Atomic-level separation of thiolate-protected metal clusters.

Fine metal clusters have attracted much attention from the viewpoints of both basic and applied science for many years because of their unique physical/chemical properties and functions, which differ from those of bulk metals. Among these materials, thiolate (SR)-protected gold clusters (Aun(SR)m clusters) have been the most studied metal clusters since 2000 because of their ease of synthesis and handling. However, in the early 2000s, it was not easy to isolate these metal clusters. Therefore, high-resolution separation methods were explored, and several atomic-level separation methods, including polyacrylamide gel electrophoresis (PAGE), high-performance liquid chromatography (HPLC), and thin-layer chromatography (TLC), were successively established. These techniques have made it possible to isolate a series of Aun(SR)m clusters, and much knowledge has been obtained on the correlation between the chemical composition and fundamental properties such as the stability, electronic structure, and physical properties of Aun(SR)m clusters. In addition, these high-resolution separation techniques are now also frequently used to evaluate the distribution of the product and to track the reaction process. In this way, high-resolution separation techniques have played an essential role in the study of Aun(SR)m clusters. However, only a few reviews have focused on this work. This review focuses on PAGE, HPLC, and TLC separation techniques, which offer high resolution and repeatability, and summarizes previous studies on the high-resolution separation of Aun(SR)m and related clusters with the purpose of promoting a better understanding of the features and the utility of these techniques.


Introduction
Fine metal clusters smaller than ~2 nm (< ~100 atoms) exhibit different geometrical/electronic structures than those of bulk metals. 1 Metal clusters often form a unique framework, such as an icosahedral structure, to suppress the surface energy instead of the close-packed structure often observed in bulk metal. In addition, metal clusters exhibit a discrete electronic structure unlike bulk metal. Because of these characteristic geometrical/electronic structures, fine metal clusters exhibit unique physical/chemical properties and functions that differ from those of bulk metals. In addition, the physical/chemical properties and functions of metal clusters vary significantly depending on the number of constituent atoms. For these reasons, fine metal clusters have attracted considerable attention for many years in the fields of both basic and applied science.
For these metal clusters, it is essential to conduct investigations on metal clusters controlled with atomic precision to understand the structures and physical/chemical properties. For this purpose, gas-phase beam experiments are superior 2−6 and they led researches of the metal clusters in the 1980ʹs and the 1990ʹs. Many unique characteristics of metal clusters were discovered during this period by observing the mass distributions and electronic structures in gas-phase beam experiments. In parallel with such physical experiments, the research on the synthesis of phosphine (PR3)-protected metal clusters was also actively pursued during this period. 7−15 The main purpose of these studies was to reveal the correlation between chemical composition and geometrical structure, and the geometrical structures of some PR3-protected metal clusters were determined by single-crystal X-ray diffraction (SC-XRD) at that time. Regarding the thiolate (SR)-protected metal clusters described below, the geometrical structure was first determined by SC-XRD in 2007; thus, the development of the researches on PR3-protected metal clusters at that time was remarkable. Since 2000, nanotechnology has been adopted as a national policy in many countries, and the main target metal clusters have shifted to SR-protected gold clusters (Aun(SR)m clusters). 16−33 Aun(SR)m clusters can be synthesized by simply mixing reagents in a solvent in air. Furthermore, Aun(SR)m clusters are stable both in solution and in the solid state because the SR group forms a strong bond with Au. Such Aun(SR)m clusters have a low threshold even for researchers who have not worked on metal cluster synthesis and show great potential for material applications. It is presumed that these factors are largely related to the explosive increase in the number of studies on Aun(SR)m clusters since 2000. 20 However, for Aun(SR)m clusters, single crystallization techniques could not be found, and thus, they could not be isolated in the early stage. Then, high-resolution separation techniques were developed to isolate Aun(SR)m clusters. In earlier studies, separation techniques that relied on differences in solubility to solvents were mainly used. 34−38 Then, atomiclevel separation techniques, such as polyacrylamide gel electrophoresis (PAGE) and liquid chromatography (LC) were developed. These methods made it possible to isolate a series of Aun(SR)m clusters and obtain knowledge on the correlation between the chemical composition and the fundamental properties (e.g., stability, 39,40 electronic structure, 41 physical/chemical properties 42,43 ) of Aun(SR)m clusters. After these separation techniques were established, the experimental conditions for synthesizing only stable metal clusters were also determined by using the features of their optical absorption spectra. As a result, several methods were established for selectively synthesizing stable Aun(SR)m clusters with atomic precision. 24,44 In addition, because crystallization was easier for isolated or selectively synthesized Aun(SR)m clusters, the geometrical structures were also determined by SC-XRD for several Aun(SR)m clusters. 45 In parallel with these studies, studies on the application of these precisely controlled Aun(SR)m and related clusters for chemical sensors, 46,47 photosensitization, 48 catalysts, 49,50 and solar cells 51,52 were conducted. 53 Thus, high-resolution separation techniques have played an extremely important role in the study of Aun(SR)m clusters. Recently, some stable metal clusters can be synthesized with atomic precision. 24,44 However, not all clusters can currently be synthesized size-selectively. Thus, the use of high-resolution separation techniques remains indispensable for understanding the correlation between the chemical composition and structure/physical properties of SR-protected metal clusters. Moreover, these separation techniques are also needed for purification of the main products and for isolation of metastable species. In addition to the use for fractionation as described above, these separation techniques are also often used to evaluate the distribution of a product and to track reaction. Despite their importance, few reviews have focused on these techniques in the study of Aun(SR)m clusters. 54 This review summarizes research on the high-resolution separation of Aun(SR)m and related clusters. In particular, we describe previous studies on PAGE, high-performance LC (HPLC), and thin-layer chromatography (TLC), which are separation techniques with high resolution and repeatability. The aim of this review is to provide a deep understanding of the features and usefulness of the three separation techniques through past research. The following section outlines the basic principles and experimental methods of PAGE, HPLC, and TLC. Then, in section 3, we briefly describe previous high-resolution separation methods that were used before the appearance of these three techniques. Next, sections 4 to 6 outline previous works on PAGE, HPLC, and TLC, respectively. Finally, section 7 summarizes the review and briefly describes future expectations.

