Three-atom-wide gold quantum rods with periodic elongation and strongly polarized excitons

Significance

Ultrasmall gold nanoparticles (e.g., comprising only dozens of atoms per core) become nonmetallic due to strong quantum size effects, manifested in the disappearance of plasmon excitation and emergence of multiple excitons in the optical absorption spectrum. While this plasmon-to-exciton transition has been clear in spherical particles, it remains unclear in non-spherical (or anisotropic) cases such as rods. In early theory, plasmon-like features in quantum rods (QRs) of gold were predicted but there has been no experimental success yet. In the current work, we have experimentally attained a periodic series of gold QRs (Au₄₂ to Au₁₁₄ protected by the same thiolate), which exhibit unusual optical properties and shed light on the theoretical prediction more than a decade ago.

Abstract

Atomically precise control over anisotropic nanoclusters constitutes a grand challenge in nanoscience. In this work, we report our success in achieving a periodic series of atomically precise gold quantum rods (abbrev. Au QRs) with unusual excitonic properties. These QRs possess hexagonal close-packed kernels with a constant three-atom diameter but increasing aspect ratios (ARs) from 6.3 to 18.7, all being protected by the same thiolate (SR) ligand. The kernels of the QRs are in a Au₁–(Au₃)_n–Au₁ configuration (where n is the number of Au₃ layers) and follow a periodic elongation with a uniform Au₁₈(SR)₁₂ increment consisting of four Au₃ layers. These Au QRs possess distinct HOMO–LUMO gaps (E_g = 0.6 to 1.3 eV) and exhibit strongly polarized excitonic transition along the longitudinal direction, resulting in very intense absorption in the near-infrared (800 to 1,700 nm). While excitons in gapped systems and plasmons in gapless systems are distinctly different types of excitations, the strongly polarized excitons in Au QRs surprisingly exhibit plasmon-like behaviors manifested in the shape-induced polarization, very intense absorption (~10⁶ M⁻¹ cm⁻¹), and linear scaling relations with the AR, all of which resemble the behaviors of conventional metallic-state Au nanorods (i.e., gapless systems), but the QRs possess distinct gaps and very long excited-state lifetimes (10 to 2,122 ns), which hold promise in applications such as near-infrared solar energy utilization, hot carrier generation and transfer. The observation of plasmon-like behaviors from single-electron transitions in Au QRs elegantly bridges the distinct realms of single-electron and collective-electron excitations and may stimulate more research on excitonics and plasmonics.

Exciton (i.e., single-electron transition in a gapped system) and plasmon (i.e., collective-electron excitation in a gapless system) are two distinctive types of excitation in materials. The plasmon excitation, as a collective and coherent oscillation of conduction electrons, imparts metal nanostructures (1–4) such as gold nanoparticles (Au NPs) and doped semiconductor quantum dots (5) (e.g., Cu_2−xSe) with elegant optical properties, which have attracted multidisciplinary scientific interest. Among the plasmonic metals, Au NPs (e.g., 5 to 100 nm) have been extensively pursued. As the dimensions of Au NPs decrease to a critical threshold, e.g., ~2.2 nm, the surface plasmon resonance (SPR) vanishes due to an evolution from metallic to nonmetallic state and the electronic structure quantization (6, 7). These ultrasmall Au NPs, called nanoclusters (NCs), display discrete energy levels and multiple optical absorption peaks of excitonic nature (8, 9). The plasmon-to-exciton transition has been clear in spherical particles, (7, 9) but it remains unclear in non-spherical (or anisotropic) cases. In theoretical work, single-electron transition between HOMO–LUMO in ultrasmall Au and Ag quantum rods (QRs) has been computationally proved to induce plasmonic behaviors (10), such as the redshift of the longitudinal excitation with increasing aspect ratio (AR) (11). Apparently, classical electrodynamics can no longer describe such quantum systems. From a quantum mechanical perspective, multiple criteria have been put forth for defining the plasmon in such QRs (12–15), but there are conflicting classifications of the longitudinal excited states of the QRs when using either collectivity or transition dipole moments as the criteria (16, 17). In some work, the electron–electron interaction scaling parameter was used for identifying the plasmon nature against single-electron transitions (18). It is noteworthy that all the calculations and criteria were based on bare QRs (without ligand protection) (19, 20), which are not possible for experimental testing, and the structures of bare QRs are difficult to obtain. Other than metal systems, plasmon research has also extended to the doped quantum dots (e.g., Ag₂Se and Cu₂Se QDs) (5), which exhibit plasmons in the infrared region when a sufficient number of carriers are doped into the quantized band (21). In both metal and semiconductor systems, some fundamental questions are i) whether few-carrier quantum systems can exhibit SPRs (21), and ii) how the particle shape (e.g., QRs) affects the quantized electronic transition (8). We aim to synthesize ligand-protected QRs with well-defined structures to investigate the potentially unusual excitonic or plasmonic behavior of peculiar quantum systems (10, 11), which may reconcile the existing discrepancies in theory (10–20) and shed light on the profound exciton–plasmon relationship.

