Assembly of silver Trigons into a buckyball-likeAg180 nanocageZhi Wanga,1, Hai-Feng Sub,1, Yuan-Zhi Tanb, Stan Scheinc,d,2, Shui-Chao Linb, Wei Liue, Shu-Ao Wange,Wen-Guang Wanga, Chen-Ho Tunga, Di Suna,2, and Lan-Sun Zhengb

aKey Lab of Colloid and Interface Chemistry, Ministry of Education, School of Chemistry and Chemical Engineering, Shandong University, Jinan, 250100,People’s Republic of China; bState Key Laboratory for Physical Chemistry of Solid Surfaces, College of Chemistry and Chemical Engineering, XiamenUniversity, Xiamen, 361005, People’s Republic of China; cCalifornia NanoSystems Institute, University of California, Los Angeles, CA 90095-1563;dDepartment of Psychology, University of California, Los Angeles, CA 90095-1563; and eSchool for Radiological and Interdisciplinary Sciences, SoochowUniversity, Jiangsu 215123, People’s Republic of China

Edited by Vivian Wing-Wah Yam, The University of Hong Kong, Hong Kong, China, and approved September 28, 2017 (received for review July 07, 2017)

Buckminsterfullerene (C60) represents a perfect combination of ge-ometry and molecular structural chemistry. It has inspired many cre-ative ideas for building fullerene-like nanopolyhedra. These includeother fullerenes, virus capsids, polyhedra based on DNA, and syn-thetic polynuclear metal clusters and cages. Indeed, the regular or-ganization of large numbers of metal atoms into one highly complexstructure remains one of the foremost challenges in supramolecularchemistry. Here we describe the design, synthesis, and characteriza-tion of a Ag180 nanocage with 180 Ag atoms as 4-valent vertices (V),360 edges (E), and 182 faces (F)––sixty 3-gons, ninety 4-gons, twelve5-gons, and twenty 6-gons––in agreement with Euler’s rule V − E +F = 2. If each 3-gon (or silver Trigon) were replaced with a carbonatom linked by edges along the 4-gons, the result would be like C60,topologically a truncated icosahedron, an Archimedean solid withicosahedral (Ih) point-group symmetry. If C60 can be described math-ematically as a curling up of a 6.6.6 Platonic tiling, the Ag180 cage canbe described as a curling up of a 3.4.6.4 Archimedean tiling. High-resolution electrospray ionization mass spectrometry reveals that{Ag3}n subunits coexist with the Ag180 species in the assembly systembefore the final crystallization of Ag180, suggesting that the silverTrigon is the smallest building block in assembly of the final cage.Thus, we assign the underlying growth mechanism of Ag180 to theSilver-Trigon Assembly Road (STAR), an assembly path that might befurther employed to fabricate larger, elegant silver cages.

supramolecular chemistry | coordination assembly | symmetry |silver cage | Goldberg cage

Symmetry is a consequence of the self-assembly of many beautifulmolecules (1–8), with assembly of C60 from a cooling carbon

plasma (9) one of the best-known examples. In nature, living or-ganisms take advantage of molecular self-assembly to construct manycomplicated macromolecules. For example, COPII protein assemblesinto two Archimedean solids, the cuboctahedron and the icosidode-cahedron (10), ferritin forms a rhombic dodecahedron (11), andspherical viruses form icosahedral cages (12, 13). Inspired by C60 andsuch biological macromolecules, scientists face the challenge ofmimicking and synthesizing comparably impressive single molecules(14, 15) from large numbers of subcomponents. However, thesynthesis of molecules as impressive as C60 has been rare––but seeAs20 (2), [{Cp*Fe(P5)}12{CuCl}10{Cu2Cl3}5{Cu(CH3CN)2}5] (3),Mo368 (16), Ti42 (17), Cd66 (18), Pd145 (19), Al56 (20), Ln104 (21),[{CpBIGFe(P5)}12{CuBr}92] (22), [{Cp*Fe(P5)}12{CuCl}20] (23),[{CpBnFe(P5)}12{CuCl}20] (24), Pd30 (25), and Ag374 (26), allPlatonic solids, Archimedean solids, or combinations of them.Nanosized silver clusters have attracted increasing research in-

terest because of their fascinating structures and potential appli-cations (27–29). Although silver clusters with up to 490 metalatoms in the core are known (30), these lack high symmetry. Silveratoms are prone to form polygons like 3- and 4-gons with the aid ofan argentophilic interaction (31) and/or ligation of thiolates. Herewe report fabrication of these polygonal building blocks commonin Platonic and Archimedean solids into a highly symmetric cage.