Polyacrylamide gel electrophoresis
When a direct current flows through a solution, the charged sample in the solution moves in the direction of the oppositely charged electrode. A method of separating a substance based on this principle is called electrophoresis. In PAGE, substances move in a three-dimensional network consisting of polyacrylamide gel. Each metal cluster can be separated by this method because the mobility of the clusters differs depending on the charge, particle size, and shape. PAGE is generally used for the separation of hydrophilic Aun(SR)m and its related clusters containing a ligand with a dissociable functional group.
In the experiment, first, a polyacrylamide-gel running layer is prepared between two plates using acrylamide and bis(acrylamide). Then, a polyacrylamide-gel stacking layer is prepared using acrylamide and bis(acrylamide) with a different concentration than that of the running layer. A sample solution containing several percent of glycerol is dropped on the upper end of the gel. Then, electrophoresis is performed by applying a voltage to the electrodes placed on the upper and lower sides of the gel. Each cluster is separated into several bands ( Figure  1A). Bands containing each metal cluster are cut out using a utility knife, and the clusters are eluted from the gel by leaving them in water and collecting them from the solution.
The device for PAGE is simple and inexpensive ( Figure 1A). In addition, when the cluster mixture is separated by PAGE, the separation of each component cluster can be visually confirmed. It is also possible to specify luminescent clusters by ultraviolet light irradiation. Moreover, PAGE is also useful for evaluating the product size and shape because the mobility of each metal Please do not adjust margins Please do not adjust margins cluster varies depending on the particle size and shape as well as the charge and the interaction with the solvent.

Liquid chromatography
Chromatography is a method used to separate a sample based on the difference in the extent of the interaction between the sample and the stationary phase. When the mobile phase is liquid, the technique is called LC.

Open column chromatography
For classical LC, the sample is loaded on the upper end of an open column with the stationary phase. Then, the mobile phase is passed through from the upper end of the column to separate the substances. Because of its simplicity, this method is often used for washing metal-SR complexes with greatly different sizes. However, there are almost no examples of Aun(SR)m and their related clusters being separated with atomic precision because it is difficult to achieve a high degree of precision using this method. Therefore, this review does not introduce separation using this method.

High-performance liquid chromatography
When a high pressure is applied in LC, the mobile phase passes through the column at a high flow rate. Consequently, the time during which the substance remains in the stationary phase is shortened, and the resolution and detection sensitivity are improved. This separation method is called HPLC to distinguish it from classical LC. The principle of separation used in HPLC is roughly divided into four types: adsorption, partition, ion exchange, and size exclusion. In addition, various other separation modes are used in actual HPLC analysis; however, these modes can be recognised as modifications or combinations of the above four separation principles in terms of the separation mechanism. The normal phase is the separation condition in which the polarity of the stationary phase is higher than that of the mobile phase. In contrast, reverse phase (RP) is the separation condition in which the polarity of the stationary phase is lower than that of the mobile phase ( Figure 1B). In the separation of Aun(SR)m and their related clusters, partition, adsorption, and size exclusion have been used as the main separation principles. The general HPLC system used for such separation consists of a mobile-phase solvent reservoir, a degasser device, a highpressure liquid pump, an injector, a column, and a detector ( Figure 1B). There are two types of mobile phases, one using a single mobile phase and the other using multiple types of mobile-phase solvents while arbitrarily changing their volume ratio. The first method is called isocratic mode, and the second method is called gradient mode. In general, a column is produced by filling a stainless-steel tube with a particulate stationary phase (column filler) at high pressure and sealing its upper and lower ends with a sintered porous stainless filter. Silica gel particles with surfaces modified by an organic layer are often used as the column filler ( Figure 1B).
HPLC has advantages of resolution and repeatability. There is also the advantage that electrospray ionization (ESI) mass spectrometry (MS) can be used for the detection. As opposed to separation by PAGE, when the HPLC apparatus and ESI mass spectrometer are directly connected (LC/MS), all the generated clusters can be directly led to the MS section. Thus, it is possible to determine the chemical composition of very minor components that cannot be detected by PAGE.

Thin-layer chromatography
There have been some reports on the separation of Aun(SR)m clusters by TLC using a planar stationary phase in recent years. The TLC plates are prepared by coating a stationary phase on a flat glass, aluminium, or plastic plate. Currently, TLC plates coated with various types of stationary phases are commercially available. The separation principles of adsorption, partition, ion exchange, and size exclusion can also be used in TLC separation.
In the experiment, the solution containing the sample is spotted 15 to 25 mm above the lower end of the TLC plate using a micropipette or a capillary tube. After drying the sample, the plate is allowed to stand with the spot facing down in a sealed container containing a solvent (the mobile phase). The sample is separated by rising of the solvent from the lower side via capillary action ( Figure 1C). The band containing each Aun(SR)m cluster is cut out with a spatula, and each Aun(SR)m cluster is collected from the plate.
With TLC, it is difficult to achieve the same degree of resolution as HPLC. However, TLC uses a less expensive and simpler experimental apparatus than HPLC. Therefore, when the distances that each Aun(SR)m cluster travel on the plate are significantly different, the target Aun(SR)m cluster can be easily and inexpensively isolated using this method. It is also one of the advantages of this method that the separation of Aun(SR)m clusters can be visually confirmed, as for PAGE.