Here, we report a periodic series of atomically precise Au QRs with a constant three-atom diameter and varying AR from 6.3 to 18.7, including Au₄₂(PET)₃₂, Au₆₀(PET)₄₄, Au₇₈(PET)₅₆, Au₉₆(PET)₆₈, and Au₁₁₄(PET)₈₀, where PET = 2-phenylethanethiolate. These ultrasmall Au QRs possess hexagonal-close packed (hcp) kernels in a Au₁–(Au₃)_n–Au₁ configuration (where n is the number of Au₃ layers) and follow a periodic elongation by four Au₃ layers. The optical spectra of these Au QRs (with E_g = 0.6 to 1.3 eV) exhibit an absorption peak in the visible region and an intense peak in the near-infrared (NIR) that is tunable by the AR, akin to their larger plasmonic nanorods (e.g., >10 nm). Theoretical simulations reveal that the longitudinal NIR peak arises from the HOMO–LUMO transition and is strongly polarized. The NIR peak wavelength and strong absorption coefficient exhibit linear scaling relations with the AR, in agreement with the behaviors of conventional nanorods, but the Au QRs have much longer excited-state lifetimes (10 to 2,122 ns). Such unusual behaviors in Au QRs reveal profound relationships between single- and collective-electron excitations in peculiar quantum systems. These Au QRs hold promise in NIR solar energy utilization, quantum emitting, and optoelectronic applications.

Results and Discussion

The series of Au QRs was synthesized by an optimized NHC-mediated method (NHC = N-heterocyclic carbene), (22) which involved two primary steps: 1) the production of insoluble Au(I)-SR polymers and 2) the subsequent reduction of Au(I)-SR using sodium borohydride (see SI Appendix, Fig. S1 for details). Five Au NCs were separated by thin-layer chromatography, which were further extracted with dichloromethane to obtain pure products (Fig. 1A and SI Appendix, Fig. S2). Electrospray ionization mass spectrometry (ESI-MS) analyses of these five products show peaks corresponding to [Au₄₂(PET)₃₂+2Cs]²⁺, [Au₆₀(PET)₄₄]²⁺, [Au₇₈(PET)₅₆]⁴⁺, [Au₉₆(PET)₆₈]⁴⁺, and [Au₁₁₄(PET)₈₀]⁴⁺ (Fig. 1 B–F), note: the charges are caused by ESI. The experimental isotope patterns match well with the calculated patterns, confirming the formulas of these five NCs. The experimental isotope patterns generally match well with the calculated ones, confirming the formulas of the five NCs. The slight deviation (<1 amu) in [Au₄₂(PET)₃₂+2Cs]²⁺ and [Au₇₈ (PET)₅₆]⁴⁺ should be caused by the low signal-to-noise ratio of the peaks. Among these five NCs, a constant mass increment corresponding to Au₁₈(PET)₁₂ was observed, hinting at a recurring structural evolution (vide infra), i.e., a periodic series.

Fig. 1.

