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

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