A geometric solution to the largest-free-sphere problem in zeolite frameworks

Foster, Martin D.; Rivin, Igor; Treacy, M.M.J.; Friedrichs, Olaf Delgado

doi:10.1016/j.micromeso.2005.08.025

Cited by 190 publications

(163 citation statements)

References 8 publications

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“…Efficient implementation can be obtained by using heap-sort data structures. Consider an easy version of this problem, in which one divides the unit square in cells, each of whose cost is 1, and the goal is to find the shortest path from (0, 0) to (1,1). It is easy to see that as the grid becomes finer and finer, Dijkstra's method always produces a stairstep path with cost 2 and does not converge to the correct answer, which is a diagonal path with minimal cost ͌ 2 (see ref.…”

Section: Fast Marching Methods For Computing the Shortest Pathsmentioning

confidence: 99%

“…They applied a form of Dijkstra's algorithm on a 3D grid with each point having assigned a cost related to the distance to the closest obstacle (closest protein atoms). Foster et al (1) exploited the Delaunay triangulation technique to find the largest free sphere in a porous material. A Delaunay triangulation of a set of points defined by the centers of framework atoms generates a set of spheres (the Delaunay circumspheres) that occupy the voids and crevices within the framework.…”

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confidence: 99%

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Navigating molecular worms inside chemical labyrinths

Harańczyk

Sethian

2009

Proc. Natl. Acad. Sci. U.S.A.

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Predicting whether a molecule can traverse chemical labyrinths of channels, tunnels, and buried cavities usually requires performing computationally intensive molecular dynamics simulations. Often one wants to screen molecules to identify ones that can pass through a given chemical labyrinth or screen chemical labyrinths to identify those that allow a given molecule to pass. Because it is impractical to test each molecule/labyrinth pair using computationally expensive methods, faster, approximate methods are used to prune possibilities, ''triaging'' the ability of a proposed molecule to pass through the given chemical labyrinth. Most pruning methods estimate chemical accessibility solely on geometry, treating atoms or groups of atoms as hard spheres with appropriate radii. Here, we explore geometric configurations for a moving ''molecular worm,'' which replaces spherical probes and is assembled from solid blocks connected by flexible links. The key is to extend the fast marching method, which is an ordered upwind one-pass Dijkstra-like method to compute optimal paths by efficiently solving an associated Eikonal equation for the cost function. First, we build a suitable cost function associated with each possible configuration, and second, we construct an algorithm that works in ensuing high-dimensional configuration space: at least seven dimensions are required to account for translational, rotational, and internal degrees of freedom. We demonstrate the algorithm to study shortest paths, compute accessible volume, and derive information on topology of the accessible part of a chemical labyrinth. As a model example, we consider an alkane molecule in a porous material, which is relevant to designing catalysts for oil processing.fast marching methods ͉ robotic navigation ͉ accessible volume

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Section: Fast Marching Methods For Computing the Shortest Pathsmentioning

confidence: 99%

mentioning

confidence: 99%

Navigating molecular worms inside chemical labyrinths

Harańczyk

Sethian

2009

Proc. Natl. Acad. Sci. U.S.A.

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“…[86] In addition, the analysis of the Voronoi network can yield other useful geometric descriptors for porous materials. Three quantities, in particular, are of particular relevance to the description of molecular adsorption and transport in porous materials (see Figure 8): [93,87,86] • the diameter of the largest included sphere, D i , which reflects the size of the largest cavity within a porous material;…”

Section: Advanced Geometrical Descriptorsmentioning

confidence: 99%

Computational characterization and prediction of metal–organic framework properties

Coudert

Fuchs

2016

Coordination Chemistry Reviews

241

203

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In this introductory review, we give an overview of the computational chemistry methods commonly used in the field of metal-organic frameworks (MOFs), to describe or predict the structures themselves and characterize their various properties, either at the quantum chemical level or through classical molecular simulation. We discuss the methods for the prediction of crystal structures, geometrical properties and large-scale screening of hypothetical MOFs, as well as their thermal and mechanical properties. A separate section deals with the simulation of adsorption of fluids and fluid mixtures in MOFs.

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“…The van der Waals radii for both of these atoms are defined as 1.35 Å, which is the published standard for these atom types in zeolites. 23 It is straightforward to include our types of atoms, with corresponding radii, into the presented framework. We believe that the approximations in the diameters of the largest included and free spheres introduced by our approximation are reasonable for the purpose of our simplified T-ring representation.…”

Section: P2mentioning

confidence: 99%

“…The default threshold diameter is set to 2.8 Å, which is based on a hard sphere often used to represent a water molecule. 23 This threshold parameter can be readjusted to correspond to other molecules, e.g., benzene. In this way, it is straightforward to visually compare the topology of a given porous material accessible to different guest species.…”

Section: P2mentioning

confidence: 99%

Chemical Hieroglyphs: Abstract Depiction of Complex Void Space Topology of Nanoporous Materials

Theisen

Smit

Harańczyk

2010

J. Chem. Inf. Model.

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In general, most porous materials are so complex that structural information cannot be easily observed with 3D visualization tools. To address this problem, we have developed a special abstract 2D representation to depict all important topological features and geometrical parameters. Our approach involves reducing these structures based on symmetry and perceived building blocks to a compressed, graph representation that allows for quick structure analysis, classification, and comparison.

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A geometric solution to the largest-free-sphere problem in zeolite frameworks

Cited by 190 publications

References 8 publications

Navigating molecular worms inside chemical labyrinths

Navigating molecular worms inside chemical labyrinths

Computational characterization and prediction of metal–organic framework properties

Chemical Hieroglyphs: Abstract Depiction of Complex Void Space Topology of Nanoporous Materials

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