Limits of economy and fidelity for programmable assembly of size-controlled triply periodic polyhedra.

We propose and investigate an extension of the Caspar-Klug symmetry principles for viral capsid assembly to the programmable assembly of size-controlled triply periodic polyhedra, discrete variants of the Primitive, Diamond, and Gyroid cubic minimal surfaces. Inspired by a recent class of programmable DNA origami colloids, we demonstrate that the economy of design in these crystalline assemblies-in terms of the growth of the number of distinct particle species required with the increased size-scale (e.g., periodicity)-is comparable to viral shells. We further test the role of geometric specificity in these assemblies via dynamical assembly simulations, which show that conditions for simultaneously efficient and high-fidelity assembly require an intermediate degree of flexibility of local angles and lengths in programmed assembly. Off-target misassembly occurs via incorporation of a variant of disclination defects, generalized to the case of hyperbolic crystals. The possibility of these topological defects is a direct consequence of the very same symmetry principles that underlie the economical design, exposing a basic tradeoff between design economy and fidelity of programmable, size controlled assembly.

Symmetric tangled Platonic polyhedra.

Conventional embeddings of the edge-graphs of Platonic polyhedra, {f, z}, where f, z denote the number of edges in each face and the edge-valence at each vertex, respectively, are untangled in that they can be placed on a sphere ([Formula: see text]) such that distinct edges do not intersect, analogous to unknotted loops, which allow crossing-free drawings of [Formula: see text] on the sphere. The most symmetric (flag-transitive) realizations of those polyhedral graphs are those of the classical Platonic polyhedra, whose symmetries are *2fz, according to Conway's two-dimensional (2D) orbifold notation (equivalent to Schönflies symbols Ih , Oh , and Td ). Tangled Platonic {f, z} polyhedra-which cannot lie on the sphere without edge-crossings-are constructed as windings of helices with three, five, seven,… strands on multigenus surfaces formed by tubifying the edges of conventional Platonic polyhedra, have (chiral) symmetries 2fz (I, O, and T), whose vertices, edges, and faces are symmetrically identical, realized with two flags. The analysis extends to the "θz " polyhedra, [Formula: see text] The vertices of these symmetric tangled polyhedra overlap with those of the Platonic polyhedra; however, their helicity requires curvilinear (or kinked) edges in all but one case. We show that these 2fz polyhedral tangles are maximally symmetric; more symmetric embeddings are necessarily untangled. On one hand, their topologies are very constrained: They are either self-entangled graphs (analogous to knots) or mutually catenated entangled compound polyhedra (analogous to links). On the other hand, an endless variety of entanglements can be realized for each topology. Simpler examples resemble patterns observed in synthetic organometallic materials and clathrin coats in vivo.

Nanoscale Dodecahedral and Fullerene-Type Organoboroxine and Borazine Cages from Planar Building Units.

Boroxine- and borazine-cage analogs to C20, C60, and C70 were calculated and compared in terms of structure, strain indicators, and physical properties relevant to nanoscale applications. The results show C60 and C70 type cages are less strained than the smaller congener, primarily due to minimized bending in the B-arylene-B segments. The smallest cage calculated has a diameter of 2.4 nm, which increases up to 4.9 nm by either variation of the polyhedron (C20 < C60 < C70-type cage) or organic spacer elongation between boron centers. All calculated cages are porous (apertures ranging from 0.6 to 1.9 nm). Molecular electrostatic potential and Hirshfeld population analysis revealed both nucleophilic and electrophilic sites in the interior and exterior cage surfaces. HOMO-LUMO gaps range from 3.98 to 4.89 eV and 5.10-5.18 eV for the boroxine- and borazine-cages, respectively. Our findings provide insights into the design and properties of highly porous boroxine and borazine cages for nanoscience.

Achieving Optical Refractive Index of 10-Plus by Colloidal Self-Assembly.