Early Studies on Separation
Many attempts were made to separate Aun(SR)m clusters based on the number of constituent atoms before the use of the above three methods (PAGE, HPLC, and TLC). 34−38 For example, Whetten et al. synthesized Aun(SClH2l+1)m clusters (SClH2l+1 = alkanethiolate) as a ligand. They gradually added a poor solvent and precipitated clusters from large to small in order. 35 In these studies, each separated Aun(SClH2l+1)m cluster was evaluated mainly using matrix-assisted laser desorption/ionization (MALDI)-MS. In the mass spectrum of each Aun(SClH2l+1)m cluster, ion peaks appeared in different mass regions (Figure 2A), which indicated that the Aun(SClH2l+1)m clusters were separated based on their size. Unfortunately, these mass spectra included only the fragmentation peaks of each Aun(SClH2l+1)m cluster. 38 Therefore, the chemical composition of each Aun(SClH2l+1)m cluster was not accurately determined at this stage. Murray et al. also separated Aun(SR)m clusters (SR = SClH2l+1 or PET) using solvent-selective extraction. 55 Although this method has been revealed to be useful for obtaining each stable Aun(SR)m clusters at atomic resolution in the later studies 56−58 and thereby often used for the isolation of Aun(SR)m clusters in a large quantities in recent studies, 59−63 unfortunately, the separated Aun(SR)m clusters could not be confirmed to be isolated at atomic resolution at this stage. However, these studies provided considerable information on the correlation between the particle size and electronic structure in the Aun(SR)m clusters ( Figure 2B). 34−38 Since then, the separation technique for Aun(SR)m clusters has progressed rapidly with the introduction of separation methods offering high resolution and repeatability and the improvement of mass spectrometers.

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Please do not adjust margins clusters in each band using MALDI-MS and ESI-MS. However, these measurements did not provide mass spectra with a high signal/noise (S/N) ratio. Therefore, at this stage, the chemical composition of each separated Aun(SG)m cluster had not been accurately determined.
Later, Negishi and Tsukuda et al. demonstrated that this method could be used to separate a mixture into each Aun(SG)m cluster with atomic precision. 41,65 They evaluated the chemical compositions of the Aun(SG)m cluster contained in each band using their homemade ESI mass spectrometer. Using their homemade apparatus, an ionized solvent containing Aun(SG)m clusters could be efficiently introduced into the mass spectrometer ( Figure 3C). 41,65 As a result, a high S/N ratio was achieved in the mass spectra, and the separated Aun(SG)m clusters were assigned as Au10−12(SG)10−12, Au15(SG) 13 Au39(SG)24, respectively ( Figure 3D). This study also clarified that Au25(SG)18 is especially stable. 65 Stable clusters with similar absorption spectra had previously been reported by Whetten et al. and Murray et al.. 66,67 This study revealed that the exact chemical composition of these clusters was Au25(SR)18.
For the Aun(SG)m clusters, Kimura et al. and Dass et al. separated larger-sized clusters up to Au~56(SG)~29 and Au43(SG)26, respectively. 68,69 In Dass's study, the chemical composition of each cluster was determined using a commercially available mass spectrometer. 69 The detection sensitivity of commercial apparatuses have improved, and in research since 2008, the chemical composition of separated clusters has been evaluated using commercial rather than homemade apparatuses.
The isolation of Aun(SG)m clusters with atomic precision enabled a deep understanding of the stability, structure, and other properties of Aun(SG)m clusters to be obtained. Tsukuda and Teranishi et al. showed that a series of Aun(SG)m clusters exhibited especially high stability against etching by excess thiol ( Figure 4A) 39 and that Au25(SG)18 could be selectively synthesized in a solution where etching is likely to occur. 44 Kojima and Tsukuda et al. experimentally demonstrated using 197 Au Mössbauer spectroscopy that Aun(SR)m clusters have a geometrical structure in which a Au core is covered by Au(I)−SR oligomers ( Figure 4B), which had been predicted by density  Figure 5A). 73 They showed that the chemical compositions of the isolated Aun(SR)m clusters differed depending on the ligand structure by comparing the chemical compositions of Aun(S(PG))m, Aun(S(SA))m, and Aun(SG)m clusters. 73 Comparison of the optical absorption spectra of these clusters with the same chemical composition revealed that the electronic structure of Aun(SR)m clusters also changes depending on the ligand structure ( Figure 5B). 73 Tsukuda et al. isolated Au25(S(PG))18 at high purity and obtained information on its geometrical structure in a later study. 74 In addition, other hydrophilic Aun(SR)m clusters were separated using PAGE by Separation using PAGE has also been applied for the isolation of other metal clusters. Bigioni et al. separated Agn(SG)m clusters using PAGE ( Figure 5C) and suggested that Agn(SG)m clusters could have a different chemical composition than Aun(SG)m clusters by comparing each gel. 79 The main product of Agn(SG)m clusters was later determined to be Ag32(SG)19 by Griffith and Bigioni et al., 80 and this chemical composition actually cannot be observed for Aun(SG)m clusters. Pradeep et al. separated Agn(SG)m clusters and showed that Ag32(SG)19 exhibits strong photoluminescence (PL). 81 Yao and Kimura et al. separated Agn(D/L-Pen)m clusters and revealed that they have higher mobility than Aun(Pen)m clusters. 82 They concluded that the mobility differences originated from the larger surface charge of the Agn(D/L-Pen)m clusters. 82 In this way, it is possible to isolate SR-protected metal clusters composed of various ligands and metal elements with atomic precision using PAGE. 83−101 By conducting research on a series of separated clusters, much knowledge has been obtained on the chemical composition and stability, electronic/geometrical structure, and physical properties of various SR-protected metal clusters.

