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Predicting structure from the attributes of a material's building blocks remains a challenge and central goal for materials science. Isolating the role of building block shape for self-assembly provides insight into the ordering of molecules and the crystallization of colloids, nanoparticles, proteins, and viruses. We investigated 145 convex polyhedra whose assembly arises solely from their anisotropic shape. Our results demonstrate a remarkably high propensity for thermodynamic self-assembly and structural diversity. We show that from simple measures of particle shape and local order in the fluid, the assembly of a given shape into a liquid crystal, plastic crystal, or crystal can be predicted.

Porous crystals made to order Controlling and predicting the structural properties of porous molecular crystals would have important implications in gas adsorption, separation and catalysis applications, but remain an unmet goal. This paper introduces a new concept of modular assembly at the molecular level for the formation of porous crystalline solids. Different large chiral molecules with intrinsic nanosize pores, or porous modules, self-assemble through chiral recognition during co-crystallization to produce solid porous frameworks. The three-dimensional structure of the final material can be predicted theoretically. The paper explores four different, albeit analogous, porous modules, which form four different porous solids. Nanoporous molecular frameworks 1 , 2 , 3 , 4 , 5 , 6 , 7 are important in applications such as separation, storage and catalysis. Empirical rules exist for their assembly but it is still challenging to place and segregate functionality in three-dimensional porous solids in a predictable way. Indeed, recent studies of mixed crystalline frameworks suggest a preference for the statistical distribution of functionalities throughout the pores 7 rather than, for example, the functional group localization found in the reactive sites of enzymes 8 . This is a potential limitation for ‘one-pot’ chemical syntheses of porous frameworks from simple starting materials. An alternative strategy is to prepare porous solids from synthetically preorganized molecular pores 9 , 10 , 11 , 12 , 13 , 14 , 15 . In principle, functional organic pore modules could be covalently prefabricated and then assembled to produce materials with specific properties. However, this vision of mix-and-match assembly is far from being realized, not least because of the challenge in reliably predicting three-dimensional structures for molecular crystals, which lack the strong directional bonding found in networks. Here we show that highly porous crystalline solids can be produced by mixing different organic cage modules that self-assemble by means of chiral recognition. The structures of the resulting materials can be predicted computationally 16 , 17 , allowing in silico materials design strategies 18 . The constituent pore modules are synthesized in high yields on gram scales in a one-step reaction. Assembly of the porous co-crystals is as simple as combining the modules in solution and removing the solvent. In some cases, the chiral recognition between modules can be exploited to produce porous organic nanoparticles. We show that the method is valid for four different cage modules and can in principle be generalized in a computationally predictable manner based on a lock-and-key assembly between modules.

We show that the different bond orders of individual carbon-carbon bonds in polycyclic aromatic hydrocarbons and fullerenes can be distinguished by noncontact atomic force microscopy (AFM) with a carbon monoxide (CO)—functionalized tip. We found two different contrast mechanisms, which were corroborated by density functional theory calculations: The greater electron density in bonds of higher bond order led to a stronger Pauli repulsion, which enhanced the brightness of these bonds in high-resolution AFM images. The apparent bond length in the AFM images decreased with increasing bond order because of tilting of the CO molecule at the tip apex.

A surprise package One of the simplest shapes for which the densest packing arrangement remains unresolved is the regular tetrahedron — despite much theoretical, computational and experimental effort. Using a novel approach involving thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, Sharon Glotzer and colleagues have worked out the densest ordered packing yet for tetrahedra, a configuration with a packing fraction of 0.8324. Unexpectedly, the structure is a dodecagonal quasicrystal, the first example of a quasicrystal formed from hard particles or from non-spherical building blocks. All hard, convex shapes pack more densely than spheres, although for tetrahedra this was demonstrated only very recently. Here, tetrahedra are shown to pack even more densely than previously thought. Thermodynamic computer simulations allow the system to evolve naturally towards high-density states, showing that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal, and yielding the highest packing fractions yet observed for tetrahedra. All hard, convex shapes are conjectured by Ulam to pack more densely than spheres 1 , which have a maximum packing fraction of φ = π/√18 ≈ 0.7405. Simple lattice packings of many shapes easily surpass this packing fraction 2 , 3 . For regular tetrahedra, this conjecture was shown to be true only very recently; an ordered arrangement was obtained via geometric construction with φ = 0.7786 (ref. 4 ), which was subsequently compressed numerically to φ = 0.7820 (ref. 5 ), while compressing with different initial conditions led to φ = 0.8230 (ref. 6 ). Here we show that tetrahedra pack even more densely, and in a completely unexpected way. Following a conceptually different approach, using thermodynamic computer simulations that allow the system to evolve naturally towards high-density states, we observe that a fluid of hard tetrahedra undergoes a first-order phase transition to a dodecagonal quasicrystal 7 , 8 , 9 , 10 , which can be compressed to a packing fraction of φ = 0.8324. By compressing a crystalline approximant of the quasicrystal, the highest packing fraction we obtain is φ = 0.8503. If quasicrystal formation is suppressed, the system remains disordered, jams and compresses to φ = 0.7858. Jamming and crystallization are both preceded by an entropy-driven transition from a simple fluid of independent tetrahedra to a complex fluid characterized by tetrahedra arranged in densely packed local motifs of pentagonal dipyramids that form a percolating network at the transition. The quasicrystal that we report represents the first example of a quasicrystal formed from hard or non-spherical particles. Our results demonstrate that particle shape and entropy can produce highly complex, ordered structures.

