Theoretical prediction

Based on GUM, there is a potential two-dimensional growth pattern, in which the growth of gold kernels in thiolate-protected gold nanoclusters can be viewed as the sequent addition of elementary blocks (tetrahedral Au4 in this case) obeying duet rule21,28. As shown in Fig. 1, there are two types of face-centered cubic (fcc) growth pattern for the kernels of Au8n+4(SR)4n+8 (n = 3, 4, 5, 6) using Au4 building blocks. Starting from the predicted Au28(SR)20 (a3 in Fig. 1)22, two Au4 units are fused with the Au14 kernel of Au28(SR)20 (a3 in Fig. 1) by sharing two gold atoms to form a new Au20 kernel, resulting in two Au36(SR)24 isomers (b2 and b3 in Fig. 1). Continuing fusing two Au4 units with the Au20 kernel of Au36(SR)24 can form an Au44(SR)28 isomer with Au26 kernel (c2 in Fig. 1). Following the same way, two different Au32 kernels can be obtained to form two Au52(SR)32 isomers (d2 and d3 in Fig. 1). Among them, the d2 of Au52(SR)32 protected by 2-phenylethanethiol (denoted as PET) was experimentally determined33. In this work, as illustrated in Fig. 1, totally four new isomers for Au8n+4(SR)4n+8 series have been theoretically predicted based on GUM. The series follow the two-dimensional growth mode (green arrows in Fig. 1), which is completely different from the one-dimensional double-helical growth for old series (blue arrows in Fig. 1).

Fig. 1: The growth patterns of Au8n+4(SR)4n+8 (n = 3–6) nanoclusters.


The values in brackets are the relative energies (eV). Note that structures of a1/b1/c1/d1 (TBBT as ligand) and a2 (CHT as ligand) are experimentally determined. The arrows in blue and green denote the one-dimensional and two-dimensional growth, respectively. According to the relative energies, b2 of Au36(SR)24 and d2 of Au52(SR)32 are the most potential candidates among the predicted isomers. Color labels: green = S, blue/magenta/yellow = Au. The C and H atoms are omitted for clarity.

All the predicted isomers (–R group is replaced by –H) were fully optimized using DFT method implemented in the Gaussian 09 program package34, including the TPSS functional35 and the all-electron basis set 6–31 G* for H and S, effective-core basis set LANL2DZ for Au. Among the predicted isomers shown in Fig. 1, the isomer b2 of Au36(SR)24 is only 0.11 eV higher in energy than b1, implying that this structure may be stable and accessible. In addition, this cluster has a large HOMO–LUMO (HOMO/LUMO: the highest/lowest occupied/unoccupied molecular orbital) gap and all positive harmonic vibrational frequencies (Supplementary Table 1), indicating its thermal and chemical stability. Thus, it motivates us to synthesize this most potential candidate based on the GUM-guided prediction.

Synthesis and characterization

The b1 and b2 isomers in Au36(SR)24 can be simultaneously synthesized using a two-step size-focusing method when DMBT was selected as the protected ligand. The two nanoclusters were denoted as Au36(DMBT)24-1D and Au36(DMBT)24-2D according to the growth modes (vide infra). Electrospray ionization mass spectra (ESI-MS) showed the m/z 5192.02 peak with +2 charge for both nanoclusters (Supplementary Fig. 1), corresponding to [Au36(DMBT)24-2e]2+ (calculation: 5192.09 Da; deviation: 0.07 Da). The observed isotopic distributions were in perfect agreement with the simulated ones, further verifying the accurate formula of Au36(DMBT)24 nanoclusters.

Figure 2a showed the optical absorption spectra of Au36(DMBT)24. Au36(DMBT)24-2D exhibited the two-step peaks at 382 and 452 nm and two broad peaks at 678 and 792 nm, respectively, while Au36(DMBT)24-1D showed the two distinct peaks at 378 and 580 nm and one shoulder peak at 432 nm. The calculated UV-vis spectra of Au36(SH)24-2D and Au36(SH)24-1D were presented in Fig. 2b to reproduce the experimental results using linear response time-dependent density functional theory (TDDFT). The lowest 450 singlet-to-singlet excitation states were evaluated. As shown in Fig. 2b, the theoretical spectra can well reproduce the results of experimental measurements. Four absorption peaks (400, 480, 654, and 855 nm) for Au36(SH)24-2D and three absorption peaks (361, 425, and 559 nm) for Au36(SH)24-1D can be observed. Further examination of the Kohn–Sham (KS) molecular orbital (MO) energy levels and atomic orbital components in each KS MO of Au36(SH)24-2D and Au36(SH)24-1D indicate that the absorption peaks mainly involve the Au(sp) → Au(sp) transitions (Fig. 2c, d). Accordingly, the optical energy gaps were determined to be 1.36 eV for Au36(DMBT)24-2D and 1.71 eV for Au36(DMBT)24-1D based on the photon-energy scaled spectra (Supplementary Fig. 2), which were consistent with the corresponding calculated values of 1.31 and 1.74 eV (Supplementary Table 1).

