From the Cover: Moving beyond the constraints of chemistry via crystal structure discovery with isotropic multiwell pair potentials

The rigid constraints of chemistry—dictated by quantum mechanics and the discrete nature of the atom—limit the set of observable atomic crystal structures. What structures are possible in the absence of these constraints? Here, we systematically crystallize one-component systems of particles interacting with isotropic multiwell pair potentials. We investigate two tunable families of pairwise interaction potentials. Our simulations self-assemble a multitude of crystal structures ranging from basic lattices to complex networks. Sixteen of the structures have natural analogs spanning all coordination numbers found in inorganic chemistry. Fifteen more are hitherto unknown and occupy the space between covalent and metallic coordination environments. The discovered crystal structures constitute targets for self-assembly and expand our understanding of what a crystal structure can look like.

Do we know all conceivable crystal structures? This question appears naïve at first, because crystallography is a mature field, but the list of reported inorganic crystal structures is not necessarily representative of all kinds of order that are possible on other scales. Atomic crystal structures are affected by the discreteness of the periodic table and the resulting constraints on chemical bonding (1). Molecular crystals (2), metal organic frameworks (3), nanoparticle superlattices (4), and other soft-matter assemblies (5) are free from these chemical constraints and can exhibit entirely new types of crystallographic order distinct from those found with atoms. A universal list of all plausible crystal structures in systems of particles ranging from the angstrom to the micrometer scale would benefit the search for—and design of—new materials.Crystal structures observed on the atomic scale are subject to the laws of quantum mechanics and to the discrete nature of the atom. The constraints of the chemical bond limit the ways in which atoms can be arranged; in particular, inorganic compounds display geometries that are specific to different kinds of bonding, for example, tetrahedral coordinations in the case of covalent bonding with sp3-hybridized orbitals, or high coordination numbers (CNs) in the case of metallic bonding. For example, in the case of water, angular information is usually directly encoded into the computational model (6, 7); however, structures with similar local arrangements have recently been observed in simulations with isotropic multiwell potentials (8, 9). In addition to known crystal structures, these tunable pair potentials can also be parametrized to model particles “in between” the discontinuous types of behaviors that are possible on the atomic scale, due to the quantized nature of the realm of electronic interactions. As a result, these interaction potentials can model systems on the mesoscopic soft-matter length scale, where particle properties and shapes are highly variable. How do these crystal structures differ from those observed on the atomic scale?Here we show that molecular dynamics simulations of single-component systems interacting via simple isotropic oscillating pair potentials (OPPs) can produce—via crystallization from disordered initial conditions—the majority of reported one-component as well as several multicomponent inorganic crystal structures (10). Our findings are obtained with pair potentials that encode coordination geometry solely via the shape of the radial function of the interaction, and contain no angular terms. We characterize simulation outcomes semiautomatically with the help of computational crystal structure identification techniques. Among the crystal structures we observe are many previously unknown structures, some resembling known ones and some surprisingly complex. The previously unknown crystal structures cluster near each other in parameter space in islands of complexity, demonstrating that certain pair potential features promote specific coordination environments, and that certain coordination environments are inherently prone to crystallographic diversity. Because the functional form of the potential is generic, chemical constraints do not play a role in our simulations, and the particles explore feasible geometries more freely. Such geometries should be accessible, if not to atomic crystals, then to colloidal crystals of nanoparticles where valence is easily tunable.