Dative, or nonoxidative, ligand coordination is common in transition metal complexes; however, this bonding motif is rare in compounds of main group elements in the formal oxidation state of zero. Here, we report that the potassium graphite reduction of the neutral hypervalent silicon-carbene complex L:SiCl₄ {where L: is:C[N(2,6-Pri₂-C₆H₃)CH]₂ and Pri is isopropyl} produces L:(Cl)Si-Si(Cl):L, a carbene-stabilized bis-silylene, and L:Si=Si:L, a carbene-stabilized diatomic silicon molecule with the Si atoms in the formal oxidation state of zero. The Si-Si bond distance of 2.2294 ± 0.0011 (standard deviation) angstroms in L:Si=Si:L is consistent with a Si=Si double bond. Complementary computational studies confirm the nature of the bonding in L:(Cl)Si-Si(Cl):L and L:Si=Si:L.

A molecular network that exhibits critical correlations in the spatial order that is characteristic of a random, entropically stabilized, rhombus tiling is described. Specifically, we report a random tiling formed in a two-dimensional molecular network of p-terphenyl-3,5,3',5'-tetracarboxylic acid adsorbed on graphite. The network is stabilized by hexagonal junctions of three, four, five, or six molecules and may be mapped onto a rhombus tiling in which an ordered array of vertices is embedded within a nonperiodic framework with spatial fluctuations in a local order characteristic of an entropically stabilized phase. We identified a topological defect that can propagate through the network, giving rise to a local reordering of molecular tiles and thus to transitions between quasi-degenerate local minima of a complex energy landscape. We draw parallels between the molecular tiling and dynamically arrested systems, such as glasses.

Complex systems in condensed phases involve a multidimensional energy landscape, and knowledge of transitional structures and separation of time scales for atomic movements is critical to understanding their dynamical behavior. Here, we report, using four-dimensional (4D) femtosecond electron diffraction, the visualization of transitional structures from the initial monoclinic to the final tetragonal phase in crystalline vanadium dioxide; the change was initiated by a near-infrared excitation. By revealing the spatiotemporal behavior from all observed Bragg diffractions in 3D, the femtosecond primary vanadium-vanadium bond dilation, the displacements of atoms in picoseconds, and the sound wave shear motion on hundreds of picoseconds were resolved, elucidating the nature of the structural pathways and the nonconcerted mechanism of the transformation.

Aluminum is considered to approach an \"ideal\" metal or free electron gas. The valence electrons move freely, as if unaffected by the presence of the metal ions. Therefore, the electron redistribution due to chemical bonding is subtle and has proven extremely difficult to determine. Experimental measurements and ab initio calculations have yielded substantially different results. We applied quantitative convergent-beam electron diffraction to aluminum to provide an experimental determination of the bonding electron distribution. Calculation of the electron distribution based on density functional theory is shown to be in close agreement. Our results yield an accurate quantitative correlation between the anisotropic elastic properties of aluminum and the bonding electron and electrostatic potential distributions.

Packing problems, such as how densely objects can fill a volume, are among the most ancient and persistent problems in mathematics and science. For equal spheres, it has only recently been proved that the face-centered cubic lattice has the highest possible packing fraction φ = π/√18 ≈ 0.74. It is also well known that certain random (amorphous) jammed packings have φ ≈ 0.64. Here, we show experimentally and with a new simulation algorithm that ellipsoids can randomly pack more densely-up to ≈ = 0.68 to 0.71 for spheroids with an aspect ratio close to that of M&M's Candies-and even approach φ ≈ 0.74 for ellipsoids with other aspect ratios. We suggest that the higher density is directly related to the higher number of degrees of freedom per particle and thus the larger number of particle contacts required to mechanically stabilize the packing. We measured the number of contacts per particle Z ≈ 10 for our spheroids, as compared to Z ≈ 6 for spheres. Our results have implications for a broad range of scientific disciplines, including the properties of granular media and ceramics, glass formation, and discrete geometry.

Intense femtosecond laser excitation can produce transient states of matter that would otherwise be inaccessible to laboratory investigation. At high excitation densities, the interatomic forces that bind solids and determine many of their properties can be substantially altered. Here, we present the detailed mapping of the carrier density-dependent interatomic potential of bismuth approaching a solid-solid phase transition. Our experiments combine stroboscopic techniques that use a high-brightness linear electron accelerator-based x-ray source with pulse-by-pulse timing reconstruction for femtosecond resolution, allowing quantitative characterization of the interatomic potential energy surface of the highly excited solid.