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NANOMATERIALS Chemically reversible isomerization of inorganic clusters Curtis B. Williamson 1 *, Douglas R. Nevers 1 *, Andrew Nelson 2 , Ido Hadar 3 , Uri Banin 3 , Tobias Hanrath 1 , Richard D. Robinson 2 Structural transformations in molecules and solids have generally been studied in isolation, whereas intermediate systems have eluded characterization. We show that a pair of cadmium sulfide (CdS) cluster isomers provides an advantageous experimental platform to study isomerization in well-defined, atomically precise systems. The clusters coherently interconvert over an ~1electron volt energy barrier with a 140millielectron volt shift in their excitonic energy gaps.There is a diffusionless, displacive reconfiguration of the inorganic core (solid-solid transformation) with first order (isomerization-like) transformation kinetics. Driven by a distortion of the ligand-binding motifs, the presence of hydroxyl species changes the surface energy via physisorption, which determines phasestability in this system. This reaction possesses essential characteristics of both solid-solid transformations and molecular isomerizations and bridges these disparate length scales. P hase transitions in solids and molecular isomerizations occupy different extremes for structural rearrangements of a set of atoms proceeding along mechanistic path- ways. Phase transformations are initiated by nucleation events (1) that are difficult to de- fine and then propagate discontinuously from lattice defects with activated regions smaller than the crystalline grains (incoherent transformation) (2). Small-molecule isomerization is a discrete process, in which the activation volume of the transition state is comparable to the size of the molecule (coherent transformation). Studies of isomerization and solid-solid transformations have thus far proceeded largely independently. Efforts to identify a system bridging these trans- formations have been made by examining the transformation of domains of reduced size, such as nanocrystals. Transformations of nanocrystals (100 to 10,000 atoms) do not mirror molecular isomerization, in that bulk-like phase transition behavior extends to the nanometer-length scale, even down to ~2 nm (2). Here we investigate the structural transformations in semiconductor clus- ter molecules at the boundary between molecular isomerizations and solid-solid phase transitions in nanocrystals (Fig. 1) by studying magic-size clusters (MSCs) (~10 to 100 atoms), as proto- typical systems. Studies of these clusters (diam- eter < 2 nm) with distinct chemical formulas revealed that the cluster structures were strongly influenced by the surface termination (25). Previous work has observed that certain types, or families, of MSCs can be converted into other MSCs (58). Thus far, however, experiments claim- ing to have observed structural reorganization have been primarily conducted in the solution phase. Clusters in solution are free to interact with each other and with unbound surfactants, monomers, or by-products, and these interac- tions promote mass transport and etching pro- cesses. For example, reports on InP clusters show irreversible structural changes, aggregation, and etching in the presence of high concentrations of amines (5). Such cases indicate a loss in the productscompositional integrity and thus that the transformation is not an isomerization. Struc- tural transformations have been proposed for the same InP clusters at lower amine concentrations (5) and in CdS clusters after changes in temper- ature (6). In the former case, the assignment to a structural transformation was made by indirect methods (9) based on changes in 31 P nuclear mag- netic resonance shifts. This measurement per- mitted identification of only ~20% of the atoms in the cluster, none of which were directly asso- ciated with the surface ligands, and the experi- ment did not rule out the possibility of etching. Substantial changes in the 31 P spectrum were observed in different solvents, bringing into question the dynamical stability of InP clusters in solution and, by extension, their status as isolated molecules undergoing discrete trans- formations. For the CdS clusters (6), the kinetics of incomplete transformations between cluster types indicated a very high activation energy (~3 eV), which is likely too large to account for merely structural reorganization energies and points instead to interparticle interactions. A primary complication of these solution-phase studies has been the lack of direct characterization of atomic structure, such as x-ray total scattering, in the native environment of transformation (5, 6) that can be used to identify the existence and extent of a structural transformation (9). We demonstrate that a class of MSCs whose local structures can be modeled with a composi- tion of Cd 37 S 20 undergoes reversible isomeriza- tion between two discrete and stable states via a chemically induced, diffusionless transformation. We preserved the composition by isolating our clusters in solid films and determined the cluster structures (fit residuals < 0.2) through analysis of their x-ray pair distribution functions (PDFs). Switching between the isomers was triggered by the absorption-desorption of water or alcohol (hydroxyl groups) with an activation barrier of ~1 eV in both directions. This chemically in- duced, reversible transformation has charac- teristics of both molecular isomerization and bulk solid-solid transformations. These clusters are an attractive starting point for merging the long- and short-length scale descriptions of such transformations as mediated by the external surface energy. We synthesized high-purity clusters (i.e., single product), characterized by a narrow excitonic absorption peak at 324 nm with negligible longer-wavelength absorption, via our high- concentration method (10). These clusters are stabilized by their mesophase (11) and immobi- lized in a thin solid film (Fig. 2A). We refer to this cluster type as a-Cd 37 S 20 . After exposure of RESEARCH Williamson et al., Science 363, 731735 (2019) 15 February 2019 1 of 5 1 Robert F. Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY, USA. 2 Department of Materials Science and Engineering, Cornell University, Ithaca, NY, USA. 3 Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University, Jerusalem 91904, Israel. *These authors contributed equally to this work. Corresponding author. Email: [email protected] (U.B.); [email protected] (T.H.); [email protected] (R.D.R.) Fig. 1. Inorganic isomerization. Isomerization is well established in small organic molecules (e.g., the cis-to-trans transformation of azobenzene), whereas bulk inorganic solids exhibit phase transformations. Although small in size, nanocrystals follow bulk-like behavior in their solid-solid transformations. At even smaller length scales, inorganic clusters isomerize with molecular- and inorganic solidlike characteristics. 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Page 1: NANOMATERIALS Chemically reversible isomerization of … · NANOMATERIALS Chemically reversible isomerization of inorganic clusters Curtis B. Williamson1*, Douglas R. Nevers1*, Andrew

