Significance: The traditional, Edisonian method of research involves taking a system and examining its properties. A preferred alternative is to target a suite of properties and then design the most appropriate system in this context. Here we illustrate such a design approach for the self-assembly of colloids grafted with single-stranded DNA. When two types of colloids grafted with complementary ssDNA sequences are mixed, DNA hybridization can lead to the formation of ordered colloidal crystals. We use the genetic algorithm to design ssDNA-grafted particles that will assemble into a desired structure. Our methodology is easily generalizable, fast and highly selective, and not only accurately reproduces the parameters relevant to four currently realized crystals but also elucidates four currently unobserved structures.

Significance: Recently, there has been an increased interest in understanding the self-assembly of DNA-grafted colloids into different morphologies. Conventional approaches assume that the critical design parameters are the size and number of DNA grafts on each particle. Stoichiometry is viewed as a secondary variable and its exact role in this context is unresolved. In contrast with these expectations, our experiments show that the equilibrium lattice structure can be tuned through variations in the imposed stoichiometry. These findings are captured through simple extensions of the complementary contact model. Stoichiometry is thus shown to be a powerful handle to control these self-assembled structures.

We introduce a mean-field theoretical framework for generalizing isotropic pair potentials to anisotropic shapes. This method is suitable for generating pair potentials that can be used in both Monte Carlo and molecular dynamics simulations. We demonstrate the application of this theory by deriving a Lennard-Jones (LJ)-like potential for arbitrary geometries along with a Weeks–Chandler–Anderson-like repulsive variant, showing that the resulting potentials behave very similarly to standard LJ potentials while also providing a nearly conformal mapping of the underlying shape. We then describe an implementation of this potential in the simulation engine HOOMD-blue and discuss the challenges that must be overcome to achieve a sufficiently robust and performant implementation. The resulting potential can be applied to smooth geometries like ellipsoids and to convex polytopes. We contextualize these applications with reference to the existing methods for simulating such particles. The pair potential is validated using standard criteria, and its performance is compared to existing methods for comparable simulations. Finally, we show the results of self-assembly simulations, demonstrating that this method can be used to study the assembly of anisotropic particles into crystal structures.