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International audience; The isoelectronic doping of dichalcogenolato nanoclusters of the type [Ag-21{E2P(OR)(2)}(12)](+) (E = S, Se) by any heteroatom belonging to groups 9-12 was systematically investigated using DFT calculations. Although they can differ in their global structure, all of these species have the same M@M-12-centered icosahedral core. In any case, the different structure types are all very close in energy. In all of them, three different alloying sites can be identified (central, icosahedral, peripheral) and calculations allowed the trends in heteroatom site occupation preference across the group 9-12 family to be revealed. These trends are supported by complementary experimental results. They were rationalized on the basis of electronegativity, potential involvement in the bonding of valence d-orbitals and atom size. TD-DFT calculations showed that the effect of doping on optical properties is sizable and this should stimulate research on the modulation of luminescence properties in the dithiolato and diseleno families of complexes.

The syntheses and the characterization of two 17-atom endohedral Ge clusters, [Co2@Ge17]6− (1a) and [Ni2@Ge17]4− (2a), are reported. The anions 1a and 2a, which close the gap between the known 16- and 18-atom Ge clusters, are investigated by single crystal X-ray diffraction and by quantum chemical calculations. The structures mark a new example on the pathway for cluster growth towards larger clusters with icosahedral symmetry. Furthermore, the [Co@Ge10]3− anion (3a) is obtained from liquid ammonia.

The topologically close-packed (TCP) structural characteristics in a model metallic glass (MG) of Cu64.5Zr35.5 have been investigated by molecular dynamics simulations. A group of structural indicators based on the largest standard cluster (LaSC) have been correlated with the non-affine displacement (D2) of atoms, so as to reveal the hidden correlation between local structures and deformation behavior of Cu64.5Zr35.5 during compression. It was found that the 15 types of Top-10 LaSCs are all TCP-like ones, among which the most numerous icosahedron (Z12 and 1-Z12) decreases in population sharply and moderately during respectively the elastic and yield region of compression; while in the fluid-flow region, the number of all Top-10 LaSCs tends to be almost constant. Low-D2 atoms prefer to link with each other; while medium-D2 atoms act as transition structures between backbone areas and deformation areas. Most interestingly, the deformation response of TCP-like atoms is not only determined by its nearest neighbor characteristics, but also depends on the linkage with other atoms. In addition, icosahedral atoms with a higher degree of medium range five-fold symmetry (MRFFS) are more resistant to the stress-induced deformation. Therefore, the TCP characteristics, including its nearest neighbor feature and the inter-connection between TCP LaSCs, are closely related with the deformation behavior of atoms, especially the MRFFS (up to 5 layers) of icosahedral atoms. These findings shed new light on the understanding of the relationship between microstructure and deformation response of MGs, which will promote the development of deformation theory of MGs.

In the present study, solid-state nuclear magnetic resonance (NMR) spectra under magic angle spinning conditions of the rhombohedral structures α-B and B12P2 are reported together with the corresponding parameter sets from first principles calculations on α-B B12X2 (X = P, As, O). With the combination of density functional theory (DFT) and the gauge-including projector-augmented wave (GIPAW) approach as the theoretical tools at hand the computed 11B parameters lead to unambiguous explanation of the measurements. Thereby, we overcome common obstacles of processing recorded NMR spectra of solid-state compounds with several crystallographic positions, in particular non-trivial signal assignments and parameter determination due to peak overlap or even unexpected intensity/area ratios. In fact, we find very good agreement between the theoretical results and measured spectra without applying fitting procedures. Using the Perdew-Burke-Ernzerhof (PBE) functional, the results of the common construction types for pseudopotentials and referencing methods for the chemical shift determination are compared. Suggestions and conclusions from experimental 11B NMR studies on parameters according to the icosahedral positions are critically discussed, for instance the early suspected correlation to chemical shifts is not confirmed. Regarding the electric field gradient (EFG) a detailed explanation for obtaining small deviations amongst all investigated structures of the icosahedral polar sites compared to the equatorial sites is given. Our results show an important link between the exohedral bonding situation of compounds with icosahedral structure elements and the main axis of the EFG and therefore, also measurable quadrupole coupling constants if certain geometrical conditions are fulfilled. Finally, this work also contributes to establishing the number of unique sites measured by solid-state NMR methods within the modification of β-B.

The reactions of K2ZnSb (0.234 mol) and Ni(CO)2(PPh3)2 (x mol) in ethylenediamine (en) solutions of 18-crown-6 at 60 °C yielded half-centered [Ni0.5@{Sb6Ni6(CO)8}]4− (x = 0.023, 1) and fully embedded [Ni@{Sb7Ni5(CO)6}]3− (x = 0.047, 2), wherein the chair-like Sb6 subunit is bicapped by two Ni3 triangles to form the single Sb6Ni6 icosahedron of 1 and by the triangular Ni2Sb and Ni3 to form the single Sb7Ni5 icosahedron of 2. Surprisingly, a smaller amount of Ni(CO)2(PPh3)2 (x = 0.016) led to the formation of the unprecedented dimer [(Sb8){Sb7Ni5(CO)4}2]6− (4), wherein the Sb7Ni5 icosahedral unit built of boat-like Sb6, Ni2Sb and Ni3 is linked together by the realgar-like Sb8 to form the icosahedral dimer 4, providing a new way of thinking for the preparation of icosahedral oligomers/polymers. A similar hexa-anionic dimer (3) can be solely obtained using PBu4+ as the countercation under the same reaction conditions. The structure and bonding of this novel series of icosahedral clusters containing polyantimony were discussed for the first time.

We report the identification and quantitative isolation of Au145(SR)60X (R = n-butyl, n-pentyl; X = halide) along with elucidation of key properties as compared to the corresponding ubiquitous chiral-icosahedral Au144(SR)60 cluster known to have a central vacancy. The stoichiometries were assessed by electrospray mass spectrometry (ESI-MS) at isotopic resolution, and induced dissociation patterns indicate the ‘extra’ (Au,Br) atoms are strongly bound components of these structures. Voltammetric and spectroscopic characterization reveals Au145(SR)60X behaviors that are qualitatively similar to yet fascinatingly distinct from those of Au144(SR)60. (1H,13C)-NMR spectra clearly show how both Au145(SR)60X and Au144(SR)60 are capped by 12 distinct ligand types of 5-fold equivalence, as was recently established for Au144(SR)60 capped by shorter ligands, demonstrating that this novel cluster shares the same chiral-icosahedral motif. Intriguingly, Au145(SR)60X is strongly near-IR luminescent, whereas under comparable conditions Au144(SR)60 barely emits. The photoluminescence pattern of Au145(SR)60X is very similar to that observed for Au25(SR)18, which contains the Au13 core. The combined results are interpreted as consistent with neutral Au145(SR)60X as a diamagnetic species, electronically and structurally similar to the corresponding Au144(SR)60 compounds.