Results and DiscussionIn our effort to use thiolates as capping ligands to construct well-ordered silver clusters, we fabricated a nanocage with 180 silveratoms (Fig. 1A and B and SI Appendix, Table S1) based on abundantargentophilic interactions (Fig. 1C and SI Appendix, Table S2). The{Ag180}

46+ (hereafter, Ag180 for short) cage has these characteristics:(i) With 180 metal atoms, it is a very large silver cage, not a cluster.(ii) It is a silver cage with icosahedral (Ih) topology. (iii) It comprises3-, 4-, 5-, and 6-gons (Fig. 1D). (iv) It has high solution stability.Solvothermal reaction (65 °C) of [Ag(iPrS)]n (iPr = isopropyl,

C3H7) and CH3SO3Ag (silver methanesulfonate) in methanol(see SI Appendix for detailed methods) gives yellow, octahedron-shaped crystals of complex 1 (SI Appendix, Fig. S1). Complex 1was fully characterized by high-resolution electrospray ionizationmass spectroscopy (HR-ESI-MS), 1H NMR on acid-digestedsolutions of crystals, thermogravimetric analysis, and single-crystal X-ray diffraction (Fig. 1 A and B and SI Appendix, Ta-ble S1), to assess solution behavior and assembly mechanism,organic ligand ratio, thermal stability, and its average structure.Because the crystals are fragile and unstable on leaving the

mother liquor, we collected X-ray diffraction data from a singlecrystal protected by Paraton oil at 100 K on a Bruker APEX II

Significance

Here we present a striking outcome from the alliance betweenchemistry and mathematics in the design, synthesis, and charac-terization of a silver cage, Ag180. In principle, the design replaceseach carbon atom of C60 with a triplet of argentophilicity-bondedsilver atoms to produce a 3.4.6.4 (1,1) polyhedron with sixty3-gons, ninety 4-gons, twelve 5-gons, and twenty 6-gons. Resultsfrom mass spectroscopy suggest an assembly mechanism in so-lution based on such triplets––the Silver-Trigon Assembly Road(STAR). Indeed, the STAR mechanism may be a general syntheticpathway toward even larger silver polyhedral cages. Besides itsfundamental appeal, this synthetic cage may be considered foruse as a molecular luminescent thermometer.

Author contributions: D.S. conceived and designed the experiments; Z.W. conducted synthe-sis and characterization; H.-F.S., Y.-Z.T., S.-C.L., W.L., S.-A.W., and D.S. performed research;H.-F.S., Y.-Z.T., S.-C.L., W.L., S.-A.W., and D.S. analyzed data; S.S. analyzed the mathematics ofthe polyhedral structure; and Z.W., S.S., W.-G.W., C.-H.T., D.S., and L.-S.Z. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

Published under the PNAS license.

Data deposition: The atomic coordinates and structure factors have been deposited in theCambridge Structural Database, Cambridge Crystallographic Data Centre, www.ccdc.cam.ac.uk (accession code CCDC 1541756).1Z.W. and H.-F.S. contributed equally to this work.2To whom correspondence may be addressed. Email: stan.schein@gmail.com or dsun@sdu.edu.cn.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1711972114/-/DCSupplemental.

12132–12137 | PNAS | November 14, 2017 | vol. 114 | no. 46 www.pnas.org/cgi/doi/10.1073/pnas.1711972114

Dow

nloa

ded

by g

uest

on

June

2, 2

020

Dow

nloa

ded

by g

uest

on

June

2, 2

020

Dow

nloa

ded

by g

uest

on

June

2, 2

020

single-crystal diffractometer. X-ray crystallographic results revealthat complex 1 crystallizes in the highly symmetric cubic spacegroup Fm-3 with a large unit-cell volume of ∼110,000 Å3 (SIAppendix, Table S1). The electron-density map provides alandscape of the overall connectivity of a giant cage with 180 Agatoms (Fig. 1C), 90 iPrS−, and 44 CH3SO3

−, and its asymmetricunit contains only 1/24th of the cage (SI Appendix, Fig. S2).The exact molar ratio of iPrS− and CH3SO3

− in 1 was furtherdeduced from the 1H NMR spectra of a DCl-digested solution ofthe crystals of 1 (SI Appendix, Fig. S3). Proton resonances with thepredicted positions and coupling patterns are clearly detected in theexpected regions. By integrating resonance peak intensities, we findthat the iPrS− and CH3SO3

− are in the proportion 1:1.005, in-dicating that they are equimolar in 1. Thermogravimetric analysis ofpolycrystalline samples of 1 (SI Appendix, Fig. S4) show that thecomplex loses guest methanol (total percentage mass loss = 3.08%)from 30 °C to 69 °C and stabilizes to 143 °C before decomposition.Based on the above data, the reliable formula of 1 can be deducedto be {[Ag180(

iPrS)90(CH3SO3)44]·(CH3SO3)46·34CH3OH} (alsodenoted as 1a·46CH3SO3·34CH3OH).This Ag180 cage has 360 Ag···Ag edges (Fig. 1C). Of these,