NANOMATERIALS

Chemically reversible isomerizationof inorganic clustersCurtis B. Williamson1*, Douglas R. Nevers1*, Andrew Nelson2, Ido Hadar3, Uri Banin3†,Tobias Hanrath1†, Richard D. Robinson2†

Structural transformations in molecules and solids have generally been studied inisolation, whereas intermediate systems have eluded characterization. We show that apair of cadmium sulfide (CdS) cluster isomers provides an advantageous experimentalplatform to study isomerization in well-defined, atomically precise systems. The clusterscoherently interconvert over an ~1–electron volt energy barrier with a 140–milli–electronvolt shift in their excitonic energy gaps. There is a diffusionless, displacive reconfigurationof the inorganic core (solid-solid transformation) with first order (isomerization-like)transformation kinetics. Driven by a distortion of the ligand-binding motifs, the presenceof hydroxyl species changes the surface energy via physisorption, which determines“phase” stability in this system. This reaction possesses essential characteristics of bothsolid-solid transformations and molecular isomerizations and bridges these disparatelength scales.

Phase transitions in solids and molecularisomerizations occupy different extremesfor structural rearrangements of a set ofatoms proceeding alongmechanistic path-ways. Phase transformations are initiated

by nucleation events (1) that are difficult to de-fine and then propagate discontinuously fromlattice defects with activated regions smaller thanthe crystalline grains (incoherent transformation)(2). Small-molecule isomerization is a discreteprocess, in which the activation volume of thetransition state is comparable to the size of themolecule (coherent transformation). Studies ofisomerization and solid-solid transformationshave thus far proceeded largely independently.Efforts to identify a system bridging these trans-formations have been made by examining thetransformation of domains of reduced size, suchas nanocrystals. Transformations of nanocrystals(100 to 10,000 atoms) do not mirror molecularisomerization, in that bulk-like phase transitionbehavior extends to the nanometer-length scale,even down to ~2 nm (2). Here we investigate thestructural transformations in semiconductor clus-ter molecules at the boundary between molecularisomerizations and solid-solid phase transitionsin nanocrystals (Fig. 1) by studying magic-sizeclusters (MSCs) (~10 to 100 atoms), as proto-typical systems. Studies of these clusters (diam-eter < 2 nm) with distinct chemical formulasrevealed that the cluster structures were stronglyinfluenced by the surface termination (2–5).

