Tolerance for Identification of Point-Groups

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.