180 are in the 3.00–3.14-Å range (SI Appendix, Table S2; numberingof Ag atoms in Fig. 2A and SI Appendix, Fig. S2) that is charac-teristic of genuine argentophilic interactions, and these bonds(purple edges in Fig. 1C) are found exclusively in the silver Tri-gons (purple-filled triangles in Fig. 1D). Another 180 Ag···Ag edgelengths, 3.19–3.67 Å (black edges in Fig. 1C) (SI Appendix, TableS2), represent very weak argentophilic interactions (32). (Due tofour disordered silver atoms, the Ag···Ag distances related to theseAg atoms are discussed based on only the main orientation.) On the

basis of these argentophilic interactions, the surface of the Ag180cage can be divided into four kinds of all-silver polygons: sixty3-gons, ninety 4-gons, twelve 5-gons and twenty 6-gons (Fig. 1D).All iPrS− ligands––appearing as just (yellow and blue) S atoms in

Fig. 2A––were ligated on the 4-gons in μ4 fashion with Ag–S dis-tances of 2.29–2.54 Å (SI Appendix, Table S2). Among the 90 iPrS−

ligands, 60 coordinate from positions outside the Ag180 cage. Theseare marked in Fig. 2A by S atoms colored yellow above all of the five4-gons surrounding each of the twelve 5-gons. The remaining 30 co-ordinate from positions inside the Ag180 cage and are marked by Satoms colored blue. Each of the twenty 6-gons share three 4-gonswith another 6-gon, and it is these 30 shared 4-gons (20 × 3/2 = 30)that have the interior iPrS− ligands marked by blue S atoms. Thus,the 4-gons around each 6-gon are capped by alternating exterior(yellow) and interior (blue) iPrS− ligands.In addition, there are 44 CH3SO3

− ligands, shown as just SO3groups in Fig. 2A. Each of the twenty 6-gons is capped by oneCH3SO3

− ligand on the outside of the cage, marked by a yellow Satom and three (red) O atoms. Each of the twelve 5-gons iscapped by two CH3SO3

− ligands, one outside the cage, alsomarked by a yellow S atom and three (red) O atoms, and oneinside, marked by a black S atom and three (red) O atoms. Dueto the large steric hindrance from the iPrS− ligands capping thesurrounding 4-gons, no CH3SO3

− ligands cap the silver 3-gons.Due to the coordination interactions between Ag atoms andO and

S donors, eight crystallographically unique Ag atoms can be dividedinto two groups without the consideration of Ag···Ag interactions.Based on interatomic distances (SI Appendix, Table S2) and asshown in Fig. 2A and SI Appendix, Fig. S2, Ag2–Ag8 coordinate

Fig. 1. Molecular structure of the nanocage Ag180.(A) Space-filling model of the structure of 1 (Ag180)established by X-ray crystallography. H atoms areomitted for clarity. Atoms colored green, red, yel-low, and gray correspond to Ag, O, S, and C. (B) Ball-and-stick model of the structure of 1 (Ag180) corre-sponding to the space-filling model in A that omits Hatoms. (C) Ball-and-stick model of only the Ag atoms(purple balls). The 180 Ag-Trigon (purple) bonds arewithin the length range for argentophilic interac-tions (SI Appendix, Table S2). The 180 (black) edgesare longer. (D) Silver 3-, 4-, 5-, and 6-gonal faces indifferent colors on the Ag180 nanocage.

Wang et al. PNAS | November 14, 2017 | vol. 114 | no. 46 | 12133

CHEM

ISTR

Y

Dow

nloa

ded

by g

uest

on

June

2, 2

020

with two sulfur atoms and one oxygen atom, whereas Ag1 co-ordinates with two sulfur atoms and two oxygen atoms.The Ag180 has a spherical shape with a bare silver cage diameter

of 2.5 nm and an overall diameter (including the ligand shell) of3.0 nm, whereas the diameter of the inner void is 1.9 nm, thus anaccessible volume of the inner cavity calculated as 3,769 Å3. Of thetotal unit-cell volume, 43.7% is occupied by disordered methanolmolecules and CH3SO3

− that are not imaged by X-ray crystallog-raphy but are revealed by the following HR-ESI-MS experiments.The HR-ESI-MS of crystals of complex 1 dissolved in

methanol (Fig. 3A) shows three sequentially charged parention species centered at m/z 5,781.11, 6,960.63, and 8,713.51 thatwe assign to {1a·40CH3SO3·15CH3OH·2H2O}6+ ({Ag3}60

6+, m/zCalc. = 5,780.84), {1a·41CH3SO3·14CH3OH·5H2O}5+ ({Ag3}60

5+,Calc. m/z = 6,960.41), and {1a·42CH3SO3·15CH3OH·H2O}4+

({Ag3}604+, Calc. m/z = 8,714.25), respectively, indicating that the

large Ag180 cage retains its structural integrity in methanol.We attribute three dominant fragment peaks below m/z = 3,000 to

