On the Balance of Simplification and Reality in Molecular Modeling of the Electron Density

Fused-sphere (van der Waals) surfaces and their variants such as solvent accessible surfaces and molecular surfaces are simple molecular models that are commonly used for many diverse purposes across a broad range of scientific disciplines due to their low computational resource demands. Fused-sphere models require atomic radii to be defined. Many different atomic radii have been proposed, with each set of radii being applicable to a relatively limited scope of molecular types or situations. The large number of differing radii sets actually serves to emphasize the simplicity of the model and its inability to accurately represent the reality of the molecule: its electron density. By measuring the similarity of fused-sphere, fuzzy fused-sphere, and calculated electron density representations of a set of small molecules via symmetric volume differences and the shape group method, it can be seen that fused-sphere models are very poor at representing the real electronic charge distribution of small molecules, especially where π bond systems, lone pair electrons, and aromatic rings are involved. Larger molecules, conceivably, will be even more poorly represented. With advances in computational power and modeling techniques to arrive at high-quality calculated electron density representations for large molecules already in existence, abandoning the use of fused-sphere models should be considered for many applications.