Self-assembly of Low-coordinated Ground States via Monotonic Pair Potentials

Monotonically decreasing radially symmetric pair potentials can lead to the self assembly of unusual low-coordinated ground states. The states include, but are not limited to, the square, honeycomb, and simple cubic crystals in two and three-dimensional Euclidean spaces $R^2$ and $R^3$. We can determine optimal potentials for targeted ground states using inverse statistical mechanical techniques. Using a linear programming method, we are able to search over a wide parameter space while still enforcing constraints such as motonicity and convexity on optimized potentials. The features present in the classes of short-ranged potentials that conform to these constraints suggest sufficient requirements for colloids to self assemble into a desired ground state.