A novel 3D coordination polymer, ∞3[{Cu3(felden)}4(btec)3]·17H2O, has been assembled using cationic trigonal nodes, [CuII3(felden)]3+, generated by a tricompartmental ligand, H3felden, which results from the Schiff condensation reaction between 2,4,6-triformylphloroglucinol and N,N-dimethylethylenediamine. The tetraanion of the 1,2,4,5-benzenetetracaboxylic acid (H4btec) was employed as a spacer. The structure of 1 shows large icosahedral cavities and channels and the magnetic interaction between the copper(II) ions within the triangles is weak and antiferromagnetic.

Two mononuclear Dy(III) compounds and one heteronuclear Dy(III)–K(I) compound, [Dy(tmpd)3(4,4′-dmpy)] (1), [KDy2(tmpd)8]·C5H6N (2) and [Dy(tmpd)3(dppz)] (3) (4,4′-dmpy = 4,4′-dimethyl-2,2′-bipyridyl, tmpd = 4,4,4-trifluoro-1-(4-methylphenyl)butane-1,3-dione, and dppz = dipyrido[3,2-a:2′,3′-c]phenazine), were synthesized by changing the organic bases and auxiliary ligands. The coordination environments of compounds 1 and 3 are different DyN2O6 configurations resulting from steric effects of different auxiliary ligands, while 2 has KF6O6 and DyO8 coordination environments because of the introduction of an organic base (CH3OK). The Dy(III) ions in compounds 1 and 2 have a triangular dodecahedral (D2d) configuration and square antiprismatic (D4d) configuration, respectively. Compound 3 contains two crystallographically equivalent Dy(III) ions of which the eight-coordinated geometries uniformly behave as distorted square antiprismatic (D4d) configurations. Compound 2 affords a novel Dy(III)–K(I) compound with unusually coordinated fluorine atoms of trifluoromethyl groups of β-diketone ligands. 2 is a centrosymmetric structure in which the central K(I) ion is located at the middle of two Dy(III) ions, resulting in an icosahedral (Ih) configuration. Magnetic investigations demonstrate that 1 and 3 display slow magnetic relaxation behaviors. The effective barriers are 94.91 K in 1 and 82.44 K in 3. The M versus H data exhibit weak butterfly-shaped hysteresis loops at 2 K for 1 and 3. The uniaxial magnetic anisotropies, magnetostructural correlations and relaxation mechanism were investigated both experimentally and theoretically. The experimental and theoretical studies indicate that compound 1 exhibits the best magnetic properties among compounds 1–3. The theoretical predictions of quantum tunneling of magnetization time and effective barriers are consistent with the corresponding experimental values. Our results indicate that the different organic bases and substituted groups of auxiliary ligands play an important role in synthetic processes, finally affording distinct structures and magnetic properties.

We report the successful synthesis of a chiroptically active Au25 cluster protected by mixed ligands of chiral bidentate S-BINAP and achiral dodecanethiol (DDT), which can be formulated as [Au25(S-BINAP)4(DDT)5X4] (X = Cl or Br). The UV-vis absorption spectral pattern is similar to that of the well-known bi-icosahedral cluster [Au25(PPh3)10(SR)5X2]2+, so the obtained cluster should also have a similar bi-icosahedral structure assembled from two vertex-sharing icosahedral Au13 units. With a closer inspection of the optical absorption, interestingly, the lowest-energy peak is red-shifted as compared to that of [Au25(PPh3)10(SR)5X2]2+. Quantum chemical calculations for model bi-icosahedral Au25 structures suggest the reason of the red shift. On the other hand, the obtained Au25 cluster exhibits a weak CD signature in the lowest-energy transition region, whereas higher-energy transitions have very large chiroptical responses with a maximum g-factor of 1.7 × 10−3. The calculations also give implications for the origin of the CD response in the Au25 cluster. We then believe that bi-icosahedral Au25 clusters with chirality will be a good prototype for understanding the influence of constituent Au13 units on the chiroptical activity of their assembling structures.

Colourless crystalline compounds of centrosymmetric [Np(NO3)6]2− were yielded from 3 M HNO3 aq in the presence of double-headed 2-pyrrolidone derivatives (L). In the obtained crystal structures, H+ was also involved as a countercation to compensate for the negative charge of [Np(NO3)6]2−, where the initial hydration around H+ was fully removed during crystallization despite it having the strongest hydration enthalpy. Instead, this anhydrous H+ was captured by L to form a [H+⋯L]n hydrogen bonded polymer. In [Np(NO3)6]2−, the Np4+ centre is twelve-coordinated with 6 bidentate NO3−, and therefore, present in an icosahedral geometry bearing inversion centre. In such a centrosymmetric system, any f–f transitions stemming from the 5f3 electronic configuration of Np4+ are electric-dipole forbidden. This is the reason why the compounds currently obtained were colourless unlike ordinary Np(IV) species, which are olive-green.

The formation of the Cu-Pt nanocontacts has been investigated by means of classical molecular dynamics simulations. The simulations of the mechanically controlled break junction experiment have been performed in wide ranges of temperatures (0-300 K) and at relative Pt concentrations (0-20%). The structure of the breaking area has been studied 2 ns before the final breaking of the nanocontacts. The length of the breaking area increases with the increase of the temperature and decreases with the increase of the relative Pt concentration. The structure of the breaking area has been investigated by means of the radial distribution function method. The breaking area usually has one of the following structures: (i) a bulk-like structure, (ii) a structure consisting of centered icosahedrons rotated 90°, or (iii) an icosahedral structure composed of pentagonal rings. The structure of the breaking area is almost independent of the temperature and the stretching direction due to the strong Cu-Pt interaction.