Previous work has observed that certain types,or families, of MSCs can be converted into otherMSCs (5–8). Thus far, however, experiments claim-ing to have observed structural reorganizationhave been primarily conducted in the solutionphase. Clusters in solution are free to interactwith each other and with unbound surfactants,monomers, or by-products, and these interac-tions promote mass transport and etching pro-cesses. For example, reports on InP clusters showirreversible structural changes, aggregation, andetching in the presence of high concentrationsof amines (5). Such cases indicate a loss in theproducts’ compositional integrity and thus thatthe transformation is not an isomerization. Struc-tural transformations have been proposed for thesame InP clusters at lower amine concentrations(5) and in CdS clusters after changes in temper-ature (6). In the former case, the assignment to astructural transformation was made by indirectmethods (9) based on changes in 31P nuclearmag-netic resonance shifts. This measurement per-mitted identification of only ~20% of the atoms

in the cluster, none of which were directly asso-ciated with the surface ligands, and the experi-ment did not rule out the possibility of etching.Substantial changes in the 31P spectrum wereobserved in different solvents, bringing intoquestion the dynamical stability of InP clustersin solution and, by extension, their status asisolated molecules undergoing discrete trans-formations. For the CdS clusters (6), the kineticsof incomplete transformations between clustertypes indicated a very high activation energy(~3 eV), which is likely too large to account formerely structural reorganization energies andpoints instead to interparticle interactions. Aprimary complication of these solution-phasestudies has been the lack of direct characterizationof atomic structure, such as x-ray total scattering,in the native environment of transformation(5, 6) that can be used to identify the existenceand extent of a structural transformation (9).We demonstrate that a class of MSCs whose

local structures can be modeled with a composi-tion of Cd37S20 undergoes reversible isomeriza-tion between two discrete and stable states via achemically induced, diffusionless transformation.We preserved the composition by isolating ourclusters in solid films and determined the clusterstructures (fit residuals < 0.2) through analysisof their x-ray pair distribution functions (PDFs).Switching between the isomers was triggered bythe absorption-desorption of water or alcohol(hydroxyl groups) with an activation barrier of~1 eV in both directions. This chemically in-duced, reversible transformation has charac-teristics of both molecular isomerization andbulk solid-solid transformations. These clustersare an attractive starting point for merging thelong- and short-length scale descriptions of suchtransformations as mediated by the externalsurface energy.We synthesized high-purity clusters (i.e., single

product), characterized by a narrow excitonicabsorption peak at 324 nm with negligiblelonger-wavelength absorption, via our high-concentration method (10). These clusters arestabilized by their mesophase (11) and immobi-lized in a thin solid film (Fig. 2A). We refer tothis cluster type as a-Cd37S20. After exposure of

RESEARCH

Williamson et al., Science 363, 731–735 (2019) 15 February 2019 1 of 5

1Robert F. Smith School of Chemical and BiomolecularEngineering, Cornell University, Ithaca, NY, USA.2Department of Materials Science and Engineering, CornellUniversity, Ithaca, NY, USA. 3Institute of Chemistry and theCenter for Nanoscience and Nanotechnology, The HebrewUniversity, Jerusalem 91904, Israel.*These authors contributed equally to this work.†Corresponding author. Email: [email protected] (U.B.);[email protected] (T.H.); [email protected] (R.D.R.)

Fig. 1. Inorganic isomerization. Isomerization is well established in small organic molecules(e.g., the cis-to-trans transformation of azobenzene), whereas bulk inorganic solids exhibitphase transformations. Although small in size, nanocrystals follow bulk-like behavior in theirsolid-solid transformations. At even smaller length scales, inorganic clusters isomerize withmolecular- and inorganic solid–like characteristics. Red and blue indicate two different structures.

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a-Cd37S20 films to methanol vapor, the exciton(first absorption) peak diminished, and a secondnarrow absorption peak emerged at 313 nm, in-dicating formation of the new species, b-Cd37S20,with an energy gap that is larger by 140 meV.Hereafter, only transformations with methanolare discussed in detail, but any hydroxyl-bearingspecies (alcohol or water) can initiate conversionof a to b.The b-Cd37S20 could be transformed back to

