SHAPE GROUPS OF THE ELECTRONIC ISODENSITY SURFACES FOR SMALL MOLECULES - SHAPES OF 10-ELECTRON HYDRIDES

An algorithm for a detailed 3-D characterization of the shapes of mole cular charge distributions is implemented in the form of a comprehensi ve package of computer programs, GSHAPE, and applied to a series of 10 -electron hydrides to critically evaluate the methodology. Attention i s paid to the effects of nuclear geometry and the size of basis on the molecular shape. The characterization is performed by computing a num ber of topological invariants (''shape groups'') associated with a con tinuum of molecular surfaces: the complete family of all electronic is odensity contours for the given molecules. These shape groups (the hom ology groups of truncated surfaces derived from isodensity contours) d epend on two continuous parameters: a density value defining the densi ty contour and a reference curvature value, to which the local curvatu res of the isodensity contours are compared. The electronic charge dis tribution is calculated at the ab initio level using basis sets rangin g from STO-3G to 6-31G*. No visual inspection is required for the cha racterization and comparison of shapes of molecular charge densities, as these are done algorithmically by the computer. However, visualizat ion of the results is one option of our program using Application Visu alization Software (AVS). For a given molecule, in a given nuclear geo metry, the technique provides a 2-D shape map, displaying the distribu tion of the shape groups 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 feat ure makes it potentially useful in the context of computer-aided drug design, where unbiased, automated shape characterization methods are v aluable tools. As examples, a variety of 2-D shape maps are discussed. (C) 1993 by John Wiley & Sons, Inc.