Crystal Structure Database Research Articles

Assessing free lattice and structure parameters from the atomic level

Data mining of lattice and structure parameters with the aid of the Inorganic Crystal Structure Database revealed a correlation between the abundance of parameter values observed and geometric features of interatomic distances. Working out this finding enabled distinguished lattice and structure parameters to be attributed to special bonds. The method is illustrated dealing with two examples of a hexagonal and a cubic structure type.

High-throughput determination of structural phase diagram and constituent phases using GRENDEL

Advances in high-throughput materials fabrication and characterization techniques have resulted in faster rates of data collection and rapidly growing volumes of experimental data. To convert this mass of information into actionable knowledge of material process–structure–property relationships requires high-throughput data analysis techniques. This work explores the use of the Graph-based endmember extraction and labeling (GRENDEL) algorithm as a high-throughput method for analyzing structural data from combinatorial libraries, specifically, to determine phase diagrams and constituent phases from both x-ray diffraction and Raman spectral data. The GRENDEL algorithm utilizes a set of physical constraints to optimize results and provides a framework by which additional physics-based constraints can be easily incorporated. GRENDEL also permits the integration of database data as shown by the use of critically evaluated data from the Inorganic Crystal Structure Database in the x-ray diffraction data analysis. Also the Sunburst radial tree map is demonstrated as a tool to visualize material structure–property relationships found through graph based analysis.

On the Way to New Possible Na-Ion Conductors: The Voronoi-Dirichlet Approach, Data Mining and Symmetry Considerations in Ternary Na Oxides.

With the constant growth of the lithium battery market and the introduction of electric vehicles and stationary energy storage solutions, the low abundance and high price of lithium will greatly impact its availability in the future. Thus, a diversification of electrochemical energy storage technologies based on other source materials is of great relevance. Sodium is energetically similar to lithium but cheaper and more abundant, which results in some already established stationary concepts, such as Na-S and ZEBRA cells. The most significant bottleneck for these technologies is to find effective solid ionic conductors. Thus, the goal of this work is to identify new ionic conductors for Na ions in ternary Na oxides. For this purpose, the Voronoi-Dirichlet approach has been applied to the Inorganic Crystal Structure Database and some new procedures are introduced to the algorithm implemented in the programme package ToposPro. The main new features are the use of data mined values, which are then used for the evaluation of void spaces, and a new method of channel size calculation. 52 compounds have been identified to be high-potential candidates for solid ionic conductors. The results were analysed from a crystallographic point of view in combination with phenomenological requirements for ionic conductors and intercalation hosts. Of the most promising candidates, previously reported compounds have also been successfully identified by using the employed algorithm, which shows the reliability of the method.

Kinase hinge binding scaffolds and their hydrogen bond patterns

Protein kinases constitute a major class of intracellular signaling molecules, and describe some of the most prominent drug targets. Kinase inhibitors commonly employ small chemical scaffolds that form hydrogen bonds with the kinase hinge residues connecting the N- and C-terminal lobes of the catalytic domain. In general the satisfied hydrogen bonds are required for potent inhibition, therefore constituting a conserved feature in the majority of inhibitor-kinase interactions. From systematically analyzing the kinase scaffolds extracted from Pfizer crystal structure database (CSDb) we recognize that large number of kinase inhibitors of diverse chemical structures are derived from a relatively small number of common scaffolds. Depending on specific substitution patterns, scaffolds may demonstrate versatile binding capacities to interact with kinase hinge. Afforded by thousands of ligand–protein binary complexes, the hinge hydrogen bond patterns were analyzed with a focus on their three-dimensional configurations. Most of the compounds engage H6 NH for hinge recognition. Dual hydrogen bonds are commonly observed with additional recruitment of H4 CO upstream and/or H6 CO downstream. Triple hydrogen bonds accounts for small number of binary complexes. An unusual hydrogen bond with a non-canonical H5 conformation is observed, requiring a peptide bond flip by a glycine residue at the H6 position. Additional hydrogen bonds to kinase hinge do not necessarily correlate with an increase in potency; conversely they appear to compromise kinase selectivity. Such learnings could enhance the prospect of successful therapy design.

