The rotational spectrum of a highly vibrationally mixed quantum state. I. Intramolecular vibrational energy redistribution (IVR) exchange narrowing of the rotational spectrum

Abstract

The description of the rotational spectrum of a single, highly vibrationally mixed molecular eigenstate is given using two formulations. The model studied is a set of anharmonically coupled normal-mode rovibrational states. In the first approach, the rotational problem is cast into the form of the single bright-state model of IVR. This eigenstate-level formulation reveals the fragmentation of the rotational spectrum as the magnitude of the anharmonic coupling is increased. It is also seen that the center frequencies of all of the molecular eigenstate rotational spectra approach the same value, determined by the ensemble average rotational constant, as the IVR rate is increased. Furthermore, this formulation provides a generalization to rotational spectroscopy. When there is extensive state mixing, the center frequency of the pure rotational spectrum of a single molecular eigenstate is determined by the expectation value of the rotational constant, and the width of the spectrum is determined by the quantum mechanical fluctuation of the rotational constant in the molecular eigenstate. The lineshape properties of the spectrum are addressed using the motional (exchange) narrowing formalism for the ensemble spectrum. This formulation provides a quantitative description of the narrowing of the rotational spectrum by an IVR exchange mechanism. Finally, the convergence of the line shape profile of the eigenstate rotational spectrum to the line shape of the ensemble spectrum is investigated using a statistical model Hamiltonian. Convergence is observed when the number of overlapping states, defined as Wrms*ρ, reaches 1. These results show that an experimental measurement of the rotational spectrum of single molecular eigenstates can provide important average properties of the rotational constant distribution, dipole moment distribution, and the IVR rate at a well-defined total energy.