This study demonstrates the developments of self-assembled optical metasurfaces to overcome inherent limitations in polarization density (P) and high refractive indices (n) within naturally occurring materials. The Maxwellian macroscopic description establishes a link between P and n, revealing a static limit in natural materials, restricting n to ≈4.0 at optical frequencies. Previously, it is accepted that self-assembly enables the creation of nanogaps between metallic nanoparticles (NPs), boosting capacitive enhancement of P and resultant exceptionally high n at optical frequencies. The work focuses on assembling gold (Au) NPs into a closely packed monolayer by rationally designing the polymeric ligand to balance attractive and repulsive forces, in that polymeric brush-mediated self-assembly of the close-packed Au NP monolayer is robustly achieved over a large-area. The resulting monolayer of Au nanospheres (NSs), nanooctahedras (NOs), and nanocubes (NCs) exhibits high macroscopic integrity and crystallinity, sufficiently enough for pushing n to record-high regimes. The systematic comparisons between each differently shaped Au NP monolayers elucidate the significance of capacitive coupling in achieving an unnaturally high n. The achieved n of 10.12 at optical frequencies stands as a benchmark, highlighting the potential of polyhedral Au NPs in advancing optical metasurfaces.

Portable wireless electrochemical sensing of breviscapine using core-shell ZIFs-derived Co nanoparticles embedded in N-doped carbon nanotube polyhedra-modified electrode.

A core-shell ZIF-67@ZIF-8-derived Co nanoparticles embedded in N-doped carbon nanotube polyhedra (Co/C-NCNP) hybrid nanostructure was prepared by a pyrolysis method. The synthesized Co/C-NCNP was modified on the screen-printed carbon electrode and used for the portable wireless sensitive determination of breviscapine (BVC) by differential pulse voltammetry. The Co/C-NCNP had a large surface area and excellent catalytic activity with increasing Co sites to combine with BVC for selective determination, which led to the improvement of the sensitivity of the electrochemical sensor. Under optimized conditions, the constructed sensor had linear ranges from 0.15 to 20.0 µmol/L and 20.0 to 100.0 µmol/L with the limit of detection of 0.014 µmol/L (3S0/S). The sensor was successfully applied to BVC tablet sample analysis with satisfactory results. This work provided the potential applications of zeolitic imidazolate framework-derived nanomaterials in the fabrication of electrochemical sensors for the sensitive detection of drug samples.

Chiral Superlattices Self-Assembled from Post-Modified Metal-Organic Polyhedra.

Metal-organic polyhedra (MOPs) are inherently porous, discrete, and solvent-dispersive, and directing them into chiral superlattices through direct self-assembly remains a considerable challenge due to their nanoscale size and structural complexity. In this work, we illustrate a postmodification protocol to covalently conjugate a chiral cholesteryl pendant to MOPs. Postmodification retained the coordination cores and allowed for reaction-induced self-assembly in loosely packed nanosized columns without supramolecular chirality. Solvent-processed bottom-up self-assembly in aqueous media facilitated the well-defined packing into twisted superlattices with a 5 nm lattice parameter. Experimental and computational results validated the role of intercholesteryl forces in spinning the nanosized MOPs, which achieved the chirality transfer to supramolecular scale with chiral optics. This work establishes a novel protocol in rational design of MOP-based chiroptical materials for potential applications of enantioselective adsorption, catalysis, and separation.

In-Cell Engineering of Protein Crystals into Hybrid Solid Catalysts for Artificial Photosynthesis.

The emergence of protein-based crystalline materials offers promising opportunities in enzyme immobilization. However, the current systems used for encapsulation of protein crystals are limited to either exogenous small molecules or monomeric proteins. In this work, polyhedra crystals were used to simultaneously encapsulate the foreign enzymes FDH and the organic photocatalyst eosin Y. These hybrid protein crystals are prepared easily by cocrystallization within a cell without a requirement for complex purification processes because they spontaneously form 1 µm scale solid particles. After immobilization within protein crystals, the recombinant FDH is recyclable and thermally stable and maintains 94.4% activity compared to the free enzyme. In addition, the incorporation of eosin Y endows the solid catalyst with CO2-formate conversion activity based on a cascade reaction. This work indicates that engineering protein crystals by both in vivo and in vitro strategies will provide robust and environmentally friendly solid catalysts for artificial photosynthesis.

Non-Covalent and Covalent Binding of New Mixed-Valence Cage-like Polyoxidovanadate Clusters to Lysozyme.

The high-resolution X-ray structures of the model protein lysozyme in the presence of the potential drug [VIVO(acetylacetonato)2] from crystals grown in 1.1 M NaCl, 0.1 M sodium acetate at pH 4.0 reveal the binding to the protein of different and unexpected mixed-valence cage-like polyoxidovanadates (POVs): [V15O36(OH2)]5-, which non-covalently interacts with the lysozyme surface, [V15O33(OH2)]+ and [V20O51(OH2)]n- (this latter based on an unusual {V18O43} cage) which covalently bind the protein. EPR spectroscopy confirms the partial oxidation of VIV to VV and the formation of mixed-valence species. The results indicate that the interaction with proteins can stabilize the structure of unexpected - both for dimension and architecture - POVs, not observed in aqueous solution.