PAGE separation for reaction control
In section 4.1, we introduced the isolation of metal clusters by PAGE. Meanwhile, fine metal clusters often exhibit a colour that depends on the number of constituent atoms. Thus, when they are separated by PAGE, the distribution of their chemical compositions can be confirmed visually. For this reason, PAGE is also often used to examine the distribution of chemical compositions of a product, optimize reaction conditions, elucidate the degraded processes, and track reactions. 102−110 For example, Tsukuda and Teranishi et al. observed that Au25(SG)18 was a major product when a triphenylphosphine (PPh3)-protected Au cluster was mixed with glutathione (GSH). They attempted to optimize the reaction conditions to selectively synthesize such a stable cluster with atomic Please do not adjust margins Please do not adjust margins precision. In this experiment, the distribution of the product under each experimental condition was first checked by PAGE separation ( Figure 6A) 44 and then estimated by ESI-MS in the final stage. The results indicated that high-purity Au25(SG)18 was present in the product ( Figure 6B). 44 Later, they mixed a series of Aun(SG)m clusters with GSH and traced the etching process using PAGE and discussed why Au25(SG)18 was selectively synthesized in the reaction between the PPh3-protected Au cluster and GSH. 39 Ackerson et al. synthesized Au102(p-MBA)44 (p-MBA = pmercaptobenzoic acid) under different gas atmospheres and examined the distribution of products using PAGE. They observed that O2 was required as a gas for radical generation when using an organic solvent during the synthesis ( Figure  7A). 111 They also showed that Au102  Figure 7B). 112 Xie et al. revealed that Au18(SG)14 could be produced as an intermediate in the synthesis of Au22(SG)18 with carbon monoxide (CO) reduction by monitoring the reaction using PAGE. 113 In this way, the use of PAGE enables the chemical composition distribution of the product to be clarified. Through the use of such PAGE separation, much knowledge has been obtained on appropriate synthesis conditions, stable conditions, and reaction mechanisms.

PAGE separation to identify luminescent cluster
Fine noble metal clusters often exhibit PL. 114,115 Au and Ag are harmless elements, unlike cadmium and arsenic, which form compound semiconductors with strong emission. 116 However, it is not easy to identify a metal cluster that emits PL with a high quantum yield from a mixture. However, if the mixture is separated by PAGE and then the gel is irradiated with ultraviolet light, it is possible to visually identify the metal cluster exhibiting PL. Therefore, PAGE has often been utilized to identify luminescent metal clusters.
Au22(SG)18, which emits red light with high quantum yield (~8%), was identified by such PAGE separation. 43 Xie et al. synthesized Aun(SG)m clusters using CO as the reduction agent and separated the mixture into each band using PAGE. The products were separated into four different Aun(SG)m clusters. Irradiation of the obtained gel with ultraviolet light revealed that Au22(SG)18, which has the lowest mobility, emits strong red PL ( Figure 8A). Based on the results of DFT calculation and X-ray absorption spectroscopy, they suggested that Au22(SG)18 has a geometrical structure in which the Au core is covered by a longer Au(I)−SG staple (RS−[Au−SR]n; n = 3,4), which differs from the structure of other Aun(SG)m clusters. They concluded that Au22(SG)18 emits PL at a high quantum yield because of the aggregation excitation emission effect caused by the long Au(I)−SG staple. Pradeep et al. succeeded in finding Ag7(S(SA))7 that emits red PL and Ag8(S(SA))8 that emits blue PL using PAGE separation ( Figure 8B). 117

PAGE separation for structural estimation
In PAGE separation, the mobility of each metal cluster depends on the particle size and shape as well as its charge and interaction with the solvent. Thus, there are several examples of the use of PAGE for structural and shape evaluation of Aun(SR)m clusters.
Ackerson et al. synthesized Aun(p-MBA)m clusters with unknown size and estimated their chemical compositions from their PAGE mobility. In their study, they first ran Au102(p-MBA) 44 and Au144(p-MBA)60 with known chemical composition through a gel and estimated the correlation between the mobility and chemical composition. Then, Aun(p-MBA)m clusters with unknown size were run through a gel at the same concentration, and the chemical composition was estimated to be Au~230(p-MBA)~88 from the mobility and the aforementioned correlation. 118

Sodium dodecyl sulfate-PAGE separation
In the PAGE separation described thus far, not only the molecular weight of the cluster but also the charge state was reflected in the mobility. Therefore, to more accurately estimate the correlation between the chemical composition and mobility, it is necessary to exclude the effect of the charge state. Adding sodium dodecyl sulfate (SDS) to the sample solution and electrophoresis solution results in an almost constant charge-to-size ratio of the cluster, eliminating the effect of charge state on the mobility. Such a SDS-PAGE solution is used in protein separation. 120 Cheng and Häkkinen et al. used SDS-PAGE for separation of Aun(SR)m clusters. 121 They replaced some ligands of Au102(p-MBA)44 with maleimide (C6Ml) to bind Au102(p-MBA)44 efficiently to nanocapsid. They confirmed using SDS-PAGE that the Au102(p-MBA)44−x(C6Ml)x bound to nanocapsid with higher efficiency than the unreacted Au102(p-MBA)44.

