How vibrational energy flows in molecules has recently become much better understood through the joint efforts of theory, experiment, and computation. The phenomenology of energy flow is much richer than earlier thought. We now know energy flow depends on the local structure of molecular vibrational state space. The details of the theoretically predicted transition from localized vibrations to free flow, where the molecule can act as its own heat bath, are now well-established experimentally. Energy flow is a quantum diffusive process leading to nonexponential decays, also seen in experiment. The slowness of energy flow in activated molecules causes substantial deviation from statistical Rice-Ramsperger-Kassel-Marcus (RRKM) theories for low barrier rate processes, such as isomerization. Quantitative calculations of rates in those cases are now possible.
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