Structures of the slightly hypoelectronic 14-vertex species Cp2M2B12H12 (M = Rh, Ir) and Cp2M′2C2B10H12 (M′ = Ru, Os) with 28 Wadean skeletal electrons, including the experimentally known Cp*2Ru2C2B10H12, have been optimized by density functional theory. All low-energy such structures have the metal atoms located at degree 6 vertices. The lowest energy structures have central M2B12 and M′2C2B10 deltahedra with three degree 6 vertices, one degree 4 vertex, ten degree 5 vertices, and the metal atoms located at non-adjacent non-antipodal degree 6 vertices similar to meta isomers of icosahedral dimetallaboranes. Slightly higher energy structures are based on the same central deltahedron but with the metal atoms located at adjacent degree 6 vertices similar to ortho isomers of dimetallaboranes. Isomeric structures with central M2B12 and M′2C2B10 central closo deltahedra, namely bicapped hexagonal antiprisms with the metal atoms in antipodal positions at the two degree 6 vertices similar to the para isomers of icosahedral dimetallaboranes, also lie at low energies.

We report an experimental and theoretical investigation of the electronic and optical properties of a series of icosahedral Au13 nanoclusters, protected using different halogen ligands (Cl, Br, and I), as well as 1,2-bis(diphenylphosphino)ethane (dppe) ligands. All three clusters are comprised of the same Au13 kernel with two halogens coordinated to the poles of the icosahedral cluster along with five dppe ligands. UV-vis absorption spectra indicate a systematic red shift from Cl to Br to I, as well as a sudden enhancement of the second excitonic peak for the I-coordinated cluster. Density functional theory (DFT) calculations suggest that all clusters possess a wide HOMO–LUMO energy gap of ∼1.79 eV and are used to assign the first two excitonic bands. Frontier orbital analyses reveal several HOMO → LUMO transitions involving halogen-to-metal charge transfers. For the I-coordinated cluster, more complicated I-to-metal charge transfers give rise to different excitation features observed experimentally. The current findings show that halogen ligands play important roles in the electronic structures of gold clusters and can be utilized to tune the optical properties of the clusters.

Endohedral metallofullerenes are key species for expanding the range of viable fullerenes, their versatility, and applications. Here we report our computational evaluation on the formation of spherical aromatic counterparts of the C60 fullerene from relativistic DFT calculations, based on the inclusion of Cr, Mo and W endohedral atoms. The resulting M@C60 endohedral fullerenes are 66-π electron neutral species exhibiting bonding properties and electronic structure mimicking the aromaticity and diamagnetic insulator behavior of alkali-C606− phases. The resulting structures are interesting candidates for further experimental realization as novel neutral building blocks for more flexible nanostructured organic materials, highlighting truly spherical aromatic neutral species retaining the truncated icosahedral structure of the seminal Buckminster fullerene.

Energetically low-lying structural isomers of the much-studied thiolate-protected gold cluster Au25(SR)18− are discovered from extensive (80 ns) molecular dynamics (MD) simulations using the reactive molecular force field ReaxFF and confirmed by density functional theory (DFT). A particularly interesting isomer is found, which is topologically connected to the known crystal structure by a low-barrier collective rotation of the icosahedral Au13 core. The isomerization takes place without breaking of any Au–S bonds. The predicted isomer is essentially iso-energetic with the known Au25(SR)18− structure, but has a distinctly different optical spectrum. It has a significantly larger collision cross-section as compared to that of the known structure, which suggests it could be detectable in gas phase ion-mobility mass spectrometry.

Herein, we report the synthesis and total structure of a Cu-rich alloy nanocluster protected by twelve adamantanethiolate ligands, i.e., [Ag13Cu10(SAdm)12]X3 (-SAdm = SC10H15, X = counterion), which was confirmed by single-crystal X-ray structure determination and electrospray ionization mass spectrometry (ESI-MS). X-ray crystallographic analysis indicated that [Ag13Cu10(SAdm)12]X3 consisted of an icosahedral Ag13 core, covered by a cage-like shell of Cu10(SAdm)12. Furthermore, density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations on the geometric and electronic structures and KS orbitals and UV-vis spectroscopy were performed on the model [Ag13Cu10(SMe)12]3+ and its monometallic analog [Ag23(SMe)12]3+. This work will deepen the understanding of core-shell Ag-Cu alloy nanoclusters.

The geometries and electronic structures of icosahedral A13C (A = Sc, Y; C = 0, ±1, ±2) clusters have been determined at a range of multiplicities at each cluster charge, using density functional theory methods. These clusters demonstrate a complex electronic structure which provides insight into the anomalously high magnetic moment of icosahedral group 3 clusters and further contextualises the role of transition metals and d-electrons within the superatomic model. Embedded deeply within the density of states for these clusters are typical superatom orbitals which are populated up to the 2S level. Above the 2S-state there are three states of apparent F symmetry, which are preferentially singly occupied, followed by an abundance of approximately degenerate P-, G-, D- and F-states at the Fermi energy, which are at most singly occupied. In spite of apparent angular symmetry and a nodal structure reminiscent of superatomic orbitals these states are actually formed from preferential overlap of the valence d-orbitals of the cluster atoms. This analysis was further contextualised through analysis of the Sc19 cluster, which shows a similar construction of Kohn–Sham states, but with the breaking of 5-fold symmetry along one of its Cartesian axes. Finally, this work clearly demonstrates the ability of d-electrons to give rise to superatomic orbitals is not just constrained by atomic species but also by the local environment of the atoms.

Atomically precise engineering on the nanocluster surface remains highly desirable for the fundamental understanding of how surface structures of a nanocluster contribute to its overall properties. In this paper, the concept of "graft-onto" has been exploited to facilitate nanocluster growth on surface structures. Specifically, the Ag2(DPPM)Cl2 complex is used for re-constructing the surface structure of Pt1Ag28 (SR)18(PPh3)4 (Pt1Ag28 , SR = 1-adamantanethiolate) and producing a size-growth nanocluster - Pt1Ag31 (SR)16(DPPM)3Cl3 (Pt1Ag31 ). The grafting effect of Ag2(DPPM)Cl2 induces both direct changes on the surface structure (e.g., size growth, structural transformation, and surface rotation) and indirect changes on the kernel structure (from a fcc configuration to an icosahedral configuration). Remarkable differences have been observed by comparing optical properties between Pt1Ag28 and Pt1Ag31 . Significantly, Pt1Ag31 exhibits high photo-luminescent intensity with a quantum yield of 29.3%, which is six times that of the Pt1Ag28 . Overall, this work presents a new approach (i.e., graft-onto) for the precise dictation of nanocluster surface structures at the atomic level.

