A useful measure of a molecule is its size. There are several possible ways of defining the size of a molecule. The definition used in MOPAC is as follows:
The first dimension is the maximum distance between any pair of atoms.
For systems of 20 or fewer atoms, this distance, and the atoms involved, is worked out explicitly. For systems of 21 or more atoms, an atom is selected; the atom, K, most distant from it is then identified, then the atom, L, most distant from K is identified. In most systems, the distance R(K-L) is the first dimension. To ensure that it is, the point half-way between K and L is selected, and atom K is then re-defined as the atom most distant from that point. A new L is determined. This sequence in repeated up to 10 times, or until atoms K and L no longer change. There is no guarantee that the first dimension is, in fact, the largest distance, but it is likely to be close to the largest possible value.
The second dimension is the maximum distance in the plane perpendicular to the first dimension between any pair of atoms.
The technique that was used in determining the first dimension for systems of over 21 atoms is used here.
The third dimension is the maximum distance between any two atoms on the line perpendicular to the plane of the first two atoms.
This quantity is explicitly calculated.
Note that the second and third dimensions do not define the smallest rectangular slot that a molecule would go through; it will normally be slightly larger than the minimum slot. Nevertheless, the "dimensions" of a molecule can be regarded as a good measure of the size of hole that the molecule could pass through. Of course, allowance must be made for the finite size of atoms.
Monatomic systems have no "dimension", linear systems have two zero "dimensions", and flat systems have one zero "dimension".