The SU(3) algebraic vibrational dynamics of inter-mode couplings: a case study of H2O, CH2Br2 and CD2Br2

An SU(3) algebraic Hamiltonian is proposed to account for the inter-mode couplings among three Morse oscillators of which two are equivalent and the third is in Fermi resonance with the other two. The parameters in the algebraic Hamiltonian are determined through the fitting with the observed eigenfrequencies. Hamiltonʹs equations in the coset representatives are then employed to study the dynamics of energy transfer in the time domain of sub-picosecond. With different coset representations, various surfaces of section of the multi-dimensional potential can be traced out. From the results by these two algorithms fruitful dynamical information is explored.