Chapter 2 - Distances

van der Waals radius

Our study of limonene showed that atoms do not approach each other closely when they are not bonded to each other. This suggests that atoms in different molecules cannot approach each other closely either and must occupy a well-defined molecular volume.

One way to measure molecular volumes is to study gas behavior over a range of temperatures. Real gases do not perfectly obey the ‘ideal’ gas law (PV = nRT), and deviations between ‘ideal’ and real behavior can give information about molecular volume.

It is also possible to measure intermolecular distances if a compound can be crystallized. One can pass X-rays through a crystalline solid and detect the X-rays when they emerge. The “bounce angle” gives information about atom positions, and one can use these data to calculate all kinds of interatomic distances.

Whatever its source, intermolecular distance data are interpreted by viewing the atoms as hard spheres. We assume that the spheres of neighboring nonbonded atoms just touch, so that the measured interatomic distance equals the sum of the atomic hard-sphere radii:


Hard-sphere radii are more commonly called van der Waals radii (or nonbonded radii). Reliable values cannot be given for these radii because they depend on the measuring technique and the molecule, but I have listed one useful set of radii in the following table.

van der Waals radii (in Å)

















These radii, like the bond radii discussed above, correlate with position in the Periodic Table:

  1. As we go left to right within a row, van der Waals radius shrinks slightly (example: C > N > O > F)

  2. As we go top to bottom within a column, van der Waals radius expands (example: F << Cl < Br < I)

Van der Waals radii can be used to study nonbonded (especially intermolecular) interactions. For example, one can compare an actual nonbonded distance with a predicted distance (the latter is obtained by summing van der Waals radii). If there is a “prediction gap”, that is, if the actual distance is substantially shorter than the predicted one, we might claim that some special force draws the atoms (molecules) together. We can also try to correlate the magnitude of this “prediction gap” with the strength of this attractive force.

This kind of analysis must be undertaken carefully because atoms are not hard spheres (they are squishy). It is also possible for another force to draw nonbonded atoms together. For example, we have seen that X-C-Y nonbonded distances are much shorter than X-C…C-Y nonbonded distances. X-C-Y distances are also much shorter than r(X) + r(Y), where r = van der Waals radius. The large “prediction gap” does not mean that X and Y attract each other, however. A much more likely explanation is that C forces X and Y to approach each other in order to make CX and CY bonds.