Designing hierarchical molecular complexity: icosahedra of addressable icosahedra

Designing the Self-Assembly of Arbitrary Shapes Using Minimal Complexity Building Blocks

The design space for self-assembled multicomponent objects ranges from a solution in which every building block is unique to one with the minimum number of distinct building blocks that unambiguously define the target structure. We develop a pipeline to explore the design spaces for a set of structures of various sizes and complexities. To understand the implications of the different solutions, we analyze their assembly dynamics using patchy particle simulations and study the influence of the number of distinct building blocks, and the angular and spatial tolerances on their interactions, on the kinetics and yield of the target assembly. We show that the resource-saving solution with a minimum number of distinct blocks can often assemble just as well (or faster) than designs where each building block is unique. We further use our methods to design multifarious structures, where building blocks are shared between different target structures. Finally, we use coarse-grained DNA simulations to investigate the realization of multicomponent shapes using DNA nanostructures as building blocks.

Symmetry-derived structure directing agents for two-dimensional crystals of arbitrary colloids

We derive properties of self-assembling rings which can template the organization of an arbitrary colloid into any periodic symmetry in two Euclidean dimensions. By viewing this as a tiling problem, we illustrate how the shape and chemical patterning of these rings are derivable, and are explicitly reflected by the symmetry group's orbifold symbol. We performed molecular dynamics simulations to observe their self-assembly and found 5 different characteristics which could be easily rationalized on the basis of this symbol. These include systems which undergo chiral phase separation, are addressably complex, exhibit self-limiting growth into clusters, form ordered "rods" in only one-dimension akin to a smectic phase, and those from symmetry groups which are pluripotent and allow one to select rings which exhibit different behaviors. We discuss how the curvature of the ring's edges plays an integral role in achieving correct self-assembly, and illustrate how to obtain these shapes. This provides a method for patterning colloidal systems at interfaces without explicitly programming this information onto the colloid itself.

Crystal Structure Prediction for Benzene Using Basin-Hopping Global Optimization

Organic molecules can be stable in distinct crystalline forms, known as polymorphs, which have significant consequences for industrial applications. Here, we predict the polymorphs of crystalline benzene computationally for an accurate anisotropic model parametrized to reproduce electronic structure calculations. We adapt the basin-hopping global optimization procedure to the case of crystalline unit cells, simultaneously optimizing the molecular coordinates and unit cell parameters to locate multiple low-energy structures from a variety of crystal space groups. We rapidly locate all the well-established experimental polymorphs of benzene, each of which corresponds to a single local energy minimum of the model. Our results show that basin-hopping can be both an efficient and effective tool for polymorphic crystal structure prediction, requiring no a priori experimental knowledge of cell parameters or symmetry.

Controlling Fragment Competition on Pathways to Addressable Self-Assembly

Addressable self-assembly is the formation of a target structure from a set of unique molecular or colloidal building blocks, each of which occupies a defined location in the target. The requirement that each type of building block appears exactly once in each copy of the target introduces severe restrictions on the combinations of particles and on the pathways that lead to successful self-assembly. These restrictions can limit the efficiency of self-assembly and the final yield of the product. In particular, partially formed fragments may compete with each other if their compositions overlap, since they cannot be combined. Here, we introduce a "completability" algorithm to quantify competition between self-assembling fragments and use it to deduce general principles for suppressing the effects of fragment incompatibility in the self-assembly of small addressable clusters. Competition originates from loops in the bonding network of the target structure, but loops may be needed to provide structural rigidity and thermodynamic stability. An optimal compromise can be achieved by careful choice of bonding networks and by promoting semihierarchical pathways that rule out competition between early fragments. These concepts are illustrated in simulations of self-assembly in two contrasting addressable targets of 20 unique components each.