Critical Point Analysis of Calculated Electron Density Maps at Medium Resolution: Application to Shape Analysis of Zeolite-Like Systems

A method, derived from the procedure implemented in the program ORCRIT which was originally developed by C.K. Johnson, is presented for the topological analysis of zeolite electron density maps. This method is an approach to shape analysis of zeolitic frameworks through the location, identification, and linkage of critical points (points where the gradient of the density vanishes) in medium resolution electron density maps. It is observed that, at 3 Å resolution, tetrahedral sites and oxygen atoms generate peaks (density maxima) and passes (saddle points), respectively. The definition of ellipsoids, built at each peak location from their three local density curvatures, is used to generate a void volume wherein atomic or molecular probes can interact. The energetic behaviour of probes of several sizes interacting with ferrierite and mordenite is qualitatively studied through a pseudo- Lennard-Jones potential approximation.