Intramolecular vibrational energy classical dynamics

If the unimolecular dissociation is not random and not in accord with Eq. (2.2) it is thought that classical bottlenecks restricting intramolecular vibrational-energy redistribution (IVR) may be manifested in the quantum dynamics [16]. Thus, there is considerable interest in identifying the nature of the unimolecular dynamics of excited molecules. In this section Monte... 

Dynaniical theories of unimolecuiar decomposition deal with the properties of vibrational/rotational energy levels, state preparation and intramolecular vibrational energy redistribution (IVR). Thus, the presentation in this chapter draws extensively on the previous chapters 2 and 4. Unimolecuiar decomposition d)mamics can be treated using quantum and classical mechanics, and both perspectives are considered here. The role of nonadiabatic electronic transitions in unimolecuiar dynamics is also discussed. 

Of course, a proper description of the fragmentation of a van der Waals molecule must be based on quantum mechanics and must account for the competition between intramolecular vibrational energy redistribution and reaction. However, approximate statistical theories of the reaction rate based on classical mechanics can be very useful in the construction of a physical picture of the relevant molecular dynamics. For that reason we examine how the classical mechanical theory of... 

The first classical trajectory study of iinimoleciilar decomposition and intramolecular motion for realistic anhannonic molecular Hamiltonians was perfonned by Bunker [12,13], Both intrinsic RRKM and non-RRKM dynamics was observed in these studies. Since this pioneering work, there have been numerous additional studies [9,k7,30,M,M, ai d from which two distinct types of intramolecular motion, chaotic and quasiperiodic [14], have been identified. Both are depicted in figure A3,12,7. Chaotic vibrational motion is not regular as predicted by tire nonnal-mode model and, instead, there is energy transfer between the modes. If all the modes of the molecule participate in the chaotic motion and energy flow is sufficiently rapid, an initial microcanonical ensemble is maintained as the molecule dissociates and RRKM behaviour is observed [9], For non-random excitation initial apparent non-RRKM behaviour is observed, but at longer times a microcanonical ensemble of states is fonned and the probability of decomposition becomes that of RRKM theory. 

Shirts R B and Reinhardt W P 1982 Approximate constants of motion for classically chaotic vibrational dynamics vague tori, semiclassical quantization, and classical intramolecular energy flow J. Cham. Phys. 77 5204-17... 

It is worth mentioning that Davis and Gray also found that at low energy, for example, when I2 is initially in a vibrational state with v < 5, no classical dissociation occurs. Furthermore, if I2 is initially in a vibrational state with 20 > V > 5, the dynamics appears to be so complicated that including only one intramolecular bottleneck does not suffice. Indeed, in the case of v = 10 Davis and Gray used two intramolecular bottlenecks to model the Hel2 fragmentation reaction. The two bottlenecks on a PSS are illustrated in Fig. 17. It is seen that... 

We denote by G the set of all the experimentally observable quantities (called physical observables) which must be reproduced. Such quantities are, for instance, the collision energy, the quantum numbers defining the intramolecular state (vibrations and the principal quantum number of rotation), the total angular momentum etc... However, there are other dynamical variables which have a clear meaning in Classical Mechanics but correspond to no physical observable because of the Uncertainty Principle. We call them phase variables and denote them globally by g. The phase variables must be given particular values to obtain, at given G, a particular trajectory. Such variables are, for instance, the various intramolecular normal vibrational phases, the intermolecular orientation, the secondary rotation quantum numbers, the impact parameter, etc... Thus we look for relationships of the type qo = qq (G, g) and either qo = qo (G, g) or po = Po (G, g)... 

It is common practice in classical computer simulations not to attempt to represent intramolecular bonds by terms in the potential energy function, because these bonds have very high vibration frequencies and should really be treated in a quantum mechanical way rather than in the classical approximation. Instead, the bonds are treated as being constrained to have fixed length, and some straightforward ways have been devised to incorporate these constraints into the dynamics (see later). 

---