Rietveld structure refinement of microcline

Compared with single-crystal X-ray diffraction, extracting structural data from X-ray powder diffraction (XRPD) seems meaningless for minerals with an available single crystal, such as alkali feldspar. However, alkali feldspar is highly abundant on Earth, and the feldspar structure is important in geology. Thus, the potential of extracting structural parameters from powder diffraction data collected using conventional Bragg–Brentano XRPD (BB-XRPD) with Cu K α radiation is worthy of exploration. BB-XRPD may be the most extensively used instrument in the laboratory and has a major advantage in terms of cost and convenience. Accordingly, by combining the Rietveld method with the General Structure Analysis System (GSAS) of BB-XRPD, a microcline structure in a natural feldspar sample with two minor impurities was refined for the first time. To extract high-quality structural data, a formula related to Si/Al–O bond lengths and Si/Al occupancies in terms of the crystal structure database and a new model are sequentially presented. The reliability of the structural data for such a low-symmetry phase as microcline is discussed and established by comparison with published single-crystal data.

Magnesium-binding architectures in RNA crystal structures: validation, binding preferences, classification and motif detection.

The ubiquitous presence of magnesium ions in RNA has long been recognized as a key factor governing RNA folding, and is crucial for many diverse functions of RNA molecules. In this work, Mg2+-binding architectures in RNA were systematically studied using a database of RNA crystal structures from the Protein Data Bank (PDB). Due to the abundance of poorly modeled or incorrectly identified Mg2+ ions, the set of all sites was comprehensively validated and filtered to identify a benchmark dataset of 15 334 ‘reliable’ RNA-bound Mg2+ sites. The normalized frequencies by which specific RNA atoms coordinate Mg2+ were derived for both the inner and outer coordination spheres. A hierarchical classification system of Mg2+ sites in RNA structures was designed and applied to the benchmark dataset, yielding a set of 41 types of inner-sphere and 95 types of outer-sphere coordinating patterns. This classification system has also been applied to describe six previously reported Mg2+-binding motifs and detect them in new RNA structures. Investigation of the most populous site types resulted in the identification of seven novel Mg2+-binding motifs, and all RNA structures in the PDB were screened for the presence of these motifs.

The Bürgi–Dunitz angle revisited: a mystery?

The Bürgi–Dunitz angle is one of those memes that most students of organic chemistry remember. It hypothesizes the geometry of attack of a nucleophile on a trigonal unsaturated (sp2) carbon in a molecule such as ketone, aldehyde, ester, and amide carbonyl. Its value obviously depends on the exact system, but is generally taken to be in the range 105-107°. A very good test of this approach is to search the crystal structure database (this was how it was originally established[1]). The search is defined as follows R can be either H or C The carbon is constrained to 3-coordinate The carbonyl oxygen is constrained to 1-coordinate QA can be any of N, O, S, Cl, F. QB can be any of H (aldehyde), C (ketone), N (amide), O (ester) or S (thioester). The distance QA…C is constrained to any intermolecular non-bonded contact ≤ the sum of the van der Waals radii of the two atoms involved and the angle QA…C=O is the Bürgi–Dunitz angle. I have also added a torsion constraint to specify that Nu has got to be ± 20° from orthogonality to the plane of the carbonyl to allow it to attack the π* orbital. The crystallographic R factor must be < 0.05, no disorder, no crystallographic errors and the temperature is either any or < 120K. With no temperature specified, 6994 hits are obtained as below. So the most probable angle (red spot) is ~90°. One important change to the search is to decrease the temperature to 120K, since structures will have less vibrational noise. The number of hits decreases to 1279, but the most probable angle if anything reduces slightly. So we have something of a mystery; this crystallographic data shows an angle of approach about 15° less than the oft quoted value. Here are some thoughts: This search is the average for all types of carbonyl, whereas the original suggestion was constrained to four types of nucleophiles and simple ketones. This search extends the interacting distance of the nucleophile and the carbon out to 3.5Å which is significantly longer than the normally considered length of ~2.85Å. The hotspots occur at about 3.15Å and not 2.85Å. There is obviously considerably more data available in 2015 than in 1974, and in particular at low temperature. The Bürgi–Dunitz angle is in fact one of two defining the trajectory, the other being the Flippin–Lodge angle which defines the displacement towards R or QB. The search above gives no direct information about this angle, but the torsion is related since it is constrained to bisect the C=O to within ± 20° and hence bisect the groups R and QB. An angle of ≤ 90° does not match to the normal explanation, which is that the nucleophile attacks the π* orbital, each lobe of which “leans out” from the centre at about 105° rather than leaning in at ≤ 90°. Decreasing the torsion range to ± 5° at 120K gives 592 hits with a hot spot at 95° Also constraining the distance QA…C to be 0.3Å less than the van der Waals sum at 120K gives 59 hits with a hot spot at 95° and 2.9Å. Well, to get to the bottom of this will require reducing the scope of both QA and QB, to find which if any of discrete values for these two variables can indeed give an angle of 105-107°. This would make for quite a good student group project; I expect a group of 8 students could sort this out quite quickly! References H. B:urgi, J. Dunitz, J. Lehn, and G. Wipff, "Stereochemistry of reaction paths at carbonyl centres", Tetrahedron, vol. 30, pp. 1563-1572, 1974. http://dx.doi.org/10.1016/S0040-4020(01)90678-7

Trigonal bipyramidal or square pyramidal: Another ten minute exploration.

This is rather cranking the handle, but taking my previous post and altering the search definition of the crystal structure database from 4- to 5-coordinate metals, one gets the following. Fe … Co … Ni … Cu … Trigonal bipyramidal coordination has angles of 90, 120 and 180°. Square pyramidal has no 120° angles, and the 180° angles might be somewhat reduced. Thus the Fe and Co series have plenty of 120, whereas the Ni and Cu series hardly any. The Ni series has many 160° values. It is clearly a serious issue that attempting any correlation with the spin states is going to be a lot of really hard work (I might next do another simple search where bond lengths can be shown to very closely correlate with low/medium/high spin states). I will not be trying a more finely grained analysis of the above plots; I just wanted to point out how very simple and quick they are to generate.

The nature of NO-bonding in N-oxide group.

The nature of the NO-bond in the N-oxide group was investigated by means of combined theoretical calculations (including QTAIM and NBO approaches) and statistical analyses of the contents of crystal structure databases. The N-O bond in the N-oxide group should be classified as the NO donating bond with an important contribution of ON back-donation (of the π-electron type, when available). The visualization of the Laplacian of electron density in the region of an oxygen valence sphere suggests the presence of two lone pairs for the imine-N-oxide group (characterized by effective ON back-donation). A detailed bonding analysis performed by means of natural resonance theory indicates that the N→O bond is of an order of magnitude clearly greater than 1. In addition, the stability of the N→O bond in various N-oxides was estimated. The analyses of the hydrogen- and halogen-bonded complexes of the N-oxides reveal strong Lewis basicity of the N-oxide group. The formation of H- and X-bonding leads to N→O bond elongation due to its structural, topological and spectroscopic characteristics. Moreover, in pyridine-N-oxide, the electron-withdrawing -NO2 group additionally stabilizes the N→O bond, whereas the opposite effect can be observed for the electron-donating-NH2 substituent. This is due to a substituent effect on the π-type ON back-donation. As a result, the oxygen atom in pyridine-N-oxide may change its availability during intermolecular interaction formation, as revealed in the interaction energy, which changes by about half of the estimated total interaction energy.

R-X≡X-R: G. N. Lewis' 100 year old idea.

As I have noted elsewhere, Gilbert N. Lewis wrote a famous paper entitled “the atom and the molecule“, the centenary of which is coming up.[1] In a short and rarely commented upon remark, he speculates about the shared electron pair structure of acetylene, R-X≡X-R (R=H, X=C). It could, he suggests, take up three forms. H-C:::C-H and two more which I show as he drew them. The first of these would now be called a bis-carbene and the second a biradical. In 1916, it was too early for Lewis to speculate what the geometries of such species might be, and in particular the C…C (or generalising, X…X) distance, and the two angles, one for each X. Well, we do not need to speculate, we can perform a search of the crystal structure database. Here it is (R < 0.05, no errors, no disorder): A little more explanation of this 4-dimensional plot is needed: The two angles are plotted as X and Y. The X…X distance is plotted as colour, with red representing the longest distances and blue the shortest The size of each “bin” is represented by the radius of the circle; small circles represent few examples, larger circles represent more examples in each “bin” defined by a regular range of angles. There are one or two off-diagonal “outliers”, each of which probably deserves individual inspection. But dealing just with the obvious clusters, the overwhelmingly largest is for both angles of ~180°, and these are the triple bonds we know and love. As far as I know, Lewis was the first to propose a triple bond between two atoms, but if anyone reading this blog knows of an antecedent, do let me know. The next cluster is for angles of ~109° and these are clearly bis-carbenes. These all occur when X ≠ C. There are two small clusters worthy of note; one ~130° and one ~90°. The latter are mostly Pb-Pb and Sn-Sn, where the bonding is unhybridised pure p. One of the limitations of searching for crystal structures is that the spin state of each molecule is never given. The biradical structure given by Lewis could well have a triplet ground state, and perhaps that might have very characteristic angles (~130° ?). It would be great to identify a genuine example of this biradical form! As usual, the search itself took around 10 minutes, and it provides much interesting food for thought; not bad for a 100-year-old idea! References G.N. Lewis, "THE ATOM AND THE MOLECULE.", J. Am. Chem. Soc., vol. 38, pp. 762-785, 1916. http://dx.doi.org/10.1021/ja02261a002

