Dimension reduction for extracting geometrical structure of multidimensional phase space: Application to fast energy exchange in the reaction O({sup 1}D)+N{sub 2}O{yields}NO+NO

One of the most fundamental problems in studying general Hamiltonian systems with many degrees of freedom is to extract a low-dimensional subsystem including the essential dynamics. In this paper, a new partial normal form (PNF) method is developed to reduce the number of coupling terms in the Hamiltonian and to simplify the dynamics analyses. The PNF method allows one to decouple many unimportant bath modes as well as the reactive mode from the system by assessing the significance of the coupling terms. The method is applied to the chemical reaction O({sup 1}D)+N{sub 2}O{yields}NO+NO, which was found to exhibit efficient energy exchange between the two NO stretching modes despite the short lifetime of the reaction intermediate [S. Kawai et al., J. Chem. Phys. 124, 184315 (2006)]. Through the analysis of the two-dimensional PNF Hamiltonian subsystem, it is found that the motion of the subsystem preserves the 'normal mode picture' of the symmetric and antisymmetric NO stretching modes despite its high energy. Then the vibrational energy, initially localized in the newly formed NO bond, is transferred to the reactants' NO bond through the beating between the symmetric and antisymmetric stretching modes. The preservation of the normal mode picture and the short period of the beating explain the fast energy exchange between the two NO bonds. This successful application proves that the PNF method can extract the essential small subspace from many-degrees-of-freedom Hamiltonian systems.