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Using a recently introduced formulation of the ground-state inverse designproblem for a targeted lattice [Pi\~neros et al., J. Chem. Phys. 144} 084502(2016)], we discover purely repulsive and isotropic pair interactions thatstabilize low-density truncated square and truncated hexagonal crystals, aswell as promote their assembly in Monte Carlo simulations upon isochoriccooling from a high-temperature fluid phase. The results illustrate that theprimary challenge to stabilizing very open two-dimensional lattices is todesign interactions that can favor the target structure over competing stripemicrophases.

Designing Pairwise Interactions that Stabilize Open Crystals: Truncated Square and Truncated Hexagonal Lattices