(A) Thin-layer chromatography separation (Upper part) of Au₄₂(PET)₃₂, Au₆₀(PET)₄₄, Au₇₈(PET)₅₆, Au₉₆(PET)₆₈, and Au₁₁₄(PET)₈₀ from the product mixture, and the photographs (Lower part) of purified Au QRs dissolved in DCM. (B–F) ESI mass spectra (Upper parts) of Au₄₂(PET)₃₂, Au₆₀(PET)₄₄, Au₇₈(PET)₅₆, Au₉₆(PET)₆₈, and Au₁₁₄(PET)₈₀, with the Lower parts showing the experimental isotope patterns of [Au₄₂(PET)₃₂+2Cs]²⁺ (m/z at 6464.81), [Au₆₀(PET)₄₄]²⁺ (m/z at 8927.96), [Au₇₈(PET)₅₆]⁴⁺ (m/z at 5762.18), [Au₉₆(PET)₆₈]⁴⁺ (m/z at 7059.90), [Au₁₁₄(PET)₈₀]⁴⁺ (m/z at 8357.99), and the simulated patterns (black).

The structures of Au₄₂ and Au₆₀ were solved by X-ray crystallography. The Au₄₂ QR possesses a rod-shaped hcp Au₂₀ kernel comprising six layers of Au₃ stacked in an a-b-a-b-a-b manner, with two more Au atoms capping the two ends (i.e., Au₁–(Au₃)₆–Au₁) (Fig. 2 A, Left) (22, 23). The two ends of the Au₂₀ kernel are protected by two pairs of interlocked Au₄(PET)₅ motifs exhibiting a ∼90° rotation relative to each other (marked in green and light green), and the body of the kernel is further protected by six monomeric Au(PET)₂ motifs (marked in icy blue). Here, we further determined the structure of Au₆₀ by growing single crystals, followed by X-ray crystallography analysis (SI Appendix, Table S1). Similar to Au₄₂, Au₆₀ also exhibits a rod-shaped structure consisting of an Au₃₂ kernel with ten Au₃ layers arranged in a hcp pattern, and two more Au atoms cap the two ends, forming a Au₁–(Au₃)₁₀–Au₁ sequence (Fig. 2 A, Right). Two pairs of interlocked Au₄(PET)₅ motifs shield the two ends of the kernel, and 12 Au(PET)₂ motifs are attached to the body of the kernel. A detailed comparison between Au₄₂ and Au₆₀ unveils a distinct evolution in the structural elongation. Compared to Au₄₂, the kernel of Au₆₀ comprises four extra Au₃ layers (marked in violet, Fig. 2A) encircled by six Au(PET)₂ motifs, which forms the Au₁₈(PET)₁₂ elongation unit (Fig. 2B and SI Appendix, Fig. S3). This elongation unit is consistent with the mass difference observed in ESI-MS analysis. Therefore, Au₆₀ is an elongated version of the Au₄₂ structure along the long axis.

Fig. 2.

(A) Illustration of the structural evolution from Au₄₂ to Au₆₀. (B) Twelve Au(PET)₂ motifs wrapping the Au₃₂ kernel of Au₆₀ along the C₃ axis. (C) Structure schematic of Au₄₂, Au₆₀, Au₇₈, Au₉₆, and Au₁₁₄ with kernel length ranging from 19.76 to 58.79 Å. Color code: yellow = S, other colors = Au, carbon tails are omitted for clarity.

Based on the two determined rod structures, the constant mass difference, and similar optical spectral features of the QR series, we infer that Au₇₈, Au₉₆, and Au₁₁₄ should be further elongated structures along the long axis, with one, two, and three more Au₁₈(PET)₁₂ elongation units added to the Au₆₀, respectively (Fig. 2C and SI Appendix, Figs. S4–S6). The rod-shaped kernels of Au₄₂, Au₆₀, Au₇₈, Au₉₆, and Au₁₁₄ share the same radius (3.15 Å, for a circle of Au₃ atomic centers), whereas the length exhibits a step-wise increase from 19.76 Å for Au₄₂ to 29.38 Å for Au₆₀, 39.02 Å for Au₇₈, 48.87 Å for Au₉₆, and 58.79 Å for Au₁₁₄. Therefore, the ARs of the kernels for Au₄₂, Au₆₀, Au₇₈, Au₉₆, and Au₁₁₄ are 6.3, 9.3, 12.4, 15.5, and 18.7, respectively. Such slender QRs (with AR > 10) are quite rare yet sufficiently stable (SI Appendix, Fig. S7). The ARs of conventional Au NRs are typically below 10.

