Designing convex repulsive pair potentials that favor assembly of kagome and snub square lattices

TL;DR

This paper designs convex, isotropic pair potentials that promote the self-assembly of particles into kagome and snub square lattices, using inverse optimization methods to maximize stability and assembly range.

Contribution

It introduces a novel inverse design strategy for convex repulsive potentials that specifically favor complex lattice structures like kagome and snub square.

Findings

Designed potentials successfully favor target lattices as ground states.

Optimizations increase the density range for stable assembly.

Greater chemical potential advantages improve thermal stability.

Abstract

Building on a recently introduced inverse strategy, isotropic and convex repulsive pair potentials were designed that favor assembly of particles into kagome and equilateral snub square lattices. The former interactions were obtained by numerical solution of a variational problem that maximizes the range of density for which the ground state of the potential is the kagome lattice. Similar optimizations targeting the snub square lattice were also carried out, employing a constraint that required a minimum chemical potential advantage of the target over select competing structures. This constraint helped discover isotropic interactions that meaningfully favored the snub square lattice as the ground state structure despite the asymmetric spatial distribution of particles in its coordination shells and the presence of tightly competing structures. Consistent with earlier published results [Pi\~neros et al. J. Chem. Phys. 144, 084502 (2016)], enforcement of greater chemical potential advantages for the target lattice in the interaction optimization led to assemblies with enhanced thermal stability.