Mining Knowledge from Crystal Structures: Oxidation States of Oxygen-Coordinated Metal Atoms in Ionic and Coordination Compounds.

We propose a universal scheme for predicting the oxidation states of metal atoms in ionic and coordination compounds with a small set of structural descriptors, which include the parameters of atomic Voronoi polyhedra. The scheme has been trained and checked with more than 35,000 crystal structures containing more than 90,000 metal atoms in the oxygen environment. The accuracy of the prediction exceeded 95%; we have detected a number of wrong oxidation states and incorrect chemical compositions in the crystallographic databases using this scheme. The scheme is easily extendable to any kind of atomic environment and can be used to search for correlations between geometrical and physical properties of crystal structures.

Topology of Intermetallic Structures: From Statistics to Rational Design.

More than 38 000 substances made only of metal atoms are collected in modern structural databases; we may call them intermetallic compounds. They have important industrial applications, and yet they are terra incognita for most of our undergraduate students. Their structural complexity and synthesis are not easily adaptable to first years laboratories, keeping them away from the standard curricula. They have been described over the years following alternative and complementary views such as coordination polyhedra, atomic layers, and polyatomic clusters. All of these descriptions, albeit relying on grounded principles, have been applied on a subjective basis and never implemented as a strict computational algorithm. Sometimes, the authors generated multiple views of the same structure reported with beautifully drawn figures and/or photos of hand-crafted models in seminal works of the precomputer age. With the use of our multipurpose crystallochemical program package ToposPro, we explored the structural chemistry of intermetallics with objective and reproducible topological methods that allow us to reconcile different structure descriptions. After computing the connectivity patterns between the metal atoms on the basis of Voronoi partitioning of the crystal space, we were able to group the 38 000 intermetallic compounds into 3700 sets of crystal structures with the same topology of atomic net. We have described the different views used in the literature and shown that 12-vertex polyhedra are the most frequent (33%) and that almost half of them are icosahedron-like (46%), followed by cuboctahedron (25%) and, unexpectedly, by bicapped pentagonal prism (13%). Looking for layers, we have found that the hexagonal lattice, which corresponds to the closest packing of spheres on a plane, exists in more than 11 000 crystal structures, confirming the close-packed nature of intermetallics. We have also applied the nanocluster approach, which goes beyond the first coordination sphere and looks for structural units as multishell clusters that assemble the whole structure. This approach shows that 41% of intermetallics can be assembled with a single nanocluster and that 22.4% of these are packed according to the face-centered cubic motif of the closest packing of spheres in three-dimensional space. We have shown that our approach can easily adopt any other building model and hence could become a platform for a universal predictive scheme. Within this scheme, all of the structural descriptors can be related to experimental data and theoretical modeling results and then can be used to synthesize new intermetallic compounds and to foresee novel materials.

Novel Heterometallic Uranyl-Transition Metal Materials: Structure, Topology, and Solid State Photoluminescence Properties.

Six new uranyl hybrid materials have been synthesized solvothermally utilizing the ligands 2,2'-bipyridine-3,3'-dicarboxylic acid (H2L) and 2,2':6',2''-terpyridine (TPY). The six compounds are classified as either molecular complexes (I0O0 connectivity), [(UO2)(L)(TPY)]·H2O (1), [Ni(TPY)2][(UO2)(L)2]·3H2O (2), and [Cu(TPY)2][(UO2)(L)2]·3H2O (3), or 3D metal-organic frameworks (MOFs, I0O3 connectivity), [Cu2(UO2)2(OH)(C2H3O2)(L)3(TPY)2]·6H2O (4), [Zn2(UO2)2(OH)(NO3)(C2H3O2)(L)3(TPY)2]·4H2O (5), and Na[Ni(UO2)3(OH)(O)(L)3]·9H2O (6). A discussion of the influence of transition metal incorporation, chelating effects of the ligand, and synthesis conditions on the formation of uranyl materials is presented. The structure of compound 6 is of particular note due to large channel-like voids with a diameter of approximately 19.6 Å. A topological analysis of 6 reveals a new topology with a 9-nodal 3,3,3,3,3,3,3,4,5-connected network, designated geg1 hereafter. Further, solid state photoluminescence experiments show emission and lifetimes values consistent with related uranyl compounds.

Visualization and Quantification of Geometric Diversity in Metal-Organic Frameworks.

With ever-growing numbers of metal-organic framework (MOF) materials being reported, new computational approaches are required for a quantitative understanding of structure-property correlations in MOFs. Here, we show how structural coarse-graining and embedding ("unsupervised learning") schemes can together give new insights into the geometric diversity of MOF structures. Based on a curated data set of 1262 reported experimental structures, we automatically generate coarse-grained and rescaled representations which we couple to a kernel-based similarity metric and to widely used embedding schemes. This approach allows us to visualize the breadth of geometric diversity within individual topologies and to quantify the distributions of local and global similarities across the structural space of MOFs. The methodology is implemented in an openly available Python package and is expected to be useful in future high-throughput studies.

Topology versus porosity: what can reticular chemistry tell us about free space in metal-organic frameworks?

We present the results of a comprehensive geometrical and topological analysis of 3D coordination networks in 33 790 coordination polymers. We have found relations between topological descriptors and free space of the networks, and have revealed topological types that promote high porosity of metal-organic frameworks.

A universal algorithm for finding the shortest distance between systems of points.

Three universal algorithms for geometrical comparison of abstract sets of n points in the Euclidean space R3 are proposed. It is proved that at an accuracy ε the efficiency of all the algorithms does not exceed O(n3/ε3/2). The most effective algorithm combines the known Hungarian and Kabsch algorithms, but is free of their deficiencies and fast enough to match hundreds of points. The algorithm is applied to compare both finite (ligands) and periodic (nets) chemical objects.