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

Abstract

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.

Keywords: crystal structures; isotropic pair potentials; self-assembly.

Fig. 1.

Schematic illustration of the OPP (Top) and the LJGP (Bottom). The OPP is characterized by a wavenumber $k$ and a phase shift $\varphi$ defining the relative well positions and their relative depths. The LJGP is the sum of a Lennard–Jones potential and a negative Gaussian potential. Parameters $r_0$ and $ϵ$ determine the position and depth of the Gaussian.

Fig. 2.

Phase diagrams of OPPs (Left) and LJGPs (Right) indicating self-assembled crystal structures. Each colored rectangle corresponds to one simulation. Colors denote different crystal structures consistently across both diagrams as specified in the color bar (top), together with Pearson symbols and representative compounds. White regions indicate simulations that assemble structures with no discernible long-range order.

Fig. 3.

Unit cells of the crystal structures reported in this study. Unit cells of all 16 known crystal structures (Left) and all 15 previously unknown crystal structures (Right) are shown. The particles are colored according to the color bar in Fig. 2; unit cell outlines are shown in black.

Fig. 4.

Coordination polyhedra in the 31 crystal structures self-assembled with OPPs and LJGPs (displayed in colors representing their structures in Figs. 2 and 3). Coordination polyhedra are grouped by CN in the range CN = 4 to 16. Reported structures are listed by Pearson symbols below the CN axis and indicated by arrows pointing to their $⟨\text{CN}⟩$ (the largest average CN observed is $⟨\text{CN}⟩=14$). Pearson symbols of previously unknown structures are labeled in bold font.