The optical absorption spectra of the five QRs are shown in Fig. 3A and SI Appendix, Figs. S8–S12. All QRs exhibit an absorption peak at ~400 nm (nearly constant) and an intense NIR-absorption peak that is AR-dependent, resembling the spectra of conventional Au nanorods (e.g., >10 nm) (1 to 3). Specifically, the NIR peaks of QRs are located at 806 nm (molar absorption coefficient ε = 1.08 × 10⁵ M⁻¹ cm⁻¹) for Au₄₂, 1,076 nm (ε = 2.97 × 10⁵ M⁻¹ cm⁻¹) for Au₆₀, 1,310 nm (ε = 6.08 × 10⁵ M⁻¹ cm⁻¹) for Au₇₈, 1,528 nm (ε = 9.06 × 10⁵ M⁻¹ cm⁻¹) for Au₉₆, and 1,727 nm (ε = 7.28 × 10⁵ M⁻¹ cm⁻¹) for Au₁₁₄ (SI Appendix, Figs. S13–S17). The strong NIR-absorption is exceptional given the ultrasmall sizes of these QRs [c.f., ε = 10^3–4 M⁻¹ cm⁻¹ for typical NCs (8), which are two orders of magnitude lower]. While previous work reported rod-shaped NCs, such as Au₃₇ (i.e., a linear assembly of three icosahedral Au₁₃ units via vertex sharing, AR~3) (24), their low ARs did not lead to similar features as in the current QRs. We further determined the optical gap (E_g) of Au₄₂ (1.33 eV), Au₆₀ (1.01 eV), Au₇₈ (0.81 eV), Au₉₆ (0.69 eV), and Au₁₁₄ (0.60 eV) by extrapolating absorbance to zero (SI Appendix, Figs. S8–S12). The E_g values display a declining tendency as the number of gold atoms increases (SI Appendix, Fig. S18). The observed size-dependent E_g can be well reproduced by the Schrödinger equation for 1D “particle in a box” (Fig. 3B), consistent with the linearly elongated structures. Furthermore, the E_g of Au QRs at the infinite length is estimated to be 0.20 eV by the 1D particle-in-a-box model.

Fig. 3.

(A) Optical absorption spectra of Au QRs (dissolved in deuterated chloroform to avoid overtone vibrational peaks in the NIR range). The error bars of the NIR peak positions for Au₄₂, Au₆₀, Au₇₈, Au₉₆, and Au₁₁₄ are 0.2, 0.2, 0.3, 0.1, and 0.1 nm, respectively. (B) Fitting of optical gaps by the Schrödinger equation for the 1D particle in a box; L: the length of Au QRs, n: the energy level, m: electron mass.

To understand the nature of the strong NIR absorption observed in ultrasmall Au QRs, DFT and TD-DFT calculations (25, 26) were performed to simulate their electronic structure and optical absorption spectra. To reduce the computational demand, we simplified the ligands on Au₄₂ as -SCH₃ and those on Au_60/78/96 as -SH; this is widely adopted in the DFT analysis of NCs (25, 26). Note: the Au₁₁₄ was not simulated due to its very large size and being computationally intractable in our attempts. As shown in Fig. 4 A–D, the experimental spectral profiles and peak positions of Au_42/60/78/96 are well reproduced by TD-DFT calculations, with the simulated NIR absorption peaks of Au_42/60/78/96 being at 1.63, 1.30, 1.08, and 0.91 eV, respectively (~0.1 eV deviated from experiment). The NIR peaks are almost entirely (96 to 99%) contributed by the HOMO–LUMO transitions in Au₄₂ to Au₉₆. The orbitals are presented in Fig. 4E; it is evident that the HOMO and LUMO orbitals of all Au QRs are primarily localized on the kernels and extend along the z-axis. Moreover, the transition dipole moments, which are related to the absorption peaks, exhibit a much stronger magnitude along the z axis, nearly an order of magnitude larger than those on the x and y axes (SI Appendix, Table S2), indicating that i) the HOMO–LUMO transition is split into radial and longitudinal components due to the rod shape, which is akin to the splitting of SPR in conventional Au nanorods (NRs) (1 to 3) and ii) the HOMO–LUMO transition occurs predominantly along the long axis (i.e., highly polarized transition), which is similar to that of conventional Au NRs.

