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Inverse Statistical Mechanics: Probing the Limitations of Isotropic Pair Potentials to Produce Ground-State Structural Extremes

Inverse statistical-mechanical methods have recently been employed to design optimized short-ranged radial (isotropic) pair potentials that robustly produce novel targeted classical ground-state many-particle configurations. The target structures considered in those studies were low-coordinated crystals with a high degree of symmetry. In this paper, we further test the fundamental limitations of radial pair potentials by targeting crystal structures with appreciably less symmetry, including those in which the particles have different local structural environments. These challenging target configurations demanded that we modify previous inverse optimization techniques. Using this modified optimization technique, we have designed short-ranged radial pair potentials that stabilize the two-dimensional kagome crystal, the rectangular kagome crystal, and rectangular lattices, as well as the three-dimensional structure of CaF$_2$ crystal inhabited by a single particle species. We verify our results by cooling liquid configurations to absolute zero temperature via simulated annealing and ensuring that such states have stable phonon spectra. Except for the rectangular kagome structure, all of the target structures can be stabilized with monotonic repulsive potentials. Our work demonstrates that single-component systems with short-ranged radial pair potentials can counterintuitively self-assemble into crystal ground states with low symmetry and different local structural environments. Finally, we present general principles that offer guidance in determining whether certain target structures can be achieved as ground states by radial pair potentials.