Bonded Atoms are Not Truly Spherical

Almost all molecular mechanics programs calculate non-bonded repulsion between atoms in molecules assuming the atoms are spherical. This is one of many examples of where the programs make a simple empirical approximation of a "reasonable" atom-atom force (or potential).

In fact experiment shows that bonded atoms are not truly spherical for purposes of atom-atom contact. The effect is demonstrated particularly dramatically for bromine by comparing Br-Br contacts determined by x-ray diffraction of a very large number of organic crystals.

The following figure uses circles, crosses, and x's to plot the positions (distance and angle) of the center of neighboring bromine atoms from the red bromine atom at the origin. The angle is defined with respect to the black carbon at the bottom right corner, to which the red bromine is bonded.

As expected most neighbors are beyond the van der Waals distance (2 * 1.85 , the vdW radius of Br), because data like these are used to determine van der Waals radii. (Neighbors beyond 5 are not even shown in the graph.) Some of the distances are expected to be less than van der Waals contact, because overall attraction between adjacent molecules should slightly compress the atoms on the surface which make the initial contact. What might seem surprising is that there are many more "too short" contacts along the C-Br axis (vertical in the plot) than perpendicular to it (to the left in the plot). Obviously the Br atom, at least when bonded to C is not spherical for van der Waals contact purposes.

There are several possible explanations for this asymmetry*, but whatever the cause, it is obvious that empirical calculations that assume a spherical bromine atom must be suspect. Just because a molecular mechanics program is complex, and expensive, doesn't mean it is right. Caveat emptor!

*) Not only the nature of Br...Br interactions but also, for example, a Br atom that is at right angles from the reference C-Br bond is closer not only to the reference C atom, but also to whatever that atom may be attached to.  These additional interactions may help keep such neighboring Br atoms at arms length.  Statistical studies like this one must be carefully controlled.

Original figure from :
S.C. Nyburg and C.H. Faerman,
A Revision of van der Waals Atomic Radii for Molecular Crystals - N, O, F, S, Cl, Se, Br, and I Bonded to Carbon.
Acta Crystallographica
B41, 274-279 (1985).