HPLC Separation
As with PAGE, there have been many reports on the separation of Aun(SR)m and related clusters using HPLC.  The main separation methods include RP partition chromatography, ionpair chromatography, hydrophilic interaction liquid chromatography, size exclusion chromatography, and chiral chromatography ( Figure 10). In the following, research examples are introduced.

Reverse phase partition chromatography
RP partition chromatography provides ease of handling and has many stationary phases with a high number of theoretical plates. Furthermore, this method also facilitates the use of LC/MS because the mobile phase used in this chromatography technique is suitable for the ionization of the cluster in ESI-MS. Because of these advantages, more than 80% of HPLC analysis uses an RP column.
In RP partition chromatography, the polarity of the stationary phase is lower than that of the mobile phase ( Figure  1B). Under this condition, the solute is in partition equilibrium between the stationary and mobile phases, and each solute is separated by a difference in the partition coefficient. In this chromatography method, silica gel supports chemically modified with an octadecyl group (C18), an octyl group (C8), a Figure. 10 Classification of HPLC used in the study of SR-protected metal clusters. The number in square brackets is the section number.

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Please do not adjust margins phenyl group (Ph), etc. are used as the stationary phase ( Figure  11A).

Separation of clusters by cluster size
Murray et al. first attempted to separate Aun(SR)m clusters using RP partition chromatography. In 2003, they synthesized a mixture of Aun(SC6H13)m clusters (SC6H13 = hexanethiolate) and attempted to separate each cluster using a C8 column. 146 The Aun(SR)m clusters with metal cores of approximately 1.5 nm were separated into multiple peaks ( Figure 12A). They estimated the size of Aun(SC6H13)m clusters contained in each fraction using methods such as optical absorption spectroscopy and electrochemical measurements and showed that smaller clusters eluted at shorter retention time. 147,148 The cluster included in the earliest eluting peak was assigned to Au38, and that included in the second eluting peak was assigned to Au140. The researchers also observed that connecting a C8 column to a Ph column improved the resolution. They succeeded in separating Au140 and Au225, which has a larger metal core, using such a connected column. 149 Negishi et al. succeeded in separating a series of Aun(SC12H25)m clusters (SC12H25 = dodecanethiolate) depending on the number of constituent atoms using such a connected column. Four distinct peaks were observed in the chromatogram, corresponding to Au102(SC12H25)44, Au130(SC12H25)50, Au144(SC12H25)60, and Au187(SC12H25)68, respectively. 150 Although isolation of Au102(SR)44 and Au144(SR)60 had been previously reported, 101,151 Au130(SR)50 and Au187(SR)68 clusters were successfully isolated for the first time in this experiment. 152,153 They also succeeded in finding an experimental condition for separating Aun(SC12H25)m clusters in a wide range from Au38(SC12H25)24 to Au~520(SC12H25)~130 at the same time ( Figure 12B). 154 In cooperation with Häkkinen and Tsukuda et al., they clarified the electronic and geometrical structures of a series of isolated Aun(SC12H25)m clusters and concluded that the transition from bulk to non-bulk occurs in the region from Au187(SC12H25)68 to Au144(SC12H25)60 in the Aun(SC12H25)m clusters ( Figure 12C). 154 Regarding this transition, the recent studies by Jin et al. 155,156 and Dass et al. 157,158 reveled that the transition from bulk to non-bulk occurs between Au279(SR)84 to Au246(SR)80 in the case of Aun(SR)m clusters including benzenthiolate in the functional group of the ligand. Knoppe et al. also studied the separation of these Aun(SC12H25)m clusters. They found the conditions for separating Au25(SC12H25)18 and Au38(SC12H25)24 with high resolution and revealed the correlation between alkyl chain length and retention time through experiments conducted under such a condition. 159 Black and Whetten et al. separated Aun(SC2H4Ph)m clusters using a capillary C18 column. Their use of a capillary column was unique, enabling suppression of the quantity of the mobile phase and thereby direct evaluation of the chemical composition of the eluted cluster with a directly connected ESI mass spectrometer ( Figure 12D). 160,161 They also succeeded in clearly separating Au104(SC2H4Ph)45, Au130(SC2H4Ph)50, Au137(SC2H4Ph)56, and Au144(SC2H4Ph)60 using a similar method. 161

Separation of clusters by charge state
As described above, in RP partition chromatography, each solute can be separated by the difference in the partition coefficient in the column. Because the charge state of the solute greatly affects the partition coefficient, separating Aun(SC2H4Ph)m clusters with different charge states can be easily achieved using RP partition chromatography.