Fig. 2: The optical absorption properties of Au36(DMBT)24 nanoclusters.


a Experimental UV-vis spectra of Au36(DMBT)24-2D and Au36(DMBT)24-1D. b Calculated UV-vis spectra of Au36(SH)24-2D and Au36(SH)24-1D. The values in the black or red are the wavelength (nm) corresponding to the absorption peaks. Molecular orbital (MO) energy level diagrams for c Au36(SH)24-2D and d Au36(SH)24-1D. The energies are in eV. Various colors are used to mark relative contributions (line length with color labels) of different orbitals. The major orbital contributions from the Au(6sp), Au(5d), and S(3p) are in olive, blue, and pink, respectively. The values in the black are the wavelength (nm) corresponding to the absorption peaks.

Single-crystal X-ray crystallography studies showed that Au36(DMBT)24-2D can be divided into a 20-atom gold kernel and eight external staple motifs (Figs. 3a and 4a). Twenty gold atoms in the kernel can be further viewed as two groups of Au4 tetrahedron which are arranged in a staggered mode, and this packing mode is in excellent agreement with the predicted two-dimensional growth (b2 in Fig. 1). The surface staple motifs can be divided into three categories: two monomeric Au1(SR)2, two trimeric Au3(SR)4, and four dimeric Au2(SR)3 (Figs. 3a and 4a). Note that both Au3(SR)4 and Au2(SR)3 staples are not in a plane (Supplementary Fig. 3). Alternatively, after cutting the gold atoms from Au1(SR)2 and Au3(SR)4 staples, the remaining 28 gold atoms can be constructed in a layer-by-layer fashion, which respectively consists of 6/8/8/6 atoms (Supplementary Fig. 4). This fashion is akin to a fcc structure of previously reported gold nanoclusters11,32,33.

Fig. 3: Crystal structures of the Au36(DMBT)24 nanoclusters.


Structural frameworks of a Au36(DMBT)24-2D and b Au36(DMBT)24-1D shown in tetrahedral Au4 networks. Color labels: yellow = S, blue/magenta/green = Au. The C and H atoms are omitted for clarity.

Fig. 4: Comparison of the Au36(DMBT)24 structures.


Structural frameworks of a Au36(DMBT)24-2D and b Au36(DMBT)24-1D shown in stacking mode. Color labels: yellow = S, blue/magenta/red = Au. The C and H atoms are omitted for clarity.

As the counterpart of Au36(DMBT)24-2D, Au36(DMBT)24-1D adopts a totally different configuration from Au36(DMBT)24-2D, although it owns a 20-Au-atom kernel as well. In fact, the helical tetrahedron in the Au36(DMBT)24-1D is along the one-dimensional growth (Figs. 3b and 4b), in contrast to Au36(DMBT)24-2D (Figs. 3a and 4a), which are excellently consistent with the growing modes of the predicted b1 and b2 of Au36(SR)24 nanoclusters (Fig. 1). Notably, the Au36(SR)24-1D and Au36(SR)24-2D can be described by superatom network (SAN) model26 with using the adaptive natural density partitioning (AdNDP) analysis36 on the Au208+ of both Au36(SR)24, which show the 12e valence electrons of Au36(SR)24 are equally distributed on six tetrahedral Au4 units, respectively (Supplementary Fig. 5). Thus, the Au20 core of each Au36(SR)24 can be viewed as a network of six 4c-2e (4c denotes 4 centers). Another notable issue is that the structural framework of Au36(DMBT)24-1D is identical to that of reported Au36(TBBT)2411. There are four non-planar and four co-planar staple motifs Au2(SR)3 in Au36(DMBT)24-1D (Supplementary Fig. 3). After cutting the Au atoms from co-planar Au2(SR)3 staples, the remaining 28 Au atoms of Au36(DMBT)24-1D are packed in a fcc structure (Supplementary Figs. 6 and 7). As we know, the previous studies showed the non-fcc vs. non-fcc isomerization appeared in the Au38(PET)24 isomers and the fcc vs. non-fcc isomerization existed in the Au42(TBBT)26 isomers15,37. Here the fcc vs. fcc isomerization is for the first time observed in the Au36(DMBT)24 isomers. In addition, Au36(DMBT)24-2D can be irreversibly converted to Au36(DMBT)24-1D at 333 K for 2 h, which indicates that the latter is more stable than the former.

To further corroborate the mechanism of two-dimensional growth in the series of Au8n+4(SR)4n+8 nanoclusters, we tried to synthesize c2 isomer of Au44(SR)28 using various synthetic methods, e.g., one-pot reduction, size-focusing, and thermal conversion (the synthesis details are shown in Methods section). Different ligands were employed such as 3-methylbenzenethiol, 4-isopropylbenzenethiol, 2,4-dimethylbenzenethiol, etc. The experimental conditions were controlled by tuning temperature and pH in different solvents. Under the above attempts, we obtained Au36(SR)24-1D, Au44(SR)28-1D, and other unknown nanoclusters, which were indicated by UV-vis (Supplementary Fig. 8) and ESI-MS spectra (Supplementary Figs. 9 and 10). The c2 isomer of Au44(SR)28 (denoted as Au44(SR)28-2D) was not obtained, which is possibly because the Au44(SR)28-2D (0.63 eV) is notably higher in energy than Au44(SR)28-1D (0 eV) (Fig. 1). In addition, as is known, the synthesis of nanoclusters involves kinetic control in the early stage and the carbon tail of the thiol ligands often plays an important role. While we believe the Au44(SR)28-2D would be attainable, their syntheses might take an exhaustive search for the right HS-R to reach the exact conditions. Therefore, we have to leave this to future work. Notably, the d2 isomer of Au52(SR)32 can be synthesized with the assistance of acid33. The Au32 kernel of Au52(TBBT)32 (d1 isomer) adopts the one-dimensional growth of the Au4 units (Supplementary Fig. 11a)32, while the kernel of Au52(PET)32 (d2 isomer) consists of 32 gold atoms that are arranged along two-dimensional direction based on the Au4 tetrahedron (Supplementary Fig. 11b). Thus, the Au52(PET)32 nanocluster further supports the possibility of the two-dimensional growth for Au4 units of Au8n+4(SR)4n+8 proposed in this work.


Au36(DMBT)24-2D is chiral, as the Au20 kernel and surface staple units are both arranged in a chiral pattern (Fig. 5a), while Au36(DMBT)24-1D is achiral due to no mirror plane occurring in the metal kernel and the surface staples (Figs. 3b and 4b). We separated the Au36(DMBT)24-2D enantiomers by high-performance liquid chromatography (HPLC) (Supplementary Fig. 12) and studied its chirality by circular dichroism (CD)38,39,40,41,42. As shown in Fig. 5b, the pair of Au36(DMBT)24-2D enantiomers showed a mirror symmetry for multiple peaks in the CD spectra, which were respectively centered at 268, 292, 329, 355, 380, 430, 487, and 615 nm in the UV-vis spectral region. The theoretically simulated CD spectra for Au36(SH)24 enantiomers agreed with the experimental spectra (Supplementary Fig. 13).

Fig. 5: Chirality of the Au36(DMBT)24-2D nanocluster.


a The enantiomers of Au36(DMBT)24-2D from top view (upper panel) and side view (lower panel). Color labels: yellow = S, blue/magenta = Au. The C and H atoms are omitted for clarity. b CD spectra of the separated enantiomers of Au36(DMBT)24-2D.

Ultrafast electron dynamics

The dynamics of excited states in the two Au36(DMBT)24 nanoclusters were studied by using transient absorption (TA) spectroscopic measurements. Figure 6a, b compared the femtosecond-resolved TA data of two isomers pumped at 400 nm. We carried out the global fitting analysis to extract the evolution associated spectra (EAS) of the isomers, as shown in Fig. 6c, d. Except for some slight wavelength shifted, the spectral characteristics showed similar features for both nanoclusters with excited-state absorption near 500 nm and ground-state bleach near 600 nm, respectively. Nonetheless, the temporal dynamics exhibited remarkable differences for the two isomers. For the Au36(DMBT)24-1D nanocluster, the experimental data can be reproduced by three processes with lifetime parameters of 0.5 ps, 7 ps, and >1 ns (Fig. 6d), respectively. In analogy to the previously reported results on Au36(TBBT)24 nanocluster, the three components can be attributed to ultrafast Sn → S1 internal conversion, structural relaxation, and carrier recombination, respectively43. However, the component of structural relaxation (~ 7 ps) was not present in the data recorded from the Au36(DMBT)24-2D nanocluster (Fig. 6c). Such a difference was explicitly manifested in the dynamics probed at 500 nm (Fig. 6e; more meticulous comparison shown in Supplementary Fig. 14), where a delayed rise in the excited-state absorption signal observed from the Au36(DMBT)24-1D sample was absent in the data recorded from the Au36(DMBT)24-2D sample. This marked difference between the electron dynamics in the two isomers is probably related to their different structures: the picosecond component with lifetime of ~7 ps in Au36(DMBT)24-1D nanoclusters is the structural relaxation due to the expansion or torsion of one-dimensional chains after excitation43, while the ~7 ps component is not observed in Au36(DMBT)24-2D nanoclusters, which may be due to the limitation of the conformation changes in the two-dimensional kernel. In addition, it was found that the carrier recombination in the Au36(DMBT)24-2D sample became slightly faster than that in the Au36(DMBT)24-1D sample (Fig. 6f). These observations are interesting that Au36(DMBT)24-2D and Au36(DMBT)24-1D have same chemical compositions, but show drastic differences in their optical features and electron dynamics.

Fig. 6: Excited-state dynamics of Au36(DMBT)24 nanoclusters.


Femtosecond-resolved transient absorption data recorded from a Au36(DMBT)24-2D and b Au36(DMBT)24-1D. Spectral features of different delay components derived from global fitting analysis for c Au36(DMBT)24-2D and d Au36(DMBT)24-1D. e Femtosecond-resolved and f nanosecond-resolved dynamic traces of the two nanoclusters.