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Variable atomic radii based on some approximate configurational invariance and transferability properties of the electron density

The purpose of this study is to design a technique that generates a variable van der Waals‐like surface for any desired charge density value of a molecule. The method is based on the recognition that for each fixed density value, within a wide range, certain shape features of the electron density contours are approximately invariant under configuration rearrangements, such as bending and stretchings in polyatomic molecules. These invariants appear in the form of spherical regions in space around the nuclei, where no density contours of a given level set value enter. These regions, the so‐called invariant cores, behave as approximately transferable quasi‐atomic spherical surfaces. We have evaluated these cores in molecules, and also approximated them in terms of the electron density of isolated atoms. The properties of these quasi‐atomic surfaces allow one to design a scale of variable atomic radii based on the size of the transferable isodensity spheres. In this work we provide a detailed description of the dependence of the diameters of these spheres on the electron density values. We show that, by using this scale of radii, it is possible to design fused‐sphere molecular models that closely mimic isodensity surfaces for a whole range of density values. The results discussed here allow one to relate molecular size with charge density. We propose the use of these scales for the construction of more realistic van der Waals model surfaces when studying molecular shape in the context of computer‐assisted molecular modeling.