Normally, molecular geometries do not exactly correspond to the idealized
point-group. Thus benzene might have slightly different bond-lengths and
angles. Of course, symmetry could be used to prevent this, but in the
discussion here we assume that the symmetry of the system is unknown. To allow
for these slight distortions, a small tolerance is built in to the tests for
symmetry elements. This starts off at 0.1Å , but may be tightened
automatically if ambiguities are detected. An example of such an ambiguity is
found in tropylium, C7H7+ ion, where the C-C distance is 1.4 Å.
Rotating the ring by 45 degrees (a C8 operation) would place the atoms at a
distance of only 0.18Å from equivalent positions. C7 and C8 would
thus give almost identical results. To resolve such ambiguities, when they
arise, the tolerance is reduced, and the test re-run.
Even with this feature, some systems still resist classification. A distorted
geometry might have some, but not all, elements of a high point group. Perhaps
a distorted benzene has a C2(z) and a C3(z), but not a C6(z),
impossible in a real system. As such it would appear to be different from all
real point groups. To accommodate such defects a descent in symmetry is
carried out. This consists of checking each point-group in turn, in order of
decreasing symmetry. Once all of the elements of a point group are satisfied,
the system is assigned to that point group, even if the system contains more
symmetry than the point group.
By these two devices, a variable tolerance and the descent in symmetry, most
systems should be identified correctly, or at least as a sub-group of the full
point group.