The main goal of this work is the design of a coarse-grained theoretical model of minimal resolution for the study of the physical properties of icosahedral virus capsids within the linear-response regime. In this model the capsid is represented as an interacting many-body system whose composing elements are capsid subunits (capsomers), which are treated as three-dimensional rigid bodies. The total interaction potential energy is written as a sum of pairwise capsomer–capsomer interactions. Based on previous work [Gomez Llorente et al., Soft Matter, 2014, 10, 3560], a minimal and complete anisotropic binary interaction that includes a full Hessian matrix of independent force constants is proposed. In this interaction model, capsomers have rotational symmetry around an axis of order n > 2. The full coarse-grained model is applied to analyse the low-frequency normal-mode spectrum of icosahedral T = 1 capsids. The model performance is evaluated by fitting its predicted spectrum to the full-atom results for the Satellite Tobacco Necrosis Virus (STNV) capsid [Dykeman and Sankey, Phys. Rev. Lett., 2008, 100, 028101]. Two capsomer choices that are compatible with the capsid icosahedral symmetry are checked, namely pentamers (n = 5) and trimers (n = 3). Both subunit types provide fair fits, from which the magnitude of the coarse-grained force constants for a real virus is obtained. The model is able to uncover latent instabilities whose analysis is fully consistent with the current knowledge about the STNV capsid, which does not self-assemble in the absence of RNA and is thermally unstable. The straightforward generalisability of the model beyond the linear regime and its completeness make it a promising tool to theoretically interpret many experimental data such as those provided by the atomic force microscopy or even to better understand processes far from equilibrium such as the capsid self-assembly.

Understanding the physicochemical processes occurring in viruses during their maturation is of fundamental importance since only mature viruses can infect host cells. Here we consider the irreversible and reversible morphological changes that occur with the dodecahedral ϕ6 procapsid during the sequential packaging of 3 RNA segments forming the viral genome. It is shown that the dodecahedral shape of all the four observed capsid states is perfectly reproduced by a sphere radially deformed by only two irreducible spherical harmonics with icosahedral symmetry and wave numbers l = 6 and l = 10. The rotation of proteins around the 3-fold axes at the Procapsid → Intermediate 1 irreversible transformation is in fact also well described with the shear field containing only two irreducible harmonics with the same two wave numbers. The high stability of the Intermediate 1 state is discussed and the shapes of the Intermediate 2 state and Capsid (reversibly transforming back to the Intermediate 1 state) are shown to be mainly due to the isotropic pressure that the encapsidated RNA segments exert on the shell walls. The hidden symmetry of the capsid and the physicochemical features of the in vitro genome extraction from the viral shell are also elucidated.

DFT calculations were carried out on bare Au32 and Au33 nanoclusters with various charges, in order to analyze their stability with respect to different cluster electron numbers. Results indicate that in addition to the neutral Au32 hollow species, significant HOMO–LUMO gaps are computed for [Au32]8+ (hollow) and [Au32]4+ (two-shell structure). Species with smaller HOMO–LUMO gaps can reach stability upon “passivation” by a ligand shell, as experimentally exemplified. Icosahedral frameworks of Ih or lower symmetry are favored for the cationic nanoclusters whereas different structures are computed for the anionic ones.

The interplay between crystalline ordering, curvature, and size dispersity make the packing of bidisperse mixtures of particles on a sphere a varied and complex phenomenon. These structures have functional significance in a broad range of systems, such as cellular organisation in spherical epithelia, catalytic activity in binary colloidosomes, and chemical activity in heterofullerenes. In this contribution, we elucidate the potential energy landscapes for systems of repulsive, bidisperse particles confined to the surface of a sphere. It is commonly asserted that particle size dispersity destroys ordered arrangements, leading to glassy landscapes. Surprisingly, across a range of compositions, we find highly ordered global minima. Moreover, a minority of small particles is able to passivate defects, stabilising bidisperse global minima relative to monodisperse systems. However, our landscape analysis also reveals that bidispersity introduces numerous defective, low-lying states that are expected to cause broken ergodicity in corresponding experimental and computational systems. Probing the global minimum structures further, particle segregation is energetically preferred at intermediate compositions, contrasting with the approximate icosahedral global packing at either end of the composition range. Finally, changing the composition has a dramatic effect on the heat capacity: systems with low-symmetry global minima have melting temperatures an order of magnitude lower than monodisperse or high-symmetry systems. This observation may provide a further example of the principle of maximum symmetry: higher symmetry global minima exhibit a larger energy separation from the minima that define the high-entropy phase-like region of configuration space, raising the transition temperature.

An ultra-light icosahedral fullerene structure is described having 12 pentagonal faces at the vertices of the regular icosahedron and 20 triangular faces, which are expanded by hexagonal faces that consist of carbon atoms. When its size exceeds a critical value, the density of the icosahedron becomes lower than that of air. Since the hollow structure deforms under atmospheric pressure, we proposed the addition of helium atoms as a means to obtaining a floatable icosahedral fullerene with pressure-resistant character. According to these requirements, the radius of the midpoint ball of the edge is 493.33 μm; the total density of the helium-filled structure is 0.18 kg m-3; and the buoyancy per cubic meter in the air is 10.88 N. Theoretical calculation and simulation are combined to explore a new approach to ultra-light materials.

