Shapes and conformations of four-atom inorganic rings and clusters A structural study using continuous shape measurements

Abstract

A structural perspective of groups of four atoms of the s and p block elements is presented, with the help of a continuous shape measures (CShM) analysis. Among the shapes of a group of N points, defined by 3N Cartesian coordinates, the reference shapes are regular polygons and polyhedra, together with univocally defined combinations thereof (e.g., two coplanar or perpendicular edge-sharing squares). This study classifies most of the structures either by their closeness to a regular shape, or by quantifying their positions along minimal interconversion pathways between two regular shapes. The many shapes described by a given pathway are generically grouped as a molecular conformation.