Determining polyhedral arrangements of atoms using PageRank

Hudelson, Matthew; Mooney, Barbara Logan; Clark, Aurora E.

doi:10.1007/s10910-012-0033-7

Cited by 23 publications

(18 citation statements)

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“…Analyzing this network via PageRank produces a mathematically unique PageRank (PR) value; each PR corresponds to a specific solvation geometry. 59,60 For example, the PR of an ion in a tricapped trigonalprismatic solvation environment is 0.148144. For each snapshot of simulation data, the calculated PR is compared to a library of PR values for different polyhedral arrangements; when the calculated PR is matched with the PR of known polyhedra, the solvation structure can be identified on a snapshot-by-snapshot basis.…”

Section: ■ Computational Methodsmentioning

confidence: 99%

Structural and Thermodynamic Properties of the Cm^III Ion Solvated by Water and Methanol

et al. 2016

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The geometric and electronic structures of the 9-coordinate Cm(3+) ion solvated with both water and methanol are systematically investigated in the gas phase at each possible solvent-shell composition and configuration using density functional theory and second-order Møller-Plesset perturbation theory. Ab initio molecular dynamics simulations are employed to assess the effects of second and third solvent shells on the gas-phase structure. The ion-solvent dissociation energy for methanol is greater than that of water, potentially because of increased charge donation to the ion made possible by the electron-rich methyl group. Further, the ion-solvent dissociation energy and the ion-solvent distance are shown to be dependent on the solvent-shell composition. This has implications for solvent exchange, which is generally the rate-limiting step in complexation reactions utilized in the separation of curium from complex metal mixtures that derive from the advanced nuclear fuel cycle.

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Section: ■ Computational Methodsmentioning

confidence: 99%

Structural and Thermodynamic Properties of the Cm^III Ion Solvated by Water and Methanol

et al. 2016

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“…Consider that eigenvalues or eigenvectors of the adjacency matrix (or its related matrices) can be related to specific edge patterns within a graph, as in the use of PageRank as a tool to identify polyhedral arrangement of particles and as a collective variable for chemical transformations. 93 , 142 , 143 Leveraging recent developments in computational topology, one can use other meaningful features to characterize the graph topology together with metric information, such as the length sequence of the minimal cycle base of a weighted graph. 144 A particular general framework is via persistent homology, which can map an input (metric or weighted) graph into a persistence diagram feature representation, via the use of the intrinsic Čech filtration over the input graph (equipped with the shortest path metric), 145 or induced by the clique complexes (for both directed or undirected graphs), 146 − 149 or induced by the so-called path homology when the input graph is directed.…”

Section: The Many-body Roadmapmentioning

confidence: 99%

The Middle Science: Traversing Scale In Complex Many-Body Systems

et al. 2021

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“…In the former, the entire hydrogen bond network of the simulated water was first converted into a graph, wherein the oxygen atoms are vertices and the intermolecular hydrogen bonds between water molecules are edges. The PageRank of the solute was then used to investigate the specific organization patterns of water about a solute, and was shown to be an effective data‐mining tool for understanding solvation structure as a function of time . This algorithm is available within the moleculaRnetworks software program .…”

Section: Introductionmentioning

confidence: 99%

ChemNetworks: A complex network analysis tool for chemical systems

2013

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Many intermolecular chemical interactions persist across length and timescales and can be considered to form a "network" or "graph." Obvious examples include the hydrogen bond networks formed by polar solvents such as water or alcohols. In fact, there are many similarities between intermolecular chemical networks like those formed by hydrogen bonding and the complex and distributed networks found in computer science. Contemporary network analyses are able to dissect the complex local and global changes that occur within the network over multiple time and length scales. This work discusses the ChemNetworks software, whose purpose is to process Cartesian coordinates of chemical systems into a network/graph formalism and apply topological network analyses that include network neighborhood, the determination of geodesic paths, the degree census, direct structural searches, and the distribution of defect states of network. These properties can help to understand the network patterns and organization that may influence physical properties and chemical reactivity. The focus of ChemNetworks is to quantitatively describe intermolecular chemical networks of entire systems at both the local and global levels and as a function of time. The code is highly general, capable of converting a wide variety of systems into a chemical network formalism, including complex solutions, liquid interfaces, or even self-assemblies.

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Determining polyhedral arrangements of atoms using PageRank

Cited by 23 publications

References 2 publications

Structural and Thermodynamic Properties of the Cm^III Ion Solvated by Water and Methanol

Structural and Thermodynamic Properties of the Cm^III Ion Solvated by Water and Methanol

The Middle Science: Traversing Scale In Complex Many-Body Systems

ChemNetworks: A complex network analysis tool for chemical systems

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Determining polyhedral arrangements of atoms using PageRank

Cited by 23 publications

References 2 publications

Structural and Thermodynamic Properties of the CmIII Ion Solvated by Water and Methanol

Structural and Thermodynamic Properties of the CmIII Ion Solvated by Water and Methanol

The Middle Science: Traversing Scale In Complex Many-Body Systems

ChemNetworks: A complex network analysis tool for chemical systems

Contact Info

Product

Resources

About

Structural and Thermodynamic Properties of the Cm^III Ion Solvated by Water and Methanol

Structural and Thermodynamic Properties of the Cm^III Ion Solvated by Water and Methanol