Van der Waals surface and radii

We may define a superposition of atomic van der Waals spheres. This defines what is called the van der Waals surface of the molecule, or a molecular shape - a concept of great importance and of the same arbitrariness as the radii themselves. 

In a similar way we may define ionic radii, to reproduce the ion packing in ionic crystals, as well as covalent radii to foresee chemical bond lengths. 

---