Phase identification and structure determination from multiphase crystalline powder samples by rotation electron diffraction

Phase identification and structure characterization are important in synthetic and materials science. It is difficult to characterize the individual phases from multiphase crystalline powder samples, especially if some of the phases are unknown. This problem can be solved by combining rotation electron diffraction (RED) and powder X-ray diffraction (PXRD). Four phases were identified on the same transmission electron microscopy grid from a multiphase sample in the Ni–Se–O–Cl system, and their structures were solved from the RED data. Phase 1 (NiSeO3) was found in the Inorganic Crystal Structure Database using the information from RED. Phase 2 (Ni3Se4O10Cl2) is an unknown compound, but it is isostructural to Co3Se4O10Cl2, which was recently solved by single-crystal X-ray diffraction. Phase 3 (Ni5Se6O16Cl4H2) and Phase 4 (Ni5Se4O12Cl2) are new compounds. The fact that there are at least four different compounds in the as-synthesized material explains why the phase identification and structure determination could not be done by PXRD alone. The RED method makes phase identification from such multiphase powder samples much easier than would be the case using powder X-ray diffraction. The RED method also makes structure determination of submicrometre-sized crystals from multiphase samples possible.

Utilizing organic and organometallic structural data in powder diffraction

The Cambridge Structural Database (CSD) is a database of small molecule organic and organometallic crystal structures elucidated using X-Ray and neutron crystallography. The CSD is distributed alongside a system of software (the Cambridge Structural Database System) to academic and industrial users. The system contains a number of applications (in particular DASH, ConQuest, and Mogul) that can be used to aid crystallographers in the solution and refinement of crystal structures from powder diffraction data, and in the interpretation of crystal structure models (in particular, Mercury). This publication uses a racemic form of ornidazole (Z′ = 3) to illustrate the efficacy of DASH in the crystal structure solution from powder diffraction data. Furthermore, numerous features in Mogul and Mercury that aid crystal structure solution and interpretation of crystallographic data are revised. Finally, a review of a new method for using database-derived geometric information directly in structural solution is presented.

Charge Anisotropy: Where Atomic Multipoles Matter Most.

Specific intermolecular interactions are largely guided by electrostatics. However, the most common model for electrostatic interactions-atomic point charges-fails to reproduce anisotropic charge distributions, such as lone pairs and sigma holes. Although this has long been known, point charges are still widely used in chemical modeling and reasoning. In this contribution, we analyze the deficiency of atomic point charges in reproducing the electrostatic potential (ESP) around molecules and find that multipole moments up to quadrupoles can, with a much lower error than point charges, reproduce the relevant ESP for all cases. Mapping the surface to the closest atom allows to compare ESP errors between atom types and to identify cases with the most urgent need for atomic multipoles. Our analysis shows that almost all heteroatoms require multipoles to correctly describe their charge distribution, with the most serious cases being nitrogen, sulfur, and halogens. Comparison with small molecule crystallography data studies supports our findings and emphasizes the need for incorporating anisotropic charge descriptions in chemical models. The scheme introduced here can be used to identify anisotropic binding preferences for atom types where there is too little coverage in crystal structure databases.

On-the-fly machine-learning for high-throughput experiments: search for rare-earth-free permanent magnets.