a-Cd37S20 (reversion) by purging the methanoland heating the MSC film (>60°C), and the re-version rate increased with temperature. Wedemonstrated a high degree of reversibility withfour complete conversion-reversion cycles (insetof Fig. 2A) in the MSC isomerization withoutcreation of other MSC families or nanocrystals(fig. S1D). This behavior in MSCs is reminiscentof reversible isomerization reactions, which arewell known in small molecules (12). We observedthat differences in the dielectric environmentonly weakly alter the absorption maximum wave-

length and that, indeed, the presence of hydroxyl-bearing species exclusively determines thefavored isomer under the temperatures appliedhere. a-Cd37S20 may be stabilized at lower tem-peratures by maintaining an anhydrous envi-ronment, and b-Cd37S20 may be stabilized athigher temperatures (e.g., up to the boiling pointof methanol) by maintaining the saturation ofhydroxyl-bearing species. The stabilization ofdifferent MSC forms within a mesophase mayhave interesting consequences for nanopar-ticle formation once growth (e.g., by orientedattachment) is initiated, as mentioned in recentreports (13).BothMSC isomers had lowphotoluminescence

(PL) quantum yields (<2.5%), which indicatesthat nonradiative decay processes dominated atroom temperature. Substantial emission fromthe clusters’ electronic transitions was present(Fig. 2B). The PL decay transients could be fitby double exponentials (inset of Fig. 2B); thelifetimes of the slower decay rates are 5.8 and

5.2 ns for a-Cd37S20 and b-Cd37S20, respectively.The corresponding nonradiative and radiativerate constants for a-Cd37S20 are therefore 4.3 ×106 and 1.7 × 108 s−1, respectively; for b-Cd37S20,they are 3.3 × 106 and 1.9 × 108 s−1, respectively(see the supplementarymaterials for calculations).We analyzed the structure of the isomers by

x-ray diffraction (XRD), noting that the XRDshoulder at 2Q ∼ 37°, where 2Q is the angle be-tween the incident and the diffracted x-ray beam,in the a-Cd37S20 is absent in the b-Cd37S20 (Fig.2C). Although the peaks are broad, we interpretthe a and b isomers as generally having “wurtzite-like” and “zinc blende–like” phases, respectively.We resolved the detailed atomic structure of thecluster isomers by fitting the PDF derived fromthe total scattering function [G(r)] using a MonteCarlo algorithm (see supplementary materialsand methods). The best-fit structures of a andb (residuals of ~0.18; fig. S2, B and C) werecomparable to InP clusters (14) (formula unit:In37P20), but with the In and P atoms replaced

Williamson et al., Science 363, 731–735 (2019) 15 February 2019 2 of 5

Fig. 2. Electronic and structure analysis. (A) Absorption spectra ofpristine cluster isomers a-Cd37S20 and b-Cd37S20, with excitonic peaks at324 and 313 nm, respectively. The two isomers switch reversibly uponalcohol adsorption and desorption (inset schematic and contour plot). Theslight deviation between cycles is associated with ambient temperaturefluctuations. (B) PL and lifetime (inset) of the isomers. a.u., arbitrary units.(C) Synchrotron XRD patterns of a and b isomers referenced to a Cu-Kasource [wavelength (l) = 0.154 nm]. Peak positions for the wurtzite

(with defining feature at 37°, asterisk) and zinc-blende phases of CdS arefrom the Joint Committee on Powder Diffraction Standards card numbers00-041-1049 and 00−010−0454, respectively. (D) PDFs of the a and bisomers. DG(r) = Ga(r) – Gb(r) is the difference in the PDF between the twoisomers and is largest for core-to-surface atom pair distances. Inset arethe fitted structures of the a and b isomers with residuals of ~0.18.(E) Radial displacement of atoms between the a and b isomer structures withrespect to distance from the cluster geometric center (X).

