as $Au_{102}(pMBA)_{44}$'s, while its surface differs substantially: on the cluster waist, six monomeric, one dimeric, and two trimeric staples (versus nine monomeric and two dimeric in $Au_{102}$), and 2-naphthalenethiolate ligands that self-organize into local tetramers through edge-to-face C–H···π and staggered π···π interactions; in the crystal these extend cluster-to-cluster into a herringbone-like zigzag chain along the needle axis. With the kernel held fixed, the optical and electrochemical HOMO–LUMO gaps (0.42 and 0.38 eV) match $Au_{102}$'s (~0.45 eV), while the TA lifetimes (2.0 ps internal conversion, 16.6 ps vibrational cooling, 420 ps excited-state decay at 480 nm pump, fluence-independent, i.e., molecular-like rather than metallic) are an order of magnitude shorter than $Au_{102}$'s reported >3 ns (measured, however, at different pump wavelengths: 400 and 600 nm). This single pair thus assigns the gap mainly to the kernel/electron count and the relaxation dynamics mainly to the surface — but only as a one-example correlation, without mechanism, without theory, and without known generality. Later work sharpened the surrounding landscape without closing the gap: Zhou et al. (2019, Science) showed carrier lifetimes vary by three orders of magnitude with kernel atomic packing (about 1 ns in hexagonal-close-packed $Au_{30}$ versus 4.7 μs in body-centered-cubic $Au_{38}$, both protected by the same ligand type) through wave-function overlap between $Au_4$ tetrahedral building blocks — a kernel channel; Zhou et al. (2019, JACS) classified 50–100-atom clusters as the regime where optical properties depend on both size and structure, while beyond ~100 atoms only size matters; Zhou et al. (2021) located the molecular-to-metallic transition near $Au_{279}$; $Au_{110}$ and $Au_{156}$ dynamics studies (2020, 2021) mapped size dependence; DFT/TDDFT on $Au_{317}(SR)_{110}$ (2022) showed few-hundred-atom ligand-protected clusters are computationally treatable; a deep-learning framework (CoLiM, 2026) began predicting core–ligand chemical compatibility before synthesis; and Gan et al. (2020) proved intercluster coupling (interparticle distance) strongly modulates photoluminescence in crystals. None of these isolates the ligand/Au–S interface at fixed kernel, and none predicts structure plus optical plus ultrafast observables for a cluster like $Au_{103}S_2(S\text{-}Nap)_{41}$.

Problem Statement

Starting from the established decoupling comparison $Au_{102}(pMBA)_{44}$ versus $Au_{103}S_2(S\text{-}Nap)_{41}$ (identical $Au_{79}$ Marks-decahedral 58-electron kernel, substantially different Au–S interfacial motif sets and ligand shell, similar HOMO–LUMO gap near 0.45 eV, but excited-state lifetimes differing by roughly an order of magnitude under non-identical measurement conditions), establish the decoupled roles of kernel and surface in ~100-atom thiolate-protected gold nanoclusters as a quantitative science. The objective is to replace the single-pair correlation with mechanism: identify and quantify the microscopic channels (electronic coupling between kernel states and surface/staple/ligand states, vibrational or phonon-mediated cooling channels, ligand-centered nonradiative decay) by which specific Au–S interfacial arrangements (monomeric/dimeric/trimeric staple compositions) and ligand–ligand interactions (C–H···π, π···π tetramers) determine excited-state relaxation pathways and lifetimes when the kernel is held fixed, explaining the kernel-to-surface relaxation pathway of electron dynamics revealed by the lifetime difference — that is, map out the respective roles of kernel and surface in determining the electronic and optical properties of these 58-electron clusters. Related open questions — whether ligand-driven, kernel-preserving surface tailoring generalizes to other thiolates, kernels, and sizes; whether predictive theoretical models of ligand-resolved structure and of optical/ultrafast observables can be built for such clusters; and whether the crystallographically observed intracluster tetramers and intercluster herringbone motifs persist in solution and surface assemblies rather than being crystal-packing artifacts — provide context for this mechanism question but are not themselves the stated objective.

A complete resolution of this mechanism question concerns the $Au_{102}$/$Au_{103}$ pair at fixed kernel: it must assign each observed transient-absorption component — the 2.0 ps internal conversion, the 16.6 ps vibrational cooling, and the 420 ps excited-state decay — together with the order-of-magnitude lifetime contrast with $Au_{102}$, to quantified channel contributions, stating for each channel class listed above whether it is dominant, minor, or negligible and giving a quantitative rate or coupling estimate for the channels that carry the decay; the listed channel classes are the candidate set to be assessed rather than an exhaustive checklist, and the resulting mechanism must be validated against the measured dynamics, either by reproducing or bounding the observed lifetimes within a stated factor or by furnishing an independently testable prediction that discriminates it from alternative explanations. Generalization of the quantified mechanism to other 58-electron, ~100-atom thiolate-protected clusters, and extension beyond excited-state relaxation to other electronic and optical properties, are desirable but not required for completion.

References

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