Abstract:
All crystalline materials can be modeled as periodic sets of atomic centers. Since crystal structures are determined in a rigid form, their strongest equivalence in practice is rigid motion (a composition of translations and rotations). A slightly weaker isometry allows mirror reflections. We developed a new descriptor PDD (Pointwise Distance Distribution), which was proved to be continuous under perturbations, computable in near-linear time, and invertible into a 3-dimensional structure for any periodic crystal in a general position. Within an hour on a modest desktop, 200+ billion comparisons of all 660+ thousand periodic crystals in the Cambridge Structural Database detected 5 pairs of geometric duplicates that differed by one atomic replacement, e.g. Cd vs Mn in HIFCAB vs JEPLIA, which is physically impossible without perturbing geometry. Five journals are investigating the integrity of the relevant papers. The more important conclusion is the Crystal Isometry Principle, which says that all real periodic crystals have unique geographic-style positions in a common continuous space parametrized by complete invariant descriptors. All relevant papers are at http://kurlin.org/research-papers.php#Geometric-Data-Science

Bio:
Vitaliy Kurlin is a universal scientist, mathematician by training, professor in computer science, now leading the Data Science Theory and Applications group in the Materials Innovation Factory at the University of Liverpool (UK) developing Geometric Data Science for crystallography, chemistry, and structural biology, details at http://kurlin.org.
 

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