Porous Salts as Platforms for Heterogeneous Catalysis.

The preparation of a new class of reactive porous solids, prepared via straightforward salt metathesis reactions, is described here. Reaction of the dimethylammonium salt of a magnesium-based porous coordination cage with the chloride salt of [CrII Cl(Me4 cyclam)]+ affords a porous solid with concomitant removal of dimethylammonium chloride. The salt consists of the ions combined in the expected ratio based on their charge as confirmed by UV-vis and X-ray photoelectron spectroscopies, ion chromatography (IC), and inductively coupled plasma mass spectrometry (ICP-MS). The porous salt boasts a Brunauer-Emmett-Teller (BET) surface area of 213 m2  g-1 . Single crystal X-ray diffraction reveals the chromium(II) cations in the structure reside in the interstitial space between porous cages. Importantly, the chromium(II) centers, previously shown to react with O2 to afford reactive chromium(III)-superoxide adducts, are still accessible in the solid state as confirmed by UV-vis spectroscopy. The site-isolated reactive centers have competence toward hydrogen atom abstraction chemistry and display significantly increased stability and reactivity as compared to dissolved ions.

Endowing Covalent Organic Frameworks with Photoresponsive Active Sites for Controllable Propylene Adsorption.

Photoresponsive covalent organic frameworks (PCOFs) have emerged as attractive candidates for adsorption, but it is challenging to construct PCOF adsorbents due to structural order loss of covalent organic frameworks (COFs) after introducing photoresponsive motifs and/or tedious steps of postmodification. Here, a facile strategy is developed, by dispersing photoresponsive metal-organic polyhedra (PMOP) into COFs, to endow COFs with photoresponsive adsorption sites. As a proof-of-concept study, a COF with pore size of 4.5 nm and PMOP with suitable molecular size (4.0 and 3.1 nm for trans and cis configuration, respectively) are selected to meet the requirements of proper accommodation space, good guest dispersion, and free isomerization. The structure of COF is well preserved after introducing PMOPs. Interestingly, the obtained photoresponsive host-guest composite (PHGC) adsorbents exhibit photomodulated adsorption capacity on propylene (C3 H6 ) and the change in adsorption capacity can reach up to 43.3% and is stable during multiple cycles. Density functional theory calculations reveal that visible-light irradiation drives the azobenzene motifs in PHGCs to the trans configuration and the adsorption sites are fully open and interact with C3 H6 . UV-light irradiation makes the azobenzene motifs transform to the cis configuration, leading to the shield of the adsorption sites and the consequent release of C3 H6 .

Cathodes Coating Layer with Li-Ion Diffusion Selectivity Employing Interactive Network of Metal-Organic Polyhedras for Li-Ion Batteries.

Surface modification of cathodes using Ni-rich coating layers prevents bulk and surface degradation for the stable operation of Li-ion batteries at high voltages. However, insulating and dense inorganic coating layers often impede charge transfer and ion diffusion kinetics. In this study, the fabrication of dual functional coating materials using metal-organic polyhedra (MOP) with 3D networks within microporous units of Li-ion batteries for surface stabilization and facile ion diffusion is proposed. Zr-based MOP is modified by introducing acyl groups as a chemical linkage (MOPAC), and MOPAC layers are homogenously coated by simple spray coating on the cathode. The coating allow the smooth transport of electrons and ions. MOPAC effectively suppress side reactions between the cathode and electrolyte and protect active materials against aggressive fluoride ions by forming a Li-ion selective passivation film. The MOPAC-coated Ni-rich layered cathode exhibited better cycle retention and enhanced kinetic properties than pristine and MOP-coated cathodes. Reduction of undesirable gas evolution on the cathode by MOPAC is also verified. Microporous MOPAC coating can simultaneously stabilize both the bulk and surface of the Ni-rich layered cathode and maintain good electrochemical reaction kinetics for high-performance Li-ion batteries.

(Bio)Functionalisation of Metal-Organic Polyhedra by Using Click Chemistry.