Advanced materials characterization techniques with ever-growing data acquisition speed and storage capabilities represent a challenge in modern materials science, and new procedures to quickly assess and analyze the data are needed. Machine learning approaches are effective in reducing the complexity of data and rapidly homing in on the underlying trend in multi-dimensional data. Here, we show that by employing an algorithm called the mean shift theory to a large amount of diffraction data in high-throughput experimentation, one can streamline the process of delineating the structural evolution across compositional variations mapped on combinatorial libraries with minimal computational cost. Data collected at a synchrotron beamline are analyzed on the fly, and by integrating experimental data with the inorganic crystal structure database (ICSD), we can substantially enhance the accuracy in classifying the structural phases across ternary phase spaces. We have used this approach to identify a novel magnetic phase with enhanced magnetic anisotropy which is a candidate for rare-earth free permanent magnet.

Thermodynamically stable lithium silicides and germanides from density functional theory calculations

Density-functional-theory (DFT) calculations have been performed on the Li-Si and Li-Ge systems. Lithiated Si and Ge, including their metastable phases, play an important technological r\^ole as Li-ion battery (LIB) anodes. The calculations comprise structural optimisations on crystal structures obtained by swapping atomic species to Li-Si and Li-Ge from the X-Y structures in the International Crystal Structure Database, where X={Li,Na,K,Rb,Cs} and Y={Si,Ge,Sn,Pb}. To complement this at various Li-Si and Li-Ge stoichiometries, ab initio random structure searching (AIRSS) was also performed. Between the ground-state stoichiometries, including the recently found Li$_{17}$Si$_{4}$ phase, the average voltages were calculated, indicating that germanium may be a safer alternative to silicon anodes in LIB, due to its higher lithium insertion voltage. Calculations predict high-density Li$_1$Si$_1$ and Li$_1$Ge$_1$ $P4/mmm$ layered phases which become the ground state above 2.5 and 5 GPa respectively and reveal silicon and germanium's propensity to form dumbbells in the Li$_x$Si, $x=2.33-3.25$ stoichiometry range. DFT predicts the stability of the Li$_{11}$Ge$_6$ $Cmmm$, Li$_{12}$Ge$_7$ $Pnma$ and Li$_7$Ge$_3$ $P32_12$ phases and several new Li-Ge compounds, with stoichiometries Li$_5$Ge$_2$, Li$_{13}$Ge$_5$, Li$_8$Ge$_3$ and Li$_{13}$Ge$_4$.

Using the Knowledge from Every Organic Crystal Structure Ever Published

The crystallographic community has done something remarkable and almost unique in science. It has operated in such a way that the data generated in virtually every experiment reported in a publication is available to all. This data, in the form of individual crystal structures, is valuable not just in itself, but as a collection. To fully exploit the results of a new structure determination, we never analyse a single structure, we analyse it in the context of every previous crystal structure. Our knowledge of molecular geometry and molecular interactions derived from these structural databases is put to routine use in almost every field of chemistry. This presentation will specifically highlight what we can learn from the world's database of small molecule crystal structures and demonstrate how we can apply that knowledge not just to increase our understanding in structural chemistry, but in structural biology too.

Survey of Bond Lengths in the Solid State for Oxides: Results and Applications

A complete survey of bond lengths from the Inorganic Crystal Structure Database (ICSD) is presented for all atoms of the Periodic Table of Elements, bonded to oxygen and in different oxidation states and coordination numbers. From over 135,000 crystal structures, a total of 33,343 coordination polyhedra and 188,462 bond distances were collected after passing a rigorous filtering process. One hundred thirty-six (136) ions in four hundred seventy-three (473) different configurations (coordination numbers) resulted. First, the bondlength distributions are visually inspected. This leads to (1) the observation and visual interpretation of known phenomena (e.g. Jahn-Teller effect), and (2) the isolation of new phenomena, as trends that are less obvious in smaller case-studies become more noticeable. Next, different applications of the data are investigated. The completeness of the survey allows the reassessment of important parameters of the solid state: ionic radii, and bond-valence parameters. Of the 473 ionic radii derived in this study, 329 revisions are made to Shannon's list of radii [1] (of which 176 were estimates), and 144 new ionic radii are derived. Next, a systematic evaluation of all bond-valence parameters published to date is done for oxides. Furthermore, using a new method of derivation, 136 new pairs of bond-valence parameters are obtained. In comparison to the previous-best published bond-valence parameters, an overall average decrease in the r.m.s.d. to the valence-sum rule of 20.7% (12.6% when weighted) is observed for the 33,343 coordination polyhedra, using the new parameters. New equations to describe the bond-length to bond-valence relation are also investigated. From an optimization between the experimental and a priori bond-valences of 54 carefully-selected crystal structures, roughly 20 relatively simple equations were selected for testing. Following a rigorous evaluation, the current exponential equation was found to be a viable choice in describing the relation. Finally, bond-length and bond-valence ranges are assigned to the 473 configurations of the atoms. Whereas the bondlength ranges are a useful aid in structure refinement, the assignment of a bond-valence range to ions allows a priori analysis of site occupancy in crystal structures.

