Global topological approach to highly excited vibration: a case study of H2O, CH2Br2 and CD2Br2

A global topological approach based on the algebraic coset representation to study highly excited molecular vibration is proposed. The algorithm allows us to elucidate ample highly excited vibrational dynamics from a global viewpoint. Topics for highly excited states studied include (1) global topological structures, (2) global symmetric and antisymmetric characters, (3) resonance overlaps and chaotic motion, (4) action transfer coefficients and (5) survival probabilities denoting the decaying of the action stored in a mode, with sample calculations for H2O, CH2Br2 and CD2Br2.