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by Cd and S, respectively. PDF analysis is aneffective tool for atomic modeling that resolvesfine features and subtle differences betweendata. Although powerful for low-symmetry anddisordered systems, extracting atomic positionsfrom PDF analysis and modeling hinges on theaccuracy of the initial inputs (15, 16). Repeatedfitting showed that a- and b-Cd37S20 structuresoccupied distinct energy minima whose separa-tion greatly exceeded possible overlap fromthermal displacements, so that the clusters’ struc-tures are unambiguously different (fig. S2D).Simulations including contributions from theorganic ligands and the mesophase assemblydetermined that the organic ligand shell doesnot substantially contribute to scattering aboveQ = 1.5 Å−1, where scattering from the inorganicstructure is dominant, so that fittingG(r) beyond2 Å even without organic contributions correct-ly resolves the positions of Cd and S (fig. S2, Band C). Our structures have a low symmetry(inset of Fig. 2D), unlike the highly symmetrictetrahedral coordination that has been reportedfor other CdS or CdSe MSCs (16, 17). We hypoth-esize that our clusters resemble the InP structurebecause our clusters are similarly passivatedwithonly carboxylate ligands, whereas previously re-ported CdS or CdSe clusters are stabilized byamines, thiols, or a mixture of ligands. The repre-sentative structures of the clusters are molecular-

like but have scattering features similar to CdScrystal phases.The difference between the a and b PDFs,

DG(r), indicates changes in the atomic positions(Fig. 2D), for which larger magnitudes signify agreater shift between the structures. AlthoughDG(r) revealed preservation of the CdS bondlengths [DG(r) ≃ 0 between 2.50 and 2.55 Å],there were appreciable differences in the bondangles [DG(r) ≠ 0 between 4 and 5 Å]. Analysisof our atomic structures indicated an overallbroader distribution of bond angles in thea-Cd37S20 than the b-Cd37S20 (fig. S2, E and F).These changes in conformation (atomic orbitaloverlap) must be the origin of the change in theexcitonic gap between clusters. The greatest dif-ference between the PDFs of the isomers waswithin the range of 5.5 to 9 Å, a range that cor-responds to atomic pairs composed of one “core”atom and one “near-surface” atom.Beyond an interatomic spacing of 12 Å, the

G(r) has oscillations that propagate to largerspacings (>30 Å). These features correspond topreferred intercluster orientations (diffractiontexturing), which are broadened by variationsin the cluster-cluster orientations (18). Our pre-vious investigation revealed that these clustersform long-range assemblies (11). Although textur-ing or preferred nanograin orientation can createchallenges in structural analysis by x-rays, these

challenges are less substantial in PDF analysis(18–20). To assign a degree of transformation,we calculated the set of displacements requiredto transform one cluster into the other (Fig. 2E).The resulting relative displacements between iso-mers increases with radial distance from thecluster’s geometric center. Despite the largemag-nitude of displacement (up to ~30% of the Cd–Sbond length for surface atoms), the connectivityof a- and b-Cd37S20 does not change. Therefore,the cluster isomerization is primarily displa-cive, characteristic of a solid-solid transforma-tion, rather than reconstructive.The Fourier transform infrared (FTIR) spectra

of a and b reveal that the isomerization stemsfrom changes in the surface structure. We iden-tify the carboxylate asymmetric stretches (nas) at1528 and 1538 cm−1, respectively (Fig. 3, A and B),and the carboxylate symmetric stretches (ns) at1410 cm−1 for both isomers. The difference (D)between nas and ns gives the ligand-bindingmotif:D < 140 cm−1 indicates a chelating bidentateconfiguration, and D > 140 cm−1 indicates abridging bidentate configuration (Fig. 3C) (21).The dominant ligand configuration in the a andb isomers is the chelating bidentate configura-tion (Da = 118 cm−1; Db = 128 cm−1), but there is astrong shoulder in the nas (1580 cm−1) in thea-Cd37S20 spectrum that points to the presenceof some bridging ligands (D = 170 cm−1) (22).

Williamson et al., Science 363, 731–735 (2019) 15 February 2019 3 of 5

Fig. 3. Organic surface analysis. (A) FTIR spectra of the carboxylasymmetric (nas) and symmetric (ns) stretches of the a-Cd37S20 andb-Cd37S20 isomers. (B) Schematic of the carboxylate stretch vibrations.(C) Observed bidentate carboxylate binding motifs. (D) O 1s XPSspectra in the a and b isomers. (E) Schematic of the ligandconfiguration on the isomer surface with chelating bidentate oleate

molecules. Methanol (green) hydrogen bonds with the oleate ligand toalter the chelating angle, which is larger in b-Cd37S20 relative toa-Cd37S20. Black, carbon; rose, oxygen; gray, cadmium; dark yellow,sulfur; red, a-Cd37S20 cadmium; orange, a-Cd37S20 sulfur; dark blue,b-Cd37S20 cadmium; light blue, b-Cd37S20 sulfur. Only one oleate is shownper cadmium atom for clarity.