Separation of clusters by ligand combination
The physical and chemical properties of Aun(SR)m clusters vary depending on the ligand type in addition to the core size. For example, the solubility in a solvent and the quantum yield of PL 166 vary depending on the functional group of the ligand. When a SR with a specific function is used as the ligand, it is possible to provide a specific function, such as molecular recognition ability 167 or catalytic ability, to the Aun(SR)m clusters. Thus, controlling the ligand composition is an extremely effective way to control the function of the cluster. If it were possible to substitute only a limited number of ligands with other SRs, strict control of the function of metal clusters might be possible as well as regular arrangement of metal clusters on the substrate. However, when Aun(SR)m clusters are synthesized using multiple types of SRs, the product typically has a distribution in the ligand combination. [168][169][170] Therefore, to realize strict control of functions and precise arrangement of clusters, it is necessary to separate the obtained mixture at high resolution depending on the ligand combination. Using RP partition chromatography, it is also possible to separate Aun(SR1)m−x(SR2)x clusters with two types of ligands (SR1 and SR2) depending on the ligand combination.
Negishi and Pradeep et al. reported that multiple ligands of Au24Pd(SC12H25)18 can be exchanged to SBB (4-tertbutylbenzenemethanethiolate) via the reaction of Au24Pd(SC12H25)18 with 4-tert-butylbenzenemethanethiol (BBSH) in solution. However, the obtained cluster had a distribution in the number of exchanged ligands. They succeeded in separating such a mixture depending on ligand composition using RP partition chromatography. 171 In this experiment, first, all the Au24Pd(SC12H25)18−x(SBB)x was adsorbed on the stationary phase. Then, Au24Pd(SC12H25)18−x(SBB)x with higher polarity was eluted sequentially by decreasing the polarity of the mobile phase using a gradient program ( Figure  14A). It is assumed that the difference in the adsorption ability to the stationary phase was also involved in this separation in addition to the difference in the partition coefficient. Niihori et al. demonstrated that such a method is applicable to the separation of various Au24Pd(SR1)m−x(SR2)x clusters with two types of SRs ( Figure 14B). 172 In later studies, Niihori et al. also succeeded in further improving the resolution, thereby enabling the separation of Au24Pd(SC2H4Ph)18-x(SC12H25)x (x = 1,2) depending on the coordination isomers ( Figure 14C). 173 Such separation revealed a preferred site for ligand exchange.

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Please do not adjust margins those of the monometallic Aun(SR)m clusters. Therefore, research on alloy clusters has recently become a hot topic. 23,53,162−165,172,174−213 To deeply understand the correlation between structure and physical/chemical properties in such an alloy cluster, it is necessary to control the chemical composition of the alloy cluster. Synthesis methods with atomic precision have already been established for several alloy clusters. However, many alloy clusters cannot yet be synthesized with atomic precision. The representative clusters are 25-atom and 38-atom clusters composed of Au and Ag (Au25−xAgx(SR)18 and Au38−xAgx(SR)24). 163,164,210,214 Using RP partition chromatography, it is also possible to separate these mixtures depending on the chemical composition of the metal core.

Ion-pair chromatography
As described in section 4, PAGE has been mainly used for the separation of hydrophilic clusters. However, if RP partition chromatography can be used for the separation of hydrophilic clusters, it becomes possible to determine the chemical composition of the separated clusters using LC/MS. Separation of such hydrophilic clusters by RP partition chromatography can be achieved by changing the hydrophilic surface of the cluster to a hydrophobic surface with an ion-pair reagent ( Figure  16A). 215 There have been several reports on the separation of hydrophilic clusters depending on the core size using such ionpair chromatography.
The first report was on the separation of Aun(NALC)m and Aun(S(PG))m clusters (NALC = N-acetyl-L-cysteine) by Murray et al. In this study, they used a C18 column for the stationary phase and tetrabutylammonium fluoride ((C4H9)4N + F − ) for the ion-pair reagent. 216 Aun(NALC)m and Aun(S(PG))m clusters were separated depending on the core size because (C4H9)4N + ions formed ion pairs with hydrophilic clusters, and therefore, the cluster surface caused a hydrophobic interaction with the stationary phase. Later, Choi et al. attempted to separate Aun(NALC)m clusters under similar experimental conditions. In the study by Murray et al., the separated Aun(NALC)m clusters were characterized by optical absorption spectroscopy. 216 However, Choi et al. separated each fraction and obtained their MALDI mass spectra ( Figure 16B). They confirmed that the Aun(NALC)m clusters could be separated depending on the chemical composition using this method. 217 They also attempted to separate Aun(NALC)m clusters using an ultra HPLC (UHPLC) instrument. The results indicated that the separation could be performed in approximately 10% of the retention time with sharper peaks appearing in the chromatogram compared with the results obtained using the normal HPLC apparatus. 218 Dong and Choi et al. conducted similar experiments on Pdn(NALC)m clusters and succeeded in separating them depending on the chemical composition. 219 Niihori et al. performed separation of Aun(SG)m clusters including the most commonly used hydrophilic ligand, SG, using ion-pair chromatography and succeeded in achieving higher-resolution separation than PAGE separation. 215 In these studies, ion-pair chromatography was used for the separation; however, the chemical composition of the separated clusters was not determined by LC/MS. Because (C4H9)4N + easily forms an ion pair with the dissociable functional group of the ligand and easily interacts with the stationary phase, a relatively high-resolution separation could be achieved when (C4H9)4N + is used as the ion-pair reagent. However, (C4H9)4N + is non-volatile and cannot be used in LC/MS because the salt precipitates during the ionization process.