{[Ag30K(iPrS)13(CH3SO3)12(OH)3]}

3+ ([{Ag3}10-α]3+, Exp. m/z =1,814.70; Calc. m/z = 1,814.74), {[Ag30K(

iPrS)13(CH3SO3)13(OH)3]}2+

([{Ag3}10-β]2+, Exp. m/z = 2,769.54; Calc. m/z = 2,769.60), and{[Ag30(

iPrS)8(CH3SO3)19Cl(CH3OH)2]}2+ ([{Ag3}10-γ]2+, Exp.

m/z = 2,871.48; Calc. m/z = 2,871.50). We assign detailed molec-ular formulae for these species based on the experimental and sim-ulated isotopic distributions (SI Appendix, Fig. S5 A–C). We found noother fragments, suggesting a coordination–disassociation equilibriumpredominantly between Ag30 and Ag180 species in solution, which isfurther evidenced by successful recrystallization of 1 in methanol.In addition, the X-ray structure shows argentophilic interac-

tions that are distributed only in silver Trigons, suggesting anassembly mechanism based on the silver Trigons. In furthersupport of this mechanism, the HR-ESI-MS of the solution aftersolvothermal reaction (Fig. 3B) reveals a series of oligomericsilver Trigons species in the m/z = 500–3,000 range with differentcharge states. The most dominant peak is {Ag3}1

1+. The otherscorrespond to integer multiples of the Ag3 Trigon, includ-ing {Ag3}2

1+, {Ag3}42+, {Ag3}5

2+, {Ag3}62+, {Ag3}7

2+, {Ag3}82+,

and [{Ag3}10-δ]2+. We assign detailed molecular formulae forthese species as well based on the experimental and simulatedisotopic distributions (SI Appendix, Fig. S5 D–K). The HR-ESI-MS of the solution after solvothermal reaction (Fig. 3B) alsoshows three Ag180 species with diminishing positive charges,[{Ag3}60-α]6+, [{Ag3}60-β]5+, and [{Ag3}60-γ]4+, almost thesame to those observed in ESI-MS of dissolved crystals of 1 inmethanol but with different numbers of solvent molecules.The rich {Ag3}n fragments and some nascent {Ag3}60 species

in the assembly process before the final crystallization of theAg180 cage suggest that the {Ag3} building block plays a specialrole in formation of the Ag180 cage. We thus assign the un-derlying growth mechanism of Ag180 to the Silver-Trigon As-sembly Road (STAR), in which silver Trigons (purple triangles inthe Schlegel diagram of the Ag180 cage shown in Fig. 2B) act asthe smallest building block that is gradually aggregated bybridging iPrS− and CH3SO3

− to form larger {Ag3}n species.We further suppose that “pentaTrigons” are assembled from

five (purple) Trigons linked to each other by iPrS− ligands toform 4-gons (Fig. 2B). These 4-gons, marked by yellow disks as inFig. 2A, have iPrS− ligands that will end up on the “outside” of

Fig. 2. STAR. (A) ORTEP plot for the crystal structure of 1a (Ag180) withnumbered crystallographically independent Ag atoms (green). C and Hatoms are omitted for clarity. Atoms, bonds, and edges in front obscure theirmirror counterparts in back. S atoms from exterior iPrS− (isopropyl sulfide–C3H7S

−) ligands “above” 4-gons are colored yellow; S atoms from interioriPrS− ligands “below” 4-gons are colored blue. Exterior CH3SO3 ligands areshown as SO3 groups above 5-gons and 6-gons with O atoms in red and Satoms in yellow. Interior CH3SO3 ligands are shown as SO3 groups below5-gons with O atoms in red and S atoms in black. (B) Ultimately, the cage isassembled from silver Trigons, the colored triangles. We suppose that five

Trigons assemble into a pentaTrigon, {Ag3}5, that includes five Trigons, pairsof argentophilic bonds that create five linking 4-gons, each with its co-ordinating iPrS− ligand on the outside (thus marked by a yellow disk), and a5-gon. As shown in these Schlegel (plane) diagrams of Ag180, pentaTrigonscould further link to each other with pairs of bonds that create a 4-gon withits iPrS− ligand on the inside (thus marked by a blue disk). (C) Assembly bydecaTrigons {Ag3}10, each composed of two linked pentaTrigons.

12134 | www.pnas.org/cgi/doi/10.1073/pnas.1711972114 Wang et al.