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Although this shoulder was absent in b-Cd37S20,the spectral area of the nas between the isomersis preserved, implying no change in the overallligand number. From the correlation of bondangles from single-crystal diffraction data to FTIRspectra for various metal carboxylates (fig. S3B),we estimated the change in the two sets of bondangles from D (23, 24): The change in the chela-ting bond angle increased by ~0.5° upon conver-sion from a to b, and ligands changing frombridging to chelating configuration in the b-Cd37S20decreased their bond angle by ~2.0°. The FTIRresults indicate that the cluster isomerizationis strongly coupled to a change in the ligand-binding modes. We hypothesize that the mod-ified ligand-binding arrangement on the clustersurface is the chemical trigger to the isomerization.X-ray photoelectron spectroscopy (XPS) showed

that theCd 3d spectra fora and bwerenot notablydifferent (fig. S4A and tables S1 and S2), sug-gesting little interaction of the Cd atoms withadsorbed methanol. However, the O 1s spectrumfor a-Cd37S20 showed a peak at 531.9 eV, whichshifts to 531.7 eV in the b-Cd37S20 spectrum. Asecond peak for b-Cd37S20was present at 534.2 eV,which is attributed to physisorbed methanol(Fig. 3D). There was no evidence of dissociatedmethoxy species, which would have an O 1s peakat energies <532 eV (25, 26).In combination, FTIR and XPS analyses indi-

cate that the presence of methanol shifts theconfiguration of ligands bound to the surfaceof the cluster. Changes in the carboxylate angleresult in a reconfiguration of Cd and S atoms atthe cluster surface, initiating the overall isom-erization of the cluster (Fig. 3E). Control exper-iments using aprotic solvents with strong toweak dielectric constants (acetone to perfluoro-hexane, respectively) (table S3) did not inducea transformation (fig. S6A). The b-Cd37S20 isformed after the adsorption of methanol on thesurface of the cluster, which arises via hydrogenbonding with the oleate ligand (Fig. 3D). Hydro-gen bonding, and not changes in the dielectricenvironment, distorts the carboxylate bond angleand initiates the necessary surface reconfigura-tion that induces the cluster isomerization. Inter-estingly, such a hydroxyl-triggered phase changein the similarly structured In37P20 cluster (fig. S5)was not spectroscopically observed (14). WhyIn37P20 lacked another stable polymorph underconditions similar to those applied here is notobvious. We suggest that further investigationsshould identify, with atomic precision, the dif-ferences in ligand conformation, binding, anddensity, between In37P20 and Cd37S20.The absorption peak of the b-Cd37S20 red shifts

to 320 nm (fig. S7A) if methanol is not present(e.g., in vacuum), forming another species thatwe term b′-Cd37S20. Reexposure to methanol rap-idly regenerated b-Cd37S20. The details of the band b′ spectra were otherwise nearly identical,indicating that the b-like structure is metastableat low temperatures and that hydroxyl is onlyrequired as an initiator. The b-to-b′ transitionshows that absorbedmethanol is not an essentialcontributor to the electronic structure. Likewise,

there are no substantial differences between theb and b′ XRD and PDF patterns (fig. S7D), im-plying that the desorbed methanol affects theexcitonic gap by way of dielectric effects.Because the spectral overlap between the ex-

citon of a- and b-Cd37S20 was small, we performedin situ time-resolved spectroscopy measurementsat temperatures of 25° to 100°C to extract kineticrate constants (Fig. 4A, fig. S8A, and table S4)through the evolution of the first absorptionpeak of a-Cd37S20. The isomerization followedfirst-order reaction kinetics and had a smalltransformation hysteresis (inset of Fig. 4A). Fora-to-b conversion, we kept the methanol partialpressure saturated; when the methanol partialpressure fell, the transformation deviated fromfirst order. In a dry or high-temperature environ-ment, the reverse transformation was also firstorder. The Arrhenius prefactor, A (Fig. 4B andtable S5), was 3.4 × 1012 s−1, which correspondsto a vibrational frequency of a transformationacross the transition state (kBT ħ−1 = 6.2 × 1012 s−1