The surface chemistry of Metal-Organic Polyhedra (MOPs) is crucial to their physicochemical properties because it governs how they interact with external substances such as solvents, synthetic organic molecules, metal ions, and even biomolecules. Consequently, the advancement of synthetic methods that facilitate the incorporation of diverse functional groups onto MOP surfaces will significantly broaden the range of properties and potential applications for MOPs. This study describes the use of copper(I)-catalysed, azide-alkyne cycloaddition (CuAAC) click reactions to post-synthetically modify the surface of alkyne-functionalised cuboctahedral MOPs. To this end, a novel Rh(II)-based MOP with 24 available surface alkyne groups was synthesised. Each of the 24 alkyne groups on the surface of the "clickable" Rh-MOP can react with azide-containing molecules at room temperature, without compromising the integrity of the MOP. The wide substrate catalogue and orthogonal nature of CuAAC click chemistry was exploited to densely functionalise MOPs with diverse functional groups, including polymers, carboxylic and phosphonic acids, and even biotin moieties, which retained their recognition capabilities once anchored onto the surface of the MOP.

3D Characterization of the Molecular Neighborhood of •OH Radical in High Temperature Water by MD Simulation and Voronoi Polyhedra.

Understanding the properties of the •OH radical in aqueous environments is essential for biochemistry, atmospheric chemistry, and the development of green chemistry technologies. In particular, the technological applications involve knowledge of microsolvation of the •OH radical in high temperature water. In this study, the classical molecular dynamics (MD) simulation and the technique based on the construction of Voronoi polyhedra were used to provide 3D characteristics of the molecular vicinity of the aqueous hydroxyl radical (•OHaq). The statistical distribution functions of metric and topological features of solvation shells represented by the constructed Voronoi polyhedra are reported for several thermodynamic states of water, including the pressurized high-temperature liquid and supercritical fluid. Calculations showed a decisive influence of the water density on the geometrical properties of the •OH solvation shell in the sub- and supercritical region: with the decreasing density, the span and asymmetry of the solvation shell increase. We also showed that the 1D analysis based on the oxygen-oxygen radial distribution functions (RDFs) overestimates the solvation number of •OH and insufficiently reflects the influence of transformations in the hydrogen-bonded network of water on the structure of the solvation shell.

Trivalent Polyhedra as Duals of Borane Deltahedra: From Molecular Endohedral Germanium Clusters to the Smallest Fullerenes.

The duals of the most spherical closo borane deltahedra having from 6 to 16 vertices form a series of homologous spherical trivalent polyhedra with even numbers of vertices from 8 to 28. This series of homologous polyhedra is found in endohedral clusters of the group 14 atoms such as the endohedral germanium cluster anions [M@Ge10]3- (M = Co, Fe) and [Ru@Ge12]3- The next members of this series have been predicted to be the lowest energy structures of the endohedral silicon clusters Cr@Si14 and M@Si16 (M = Zr, Hf). The largest members of this series correspond to the smallest fullerene polyhedra found in the endohedral fullerenes M@C28 (M = Zr, Hf, Th, U). The duals of the oblate (flattened) ellipsoidal deltahedra found in the dirhenaboranes Cp*2Re2Bn-2Hn-2 (Cp* = η5-Me5C5; 8 ≤ n ≤ 12) are prolate (elongated) trivalent polyhedra as exemplified experimentally by the germanium cluster [Co2@Ge16]4- containing an endohedral Co2 unit.

Potassium and Cesium Fluorinated ß-Diketonates: Effect of a Cation and Terminal Substituent on Structural and Thermal Properties.

As potential precursors for the synthesis of fluoroperovskites, a family of heavy alkali metal (MI = K, Cs) fluorinated ß-diketonates were prepared and characterized by elemental analysis, IR, and powder-XRD. The crystal structures of the new six complexes, MI(ß-dikF)(H2O)X, X = 0 or 1, were also determined. The structural diversity of this poorly explored class of complexes was discussed, including the preferred types of cation polyhedra and the ligand coordination modes, and the thermal properties of the metal ß-diketonates were studied by TG-DTA in an inert (He) atmosphere. The data obtained allowed us to reveal the effect of the metal cation and the terminal substituent on the structural and thermal features of this family of complexes.

Multifaceted Structurally Coloured Materials: Diffraction and Total Internal Reflection (TIR) from Nanoscale Surface Wrinkling.