Evaluation of Polymorphism Influence in the Finasteride

Finasteride is a specific competitive inhibitor of steroid type-II 5α-reductase, an intracellular enzyme that converts testosterone to dihydrotestosterone (DHT) and is widely used for the treatment of benign prostatic hyperplasia (BPH), prostate cancer , and androgenetic alopecia. Polymorphs are known to give rise to significant differences in the physicochemical properties of the compound as melting point, density, morphology, solubility and colour. Thus, proper monitoring of solid-state forms, both qualitative and quantitative, is crucial in order to ensure high-quality products. The crystal structures of finasteride appear in the Cambridge Crystal Structure Database (CSD) under the codes WOLXOK01 and WOLXOK02 for Form I and WOLXOK03 for Form II. In this context, the aim of this work was study the behavior of the chemical structure and physicochemical properties of polymorphic forms, and to evaluate the possible influence in the dissolution profile and stability of capsules. A stability study was carried out at 500C for 3 months. The Form II of finasteride was obtained by heating Form I to 2350C for 30 minutes. The techniques X-ray diffraction, infrared spectroscopy and thermal analysis were applied to characterize the Forms. The solubility of finasteride polymorphs was determined by equilibrium solubility method. For the dissolution test, water was used as dissolution medium and the basket apparatus at 100 rpm. The samples were analyzed by HPLC at 210 nm. Differences in X-ray diffraction and infrared spectra of the two polymorphs were observed. The DSC curves showed Form I melting peak at 2570C and solid-solid transformation to Form II at about 2300C. In the solubility study was observed higher Form II solubility than Form I in most evaluated pHs. The interaction of the Forms I and II with capsule excipients may have been different since the dissolution profile of the capsules showed higher release to the Form I. In the stability study, the finasteride content was stable for two Forms, however, the dissolution profile of Form II showed greater decline than the Form I. In conclusion, the results show that the dissolution profiles polymorphism may influence the quality of finasteride capsules, being necessary there be a polymorphic quality control for this dosage Form. Acknowledgments: PNPD CAPES and FAPEMIG

Exploration for Two-Dimensional Electrides via Database Screening andAb InitioCalculation

Inspired by the recent demonstration that Ca2N is a two-dimensional electride in which electrons near the Fermi level float between ionic layers, we have conducted a systematic search for 2D electrides by an approach combining crystal structure databases and ab initio electronic structure calculations. Starting from a set of working hypotheses, we have identified six 2D metallic electrides, of which one is nonmagnetic and five are nearly ferromagnetic ferrimagnets with a distinct spin texture. The latter five materials are the first magnetic electrides reported at ambient pressure.8 MoreReceived 9 November 2013DOI:https://doi.org/10.1103/PhysRevX.4.031023This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical Society

A comparative study of crystallographic van der Waals radii

Abstract Important data sets of crystallographic van der Waals radii covering major portions of the Periodic Table are reviewed, including those originally published in Pauling’s pioneering work in the late 1930s, together with other more recent data sets. The van der Waals radii for rare gases are determined next from short contact distances in crystallographic data, as an illustration of the value of crystal structure databases for the direct determination of van der Waals radii for non-metallic elements. Then, van der Waals radii for the other non-metallic and metallic elements, as presented in the literature and having been determined using various approaches, are compared systematically. Finally, certain outstanding problems related to the derivation and application of van der Waals radii are discussed, and further investigations of crystallographic van der Waals radii are suggested.