Intramolecular Dynamics: Regular and Stochastic Vibrational States of Molecules

The nature of molecular vibrational states at low and high energies has been studied both classically and quantum mechanically. At low energies the classical vibrational motion is highly "regular" (quasi-periodic) in the usual harmonic normal mode regime. Interestingly enough, it can still remain so when the motion is anharmonic. However, at high enough vibrational energies numerical calculations indicate that the classical mechanical motion usually becomes chaotic (frequently termed "stochastic") although still deterministic, of course. The corresponding quantum mechanical behavior is discussed using semi-classical ideas, and a method of calculating eigenvalues in the quasi-periodic regime is described. A definition of quantum stochasticity is proposed in terms of overlapping avoided crossings in quantum mechanical eigenvalue versus perturbation parameter plots. Some implications for phenomena such as intramolecular relaxation, spectra, unimolecular reactions, and infrared multiphoton dissociation of molecules are described