at 300 K, where kB is the Boltzmann constant, Tis temperature, and ħ is the Planck constant) andagrees with measured prefactors for adsorption-desorption and solid-solid transformation pro-cesses (27, 28). We observed a smaller reversionprefactor (9.3 × 109 s−1), on the order of thoseobserved in some solid-solid transformations (29).Correspondence between the kinetic parametersfrom the optical experiments to those found fromin situ diffraction confirmed the lack of structuralintermediates (fig. S8, F toH), as did the isosbesticpoints in the optical absorption (fig. S1C).The activation energy (Ea) values for the con-

version and reversion processes were 0.99 ± 0.04

and 0.87 ± 0.08 eV (95.5 and 84.0 kJ mol−1),respectively. In comparison, first-principles cal-culations have shown that the binding energy ofcarboxylic acids onto (Cd33Se33) is ~0.7 to 1.5 eV,with larger values for binding on higher-indexfacets (30). Compared to previously reported en-ergies for a similarly described MSC that wasunpurified, tested in dilute solutions, and onlypartially transformed, our activation energies area factor of three smaller and align more closelywith common structural transformation energies(i.e., solid-solid transformation and isomerization)(6). Our lower activation energy from more rigo-rous experiments better agreeswith the lowdegreeof local structural change during the conversionas inferred from direct characterization methods,such as pair distribution analysis.We used the Eyring equation to derive the

Gibbs free energy of the transition state, DG‡

(table S6), and the apparent values for the en-thalpy and entropy of the transition state (DH‡

and DS‡, respectively) (Fig. 4C). The DH‡ for theconversion and reversion processes are 0.96 ±0.04 and 0.84 ± 0.07 eV, respectively. The dif-ference in DH‡ between the processes may berelated to the nonequilibrium desorption of phy-sisorbed methanol in the reversion process. Toinvestigate the possibilities of chemisorption andsteric interactions, we performed the reversionprocess on b-Cd37S20 produced from alcoholswith increasing alkyl chain length (fig. S8H) andfound that DG‡ was independent of the alcohol.We conclude that the DH‡ is predominantly thefree energy to relax the inorganic core after thechange in the chemical potential at the ligand-coreinterface. Because we were unable to isolate the

Williamson et al., Science 363, 731–735 (2019) 15 February 2019 4 of 5

Fig. 4. Transformationkinetics andthermodynamics.(A) Kinetics ofconversion andreversion processes.Both are firstorder: rate = e−kt,

where k is the rateconstant and t istime. Inset is ahysteresis diagramfor the transformedfraction at a reactiontime of 5 min.(B) Arrhenius plotfor the transformationkinetics with fits(dashed lines).ln(k), natural logof the rate constant.(C) Reaction coordinatediagram of the revers-ible transformation.The Gibbs free energiesof the transition state forconversion and rever-sion, DGC

‡ and DGR‡,

respectively, are the same. b-Cd37S20 transforms to b′-Cd37S20 upon removal of adsorbed alcoholwith an entropic shift (TDSads

‡).

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two isomers in coexistence with each other, thetransformation must be kinetically controlled,and comparison to thermodynamic parameters,such as enthalpies of mixing [which are 1000-foldsmaller (31)] cannot be made. The weak temper-ature dependence implies that the transformationis predominantly enthalpic, and the mean dif-ference in DS‡ of the transformation (DS‡conversion −DS‡reversion) of +0.52 meV K−1 is consistent withH-bonding entropies. As implied by Fig. 4C, thea-Cd37S20 structure becomes thermodynami-cally unstable and converts into b-Cd37S20, owingto changes in the surface energy. Removal of thesurface-energy perturbation by desorption of hy-droxyl raises the free energy of b-Cd37S20, likewiserendering it thermally unstable and reverting tothe a form.A coherent transition between two clusters

implies conservation of binding coordination,a single rate constant for the reaction, and sim-ultaneous transformation of the entire clus-ter rather than growth from a nucleation site(2, 32, 33). On the basis of the transformationkinetics and the lack of any observable inter-mediates, the upper bound on the lifetime ofan intermediate state must be on the order of10−13 s (see supplementary materials for calcula-tions), a time scale comparable to bond vibrations(33) and the lifetime of molecular transitionstates (34); additionally, to achieve the samerate of transformation for the MSC in an inco-herent process, a phase boundary would need tomove at a velocity comparable to the speed ofsound of the bulk material (28, 35). The smallatomic displacements shown from PDF analysisindicate a structural reconfiguration without achange in coordination number. Our experimen-tal kinetics are thus consistent with a coherentatomic displacement occurring in a single stepacross the entire cluster, therefore bridging ourunderstanding of molecular isomerization andsolid-solid transformation.

