Preface 1 Pendulum Dynamics 1.1 Pendulum dynamics 1.2 Morse oscillator 1.3 Hamilton's equations of motion 1.4 Pendulum dynamics as the basic unit for resonance 1.5 Standard map and KAM theorem 1.6 Conclusion References 2 Algebraic Approach to Vibrational Dynamics 2.1 The algebraic Hamiltonian 2.2 Heisenberg's correspondence and coset representation 2.3 An example: The H20 case 2.4 su(2) dynamical properties Reference Appendix: The derivation of raising and lowering operators 3 Chaos 3.1 Definition and Lyapunov exponent: Tent map 3.2 Lyapunov exponent in Hamiltonian system 3.3 Period 3 route to chaos 3.4 Resonance overlapping and sine circle mapping 3.5 The case study of DCN 3.5.1 The chaotic motion 3.5.2 Periodic trajectories 3.5.3 Chaotic motion originating from the D-C stretching References Appendix: Calculation of the maximal Lyapunov exponent 4 C-H Bending Motion of Acetylene 4.1 Introduction 4.2 Empirical C-H bending Hamiltonian 4.3 Second quantization representation of Heft 4.4 su(2) ○ su(2) represented C-H bending motion 4.5 Coset representation 4.6 Modes of C-H bending motion 4.7 Reduced Hamiltonian of C-H bending motion 4.8 su(2) origin of precessional mode 4.9 Nonergodicity of C-H bending motion 4.10 Intramolecular vibrational relaxation References 5 Assignments and Classification of Vibrational Manifolds 5.1 Formaldehyde case 5.2 Diabatic correlation, formal quantum number and level reconstruction 5.3 Acetylene case 5.4 Background of diabatic correlation 5.5 Approximately conserved quantum number 5.6 DCN case 5.7 Density p in the coset space 5.8 Lyapunov exponent analysis References 6 Dixon Dip 6.1 Significance of level spacings 6.2 Dixon dip 6.3 Dixon dips in the systems of Henon-Heiles and quartic potentials 6.4 Destruction of Dixon dip under multiple resonances 6.5 Dixon dip and chaos References 7 QuantiT.ation by Lyapunov Exponent and Periodic Trajectories 7.1 Introduction 7.2 Hamiltonian for one electron in multiple sites 7.3 Quantization: The least averaged Lyapunov exponent 7.4 Quantization of H20 vibration 7.5 Action integrals of periodic trajectories: The DCN case 7.6 Retrieval of low quantal levels of DCN 7.7 Quantization of Henon-Heiles system 7.8 Quantal correspondence in the classical AKP system 7.9 A comment References 8 Dynamics of DCO/HCO and Dynamical Barrier Due to Extremely Irrational Couplings 8.1 The coset Hamiltonian of DCO 8.2 State dynamics of DCO 8.3 Contrast of the dynamical potentials of D-C and C-O stretchings 8.4 The HCO case 8.5 Comparison of the dynamical potentials 8.6 A comment: The IVR role of bending motion 8.7 Dynamical barrier due to extremely irrational couplings: The role of bending motion References 9 Dynamical Potential Analysis for HCP, DCP, N20, HOC1 and HOBr 9.1 Introduction 9.2 The coset represented Hamiltonian of HCP 9.3 Dynamical potentials and state properties inferred by action population 9.4 State classification and quantal environments 9.5 Localized bending mode 9.6 The condition for localized mode 9.7 On the HPC formation 9.8 The fixed point structure 9.9 DCP Hamiltonian 9.10 Dynamical similarity between DCP and HCP 9.11 N20 dynamics 9.12 The cases of HOC1 and HOBr 9.13 A comment References Appendix 10 Chaos in the Transition State Induced by the Bending Motion 10.1 Chaos in the transition state 10.2 The cases of HCN, HNC and the transition state 10.3 Lyapunov exponent analysis 10.4 Statistical analysis of the level spacing distribution 10.5 Dixon dip analysis 10.6 Coupling of pendulum and harmonic oscillator 10.7 A comment References Appendix: Author's Publications Related to this Monograph