Fig. 4.

Experimental absorption spectra (black lines) of (A) Au₄₂(PET)₃₂, (B) Au₆₀(PET)₄₄, (C) Au₇₈(PET)₅₆, and (D) Au₉₆(PET)₆₈, and TDDFT-simulated absorption spectra (violet lines) of Au₄₂(SCH₃)₃₂, Au₆₀(SH)₄₄, Au₇₈(SH)₅₆, and Au₉₆(SH)₆₈. (E) The HOMO and LUMO orbitals of Au₄₂(SCH₃)₃₂, Au₆₀(SH)₄₄, Au₇₈(SH)₅₆, and Au₉₆(SH)₆₈. The % value represents the proportion of the HOMO–LUMO transition in the simulated NIR peak. The x/y/z axes on the right represent the orientations of Cartesian coordinates, corresponding to the directions of electric transition dipole moments from the ground to the excited state, with the values on these axes denoting the magnitude of the electric transition dipole moment transitioning from the ground state to an excited state.

A strong transition dipole moment is a prerequisite for an excited state to display plasmonic behavior. The series of ultrasmall Au QRs exhibit significantly higher oscillator strength (f), e.g., f = 1.05 for Au_42, in comparison to f = 4.536 × 10^–4 for spherical [Au₂₅(SH)₁₈]⁻) (26). The large f values are consistent with the high absorption coefficients observed experimentally for the Au QRs. To understand the enhanced oscillator strengths, we further analyzed the hole–electron distributions to ascertain the characteristics of the S₁ (NIR) state (the lowest excited state). The distributions of hole and electron for the S₀→S₁ excitation at the optimized S₀ geometry of each QR are shown in SI Appendix, Fig. S19. Interestingly, a substantial overlap between the hole and electron was found in the S₀→S₁ transition as indicated by a Sr index (27) ( $\mathrm{S}\mathrm{r} =\int \sqrt{{\rho }^{\mathit{hole}}\left(\mathit{r}\right) {\rho }^{\mathit{ele}}\left(\mathit{r}\right)}d\mathit{r}$ ), for example, Au₄₂ with Sr = 0.73. This result suggests that the distribution of electron remains largely unchanged after excitation, which is indicative of a local excitation feature (D = 0.011 Å, where D is a metric that measures the distance between the electron and the hole after excitation), thus, it gives rise to a high oscillator strength in Au₄₂. As the AR of the Au QRs increases, the overlap between electron and hole intensifies, hence, the higher f values (SI Appendix, Fig. S20A), and the integral of μ_S0→S1 = <S₀|−r|S₁> escalates, reinforcing the transition dipole moment between electronic states. Meanwhile, the ellipticity of the contour surface of electron and hole is amplified, which implies a stronger electronic transition along the longitudinal axis compared to other directions, leading to an anisotropic oscillation that is reminiscent of plasmon splitting in metallic nanorods.

The computed orbital diagrams are shown in Fig. 5A, in which the HOMO–LUMO gaps of Au QRs shrink as the AR increases, while the oscillator strength along the z-axis and the ratio of longitudinal-axis to transversal-axis transition dipole moments show an increasing trend (SI Appendix, Table S2). These observations show that the electronic transition becomes progressively confined to the longitudinal axis. Additionally, a linear relationship is observed between the HOMO–LUMO gap and the AR (Fig. 5B). The oscillator strength also shows a linear dependence on the AR (SI Appendix, Fig. S20A) and so is the computed NIR absorption peak (SI Appendix, Fig. S20B), thus the computed trends are consistent with experiment.