A water molecule encapsulated inside a C60 fullerene cage behaves almost like an asymmetric top rotor, as would be expected of an isolated water molecule. However, inelastic neutron scattering (INS) experiments show evidence of interactions between the water molecule and its environment [Goh et al., Phys. Chem. Chem. Phys., 2014, 16, 21330]. In particular, a resolved splitting of the 101 rotational level into a singlet and a doublet indicates that the water molecule experiences an environment of lower symmetry than the icosahedral symmetry of a C60 cage. Recent calculations have shown that the splitting can be explained in terms of electrostatic quadrupolar interactions between the water molecule and the electron clouds of nearest-neighbour C60 molecules, which results in an effective environment of S6 symmetry [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274 and Bacic et al., Faraday Discussions, 2018, 212, 547-567]. We use symmetry arguments to obtain a simple algebraic expression, expressed in terms of a linear combination of products of translational and rotational basis functions, that describes the effect on a water molecule of any potential of S6 symmetry. We show that we can reproduce the results of the electrostatic interaction model up to ≈12 meV in terms of two unknown parameters only. The resulting potential is in a form that can readily be used in future calculations, without needing to use density functional theory (DFT) for example. Adjusting parameters in our potential would help identify whether other symmetry-lowering interactions are also present if experimental results that resolve splittings in higher-energy rotational levels are obtained in the future. As another application of our model, we show that the results of DFT calculations of the variation in energy as a water molecule moves inside the cage of an isolated C60 molecule, where the water molecule experiences an environment of icosahedral symmetry, can also be reproduced using our model.

We present computational discoveries of new structural phases of the B2O compound exhibiting novel bonding networks and electronic states at ambient and elevated pressures. Our advanced crystal structure searches in conjunction with density functional theory calculations have identified an orthorhombic phase of B2O that is energetically stable at ambient pressure and contains an intriguing bonding network of icosahedral B12 clusters bridged by oxygen atoms. As pressure increases above 1.9 GPa, a structural transformation takes the orthorhombic B2O into a pseudo-layered trigonal phase. We have performed extensive studies to investigate the evolution of chemical bonds and electronic states associated with the B12 icosahedral unit in the orthorhombic phase and the covalent B-O bonds in the trigonal phase. We have also examined the nature of the charge carriers and their coupling to the lattice vibrations in the newly identified B2O crystals. Interestingly, our results indicate that both B2O phases become superconducting at low temperatures, with transition temperatures of 6.4 K and 5.9 K, respectively, in the ambient and high-pressure phase. The present findings establish new B2O phases and characterize their structural and electronic properties, which offer insights and guidance for exploration toward further fundamental understanding and potential synthesis and application.

Four-fold aryl substituted o-carborane derivatives with defined patterns of substitution at the antipodal region of the cluster carbon atoms have been achieved. It is proven that this region is congested but lacks steric hindrance. Also, the two antipodal sites Cc–Cc and B9–B12 are affected very distinctly by electron donor substituents., This work has been supported by the Spanish Ministerio de Economı´a y Competitividad (CTQ2016-75150-R), the Generalitat de Catalunya (2017SGR1720) and European Union’s Horizon 2020 Marie Skłodowska-Curie grant agreement MSCA-IF-2016- 751587., We acknowledge support of the publication fee by the CSIC Open Access Support Initiative through its Unit of Information Resources for Research (URICI

Comparable systems are of great significance for understanding the structure-property relationship. Herein, a new Au13Cu2 nanocluster protected by phenylethanethiol (PET) and triphenylphosphine (TPP) is synthesized and structurally determined, including an icosahedral Au13 and two CuS3 configurations. Based on previous work, a comparable system was formed-only the surface coordination of Cu atoms changes from Cu-N to Cu-S, which results in a tremendous change in the optical properties. Based on this, the effect of the coordination mode on the structure and optical properties was primarily investigated in both experiment and theory. And the results demonstrate that changing the coordination mode from Cu-N to Cu-S has a significant effect on the electronic structure. This work will offer new insights into ligand engineering.

Atomically precise nanoclusters of coinage metals in the 1-3 nm size regime have been intensively pursued in recent years. Such nanoclusters are attractive as they fill the gap between small molecules ( 3 nm). This intermediate identity endows nanoclusters with unique physicochemical properties and provides nanochemists opportunities to understand the fundamental science of nanomaterials. Metal nanoparticles are well known to exhibit plasmon resonances upon interaction with light; however, when the particle size is downscaled to the nanocluster regime, the plasmons fade out and step-like absorption spectra characteristic of cluster sizes are manifested due to strong quantum confinement effects. Recent research has revealed that nanoclusters are commonly composed of a distinctive kernel and a surface-protecting shell (or staple-like metal-ligand motifs). Understanding the kernel configuration and evolution is one of the central topics in nanoscience research. This Review summarizes the recent progress in identifying the growth patterns of atomically precise coinage nanoclusters. Several basic kernel units have been observed, such as the M4, M13 and M14 polyhedrons (where, M = metal atom). Among them, the tetrahedral M4 and icosahedral M13 units are the most common ones, which are adopted as building blocks to construct larger kernel structures via various fusion or aggregation modes, including the vertex- and face-sharing mode, the double-strand and alternate single-strand growth, and cyclic fusion of units, as well as the fcc-based cubic growth pattern. The identification of the kernel growth pathways has led to deeper understanding of the evolution of electronic structure and optic properties.

Herein, we report the first silver-rich nanocluster containing an open icosahedral Au1Ag12 core. This nanocluster is determined to be [Au1Ag24(Dppm)3(SR)17]2+ (where Dppm is short for bis-(diphenylphosphino)methane and SR is short for cyclohexyl mercaptan) by single-crystal X-ray diffraction and electrospray ionization mass spectrometry (ESI-MS). The Au1Ag24 consists of an open icosahedral Au1Ag12, which contains six free valence electrons surrounded by a big ring motif Ag12(Dppm)3(SR)15 and two SR groups. Density Functional Theory (DFT) provided insight into the relationship between the structure and its performance.

The putative global minimum of clusters with formula B10M2 (M = Rh, Ir) corresponds to icosahedral structures formed by two alternately stacked B5 rings with the metals located at the top and bottom vertices. These structures are the closest approximation of molecular clusters to the elusive icosahedral boron. A detailed analysis of the chemical bonding revealed that the covalent character between the transition metal and the boron framework as well as the strong delocalization throughout the structure enhances the stabilization of the icosahedral form.

