The following chemicals were used: tetrachloroauric(III) acid (HAuCl₄·3H₂O, >99.99 % metals basis, Sigma-Aldrich Corporation, St. Louis, MO, USA), tetraoctylammonium bromide (TOAB, ≥98%, Fluka Chemicals Limited, Gillingham, Medway, UK), phenylethanethiol (PhC₂H₄SH, 99%, Acros Organics, Thermo Fisher Scientific, NJ, USA), and sodium borohydride (99.99%, metals basis, Sigma-Aldrich). The solvents include toluene (HPLC grade, ≥99.9%, Sigma-Aldrich), ethanol (absolute, 200 proof, PHARMCO-AAPER, Shelbyville, KY, USA). Pure water was from Wahaha Co. LTD (Hangzhou, China). All glassware was thoroughly cleaned with aqua regia (HCl: HNO₃ = 3:1 vol), rinsed with copious pure water, and then dried in an oven prior to use.

All UV-visible (vis) absorption spectra of Au nanoclusters in either toluene or methylene chloride were recorded using a Hewlett-Packard (HP, Palo Alto, CA, USA) 8453 diode array spectrophotometer. Electrospray ionization mass spectra were acquired using a Waters Q-TOF (Waters Corporation, Milford, MA, USA) mass spectrometer equipped with a Z-spray source. The sample solution (approximately 1 mg/mL) dissolved in toluene was diluted in dry methanol (50 mM cesium acetate CsAc, 1:2 vol). The sample was directly infused at 5 μL/min. The source temperature was kept at 70°C. The spray voltage was kept at 2.20 kV; the cone voltage, at 60 V.

HAuCl₄·3H₂O (0.1612 g, 0.41 mmol) was dissolved in 5 mL water, and tetraoctylammonium bromide (TOAB, 0.2541 g, 0.465 mmol) was dissolved in 10 mL toluene. These two solutions were combined in a 25-mL tri-neck, round-bottom flask. The solution was vigorously stirred (approximately 1,100 rpm) with a magnetic stir bar to facilitate phase transfer of Au(III) salt into the toluene phase. After approximately 15 min, phase transfer was completed; the clear aqueous phase was then removed. The toluene solution was cooled down to 0 °C in an ice bath over a period of approximately 30 min under constant magnetic stirring. After that, magnetic stirring was reduced to a slow speed (approximately 100 rpm), PhC₂H₄SH (0.20 mL, approximately threefold the moles of gold) was added, and the solution was kept under slow stirring. The solution color changed slowly from deep red to faint yellow and to colorless over approximately 1 h. After that, the speed of magnetic stirring was increased from approximately 100 to 400 rpm. At the same time, 1 mL aqueous solution of NaBH₄ (0.44 mol/L, freshly made with ice-cold water) was dropwise added to the toluene solution over a 15-min period using a 1-mL syringe. The color of the solution turned black gradually. After the dropwise addition of NaBH₄, the reaction was allowed to further proceed overnight. The optical absorption spectrum of the crude reaction product (diluted with toluene) shows a distinct absorption band at approximately 800 nm.

The aqueous layer at the bottom of the flask was removed using a syringe, and the toluene solution was concentrated by rotary evaporation at room temperature. Ethanol (approximately 50 mL) was added to precipitate the Au nanoclusters. The brown, turbid solution was allowed to stand on bench for several hours. The precipitate was collected and redissolved in toluene. This precipitation/dissolution process was repeated with ethanol. The crude mixture was extracted with methylene chloride/acetonitrile (1:9 vol) to remove a small amount of Au₂₀(SC₂H₄Ph)₁₆ (its optical absorption band at approximately 485 nm) 51 . After Au₂₀ was removed from the product, Au₂₄(SC₂H₄Ph)₂₀ nanoclusters were removed by a second extraction with methylene chloride/acetonitrile (1:2 vol) 50 . The final remaining product was collected and characterized by mass spectrometry.

Starting with an Au(III) salt precursor, the synthesis of gold nanoclusters involves two primary stages: (a) reduction of Au(III) to Au(I) by HSR, during which the formed Au(I) intermediate species spontaneously aggregates into polymeric Au(I) species (unknown structure), and (b) reduction of Au(I) to Au _n (SR) _m nanoclusters by NaBH₄.

