Continuous Invariant-Based Maps of the Cambridge Structural Database.

The Cambridge Structural Database (CSD) played a key role in the recently established crystal isometry principle (CRISP). The CRISP says that any real periodic crystal is uniquely determined as a rigid structure by the geometry of its atomic centers without atomic types. Ignoring atomic types allows us to study all periodic crystals in a common space whose continuous nature is justified by the continuity of real-valued coordinates of atoms. Our previous work introduced structural descriptors pointwise distance distributions (PDD) that are invariant under isometry defined as a composition of translations, rotations, and reflections. The PDD invariants distinguished all nonduplicate periodic crystals in the CSD. This paper presents the first continuous maps of the CSD and its important subsets in invariant coordinates that have analytic formulas and physical interpretations. Any existing periodic crystal has a uniquely defined location on these geographic-style maps. Any newly discovered periodic crystals will appear on the same maps without disturbing the past materials.

Analogy Powered by Prediction and Structural Invariants: Computationally Led Discovery of a Mesoporous Hydrogen-Bonded Organic Cage Crystal.

Mesoporous molecular crystals have potential applications in separation and catalysis, but they are rare and hard to design because many weak interactions compete during crystallization, and most molecules have an energetic preference for close packing. Here, we combine crystal structure prediction (CSP) with structural invariants to continuously qualify the similarity between predicted crystal structures for related molecules. This allows isomorphous substitution strategies, which can be unreliable for molecular crystals, to be augmented by a priori prediction, thus leveraging the power of both approaches. We used this combined approach to discover a rare example of a low-density (0.54 g cm-3) mesoporous hydrogen-bonded framework (HOF), 3D-CageHOF-1. This structure comprises an organic cage (Cage-3-NH2) that was predicted to form kinetically trapped, low-density polymorphs via CSP. Pointwise distance distribution structural invariants revealed five predicted forms of Cage-3-NH2 that are analogous to experimentally realized porous crystals of a chemically different but geometrically similar molecule, T2. More broadly, this approach overcomes the difficulties in comparing predicted molecular crystals with varying lattice parameters, thus allowing for the systematic comparison of energy-structure landscapes for chemically dissimilar molecules.