Shape groups of the electronic isodensity surfaces for small molecules: Shapes of 10‐electron hydrides

Abstract

AbstractAn algorithm for a detailed 3‐D characterization of the shapes of molecular charge distributions is implemented in the form of a comprehensive package of computer programs, GSHAPE, and applied to a series of 10‐electron hydrides to critically evaluate the methodology. Attention is paid to the effects of nuclear geometry and the size of basis on the molecular shape. The characterization is performed by computing a number of topological invariants (“shape groups”) associated with a continuum of molecular surfaces: the complete family of all electronic isodensity contours for the given molecules. These shape groups (the homology groups of truncated surfaces derived from isodensity contours) depend on two continuous parameters: a density value defining the density contour and a reference curvature value, to which the local curvatures of the isodensity contours are compared. The electronic charge distribution is calculated at the ab initio level using basis sets ranging from STO‐3G to 6‐31G**. No visual inspection is required for the characterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visualization of the results is one option of our program using Application Visualization Software (AVS). For a given molecule, in a given nuclear geometry, the technique provides a 2‐D shape map, displaying the distribution of the shape gruops as a function of the local curvature and the level set value (the value of the charge density at the contour). The computer program GSHAPE performs the analysis automatically. This feature makes it potentially useful in the context of computer‐aided drug design, where unbiased, automated shape characterization methods are valuable tools. As examples, a variety of 2‐D shape maps are discussed. © John Wiley & Sons, Inc.