Dow

nloa

ded

by g

uest

on

June

2, 2

020

the cage (Fig. 1 A and B). We then suppose that the Ag180 cage as-sembled itself from 12 pentaTrigons linked to each other by iPrS−

ligands to form additional 4-gons. These latter 4-gons have iPrS− li-gands that end up on the “inside” of the cage and are thus marked byblue disks in Fig. 2B (as in Fig. 2A). An interesting feature of this pathis that the formation of pentaTrigons and their attachments to makeAg180 appear not to require independent generation of hexagons andtheir surrounding 4-gons. However, the prominence of {Ag3}10 incages dissolved in methanol suggests a path that relies on initialassembly of pentaTrigons into decaTrigons {Ag3}10, as marked byadjacent pairs of pentaTrigons with Trigons of the same color inFig. 2C) and then assembly of six of the latter into the Ag180 cage.In the Ag180 cage, Ag···Ag edge lengths in 3-gons, 4-gons, and

5-gons are not exactly equal; 5-gons are not equiangular, and 6-gonscentered on the presumed threefold axis are also not equiangular (SIAppendix, Table S2). For these reasons, although the Ag180 cage hasmirror planes––as can be appreciated from Figs. 1 and 2A, where the“front” half of the cage is in perfect register with and thus occludesthe “back” half of the cage––it does not have all of the symmetries ofa geometrically icosahedral structure. Nonetheless, the overall to-pology of the Ag180 cage is icosahedral. Likewise, C60 has two dif-ferent bond lengths (33), longer in the five bonds within pentagonsand shorter in the three remaining bonds within 6-gons, so it re-sembles but is not identical to the truncated icosahedron.The similarities go deeper. Replacing each atom of the trun-

cated icosahedron (Fig. 4A, heavier lines) with a triangle (rep-resenting a silver Trigon) produces an icosahedral cage withthree times as many (3 × 60 = 180) vertices, sixty 3-gons, ninety4-gons, twelve 5-gons, and twenty 6-gons, a cage with the same(icosahedral) topology as Ag180 (Fig. 4A, lighter lines; Fig. 4B).Indeed, both the truncated icosahedron (or C60) and the Ag180cage are the (1,1) members of a series of icosahedral cages,where the (1,1) Goldberg indices specify the triangle that is gluedto each of the 20 triangles of an icosahedron to produce the finalicosahedral cage (12, 34–36) (Fig. 4 C and D; see “Goldbergindices and Goldberg cages” in SI Appendix).

As noted, in the Ag180 cage all of the 4-gons surrounding a5-gon coordinate with an iPrS− ligand on the outside of the cage,so those 4-gons are marked by yellow disks (Fig. 4B). By contrast,of the six 4-gons surrounding a 6-gon, yellow alternates withblue: Three of the 4-gons are shared with a 5-gon and are alreadymarked by yellow disks, whereas the other three are shared be-tween 6-gons, coordinate with an iPrS− ligand on the inside ofthe cage, and are marked by blue disks. Thus, there appear to betwo rules for assembly of Ag180. (i) All of the 4-gons surroundinga 5-gon are marked by yellow disks; (ii) To minimize sterichindrance, each triangle is surrounded by two 4-gons marked byyellow disks and one 4-gon marked by a blue disk. Therefore, forthe triangles surrounding the 5-gon, already surrounded by two“yellow 4-gons,” the third 4-gon must be blue.Examination of Fig. 4D suggests that only 3.4.6.4 cages with

T (= i2 + ij + j2) divisible by 3, e.g., T = 3, 9, and 12 [(i, j) = (1,1),(3,0), and (2,2)], obey both rules. By contrast, for T = 1 [(i,j) = (1,0)],all three 4-gons surrounding a 3-gon are yellow (outer iPrS− ligand).For T = 4 [(i,j) = (2,0)], the first rule causes some 3-gons to besurrounded by one yellow 4-gon and two blue 4-gons (inner iPrS−

ligand). For T = 7 [(i,j) = (2,1)], the first rule requires some 4-gons(marked by red) to be impossibly both yellow (outside) and blue(inside). For T = 9 and 12, the second rule requires that somespecial hexagons––those in the (1,1) position with respect to apentagon or another special hexagon––be surrounded by all yellow4-gons. There is no rule against that arrangement, and these cagespass, as would all cages with T divisible by 3. However, these largercages could not be built exclusively from pentaTrigons. Instead,they could be built from a combination of pentaTrigons and hex-aTrigons (SI Appendix, Fig. S6).However, we have not seen these larger cages with 9 × 60 =

540 or 12 × 60 = 720 silver atoms. We supposed that sterichindrance was responsible, currently set “just right” by the iPrS−

for Ag180. However, when we replaced the propyl group in theiPrS− ligand with an ethyl group, we still produced Ag180, asindicated by the similar unit-cell parameters. Therefore, wesuggest that STAR with pentaTrigons and decaTrigons maybe the dominant factor in determining the outcome of the synthesis.Although assembly of Ag180 relies on aggregation of Trigons,

breakdown appears to follow a different path. The crystal of 1 candissolve in water, but except for very small fragments like Ag6 (SIAppendix, Fig. S5L), Ag180-related molecular ion peaks are notdetected. Dissolution of 1 into other solvents shows that the Ag180cage can be stabilized in many other solvents but with differentdisassociation degrees. These solvents include n-propanol, ethanol,acetone, and dichloromethane (SI Appendix, Fig. S7 A–D), butthese solutions also show increasing amounts of Ag130. Indeed, for1 dissolved in the aprotic solvents dimethylformamide and aceto-nitrile (SI Appendix, Fig. S7 E and F), the fragment peaks are solelyAg130 species with different charge states. The number 130 is notdivisible by three, so the structure of Ag130 cannot contain silverTrigons exclusively. Of course, it is possible to imagine Ag130structures with a spherical shape or conversely with a bowl shape.Further work would be required to elucidate its actual structure.The solid-state diffuse reflectance UV/Vis spectra of a crys-