The sub-nanometer cavity of fullerene cages is an ideal platform to accommodate otherwise unstable species for accurate structural characterization with, for example, rather accurate single crystal X-ray diffraction (XRD) crystallography. Herein, we report the successful entrapment of an isolated Ti3C3 moiety inside the icosahedral-C80 cage to form Ti3C3@Ih-C80via an arc-evaporation process in the gas phase. The single crystal XRD crystallographic results unambiguously reveal that the C3-unit adopts an unprecedented cyclopropane-like structure which coordinates with the three titanium atoms in an unexpected fashion where the triangular C3-unit is nearly perpendicular to the Ti3-plane. The intercalation of a cyclopropanated C3-unit into the titanium layer is thus unambiguously confirmed. The theoretical results reveal that the Ti3C3 cluster transfers six electrons to the Ih-C80 cage so that each titanium atom has a positive charge slightly above +2 and the C3-unit is negatively charged with about −1. It is noteworthy that this is the first observation of the cyclopropane-coordination fashion in any reported organometallic complex, providing new insights into coordination chemistry.

The CeGaCu amorphous alloy has a good glass-forming ability and many special properties. However, its structure at the atomic scale is unclear. We systematically investigated the structure evolution of Ce70GaxCu30−x (x = 6, 10, 13) glass formation melts by ab initio molecular dynamics (AIMD) simulations. Based on the trajectories from the simulations, the pair-correlation function, coordination numbers, chemical short-range order, Voronoi polyhedra and electronic structures were discussed. Our results show that the concentration of Ga- and Cu-centered icosahedral (-like) clusters in Ce70Ga10Cu20 melts are larger than those in Ce70Ga6Cu24 and Ce70Ga13Cu17 melts. Furthermore, electronic analysis showed that the hybridization between Ga 4p and Cu 3d (Ce 5d) orbitals is strong and that of Cu 3d orbitals and Ga 4p orbitals was strengthened in Ce70Ga10Cu20 melts, which means that the interactions between Ga and Cu atoms nearby were enhanced in the Ce70Ga10Cu20 melts. The stability of the Ga- or Cu-centered icosahedral clusters increased accordingly, which favored their glass-forming ability. Our investigation helps people obtain an increased understanding of the glass-forming ability from the viewpoint of chemical interactions for metallic glasses.

Here we show the encapsulation of 35 nm diameter, nearly-spherical, DNA origami by self-assembly of SV40-like (simian virus 40) particles. The self-assembly of this new type of nanoparticles is highly reproducible and efficient. The structure of these particles was determined by cryo-EM. The capsid forms a regular SV40 lattice of T = 7d icosahedral symmetry and the structural features of encapsulated DNA origami are fully visible. These particles are a promising biomaterial for use in various medical applications.

Cage clusters are a discrete chemically and topologically diverse family of molecule-based functional materials. Presented here are two isostructural M48 (M = CoII for LSHU01, NiII for LSHU02) cage clusters with a merohedral icosahedral cage structure featuring 12 M4-TC4A (H4TC4A, p-tert-butylthiacalix[4]arene) second building units as vertices and 18 asymmetric 5-(1H-tetrazol-1-yl)isophthalate ligands as faces. They are the highest-nuclearity cage compounds of CoII and NiII. The activated Co48 cage exhibited high selectivity in the sorption of C3H8 over CH4 under ambient conditions. Frequency response experiments indicated that the extrinsic voids and matrix interface of the activated crystalline samples are primarily responsible for the observed gas adsorption performance.

In this work, we report a controlled self-assembly of three M13 icosahedral building-blocks into cyclic Pt3Ag33 or Pt3Au12Ag21 nanoclusters. Compared to the previously reported Pt2Ag23 and Pt1Ag12 nanoclusters, the Pt3Ag33 nanoclusters exhibit a red-shift in both the optical absorption and photoluminescence due to the assembly of an additional Pt1Ag12 icosahedron.

The atomic structures of many atomically precise nanosized ligand protected gold clusters have been resolved recently. However, the determination of the atomic structures of large sized ligand protected gold clusters containing metal atoms over ∼100 is still a grand challenge. The lack of structural information of these larger sized clusters has greatly hindered the understanding of the structure evolution and structure-property relations of ligand protected gold nanoclusters. In this work, we theoretically studied the structure evolution of a series of large sized Au145-3N(SR)60-2N (N = 1-8) clusters based on an "[Au2@Au(SR)2] fragmentation" pathway starting from a model Au145(SR)60 cluster. Through comprehensively searching the atomic structure of various clusters and evaluating their stabilities by means of first principles calculations, the stabilization mechanism of experimentally reported Au130(SR)50 and Au133(SR)52 clusters is first rationalized. Our studies indicated that Au130(SR)50 and Au133(SR)52 are two critical sized clusters on which the gold cores underwent configuration transitions between decahedral and icosahedral cores. The energy comparisons of various cluster isomer structures indicated that the Au130(SR)50, Au127(SR)48, Au124(SR)46 and Au121(SR)44 clusters favored a decahedral core, while the Au133(SR)52, Au136(SR)54, Au139(SR)56, and Au142(SR)58 clusters preferred icosahedral gold cores. Furthermore, we also find that the cuboctahedral gold core is less stable in the cluster size region between ∼120 and ∼140 gold atoms. The optical absorption properties and relative thermodynamic stabilities of the Au145-3N(SR)60-2N (N = 1-8) clusters are also surveyed by density functional theory (DFT) and time-dependent DFT calculations.

A recent study implied that a hetero-biicosahedral 25-atom cluster composed of two kinds of icosahedral 13-atom clusters could serve as a molecular rectifier and dipole material. However, no hetero-biicosahedral 25-atom clusters containing three types of ligands, in this case, phosphines, halogens, and thiolates, have been reported. In this study, we selectively synthesized [Au24Pd(PPh3)10(SC2H4Ph)5Cl2]Cl (Au = gold, Pd = palladium, PPh3 = triphenylphosphine, SC2H4Ph = phenylethanethiolate, Cl = chloride), in which one Au was replaced with a Pd. The single-crystal X-ray structural analysis demonstrated that [Au24Pd(PPh3)10(SC2H4Ph)5Cl2]Cl was a hetero-biicosahedral 25-atom cluster in which the central atom of one icosahedral Au13 core was replaced by a Pd atom. Optical absorption spectroscopy suggested that the electronic structure of each individual icosahedral 13-atom core in [Au24Pd(PPh3)10(SC2H4Ph)5Cl2]+ was reasonably well maintained, similar to the case of [Au25(PPh3)10(SC2H4Ph)5Cl2]2+. Density functional theory calculation revealed that the peak splitting in the region below 2.2 eV of the optical absorption spectrum of [Au24Pd(PPh3)10(SC2H4Ph)5Cl2]+ is due to the splitting of HOMOs and also suggested that this cluster has dipole moment. Electrochemical measurements showed that [Au24Pd(PPh3)10(SC2H4Ph)5Cl2]+ was relatively stable to reduction. These results are expected to contribute to the development of molecular rectifiers and dipole materials based on hetero-biicosahedral 25-atom clusters.

