Statistical properties of molecular spectra and molecular dynamics: Analysis of their correspondence in NO2 and C2H+4

Correspondence between the spectral statistics and classical dynamics of NO2 and C2H+4 is investigated. Particular focus is given to the role of the lower of the two coupled adiabatic surfaces on the dynamics and level statistics, which is found to yield the main contribution to the level statistics of NO2 and C2H+4. The specific features of the potential surfaces characterizing each molecule that contribute to their spectral and dynamical properties are identified. Classical dynamics simulations run on the lower adiabatic surface correspond closely with results of the statistical analysis of the energy levels on this surface: The correspondence sought between the phase space fraction that is chaotic, qcl, and parameter q determined by the level statistics, is confirmed in our analysis. The classical analysis moreover reveals qualitatively distinct trends in the relation between qcl and the total energy of each molecule, the cause of which is investigated in detail. Classical simulations are also carried out on the coupled-surface potential using the Meyer–Miller analog Hamiltonian, from which comparisons with level statistics of the corresponding Hamiltonian are drawn. The effect of surface coupling is to enhance q by about 10% for NO2 and by about 30% for the less chaotic C2H+4.