talline sample of 1 exhibits a main absorption band centered at346 nm and a shoulder peak at 423 nm tailed to 700 nm (SIAppendix, Fig. S8). The UV (346 nm) absorption peaks can beattributed to the n→ π* transition of iPrS−, and the visible region(423 nm with its tail) can be attributed to the charge-transfertransition from the S 3p to Ag 5s orbitals.We investigated the solid-state luminescence of 1, which re-

veals weak near-infrared emission with a maximum λem = 723 nmfor excitation at 365 nm at room temperature (Fig. 5A). Theemission of 1 may be due to the ligand-to-metal charge transfer,with charge transfer from S 3p to Ag 5s orbitals, a transitionperturbed by Ag···Ag interactions37. For checking possible ther-mochromic luminescence of 1, we collected its emission spectra

Fig. 3. HR-ESI-MS. (A) Positive ion mode HR-ESI-MS of the crystals of 1dissolved in methanol. (B) Positive ion mode HR-ESI-MS of the reactionmixture after solvothermal reaction. Molecular species with the samenumber of silver atoms are distinguished by Latin characters α, β, γ, δ, etc.

Wang et al. PNAS | November 14, 2017 | vol. 114 | no. 46 | 12135

CHEM

ISTR

Y

Dow

nloa

ded

by g

uest

on

June

2, 2

020

from room temperature down to 93 K. As 1 is cooled from 293 to93 K, the maximum emission wavelength shifted from 723 to693 nm (Δem = 30 nm), and the intensity of luminescence in-creased nearly 10-fold (Fig. 5 A and B). The emission colorevolution of a selected crystal at the different temperatures isalso shown in Fig. 5C. The increased intensity of emission uponcooling may be caused by reduction of the nonradiative decayat low temperature, whereas the 30-nm hypsochromic-shiftedemission may be ascribed to the significantly restricted swingof iPr groups at low temperature (37). Moreover, 1 shows alinear correlation between maximum emission intensity (Imax)and temperature (T) in the range of 93–193 K. The excellentlinearity between Imax and T could provide a calibration curvefor a molecular luminescent thermometer at low temperature.For comparison, we also measured luminescent spectra for the [Ag

(iPrS)]n precursor from 293 to 93 K (λex = 365 nm; SI Appendix, Fig.S9A). The data reveal a maximum emission peak at 545 nm at roomtemperature but no obvious shift in peak wavelength with cooling to93 K (SI Appendix, Fig. S9B). The data also reveal a sixfold en-hancement of emission intensity from 293 to 93 K. The smaller shiftin peak emission wavelength (Δem < 5 nm) and the smaller intensityenhancement makes [Ag(iPrS)]n less useful than 1 as a thermochro-mic luminescent material. Moreover, the linearity between Imax and T

of [Ag(iPrS)]n is acceptable only from 173 to 293 K (SI Appendix, Fig.S9B), which makes [Ag(iPrS)]n less attractive as a potential molecularluminescent thermometer in the lower temperature range.We have presented the synthesis and characterization of a re-

markable silver cage, Ag180. This achievement may be regarded asthe product of an alliance between chemistry and mathematics,which suggested that we paste the argentophilicity-bonded silverTrigons in the arrangement of the vertices of the 6.6.6 (1,1)Archimedean polyhedron (with twelve 5-gons and twenty 6-gons)to form a 3.4.6.4 (1,1) polyhedron (with sixty 3-gons, ninety 4-gons,twelve 5-gons, and twenty 6-gons). Moreover, the cage’s structuralfeatures, combined with the mass spectroscopy analysis, suggest thegrowth mechanism––the STAR––in solution for this nanocage.Indeed, the STAR mechanism may be a general synthetic pathwaytoward larger silver polyhedral cages like Ag540 and Ag720. Besidesthe fundamental interest of this synthetic cage, we foresee appli-cations including its use as a molecular luminescent thermometer.

Materials and MethodsWe prepared the precursors of (AgiPrS)n according to the literature but usediPrSH instead (38). All of the chemicals and solvents we used in the syntheseswere of analytical grade, and we used them without further purification.See SI Appendix for further detailed methods.