In this work, we have identified several important factors for the synthesis of nanoclusters Au₃₉ and Au₄₀, including the stirring speed of the reaction mixture, the addition speed, and the amount of NaBH₄ solution to reduce Au(I) into clusters. The synthetic conditions reported in this work differ from the previous syntheses of Au₁₉(SC₂H₄Ph)₁₃, Au₂₀(SC₂H₄Ph)₁₆ and Au₂₄(SC₂H₄Ph)₂₀ (see ‘Methods’ section) 50 51 52 . Specifically, in the present work, our major modification lies in the stirring speed of the Au(I) intermediate solution when reduced by NaBH₄. In a previous work, Au₂₀(SC₂H₄Ph)₁₆ and Au₂₄(SC₂H₄Ph)₂₀ were synthesized by controlling the stirring speed for the reduction step of Au(I) by NaBH₄; for example, approximately 50 rpm for Au₂₀(SC₂H₄Ph)₁₆ and approximately 100 rpm for Au₂₄(SC₂H₄Ph)₂₀.

To synthesize larger-sized nanoclusters, we rationalize that the kinetics of the reduction reaction of Au(I) intermediate species by NaBH₄ may be important for potential size control. Motivated by that, we systematically varied the synthetic conditions and also compared with the typical method for Au₂₅(SC₂H₄Ph)₁₈ synthesis. Interestingly, we found that with the stirring speed being increased to approximately 400 rpm, the crude product (Figure 1A) shows an optical spectrum different from that of Au₂₄(SC₂H₄Ph)₂₀ or Au₂₀(SC₂H₄Ph)₁₆ (Figure 1B,C). A new absorption peak centered at approximately 800 nm was observed (Figure 1A), indicating that some new species have been formed in this controlled reduction process. Of note, the small peak at approximately 700 nm (Figure 1A) is due to the concurrent formation of a small amount of Au₂₄(SC₂H₄Ph)₂₀ clusters as impurities in the synthesis of the new clusters. To remove Au₂₄ and possible Au₂₀ impurities from the product, the clusters in the crude product were precipitated by adding ethanol, and the crude product was then extracted with CH₂Cl₂/CH₃CN (1:9 vol) to selectively dissolve Au₂₀(SC₂H₄Ph)₁₆ from the product. The remained undissolved produce was followed by a second extraction with CH₂Cl₂/CH₃CN (1:2 vol) to remove Au₂₄(SC₂H₄Ph)₂₀. The final remaining product is largely free of Au₂₄ and Au₂₀ impurities, as evidenced in the disappearance of the 700-nm band in the optical spectrum (Figure 1A, red profile). The relatively pure product is subject to further characterization for cluster formula determination.

We employ electrospray ionization mass spectrometry (ESI-MS) to determine the composition of the new gold cluster product. A solution of cesium acetate (CsAc, 50 mM, in dry methanol) was added to a toluene solution of gold clusters at 1:1 or 1:2 (vol). ESI-MS detects the cluster-Cs adducts that are positively charged due to Cs⁺ addition to the cluster surface.

The low-mass portion of the spectrum consists of all [CsAc] _x Cs⁺ signals (Figure S1 in Additional file 1), and residual Au₂₄(SC₂H₄Ph)₂₀Cs was also observed at m/z 7,603 (calculated FW = 7604 for mono-Cs adduct). The high-mass portion (Figure 2) shows two peaks at m/z 11,793 and 12,127 (Figure 2A, unsmoothed spectrum; Figure 2B, smoothed). These two signals are corresponding to the new clusters formed in the controlled reduction process. Both peaks indicate +1 ions, evidenced by the unity spacing of the isotope-resolved peaks (see Figure 2A inset, for m/z 11,793). After subtracting one Cs⁺ ion (FW = 133), the masses of the two new clusters are determined to be 11,660 and 11,994 Da. Unfortunately, isolation of these two mixed clusters into pure ones has not been successful so far.

