How does vibrational energy flow fill the molecular state space?

The experimental and theoretical evidence suggests that vibrational wave functions at high energy or in large molecules are not mixed to the maximum extent possible. One consequence is that average vibrational survival probabilities slow to a power law decay t^-δ/2 with a small value of δ. An approximate formula is presented for estimating δ from the vibrational Hamiltonian and tested by comparing with wave packet propagations on an experimentally fitted potential surface of SCCl₂ in six degrees of freedom. Characterization of the wave packet by a dispersion parameter D furthermore shows that the state space accessed during vibrational energy flow remains nearly as compact as allowed by the decay law, opening the possibility for coherent control on a low-dimensional manifold embedded in the full vibrational state space.