Assembly of bimetallic complexes on boron clusters by coordination of coinage metal cations to Ru–B single bonds., In this work, we introduce a novel approach for the selective assembly of heterometallic complexes by unprecedented coordination of coinage metal cations to strained single ruthenium–boron bonds on a surface of icosahedral boron clusters. M(i) cations (M = Cu, Ag, and Au) insert into B–Ru bonds of the (BB)–carboryne complex of ruthenium with the formation of four-membered B–M–Ru–B metalacycles. Results of theoretical calculations suggest that bonding within these metalacycles can be best described as unusual three-center-two-electron B–M···Ru interactions that are isolobal to B–H···Ru borane coordination for M = Cu and Ag, or the pairs of two-center-two electron B–Au and Au–Ru interactions for M = Au. These transformations comprise the first synthetic route to exohedral coinage metal boryl complexes of icosahedral closo-{C2B10} clusters, which feature short Cu–B (2.029(2) Å) and Ag–B (2.182(3) Å) bonds and the shortest Au–B bond (2.027(2) Å) reported to date. The reported heterometallic complexes contain Cu(i) and Au(i) centers in uncharacteristic square-planar coordination environments. These findings pave the way to rational construction of a broader class of multimetallic architectures featuring M–B bonds.

We present a new data-driven inverse design platform for self-assembling materials that we term “landscape engineering”. The essence of the approach is to sculpt the self-assembly free energy landscape to favor the formation of target aggregates by rational manipulation of building block properties. The approach integrates nonlinear manifold learning with hybrid Monte Carlo techniques to efficiently recover self-assembly landscapes, which we subsequently optimize using the covariance matrix adaptation evolutionary strategy (CMA-ES). We demonstrate the effectiveness of this technique in the design of anisotropic patchy colloids to form hollow polyhedral capsids. In the case of icosahedral capsids, our approach discovers a building block possessing a 76% improvement in the assembly rate over an initial expert-designed building block. In the case of octahedral clusters, our platform produces a building block with a 60% yield despite being challenged with a poor initial building block design incapable of forming stable octahedra.

Due to distinctive quantum confinement effects, ultrasmall gold nanoparticles usually exhibit interesting electronic structure and molecular-like properties. However, the lack of atomically-precise structural information makes the understanding of them almost impossible, such as understanding the relationships between their compositions and unique properties. Herein, by reducing a diphosphine AuI precursor (Au2(dppm)2Cl2; dppm = Ph2PCH2PPh2) with or without a S2- releasing reagent, we enriched our knowledge of the members in the families of Au13 and Au8 by the structural determinations of two new dppm-protected gold nanoclusters, [Au13(dppm)6]5+ (SD/Au1) and [Au8(dppm)4S2]2+ (SD/Au2), respectively. Within SD/Au1, the Au13 kernel significantly deviates from the ideal Ih icosahedron by the elongation of three surface Au-Au bonds to ∼3.5 A, giving it C3 symmetry, whereas SD/Au2 has a novel heart-shaped C2 symmetric Au8S2 core (central Au4 tetrahedron + two Au2S units) protected by four μ2-dppm ligands in the outer shell. Of note, SD/Au1 represents a rare Au13 nanocluster with an opened icosahedral geometry, and SD/Au2 shows a new edge-shared "core + 4exo" structure type that has never been observed before. The electronic structures and optical absorption spectra of these systems are correlated with time-dependent density functional theory (TDDFT) calculations. Based on the spherical jellium model, the stability of the Au13 and Au8 nanoclusters can be ascribed to 8- and 2-electron superatoms with 1S21P6 and 1S2 configurations, respectively. Interestingly, the cluster SD/Au2 exhibits bright yellow luminescence with an emission maximum at 591 nm that slightly hypsochromically shifts to 581 nm upon cooling to 93 K. Our findings not only enrich the family of diphosphine-protected ultrasmall gold nanoclusters, but also demonstrate the rich variations of gold kernels during the transformation from a simple AuI precursor to Au nanoclusters.

As a fundamental building block in ultrasmall, noble metal nanoclusters, icosahedral AuxM13−x structures have recently attracted extensive research interest. In this study, density functional theory (DFT) and time-dependant DFT calculations have been carried out to investigate the structure–property (optical and electronic) relationships of a series of Au13 and AuxM13−x (M = Au, Ag, Cu, and Pd) nanoclusters co-protected by phosphine and chloride ligands. It was found that the size of the peripheral ligands significantly affects the geometric structure: the larger exterior ligands (with a larger cone angle) result in relatively longer Au–M bond distances and weaker metallic interactions within the AuxM13−x core. Therefore, the optical peak (in the UV-vis spectrum) corresponding to the HOMO → LUMO transition red-shifts accordingly. When different foreign atom(s) are incorporated, the preferential doping site is different, and the electronic and optical structures alter accordingly.

In this study, molecular dynamics simulation was used to investigate the effects of nanocluster size and its composition on the thermodynamic stability and structural evolutions of icosahedral Pd@Au@Pd three-shell nanoalloys. It was concluded that the thermal stability of Pd@Au@Pd nanoalloys is significantly dependent on their size and composition in such a way that the increase of nanoparticle size and the decrease of its Au concentration leads to the increase of its melting point. Also, the total mechanism of melting does not depend on nanoparticle size and its composition. The melting process starts from the surface of the nanocluster and leads to the segregation of Au atoms on the surface and the aggregation of Pd atoms in the core region. The final stable structure after the melting point is dependent on the nanoparticle size. For small nanoclusters, a Janus-like structure is formed after the melting point. However, for larger nanoclusters there is a competition between Janus-like and core–shell structures and after the creation of an unstable dumbbell-like intermediate structure, a stable Pd@Au core–shell structure is obtained after the melting point.