Fig. 4. Relationship between cages like Ag180 andicosahedral fullerenes. (A) The relationship betweenthe C60 buckyball (thick lines) and the Ag180 cage(thin lines). Replacing each silver 3-gon by a carbonatom and each silver 4-gon by an edge produces thesame topology as C60, the truncated icosahedron.(B) All of the 4-gons surrounding a 5-gon are markedwith small yellow disks, marking coordination withan iPrS− ligand on the outside of the cage. Each tri-angle (or Trigon in Fig. 3A) is surrounded by two4-gons marked by these small yellow disks and one4-gon marked by a small blue disk, the latter in-dicating coordination with an iPrS− ligand on theinside of the cage. (C) Equilateral triangular cutoutswith various (i, j) indices and T numbers drawn over6.6.6 tilings. (D) Equilateral triangles with various (i,j) indices and T numbers (T = i2 + ij + j2) drawn over3.4.6.4 tilings. The letter P in the 6-gons at the cor-ners of the Goldberg triangle are a reminder thatthose 6-gons in the tiling become Pentagons in thecage. The large yellow disks mark special hexagonsthat are surrounded by only yellow 4-gons. These areseen only in larger 3.4.6.4 cages with T divisible by 3,like T = 9 and 12. The red disks mark 4-gons that therules require have their iPrS− ligand on both the in-side and the outside, thus a forbidden configuration.

12136 | www.pnas.org/cgi/doi/10.1073/pnas.1711972114 Wang et al.

Dow

nloa

ded

by g

uest

on

June

2, 2

020

ACKNOWLEDGMENTS. We are deeply grateful to the anonymous reviewerwho provided many constructive suggestions for improvement of thecrystallographic data, including the very helpful suggestion to use Para-ton oil to protect the fragile crystal. D.S. was supported by the NationalScience Foundation of China (Grant 21571115) and the Young Scholars

Program of Shandong University (Grant 2015WLJH24). H.-F.S., Y.-Z.T.,and L.-S.Z. were supported by the National Science Foundation ofChina (Grants 21227001 and 21701133). D.S., W.-G.W., and C.-H.T. weresupported by the Fundamental Research Funds of Shandong University(Grant 104.205.2.5).

1. Kroto HW, et al. (1985) C60: Buckminsterfullerene. Nature 318:162–163.2. Moses MJ, Fettinger JC, Eichhorn BW (2003) Interpenetrating As20 fullerene and Ni12

icosahedra in the onion-skin [As@Ni12@As20]3- ion. Science 300:778–780.

3. Bai J, Virovets AV, Scheer M (2003) Synthesis of inorganic fullerene-like molecules.

Science 300:781–783.4. Xie SY, et al. (2004) Capturing the labile fullerene[50] as C50Cl10. Science 304:699.5. Grimes JM, et al. (1998) The atomic structure of the bluetongue virus core. Nature

395:470–478.6. Douglas SM, et al. (2009) Self-assembly of DNA into nanoscale three-dimensional

shapes. Nature 459:414–418.7. Kong XJ, Long LS, Zheng Z, Huang RB, Zheng LS (2010) Keeping the ball rolling:

Fullerene-like molecular clusters. Acc Chem Res 43:201–209.8. Müller A (2003) Chemistry. The beauty of symmetry. Science 300:749–750.9. Kratschmer W, Lamb LD, Fostiropoulos K, Huffman DR (1990) Solid C60: A new form of

carbon. Nature 347:354–358.10. Stagg SM, et al. (2006) Structure of the Sec13/31 COPII coat cage. Nature 439:234–238.11. Lawson DM, et al. (1991) Solving the structure of human H ferritin by genetically

engineering intermolecular crystal contacts. Nature 349:541–544.12. Caspar DLD, Klug A (1962) Physical principles in the construction of regular viruses.

Cold Spring Harb Symp Quant Biol 27:1–24.13. Baker TS, Olson NH, Fuller SD (1999) Adding the third dimension to virus life cycles:

Three-dimensional reconstruction of icosahedral viruses from cryo-electron micro-

graphs. Microbiol Mol Biol Rev 63:862–922.14. Sun Q-F, et al. (2010) Self-assembled M24L48 polyhedra and their sharp structural

switch upon subtle ligand variation. Science 328:1144–1147.15. Bale JB, et al. (2016) Accurate design of megadalton-scale two-component icosahe-

dral protein complexes. Science 353:389–394.16. Müller A, Beckmann E, Bögge H, Schmidtmann M, Dress A (2002) Inorganic chemistry

goes protein size: A Mo368 nano-hedgehog initiating nanochemistry by symmetry

breaking. Angew Chem Int Ed Engl 41:1162–1167.17. Gao M-Y, et al. (2016) Fullerene-like Polyoxotitanium cage with high solution sta-

bility. J Am Chem Soc 138:2556–2559.18. Argent SP, et al. (2012) High-nuclearity metal-organic nanospheres: A Cd66 ball. J Am

Chem Soc 134:55–58.19. Tran NT, Powell DR, Dahl LF (2000) Nanosized Pd145(CO)x(PEt3)30 containing a capped

three-shell 145-atom metal-core geometry of pseudo icosahedral symmetry. Angew

Chem Int Ed 39:4121–4125.

