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

## TL;DR

This paper develops purely repulsive isotropic pair interactions that stabilize and promote the assembly of low-density truncated square and hexagonal crystals, addressing the challenge of favoring open lattice structures over competing phases.

## Contribution

It introduces a method to design interactions that stabilize specific open crystal lattices, demonstrated on truncated square and hexagonal structures.

## Key findings

- Designed interactions successfully stabilize target lattices.
- Monte Carlo simulations confirm assembly from high-temperature fluids.
- Interactions favor open lattices over competing phases.

## Abstract

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