Determining polyhedral arrangements of atoms using PageRank

Abstract

Polyhedral representations of the geometric arrangements of atoms and molecules is a pervasive tool in chemistry for understanding chemical bonding and electrostatic interactions. Yet the structural organization within very large systems is often difficult to quantify. In this work, we illustrate that PageRank, when combined with the chemical constraints of a system, can be used to uniquely identify the polyhedral arrangements of atoms and molecules. The PageRank algorithm can be used on any network that can be represented as a graph: a mathematical object where individual points, or vertices, are joined by edges. It is thus well-suited for chemical systems where atoms (considered vertices) are connected to each other via chemical bonding (considered edges) or other forces. This has been implemented in a recently reported series of R-scripts, moleculaRnetworks, and the example provided herein illustrates that the polyhedral arrangement of solvent molecules about a solute results in a unique PR value for the solute and enables rapid identification of the local geometry in the condensed medium. More generally PR can be used as a chemoinformatic tool to search for specific structural patterns within any database of geometric configurations.