20. Huber M, Schnepf A, Anson CE, Schnöckel H (2008) Si@Al56[N(2,6-iPr2C6H3)SiMe3]12:

The largest neutral metalloid aluminum cluster, a molecular model for a silicon-pooraluminum-silicon alloy? Angew Chem Int Ed Engl 47:8201–8206.

21. Peng J-B, et al. (2014) Beauty, symmetry, and magnetocaloric effect—four-shellkeplerates with 104 lanthanide atoms. J Am Chem Soc 136:17938–17941.

22. Heinl S, Peresypkina E, Sutter J, Scheer M (2015) Giant spherical cluster with I-C140

fullerene topology. Angew Chem Int Ed Engl 54:13431–13435.23. Scheer M, Schindler A, Gröger C, Virovets AV, Peresypkina EV (2009) A spherical molecule

with a carbon-free I(h)-C80 topological framework. Angew Chem Int Ed Engl 48:5046–5049.24. Dielmann F, et al. (2015) Tunable porosities and shapes of fullerene-like spheres.

Chemistry 21:6208–6214.25. Fujita D, et al. (2016) Self-assembly of tetravalent Goldberg polyhedra from 144 small

components. Nature 540:563–566.26. Yang H, et al. (2016) Plasmonic twinned silver nanoparticles with molecular precision.

Nat Commun 7:12809.27. Desireddy A, et al. (2013) Ultrastable silver nanoparticles. Nature 501:399–402.28. Corrigan JF, Fuhr O, Fenske D (2009) Metal chalcogenide clusters on the border be-

tween molecules and materials. Adv Mater 21:1867–1871.29. Fuhr O, Dehnen S, Fenske D (2013) Chalcogenide clusters of copper and silver from

silylated chalcogenide sources. Chem Soc Rev 42:1871–1906.30. Anson CE, et al. (2008) Synthesis and crystal structures of the ligand-stabilized

silver chalcogenide clusters [Ag154Se77(dppxy)18], [Ag320(StBu)60S130(dppp)12],[Ag352S128(StC5H11)96], and [Ag490S188(StC5H11)114]. Angew Chem Int Ed Engl47:1326–1331.

31. Schmidbaur H, Schier A (2015) Argentophilic interactions. Angew Chem Int Ed Engl54:746–784.

32. Che CM, et al. (2000) Spectroscopic evidence for argentophilicity in structurally charac-terized luminescent binuclear silver(I) complexes. J Am Chem Soc 122:2464–2468.

33. Liu S, Lu YJ, Kappes MM, Ibers JA (1991) The structure of the c60 molecule: X-raycrystal structure determination of a twin at 110 k. Science 254:408–410.

34. Goldberg M (1937) A class of multi-symmetric polyhedra. Tohoku Math J 43:104–108.35. Fowler PW, Manolopoulos DE (1995) An Atlas of Fullerenes (Clarendon, Oxford), pp

18–23.36. Schein S, Gayed JM (2014) Fourth class of convex equilateral polyhedron with polyhedral

symmetry related to fullerenes and viruses. Proc Natl Acad Sci USA 111:2920–2925.37. Yam VWW, Lo KKW (1999) Luminescent polynuclear d10 metal complexes. Chem Soc

Rev 28:323–334.38. Li B, et al. (2014) Thermochromic luminescent nest-like silver thiolate cluster. Chemistry

20:12416–12420.

Fig. 5. Emission spectroscopic properties of 1. (A) Luminescence spectra as a function of temperature from 93 to 293 K in the solid state for excitation at365 nm. (B) Variation of maximum emission intensity (black circles; the red solid line is a linear fit in the range of 93–193 K) and peak emission wavelength(blue diamonds) from 93 to 293 K. (C) Photographs of a selected crystal of 1 irradiated with 365-nm UV light at the temperatures indicated.

Wang et al. PNAS | November 14, 2017 | vol. 114 | no. 46 | 12137

CHEM

ISTR

Y

Dow

nloa

ded

by g

uest

on

June

2, 2

020

Correction

CHEMISTRYCorrection for “Assembly of silver Trigons into a buckyball-likeAg180 nanocage,” by Zhi Wang, Hai-Feng Su, Yuan-Zhi Tan, StanSchein, Shui-Chao Lin, Wei Liu, Shu-AoWang, Wen-Guang Wang,Chen-Ho Tung, Di Sun, and Lan-Sun Zheng, which was first pub-lished October 27, 2017; 10.1073/pnas.1711972114 (Proc Natl AcadSci USA 114:12132–12137).The editors note that the name of the NAS member responsible

for handling the article was inadvertently omitted. The byline shouldappear as follows: “Edited by Vivian Wing-Wah Yam, The Uni-versity of Hong Kong, Hong Kong, China, and approved September28, 2017 (received for review July 07, 2017).” The online version hasbeen corrected.

Published under the PNAS license.

www.pnas.org/cgi/doi/10.1073/pnas.1719225114

www.pnas.org PNAS | November 28, 2017 | vol. 114 | no. 48 | E10505

CORR

ECTION