To deduce the formulas of the two new Au _n (SC₂H₄Ph) _m clusters based upon the ESI-MS data, we first determine the minimum value of the gold atom number (n), which corresponds to the limiting case of Au(I):SR complexes, i.e., when n = m. This gives rise to 11,660/337 approximately 35 for the peak of m/z 11,660. We then construct candidate formulas by systematically increasing n starting from 35. For example, for n = 36, we list two closest matches to the ESI-determined mass of 11,660 Da, one with the smallest negative deviation, i.e., (n, m) = (36, 33), and the other with the smallest positive deviation, i.e., (n, m) = (36, 34), see Table 1; note that other m values for n = 36 are not pursued since they deviate more from the ESI mass of 11,660 Da. Following this method, one can list all the possible formulas until the limiting case of 11,660 Da consisting of all gold atoms, which is the upper limiting case since a certain number of thiolate ligands must be present to protect the metal core. By comparing the candidate formulas with the ESI-MS-determined precise mass of 11,660 Da, we readily obtain the Au₃₉(SC₂H₄Ph)₂₉ formula (calculated FW = 11661; deviation, 1 Da), as reflected in Table 1. Similarly, the cluster of 11,993 Da is determined to be Au₄₀(SC₂H₄Ph)₃₀ (calculated FW = 11,995; deviation, 2 Da). A deviation of 0.5 to 2 Da is reasonable at this high mass range.

The attainment of two new nanoclusters, Au₃₉(SC₂H₄Ph)₂₉ and Au₄₀(SC₂H₄Ph)₃₀, demonstrates the feasibility of controlling cluster size via controlled reduction. Herein, we discuss some insights obtained regarding the synthetic processes of Au₂₀, Au₂₄, and Au_39/40. These four cluster species belong to a new series, as Au₂₀ and Au₂₄ are formed concurrently, albeit in small amounts, in the synthesis of Au_39/40 nanoclusters. However, by controlling the reaction process, one may selectively produce Au₂₀, Au₂₄, or Au_39/40. When using Au(III) as the starting material for nanocluster synthesis, two primary stages include (a) the reduction of Au(III) to Au(I) by HSR and (b) the conversion of Au(I) to Au _n (SR) _m clusters by reduction with NaBH₄. Factors that are important for Au _n size control with n = 20, 24, 39 and 40 include (a) the stirring speed of the reaction mixture, (b) the addition speed of NaBH₄, and (c) the amount of NaBH₄ added (vide infra).

We found the stirring speed is quite important for controlling the size and monodispersity of gold clusters. As listed in Table 2, during stage I, the stationary condition favors the formation of Au₂₀(SR)₁₆ nanoclusters, while slow stirring (50 to 100 rpm) favors the formation of Au₂₄(SR)₂₀, Au₃₉(SR)₂₉, and Au₄₀(SR)₃₀.

During stage II (the reduction of Au(I) by NaBH₄), the stirring speed is even critical for the selective formation of Au₂₀, Au₂₄, or Au_39/40. A slow stirring (approximately 50 rpm) during stage II favors the formation of Au₂₀(SC₂H₄Ph)₁₆, while a slightly higher speed of stirring (approximately 100 rpm) favored the formation of Au₂₄(SC₂H₄Ph)₂₀, and with further increased speed to approximately 400 rpm, we obtained new clusters of Au₃₉(SC₂H₄Ph)₂₉ and Au₄₀(SC₂H₄Ph)₃₀. This controlled reaction process for tuning cluster size is quite interesting. We believe that the aggregated Au(I)SR species are broken into small fragments upon reduction or partial reduction by NaBH₄. Different stirring speed for stage II would influence the kinetics of the reduction reaction of Au(I)SR, and the different stirring speeds also give rise to different sheering forces that would break polymeric Au(I)SR into different sized fragments; such different sized fragments seem to subsequently grow into different sized clusters based upon our results.