Hydrophilic interaction liquid chromatography
In this way, by using an ion-pair reagent, it is possible to separate the hydrophilic clusters depending on the core size using RP partition chromatography. In addition, when a volatile ion-pair reagent is used, the chemical composition of the separated clusters can be determined using an ESI mass spectrometer directly connected with RP partition chromatography. However, if a hydrophilic interaction liquid chromatography (HILIC) column 224 were used for the separation of the hydrophilic clusters, even ion-pair reagents become unnecessary, and the separation and evaluation of hydrophilic clusters would be facilitated.  Figure 17A). They used two columns (a ZIC-cHILIC and Amido-80 column; Figure 11B). The Aun(SG)m clusters were separated with high resolution. 211 In this study, they detected the Aun(SG)m clusters that had never been reported ( Figure 17B). All the synthesized clusters were introduced to the mass spectrometer, unlike the case using PAGE ( Figure 17A). Thus, small species that have almost never been observed before were also detected in addition to the previously reported stable species. The use of the HILIC column also enabled the separation of Aun−xMx(SG)m alloy clusters depending on the number of constituent atoms. The chemical composition evaluation by LC/MS resulted in the discovery of new Aun−xPdx(SG)m clusters, such as Au14Pd(SG)13, Au24Pd(SG)18, and Au28Pd(SG)20, which had not been reported until then. Stamplecoskie et al. also separated Agn(SG)m clusters using an amide column and revealed the size dependence of the optical properties of Agn(SG)m clusters 225 (although the technique is not described as HILIC in the original paper, it is speculated that each Agn(SG)m cluster was separated in HILIC mode from the experimental conditions).

Size exclusion chromatography
In the RP partition chromatography and the HILIC described above, a chemical interaction (partitioning and/or adsorption) occurs between the stationary phase and clusters, and accordingly, the difference in the mobility of each cluster results in separation of the clusters. However, in size exclusion chromatography (SEC), each cluster is separated by physical size. Therefore, when separating the clusters using the size exclusion mode, a stationary phase that does not interact with the clusters must be selected. SEC is divided into gel permeation chromatography (GPC) and gel filtration chromatography (GFC). In GPC, the mobile phase is an organic solvent, and in GFC, the mobile phase is an aqueous solvent. In these separations, Aun(SR)m clusters elute from the column in the order from largest to smallest.

Gel permeation chromatography
It is reasonable to first consider using SEC for the separation of Aun(SR)m clusters depending on the core size. Wilcoxon et al. attempted to separate Aun(SR)m clusters using GPC in 2000. 226 In this study, porous organics were used as the stationary phase ( Figure 11C). When this experiment was conducted, it was not yet possible to determine the chemical composition of Aun(SR)m clusters with atomic precision. Therefore, in their earlier work, they synthesized Aun(SClH2l+1)m clusters with similar metal core sizes (~2 nm) using several SClH2l+1 with different alkyl chain lengths (l = 6−18). Then, the thickness of the ligand layer in each Aun(SClH2l+1)m cluster (l = 6−18) was studied by comparing their retention times. Regarding the thickness of the ligand layer, Tsukuda et al. also later studied Pdn(SClH2l+1)m clusters (l = 10, 12, 14, 16, or 18). 227 Wilcoxon et al. then performed size separation of Aun(SClH2l+1)m and Agn(SC12H25)m clusters with a metal core size of 1.3-8.0 nm. They obtained knowledge on the correlation between the particle size and electronic structure from their findings. 228,229 Tsukuda et al. succeeded in separating Aun(SC18H37)m clusters with higher resolution by recycling ( Figure 18A), 230 and successfully isolated Aun(SClH2l+1)m clusters (l = 12, 18) having Au55 as the metal core with high purity. 231 In a later study, Jin et al. revealed that this cluster has the chemical composition of Au55(SR)31 using ESI-MS ( Figure 18B). 232 Jin et al. also succeeded in separating Au38(SC2H4Ph)24 and Au40(SC2H4Ph)24, whose chemical compositions are very similar, using GPC. 233 GPC is also utilized for tracking reactions. Negishi et al. traced the growth of Agn(SBB)m clusters using GPC. The clusters were observed to settle in a stable cluster at 96 h under their reaction conditions ( Figure 18C). 234 Jin et al. and Zhu et al. also used GPC to track several reactions and discovered a method to size-selectively synthesize Aun(SR)m clusters, such as Au19(SC2H4Ph)13, Au20(SC2H4Ph)16, and Au24(SC2H4Ph)20, with atomic precision. 235,236

Gel filtration chromatography
For the separation of hydrophilic clusters, there have only been a few reports on the separation by GFC because PAGE is frequently used for these clusters. Thus, the purpose of GFC separation is limited to cluster purification ( Figure 18D). 237 Inouye et al. used GFC to purify mercaptoacetic acid (MAA)protected Pt clusters (Ptn(MAA)m). In this experiment, they used a stationary phase consisting of porous silica ( Figure 11D). They succeeded in isolating Pt5(MAA)8, which emits blue light, and Pt8(C2H2O2S)8, which emits green light, with high purity using GFC. 238

