Systematic enumeration of crystalline networks

Friedrichs, Olaf Delgado; Dress, Andreas; Huson, Daniel H.; Klinowski, Jacek; Mackay, Alan L.

doi:10.1038/23210

Cited by 290 publications

(236 citation statements)

References 10 publications

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“…The scope of these methods has improved in recent years, providing the ability to predict possible stable phases of a wide range of materials. For example, these methods have been used for the successful prediction of single [18][19][20][21][22] and multicomponent 19,[23][24][25][26] organic molecular crystals [27][28][29][30] , high-pressure phases of materials [31][32][33] , and other crystalline network structures such as zeolites or carbon polymorphs [34][35][36] . Progress in this field for organic molecular crystals is regularly assessed in a series of blind tests of structure prediction 37 .…”

Section: Introductionmentioning

confidence: 99%

Powder crystallography of pharmaceutical materials by combined crystal structure prediction and solid-state 1H NMR spectroscopy

Baias

Widdifield

Dumez

et al. 2013

Phys. Chem. Chem. Phys.

163

251

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A protocol for the ab initio crystal structure determination of powdered solids at natural isotopic abundance by combining solid-state NMR spectroscopy, crystal structure prediction, and DFT chemical shift calculations was evaluated to determine the crystal structures of four small drug molecules: cocaine, flutamide, flufenamic acid, and theophylline. For cocaine, flutamide and flufenamic acid, we find that the assigned 1 H isotropic chemical shifts provide sufficient discrimination to determine the correct structures from a set of predicted structures using the root-mean-square deviation (rmsd) between experimentally determined and calculated chemical shifts. In most cases unassigned shifts could not be used to determine the structures. This method requires no prior knowledge of the crystal structure, and was used to determine the correct crystal structure to within an atomic rmsd of less than 0.12 Å with respect to the known reference structure. For theophylline, the NMR spectra are too simple to allow for unambiguous structure selection.

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Section: Introductionmentioning

confidence: 99%

Powder crystallography of pharmaceutical materials by combined crystal structure prediction and solid-state 1H NMR spectroscopy

Baias

Widdifield

Dumez

et al. 2013

Phys. Chem. Chem. Phys.

163

251

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“…The rich polymorphism of silica, especially in its low-density forms, allows for fine-tuning of applications (e.g., gas separation membranes) by choosing the best suited polymorph. In addition, 100 000þ hypothetical silica polymorphs have been predicted theoretically as fourfold-connected networks (4CNs) [3][4][5][6][7], a large fraction of which, after accurate theoretical evaluation as silica materials, were found to have comparable energetics to experimentally prepared polymorphs [8,9]. Similarly rich polymorphism has only been further observed for a select group of other inorganic solids, for example, aluminophosphates (AlPO 4 ).…”

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confidence: 99%

“…Arguably, the most thorough study of the energy landscape of any TBSlike system to date was that recently applied to BN [22] which sampled systems with up to only eight atoms per unit cell finding only two hypothetical TBS polymorphs (see above). Evidently, to date, such studies have yielded only a very small number of hypothetical TBS polymorphs with respect to those derived for silica from the enumeration of 4CNs [3][4][5][6][7]. Following this latter topological approach we here sample directly the large and diverse set of 4CNs (with up to 48 atoms per unit cell when realized as a TBS) from a variety of sources.…”

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confidence: 99%

Apparent Scarcity of Low-Density Polymorphs of Inorganic Solids

2010

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For most inorganic solids, very few dense polymorphs and no low-density polymorphs are observed. Taking a wide range of tetrahedrally-coordinated binary solids (e.g., ZnO, GaN) as a prototypical system, we show that the apparent scarcity of low-density polymorphs is not due to significant structural or energetic limitations. Using databases of periodic networks as sources of novel crystal structures, followed by ab initio energy minimization, we predict a dense spectrum of low-density low-energy polymorphs. The diverse range of materials considered indicates that this is likely to be a general phenomenon. DOI: 10.1103/PhysRevLett.104.175503 PACS numbers: 61.50.Ah, 61.66.Fn, 71.15.Nc, 82.75.Fq The structure and properties of inorganic solids are intimately linked to such an extent that even different structures of the same composition (so-called polymorphs) often have widely differing properties and applications. For boron nitride (BN), for example, the soft hexagonal layered polymorph (h-BN) is used as a lubricant, while the cubic polymorph (wurtzite structure) is extremely hard and is employed as an industrial abrasive. Germanium also exhibits more than one polymorph (or more strictly ''allotrope'' for elemental systems) having very different optical properties; with the diamond structured -germanium having an indirect band gap, and the recently synthesized lowdensity clathrate-II structure [1] a direct gap. Evidently, having access to more than one polymorph can significantly extend the range of properties and applications of a particular compound. For the vast majority of inorganic solids, however, typically only three or fewer distinct polymorphs have been prepared experimentally and a similarly small number of hypothetical polymorphs have been proposed. Moreover, where more than one polymorph is known, these extra phases very rarely have a significantly lower density than the most stable polymorph.In stark contrast to this situation, silica (SiO 2 ) has been prepared as more than 40 polymorphs [2], the majority of which are considerably less dense than -quartz; the most stable polymorph under ambient conditions. The rich polymorphism of silica, especially in its low-density forms, allows for fine-tuning of applications (e.g., gas separation membranes) by choosing the best suited polymorph. In addition, 100 000þ hypothetical silica polymorphs have been predicted theoretically as fourfold-connected networks (4CNs) [3][4][5][6][7], a large fraction of which, after accurate theoretical evaluation as silica materials, were found to have comparable energetics to experimentally prepared polymorphs [8,9]. Similarly rich polymorphism has only been further observed for a select group of other inorganic solids, for example, aluminophosphates (AlPO 4 ). A tantalizing hint that there may as yet exist a greater pool of experimentally accessible polymorphs for many other inorganic solids is given by the recent low temperature deposition synthesis of the tetrahedral wurtzite polymorph of LiBr [10] (after previous theor...

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“…Yet systematic derivation of these graphs remains surprisingly undeveloped, with some notable exceptions [1][2][3][4][5][6][7]. There are many possible graphs in 3D Euclidean space, E 3 , not all of which are relevant to condensed matter.…”

Section: Introductionmentioning

confidence: 99%

From 2D hyperbolic forests to 3D Euclidean entangled thickets

Hyde

Oguey

2000

Eur. Phys. J. B

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Abstract.A method is developed to construct and analyse a wide class of graphs embedded in Euclidean 3D space, including multiply-connected and entangled examples. The graphs are derived via embeddings of infinite families of trees (forests) in the hyperbolic plane, and subsequent folding into triply periodic minimal surfaces, including the P, D, gyroid and H surfaces. Some of these graphs are natural generalisations of bicontinuous topologies to bi-, tri-, quadra-and octa-continuous forms. Interwoven layer graphs and periodic sets of finite clusters also emerge from the algorithm. Many of the graphs are chiral. The generated graphs are compared with some organo-metallic molecular crystals with multiple frameworks and molecular mesophases found in copolymer melts.PACS. 61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling -61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling -61.30.Cz Theory and models of liquid crystal structure

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Systematic enumeration of crystalline networks

Cited by 290 publications

References 10 publications

Powder crystallography of pharmaceutical materials by combined crystal structure prediction and solid-state 1H NMR spectroscopy

Powder crystallography of pharmaceutical materials by combined crystal structure prediction and solid-state 1H NMR spectroscopy

Apparent Scarcity of Low-Density Polymorphs of Inorganic Solids

From 2D hyperbolic forests to 3D Euclidean entangled thickets

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