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Intramolecular vibrational energy redistribution (IVR) impacts the dynamicsof reactions in a profound way. Theoretical and experimental studies areincreasingly indicating that accounting for the finite rate of energy flow iscritical for uncovering the correct reaction mechanisms and calculatingaccurate rates. This requires an explicit understanding of the influence andinterplay of the various anharmonic (Fermi) resonances that lead to thecoupling of the vibrational modes. In this regard, the local random matrixtheory (LRMT) and the related Bose-statistics triangle rule (BSTR) model haveemerged as a powerful and predictive quantum theories for IVR. In thisPerspective we highlight the close correspondence between LRMT and theclassical phase space perspective on IVR, primarily using model Hamiltonianswith three degrees of freedom. Our purpose for this is threefold. First, thisclearly brings out the extent to which IVR pathways are essentially classical,and hence crucial towards attempts to control IVR. Second, given that LRMT andBSTR are designed to be applicable for large molecules, the exquisitecorrespondence observed even for small molecules allows for insights into thequantum ergodicity transition. Third, we showcase the power of modern nonlineardynamics methods in analysing high dimensional phase spaces, thereby extendingthe deep insights into IVR that were earlier gained for systems witheffectively two degrees of freedom. We begin with a brief overview of recentexamples where IVR plays an important role and conclude by mentioning theoutstanding problems and the potential connections to issues of interest inother fields.

Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective