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Point Group Determination

The eigenvalues
of the moment of inertia tensor are first inspected to see if there should be a principal
rotation axis of order 3 or more. Degeneracy is assumed if the difference between two principal
moments of inertia, divided by the trace of the inertia tensor, is less than some tolerance,
which is initially set to . This tolerance can be changed with the keyword *TOLE*.
Symmetry elements are then sought depending upon this first
result, and are diagnosed when rotation or reflection operations produce the same geometry
correct to in each Cartesian coordinate. This tolerance can be changed with the
keyword *TOLD*. If symmetry elements expected for the
calculated principal moments of inertia are not found then the first tolerance is divided by
ten and the whole procedure repeated with a warning message about `accidental degeneracy'.
If the first tolerance falls below the routine gives up.
Point group determination should work for small molecules belonging to all point groups with
principal axes of order less than 6. Higher order rotation axes can be sought using the
keyword *AXIS*. Problems due to the tolerances occur for larger molecules,
particularly those with high symmetry.

David Wales
2018-06-23