Fig. 5.

(A) Kohn–Sham orbital energy level diagrams of Au₄₂, Au₆₀, Au₇₈, and Au₉₆. (B) The HOMO–LUMO gap vs. the AR. (C) Variation of longitudinal extinction peak for simulated Au nanorods (diameter =10 nm, ARs from 2 to 20) (28) and ultrasmall Au QRs as the AR increases. (D) Variation of extinction coefficient for Au nanorods and ultrasmall Au QRs as the AR increases. (E) The ns-TA kinetics at 400 nm excitation and corresponding fits of Au₄₂, Au₆₀, Au₇₈, Au₉₆, and Au₁₁₄. (F) The E_g gap–dependent excited state lifetimes of Au₄₂, Au₆₀, Au₇₈, Au₉₆, and Au₁₁₄ (the error bars of excited state lifetimes are 71.8, 8.2, 4.5, 1.9, and 0.7 ns, respectively).

The plasmon-like behavior of the Au QRs is also manifested in several scaling relationships. It is well known that conventional Au NRs show two distinctive SPRs due to the anisotropic shape, i.e., the transverse SPR and the longitudinal one (1–3, 29). The latter peak position exhibits a linear increase from the visible to NIR with increasing AR (30–33), and the extinction coefficient of the longitudinal SPR also shows a linear enhancement with increasing AR. However, the ARs of plasmonic Au NRs with extinction coefficients reported are no more than 10 (28, 34, 35). Thus, in order to do a comparison with the high ARs (6 to 18.7) of our ultrasmall Au QRs, we employed Finite-Difference Time-Domain (FDTD) calculations (36) to calculate the optical spectra of plasmonic Au NRs (fixed diameter of 10 nm and increasing AR from 2 to 20) to remediate the insufficiency of available data of conventional Au NRs. As displayed in Fig. 5C and SI Appendix, Fig. S21, a linear relationship is seen in plasmonic Au NRs, even with AR reaching 20. This linear correlation between the peak wavelength and AR also remains valid in the five ultrasmall Au QRs (Fig. 5C), suggesting a common feature between the classical rods and QRs. Additionally, a linear correlation between the extinction coefficient of the longitudinal SPR and the AR of plasmonic Au NRs (28) (Fig. 5 D, Left) is also observed in ultrasmall Au QRs (Fig. 5 D, Right), except for Au₁₁₄; note that the declined absorption coefficient of Au₁₁₄ is not yet understood since its TD-DFT simulation is very challenging and thus not pursued. The absorption coefficients per Au atom for the QRs and conventional NRs are roughly on the same order of magnitude (10³ to 10⁴) (SI Appendix, Fig. S22). Furthermore, the longitudinal SPR peak position of plasmonic Au NRs is known to depend on the refractive index (RI) of the surrounding medium, and a linear dependence is seen as the RI increases. (35, 37) In the Au QRs, one can also observe a linear dependence (SI Appendix, Figs. S23–S27), albeit the sensitivity is less (Table 1). Taken together, all the scaling relations suggest that the five Au QRs possess plasmon-like characteristics when compared with the conventional Au NRs.

Table 1.

RI sensitivity of the longitudinal peak of Au QRs

Sample	AR	RI Sensitivity (peak shift/RI variation)
Au42	6.3	24.1
Au60	9.3	62.7
Au78	12.4	103.5
Au96	15.5	134.8
Au114	18.7	201.4

