Van der Waals radii are used to construct a special
kind of molecular model called a space-filling model. These
models are constructed by drawing each atom as a van der Waals sphere
with the atom’s nucleus at the center of the sphere.
Space-filling models are useful because they show
how much space an atom (or molecule) occupies. You can see this
easily by comparing space-filling models with traditional ball-and-stick
models like those in the following figure. The latter do not provide
anything like a realistic sense of molecular size.
Ball-and-stick (top) and space-filling models
On the other hand, you can also see that it is much
harder to establish bond patterns in a space-filling model. Bonds
can be located if you recall that bond distances are much smaller
than nonbonded distances. A bond must exist between any two atoms
that create strongly overlapping spheres.
I mentioned above that van der Waals radii are also
used to assess nonbonded interactions. The same kind of assessment
can be accomplished using space-filling models. The visual counterpart
of a distance “prediction gap” is a model that contains
two overlapping nonbonded atoms.
The following figure compares ball-and-stick and space-filling
models of three water molecules. The molecules have been positioned
so that they occupy roughly the same positions that they might occupy
in an ice crystal.
Three water molecules (from
The ball-and-stick model does not reveal much, but
the space-filling model clearly shows that the central oxygen atom
substantially overlaps with a hydrogen atom in another water molecule.
Distance measurements confirm that the nonbonded OH distance (1.8
Å) is much shorter than the sum of the van der Waals radii
(1.2 + 1.4 = 2.6 Å).
These observations suggest that water molecules strongly
attract each other. This conclusion is supported by some of water’s
other strange properties, and chemists have decided that this attractive
force deserves a special name. They call it a hydrogen bond.
Some scientists claim that water’s hydrogen bonds are responsible
for life itself.