REFERENCES AND NOTES

1. C. M. Wayman, Annu. Rev. Mater. Sci. 1, 185–218 (1971).2. C. C. Chen, A. B. Herhold, C. S. Johnson, A. P. Alivisatos,

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ACKNOWLEDGMENTS

The authors thank P. Ko and M. Steigerwald. Funding: Thiswork was supported in part by the National Science Foundation(NSF) under award nos. CMMI-1344562 and CHE-1507753.U.B. acknowledges funding from the European Research Council(ERC) under the European Union’s Horizon 2020 research andinnovation program (grant no. 741767). U.B. also thanks theAlfred & Erica Larisch memorial chair. This work also made useof the Cornell Center for Materials Research Shared Facilities,which are supported through the NSF MRSEC (MaterialsResearch Science and Engineering Centers) program (grantDMR-1719875). This work includes research conducted atthe Cornell High Energy Synchrotron Source (CHESS), whichis supported by the NSF and the National Institutes ofHealth–National Institute of General Medical Sciences underNSF award DMR-1332208. R.D.R. thanks the U.S. FulbrightScholar and Hebrew University for partial funding during thiswork. Author contributions: C.B.W. synthesized and preparedsamples for ultraviolet-visible absorption spectroscopy,FTIR spectroscopy, XPS spectroscopy, and kinetic analysis.C.B.W. and D.R.N. prepared samples for x-ray total scatteringand diffraction. C.B.W., D.R.N., and A.N. contributed to thePDF analysis of the total scattering data. I.H. and U.B.acquired and analyzed fluorescence spectroscopy and lifetimemeasurements. All authors contributed to the interpretation ofresults and preparation of manuscript. Competing interests:None declared. Data and materials availability: All dataneeded to evaluate the conclusions in the paper are presentin the paper or the supplementary materials.

SUPPLEMENTARY MATERIALS

www.sciencemag.org/content/363/6428/731/suppl/DC1Materials and MethodsSupplementary TextFigs. S1 to S10Tables S1 to S6References (36–48)

30 July 2018; resubmitted 17 September 2018Accepted 16 January 201910.1126/science.aau9464

Williamson et al., Science 363, 731–735 (2019) 15 February 2019 5 of 5

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Page 6: NANOMATERIALS Chemically reversible isomerization of … · NANOMATERIALS Chemically reversible isomerization of inorganic clusters Curtis B. Williamson1*, Douglas R. Nevers1*, Andrew

Chemically reversible isomerization of inorganic clustersCurtis B. Williamson, Douglas R. Nevers, Andrew Nelson, Ido Hadar, Uri Banin, Tobias Hanrath and Richard D. Robinson

DOI: 10.1126/science.aau9464 (6428), 731-735.363Science 

, this issue p. 731Scienceunder vacuum. This transition is driven by distortion of the ligand shell and shifts the excitonic energy gap of the clusters.

like structure upon exposure to methanol, and then transforms back−, which has a zinc blende20S37-Cdβisomerizes to phase, which has a wurtzite-like crystal structure,20S37-Cdαligands, undergo a reversible isomerization. The initial

which are about 2 nanometers in diameter and expose a large fraction of surface atoms capped by bidentate oleate show that magic-size cadmium sulfide (CdS) crystalline clusters,et al.phase transformations of crystals. Williamson

Structural rearrangements at the atomic scale can range from isomerization of small molecules to solid-solidCluster isomerization

ARTICLE TOOLS http://science.sciencemag.org/content/363/6428/731

MATERIALSSUPPLEMENTARY http://science.sciencemag.org/content/suppl/2019/02/13/363.6428.731.DC1

REFERENCES

http://science.sciencemag.org/content/363/6428/731#BIBLThis article cites 44 articles, 3 of which you can access for free

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