The atomic-structure characterization of alloy nanoclusters (NCs) remains challenging but is crucial in order to understand the synergism and develop new applications based upon the distinct properties of alloy NCs. Herein, we report the synthesis and X-ray crystal structure of the Pt1Ag28(S-Adm)18(PPh3)4 nanocluster with a tetrahedral shape. Pt1Ag28 was synthesized by reacting Pt1Ag24(SPhMe2)18 simultaneously with Adm-SH (1-adamantanethiol) and PPh3 ligands. A tetrahedral structure is found in the metal framework of Pt1Ag28 NC and an overall surface shell (Ag16S18P4), as well as discrete Ag4S6P1 motifs. The Pt1Ag12 kernel adopts a face-centered cubic (FCC) arrangement, which is observed for the first time in alloy nanoclusters in contrast to the commonly observed icosahedral structure of homogold and homosilver NCs. The Pt1Ag28 nanocluster exhibits largely enhanced photoluminescence (quantum yield QY = 4.9%, emission centered at ∼672 nm), whereas the starting material (Pt1Ag24 NC) is only weakly luminescent (QY = 0.1%). Insights into the nearly 50-fold enhancement of luminescence were obtained via the analysis of electronic dynamics. This study demonstrates the atomic-level tailoring of the alloy nanocluster properties by controlling the structure.

Hierarchical metal nanostructures which exhibit an open structure and a high density of twin defects accessible to reactants hold great promise in catalysis. Here, we report a facile synthesis of Pt-Cu hierarchical quasi great dodecahedrons (HQGDs) which present 5-fold symmetry and are composed of multiple ordered branched units with a frame structure. HQGDs evolve from icosahedral seeds with multiple {111} twin planes, followed by the growth of higher-order branches. Owing to the unique frame structure associated with multiple twin defects, HQGDs showed much higher HER catalytic activity and better durability relative to commercial Pt/C.

We report the synthesis, characterization and DFT studies of a transition-metal-encapsulated superatom compound, [K(2,2,2-crypt)]3[Au@Pb12]·2py, which adopts a distorted symmetry instead of the icosahedral structure due to the second-order Jahn–Teller effect. DFT computations revealed its chemical bonding nature and aromatic character, and assigned the formal electronic structure as [Au−@Pb122−]3−.

We report four new copper-rich open-framework chalcogenides (COCs) with the formulas [Cu8Ge6Se19](C5H12N)6 (1a), [Cu8Sn6Se19](C6H12N2)4(H2O)13 (1b), [Cu16Ge12S36][Ni(en)3]4(en)xCl1.5 (1c), and [Cu7Ge4Se13](C6H21N4) (2). Single-crystal X-ray diffraction analyses suggest that all of these compounds with pcu-type topology are completely built on icosahedral clusters. Of particular interest, the connection units linking the icosahedral clusters in 1a–1c are pure dimeric units in three axial directions. Such a case is unprecedented among previously reported COCs and pushes up the length limit of the connection mode, thereby resulting in the largest solvent-accessible space in COCs. Compound 2 is built on an intriguing and unprecedented mixed-metal Cu7GeSe13 cluster. The copper-rich nature of these compounds gives rise to a narrow band gap in the near-infrared range, making them hold promise for photoelectric applications.

An unprecedented silver-centered P-tetracapped [Ag@Ag4(μ3-P)4] tetrahedron inscribed within a N12 icosahedral cage has been discovered in the novel family of luminescent clusters. The latter are easily self-assembled by reacting AgI salts with tris(2-pyridyl)phosphine (Py3P).

We present an extensive density-functional and wave function theory study of partially fluorinated B12Fn0/− (n = 1–6) series, which show that the global minima of B12Fn0/− (n = 2–6) are characterized to encompass a central boron double chain (BDC) nanoribbon and form stable BF2 groups at the corresponding BDC corner when n ≥ 3, but the B12F0/− system maintains the structural feature of the well-known quasi-planar C3v B12. When we put the spotlight on B12F60/− species, our single-point CCSD(T) results unveil that albeit with the 3D icosahedral isomers not being their global minima, C2 B12F6 (6.1, 1A) and C1 B12F6− (12.1, 2A) as typical low-lying isomers are 0.60 and 1.95 eV more stable than their 2D planar counterparts D3h B12F6 (6.7, 1A′) and C2v B12F6− (12.7, 2A2), respectively, alike to B12H60/− species in our previous work. Detailed bonding analyses suggest that B12Fn0/− (n = 2–5) possess ribbon aromaticity with σ plus π double conjugation along the BDC nanoribbon on account of their total number of σ and π delocalized electrons conforming the common electron configuration (π2(n+1)σ2n). Furthermore, the simulated PES spectra of the global minima of B12Fn− (n = 1–6) monoanions may facilitate their experimental characterization in the foreseeable future. Our work provides new examples for ribbon aromaticity and powerful support for the F/H/Au/BO analogy.

Based on a newly constructed Ni–Zr potential, Molecular dynamics and Monte Carlo simulations predict the amorphization driving force for each alloy and pinpoint the optimized value of 40 at% Zr. Through a variety of local structural analysis methods, it is revealed that NixZr100−x MGs exhibit a combination of icosahedral-, fcc- and hcp-like configurations, while the icosahedra or distorted icosahedra cover a dominant fraction. Interestingly, the lower-CN clusters, such as 〈0,2,8,1〉, may play a significant role in atomic mobility, while the icosahedron is less sensitive to the faster mobility.

In this work, two probabilistic and thermodynamic limits for formation of a bimetallic nanocluster from a homogeneous gas phase were obtained in order to investigate the related phenomena using molecular dynamics simulation. Therefore, by application of some simple assumptions from thermodynamics and statistical mechanics, a new expression for composition of the nanocluster was derived which depends only on the initial conditions of the system and one adjustable parameter. This expression can be easily fitted to the results of molecular dynamics and can be used as a measure of the thermodynamic contribution in the cluster formation process. Then, molecular dynamics simulations were performed for several systems containing the same total number of metallic atoms and different concentrations of Ag and Au atoms. The results of this study exhibited that depending on different initial compositions of Ag and Au types, fcc and icosahedral structures are formed. Moreover, increase of the initial Ag concentration leads to products whose compositions are more controlled by probability limits. However, longer simulation times indicated that creation of more thermodynamically favoured nanoclusters depends on the formation of more probable ones in the early stages of the simulation.