Chiral chromatography
In chiral chromatography, a compound is separated into optical isomers by utilizing the difference in interaction between the compound and a stationary phase with chirality. The stationary phase is composed of silica gel chemically modified with a chiral compound, such as cellulose. (Figure 11E). A "three-point bond model" has been proposed for the separation mechanism of the optical isomers. 239 According to this mechanism, a compound and a chiral stationary phase form a diastereometric aggregate because of interaction at three binding sites. Because the binding energy of such an aggregate differs depending on the optical isomer ( Figure 11E), a difference in the retention time of each optical isomer is observed. Interactions forming aggregates include hydrogen-bond formation, charge-transfer complex formation, ion-pair formation, coordination bonding to metals, and dipole-dipole interaction. In the actual separation, these interactions contribute singly or in combination.
Kornberg et al. determined the geometrical structure of the Aun(SR)m cluster for the first time in 2007, revealing that the Aun(SR)m cluster consisted of a Au core covered with multiple Au(I)-SR staple and that Au102(p-MBA)44 has optical isomers. 240 Since then, many Aun(SR)m clusters have been revealed to have optical isomers by SC-XRD analysis. 61, 241−243 Bürgi et al. succeeded for the first time in separating Au38(SC2H4Ph)24 ( Figure 19A) into chiral isomers using chiral chromatography in 2010 ( Figure 19B). 244 In this study, a stationary phase in which cellulose was chemically modified on the silica surface was used. The separation resulted in obtaining much information on the physical/chemical properties of the chiral Aun(SR)m clusters, which were previously unknown. For example, for the chemical properties, it was revealed that when one of the optical isomers of Au38(SC2H4Ph)24 was left in a solvent at 80 °C, racemization proceeded and the enantiomeric excess became 27% in 15 min. 245 The researchers performed the same separation and reaction tracking for Au40(SC2H4Ph)24 and observed that Au40(SC2H4Ph)24 does not racemize unless it is left in solution at a higher temperature. 246 The researchers also revealed that the two optical isomers had different reaction rates in the ligand exchange reaction with 1,1'binaphthyl-2,2'-dithiol (R-BINAS), which has optical isomerism. 247 It was also clarified that introducing R-BINAS into the ligand layer by ligand exchange improves the stability of the cluster and can suppress racemization of the optical isomer ( Figure 19C). 248 Soai and Negishi et al. studied the asymmetric autocatalytic reaction (Soai reaction 249 ) in which a chiral compound asymmetrically synthesizes itself and selfproliferates using each optical isomer of Au38(SC2H4Ph)24. This study revealed that each optical isomer of Au38(SC2H4Ph)24 can be used as an asymmetric catalyst. 250 Chiral chromatography has also been used for optical separation of other Aun(SR)m and related clusters. [251][252][253][254][255][256][257][258][259][260][261] The use of such chiral chromatography is expected to provide a deeper understanding of the asymmetric catalytic activity and circularly polarized light emission 262 of each optical isomer in the future.

Thin-Layer Chromatography Separation
TLC uses an inexpensive and simple device different from that used for HPLC. Furthermore, in TLC, the separation can be visually confirmed similarly to PAGE. The use of preparative thin-layer chromatography (PTLC) using a thicker silica gel than that used in TLC makes it possible to isolate each cluster on a relatively large scale. Therefore, TLC is often used to confirm the purity of a product. When Wu and Jin et al. elucidated the geometrical structure of Au144(SR)60 by SC-XRD, PTLC was used to increase its purity. 263 For a mixture of Aun(SR)m and related clusters composed of clusters with great difference in size and charge state, this method can be used for the separation of clusters depending on the size and charge state.

Summary and Outlook
This review summarized previous research on the highresolution separation of Aun(SR)m and related clusters by focusing on PAGE, HPLC, and TLC. From this summary, the following characteristics of each separation method were revealed.

PAGE:
Main target: hydrophilic clusters Advantages: i) inexpensive and simple, ii) possible to separate clusters containing 40 or less atoms with atomic precision, iii) possible to confirm separation visibly by the naked eye Because the precise synthesis techniques of Aun(SR)m and related clusters have progressed rapidly in the last 20 years, many studies on their separation have been reported. We hope that this review will provide guidelines to understand the characteristics of each separation method and enable the selection of an appropriate separation method for the target experiment.
In addition, it is hoped that the established techniques will be used more widely in the future for the separation of metal clusters. The chemical properties of Aun(SR)m and related clusters have still not been clarified completely. For example, although it has been revealed that many Aun(SR)m and related clusters have a chiral structure, the asymmetric catalytic activity and circularly polarized luminescence of each optical isomer have not yet been revealed. It is expected that these physical/chemical properties can be elucidated by studying each optical isomer separated by chiral chromatography. In addition, metal exchange between Aun−xMx(SR)m clusters has been shown to occur in solution. 20 However, there are still many unclear points about the mechanism of the metal exchange reaction. A deep understanding of this mechanism could be obtained if the reaction proceeded using Aun−xAgx(SR)m clusters isolated with atomic precision 211,212 and the reaction process was tracked using LC/MS. In future studies, the effective use of established separation techniques is expected to provide a deep understanding of the functions and properties of Aun(SR)m and related clusters.
Furthermore, there are some helpful separation/analysis techniques that should be actively incorporated in future research on metal clusters. For example, MS/MS in LC/MS is useful not only for determining the chemical composition of a product but also for analysing the structure of the product. 269 An introduction of two-dimensional HPLC is also interesting for analysis. 270 If such a method is introduced, comprehensive twodimensional separation could be realised using two different separation modes. For instance, an optical isomer generated based on the position of an exchange ligand is expected to be isolated by this method.
As introduced in this review, separation/analysis techniques for metal clusters have been developing with the improvement of separation and analysis equipment. HPLC columns and mass spectrometers are still being improved day after day. We hope that the separation and analysis techniques for metal clusters will continue to evolve in the future with researchers being conscious of the latest techniques available for each device and continuing to actively incorporate such techniques into research on metal clusters.