To further probe the electronic properties of these ultrasmall Au QRs, we investigated the excited-state dynamics using time-resolved optical spectroscopy. The overall excited-state lifetimes of these Au QRs can be obtained by conducting nanosecond transient absorption spectroscopy, as detailed in SI Appendix, Figs. S28–S33. A notable observation is the exponential decrease in the excited-state lifetime of Au QRs with shrinking E_g (Fig. 5 E and F and SI Appendix, Fig. S34), which agrees with the energy gap law (38); note that the optical gap is the same as the HOMO–LUMO gap based on the DFT analysis of these Au QRs. Furthermore, we found that the exciton lifetime (2,122 ns) of Au₄₂ is ~212 times longer than that of Au₁₁₄ (10 ns), indicating a significant intensification of intramolecular interactions within the Au₁₁₄ due to its significant elongation. Additionally, this series of Au QRs displayed fluence-independent dynamics in the femtosecond transient absorption (SI Appendix, Fig. S35), which is in contrast with conventional Au NRs that are metallic and exhibit fluence-dependent dynamics (2, 5, 9). The fluence-independent electron dynamics in the QRs is due to the presence of E_g (1.33 to 0.6 eV for Au₄₂ to Au₁₁₄), albeit these Au QRs show plasmon-like behaviors. Therefore, the Au QRs present some major differences from the classical plasmons in gapless systems, such as the less sensitivity to refractive-index changes and the long excited-state lifetimes of Au QRs. It is noteworthy that the excited state lifetimes of these ultrasmall Au QRs range from 10 to 2,122 ns and are significantly longer than those of metallic-state Au NRs (~hundreds of femtoseconds) (5, 39), which highlights the potential of Au QRs in NIR solar energy conversion and NIR photocatalysis applications. In addition, such Au QRs may act as NIR quantum emitters for quantum information telecommunications.

The observation of plasmon-like behavior in Au QRs is intriguing. On the other hand, such QRs possess distinct HOMO–LUMO gaps, thus the electronic excitations in QRs exhibit some important differences from the classical SPRs in conventional NRs. Here, it is also worth comparing with the plasmons of self-doped QDs in the infrared region (5, 21, 40, 41), such as the doped Ag₂Se QDs (41). The Au QRs and Ag₂Se QDs both show a femtosecond-order dephasing time and possess quality factors of about 10, SI Appendix, Table S3. Future work may reveal more insights into the intriguing behavior of the Au QRs.

Conclusion

In summary, this work demonstrates that single-electron transition in molecular-state Au QRs (E_g = 0.6 to 1.33 eV) may exhibit plasmon-like behavior, manifested in several aspects, including the strongly polarized longitudinal component due to the rod shape, the intense NIR peak (10^5–6 M⁻¹ cm⁻¹), and its linear scaling relations with the AR. The excited states of these ultrasmall Au QRs exhibit long lifetimes (10 to 2,122 ns), being significantly longer than that of the classical plasmons (i.e., hundreds of femtoseconds), which renders the QRs quite promising in applications that require long lifetimes of carriers, such as NIR photocatalysis and solar cells (42). The intriguing relationship between excitons and plasmons in such Au QRs and this periodic series of materials may present opportunities for future research in exciton-plasmon hybrids (4, 42), quantum optics (10), and NIR solar energy conversion applications (4).

Materials and Methods

Details of the synthesis and isolation of Au₄₂(PET)₃₂, Au₆₀(PET)₄₄, Au₇₈(PET)₅₆, Au₉₆(PET)₆₈, and Au₁₁₄(PET)₈₀ are provided in SI Appendix. Characterizations include the electrospray ionization mass spectrometry, optical absorption, femtosecond and nanosecond transient absorption, and single-crystal X-ray crystallography (see details in SI Appendix). Furthermore, DFT and TDDFT calculations were performed on ligand-simplified model NCs: Au₄₂(SCH₃)₃₂, Au₆₀(SH)₄₄, Au₇₈(SH)₅₆, and Au₉₆(SH)₆₈ with the Gaussian 16 package (note: Au₁₁₄(SH)₈₀ was not computationally tractable and thus not pursued). Finite-difference time-domain (FDTD) simulations of plasmonic Au nanorods (fixed 10 nm diameter and various ARs) were performed and compared with the Au QRs. SI Appendix, Figs. S1–S35 and SI Appendix, Tables S1–S5 are also provided in SI Appendix.

Supplementary Material

Appendix 01 (PDF)

Dataset S01 (CIF)

Data, Materials, and Software Availability

All study data are included in the article and/or SI Appendix.