THE 2345-MULTIMODE RESONANCE IN ACETYLENE - A BIFURCATION-ANALYSIS

This paper reports on a classical phase space bifurcation analysis of the 2345 Fermi resonance of acetylene. The 2345 Fermi resonance is a m ultimode nonlinear, resonance coupling that is important to the vibrat ional dynamics and energy flow of highly excited acetylene. The bifurc ation analysis is performed on an integrable Hamiltonian that represen ts a planar five-mode model of acetylene in which the nu(2), nu(3), nu (4), and nu(5) vibrational modes are nonlinearly coupled through the 2 345 Fermi resonance. The phase space structures of the 2345 Fermi reso nance are shown to be analogous to but more complicated than phase spa ce structures of the two-mode, 1:1 and 2:1 Fermi resonance. The result s are presented in terms of bifurcation diagrams and molecular catastr ophe maps. The bifurcation analysis of this multidimensional system wi th a complicated multimode resonance is a step beyond the simple integ rable, resonantly coupled two-mode systems that are now well understoo d. Analysis of this integrable system also represents a necessary step toward using a multiresonance, i.e., ''chaotic'' model to decipher th e vibrational spectra of highly excited acetylene, based on knowledge of the anharmonic modes born from bifurcations of the low-energy norma l modes. (C) 1995 American Institute of Physics.