Eigenstate-resolved unimolecular reaction dynamics: Ergodic character of S formaldehyde at the dissociation threshold

Abstract

The Stark level‐crossing spectra of S₀ D₂CO are analyzed for evidence of energy level correlations and quantum ergodicity. The analysis for short and long range level correlations gives an apparent energy level spacing distribution which lies between the Poisson and GOE limits. However, the Stark level‐crossing method diminishes any existing correlations. The true level spacing distribution must be closer to the Gaussian orthogonal ensemble (GOE) than to the Poisson limit. Complete distributions of S₁−S₀ coupling matrix elements and S₀ dissociation rates are reported and subjected to statistical tests for ergodicity. The distribution of S₁−S₀ coupling matrix elements indicates that the dynamics of intramolecular vibrational redistribution of energy (IVR) is very nearly quantum ergodic. There is strong coupling and free flow of energy among vibrational degrees of freedom in this molecule above its dissociation threshold. The average S₀ decay rate can be accounted for by RRKM theory with tunneling corrections. The large variation about the average is interpreted as quantum statistical fluctuations. These fluctuations serve as a probe of the transition state. The existence of several open decay channels is inferred, and the presence of a low frequency vibrational motion near the transition state geometry is suggested. The distribution of coupling matrix element phase angles is derived from lineshape asymmetries which arise from interfering decay channels. The phase angle distribution is shown to be consistent with the matrix element and decay rate distributions, thereby providing an independent verification of these quantities. All of these distributions are quantitatively consistent with the hypothesis that the wavefunction coefficients of the molecular eigenstates of S₀ D₂CO at its dissociation threshold are Gaussian random when projected onto the eigenfunctions of a separable Hamiltonian.