Dynamical symmetries

Dynamical symmetries are discussed with special reference to practical, approximate procedures for their determination. It is argued that for realistic molecular problems there is an intermediate time scale which is of interest and is typically of the order of a vibrational period. Much faster variations tend to get averaged over (i.e., eliminated in an adiabatic fashion) while much slower variations can be treated in the sudden approximation. The result is a self-consistent procedure which can also be derived from a variational principle. The stability of the self-consistent procedure is closely related to the separation of time scales and to the utility of constraints in the information theory approach. Also discussed are the symmetries of bound vibrational states.