Regarding the aggregated Au(I)SC₂H₄Ph species in the solution, structural characterization (e.g., by NMR or X-ray diffraction) is still difficult to carry out as the Au(I) intermediate species is poorly soluble in common solvents. Thermal gravimetric analysis determined the composition of Au(I):SR to be 1:1, but the aggregation degree (e.g., how many repeat units in [Au(I)SC₂H₄Ph] _x ) and what structures [Au(I)SC₂H₄Ph] _x may adopt are all unknown yet. Possible structures of [Au(I)SC₂H₄Ph] _x include linear chains, ring 53 54 55 56 57 , or lamellar structures. The characterization of Au(I)SR still need major efforts in future work.

In addition to the stirring speed during stage II, the addition speed of NaBH₄ (aqueous solution) to reduce Au(I) into clusters also plays an important role in controlling the final cluster size. We have tested that, in the synthesis of Au₂₀(SC₂H₄Ph)₁₆, if the initial drops of NaBH₄ solution (0.44 mol/L, 1 mL) were added rapidly, the light yellow solution of Au(I) aggregates would rapidly become brown or deep black, and the product would contain more Au₂₄ and Au_39/40 clusters, instead of the predominant Au₂₀ as the case of very slow addition of NaBH₄ (over a period of approximately 30 min) (entry 1, Table 2). After optimization, we found that adding NaBH₄ (0.44 mol/L, 1 mL, same concentration and amount as the Au₂₀ synthesis) over a period of approximately 15 min gave rise to predominant Au₂₄ (under approximately 100 rpm stirring condition) or Au_39/40 (under approximately 400 rpm stirring condition); see entries 2 and 3 of Table 2. Thus, controlled reduction of Au(I) is very important for size selective formation of Au₂₀, Au₂₄, or Au_39/40. The selective formation of Au_39/40 over Au₂₄ - which differ only in the stirring speed during stage II (i.e., 400 vs 100 rpm, Table 2) - should be due to the different reaction kinetics in the reduction process of Au(I) species into clusters. In a recent synthetical work on gold/phosphine nanocluster synthesis, Pettibone and Hudgens identified a growth-etching cyclic process that occurs around the most stable cluster species to form monodisperse product 4 58 59 . This size selective growth mechanism provides important information on the gold/phosphine system. The reaction kinetics of the gold/thiol system, however, still needs significant input in order to unravel the details of the kinetic process. Mass spectrometric monitoring of the reaction intermediates would provide valuable information and should be pursued in future work.

With respect to the growth of Au₂₀, Au₂₄, and Au_39/40 nanoclusters, an interesting question arises naturally: why the ubiquitous Au₂₅ nanocluster is not formed under these conditions (entries 1 to 3, Table 2). The synthesis of Au₂₅(SC₂H₄Ph)₁₈ is typically done under experimental conditions of fast stirring and rapid reduction of Au(I) with large excess of NaBH₄ (approximately 10 equivalents (eq) of NaBH₄ per mole of gold). An important difference lies in that the syntheses of Au₂₀, Au₂₄, and Au_39/40 clusters all involve 1 eq of NaBH₄ per gold, i.e., 1 mL of NaBH₄ solution (0.44 mol/L), Table 2. This implies that the degree of reduction of Au(I) might affect the cluster size, and the formation of Au₂₅ clusters might necessitate over reduction of Au(I) with a large excess of NaBH₄.

To find out whether the reduction degree of Au(I) species affect the final cluster size, we adopt the same stirring conditions as the synthesis of Au₂₄ and Au_39/40 (see entry 4, Table 2), but we add more NaBH₄ (e.g., 5 eq, rather than 1 eq for the synthesis of Au₂₄ and Au_39/40). The addition speed of NaBH₄ solution is kept comparable to the syntheses of Au₂₄ and Au_39/40 clusters. Interestingly, dropwise addition of 5 eq of NaBH₄ does result in selective formation of Au₂₅, instead of Au₂₄ or Au_39/40, evidenced by its characteristic spectroscopic features (see Figure S2 in Additional file 1). Thus, the growth of Au₂₅ nanoclusters does require a rich reductant (NaBH₄), as opposed to lean NaBH₄ for Au₂₀, Au₂₄, and Au_39/40 synthesis. The fast stirring and rapid addition of NaBH₄ seem not the key to the synthesis of Au₂₅ nanoclusters.