We investigate the combined effects of surface diffraction and total internal reflection (TIR) in the design of 3-dimensional materials exhibiting distinct structural colour on various facets. We employ mechanical wrinkling to introduce surface diffraction gratings (from the nano to the micron scales) on one face of an elastomeric rectangular parallelepiped-shaped slab and explore the roles, in the perceived colours, of wrinkling pattern, wavelength, the directionality of incident light and observation angles. We propose a simple model that satisfactorily accounts for all experimental observations. Employing polydimethylsiloxane (PDMS), which readily swells in the presence of various liquids and gases, we demonstrate that such multifaceted colours can respond to their environment. By coupling a right angle triangular prism with a surface grating, we demonstrate the straightforward fabrication of a so-called GRISM (GRating + prISM). Finally, using a range of examples, we outline possibilities for a predictive material design using multi-axial wrinkling patterns and more complex polyhedra.

The Marriage of Sierpinski Triangles and Platonic Polyhedra.

Fractal structures with self-similarity are of fundamental importance in the fields of aesthetic, chemistry and mathematics. Here, by taking advantage of constructs the rational geometry-directed precursor design, we report the construction of two fascinating Platonic solids, the Sierpinski tetrahedron ST-T and the Sierpinski octahedron ST-O, in which each possesses a fractal Sierpinski triangle on their independent faces. These two discrete complexes are formed in near-quantitative yield from the multi-component self-assembly of truncated Sierpinski triangular kernel L1 with tribenzotriquinacene-based hexatopic and anthracene-based tetratopic terpyridine ligands (L3 and L4 ) in the presence of metal ions, respectively. The enhanced stabilities of the 3D discrete structures were investigated by gradient tandem mass spectrometry (gMS2 ). This work provides new constructs for the imitation of complex virus assemblies and for the molecular encapsulation of giant guest molecules.

Interconversion of Highly Entangled Polyhedra into Concave Polyhedra by Nitrate-Induced Ternary Coordination.

Entangled (M3 L2 )n polyhedral complexes represent a unique class of supramolecular architectures that are stabilized by relatively weak metal-acetylene interactions in cooperation with conventional metal-pyridyl coordination. Counter-anion exchange of these complexes with a nitrate (NO3 - ) ion triggered formal metal insertion between the metal centers, and a heteroleptic ternary coordination mode with acetylenic, pyridyl, and nitrate donors was generated on the metal centers. As a result, the main frameworks of the polyhedral complexes M18 L12 and M12 L8 were formally extended into a new series of concave polyhedra having the compositions M21 L12 and M13 L8 , respectively. This transformation also resulted in the local disconnection of the highly entangled trifurcate topology of the framework, providing clues toward the skeletal editing of extended and complex three-dimensional (3D) architectures.

The Telluraboranes closo-TeB5 Cl5 and closo-TeB11 Cl11 with Exceptionally Long Body Diagonals: Synthetic and Bonding Motifs for Innovative Octahedral and Icosahedral Geometries.

Six-vertex closo-TeB5 Cl5 (1) and twelve-vertex closo-TeB11 Cl11 (2) telluraboranes have been prepared via co-pyrolysis of B2 Cl4 with TeCl4 in vacuo at temperatures between 360 °C and 400 °C. Both compounds are sublimable, off-white solids, and they have been characterized by one- and two-dimensional 11 B NMR and high-resolution mass spectroscopy. Both ab initio/GIAO/NMR and DFT/ZORA/NMR computations support octahedral and icosahedral geometries for 1 and 2, respectively, as expected due to their closo-electron counts. The octahedral structure of 1 has been confirmed by single-crystal X-ray diffraction on an incommensurately modulated crystal. The corresponding bonding properties have been analyzed in terms of the intrinsic bond orbital (IBO) approach. 1 is the first example of a polyhedral telluraborane with a cluster size smaller than 10 vertices.

Retrosynthetic Analysis Applied to Clip-off Chemistry: Synthesis of Four Rh(II)-Based Complexes as Proof-of-Concept.

Clip-off Chemistry is a synthetic strategy that our group previously developed to obtain new molecules and materials through selective cleavage of bonds. Herein, we report recent work to expand Clip-off Chemistry by introducing into it a retrosynthetic analysis step that, based on virtual extension of the products through cleavable bonds, enables one to define the required precursor materials. As proof-of-concept, we have validated our new approach by synthesising and characterising four aldehyde-functionalised Rh(II)-based complexes: a homoleptic cluster; a cis-disubstituted paddlewheel cluster; a macrocycle; and a crown.