Intramolecular Dynamics Statistical Theories

4 Intramolecular Dynamics Statistical Theories In sections A—7 we review theoretical and experimental work related to the internal dynamics in unimolecular reactions as opposed to collisional energy transfer. 

In unimolecular fragmentation reactions we have coupling of quasi-bound or resonance scattering states to dissociation continua, considering the fragments as part of a single supermolecule [equation (34)]. A are highly excited, metastable 

Assuming exponential decay of A with specific rate constants (j) for the metastabk states j , one gets a genoal averaged rate omstant with populations [see equation (31)]  

In the high-pressure limit of thermal unimolecular reactions (Section 7) one has Boltzmann populations/(j) of excited states  

Molecular Collision Theory, Acsdmic Press, London, 1974. 

---

Shalashilin and Thompson [46-48] developed a method based on classical diffusion theory for calculating unimolecular reaction rates in the IVR-limited regime. This method, which they referred to as intramolecular dynamics diffusion theory (IDDT) requires the calculation of short-time ( fs) classical trajectories to determine the rate of energy transfer from the bath modes of the molecule to the reaction coordinate modes. This method, in conjunction with MCVTST, spans the full energy range from the statistical to the dynamical limits. It in essence provides a means of accurately... 

This hnding concerning quantum transport in classically chaotic systems sheds new light on quantum effects in unimolecular reaction dynamics. For example, one expects that intramolecular bottlenecks associated with canton, if treated quantum mechanically, would be more effective than in a classical statistical theory even when nh is smaller than the reaction flux crossing the intramolecular dividing surface. Clearly, it would be interesting to examine realistic molecular systems in a similar fashion. 

S. A. Rice, Overview of the dynamics of intramolecular transfer of vibrational energy, Adv. Chem. Phys. 47 117 (1981) P. Brumer, Intramolecular energy transfer theory for the onset of statistical behavior, Adv. Chem. Phys. 47 202 (1981) P. Brumer and M. Shapiro, Chaos and reaction dynamics, Adv. Chem. Phys. 70 365 (1988). 

It is important to have knowledge, on the molecular or microscopic level, of the elementary act that occurs during the course of chemical change. Work in this field, referred to as-reaction dynamics or molecular dynamics, deals with the intermolecular and intramolecular motions that occur in a chemical reaction and the quantum states of the reactant and product molecules. There are two main reasons for studying chemical dynamics. One is to test the validity of the statistical theories that were outlined in the preceding section. The other is that there are important applications (e.g., lasers) in which it is necessary to have information about the energy states of products of reaction, information that is not provided by the statistical theories. 

Before considering how the intramolecular dynamics determines the absolute value of the unimolecular reaction rate, and how van der Waals molecules can serve as a vehicle for the study of those intramolecular processes that compete with reaction, we ask if the characteristic features of the fragmentation reactions described in this section can be interpreted using perturbation theory. This approach is at the opposite end of the spectrum from the statistical theory of unimolecular reaction rate, since it focuses attention on state-to-state transitions. We shall see that such an analysis has some successes and some failures. 

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... 

Given the prominence of statistical theories in chemical reaction dynamics and kinetics, it was natural to use these theories in modeling studies of Sn2 reactions. However, more recent detailed examinations of Sn2 reactions of the type in reaction [83] have discovered a range of important nonstatistical attributes, arising from weak couplings between the X ---CH3Y intermolecular modes and CH3Y intramolecular modes. A particularly important feature of this work has been a close relationship between computational, experimental,and theoretical studies.The computational studies include quantum-dynamical and full-dimensional trajectory calculations. 

So far we have discussed statistical and dynamical theories that have largely been based on a quadratic expansion of the PES about the reaction path (albeit with a limited account of anharmonicity in some vibrational modes). Still within that same spirit, very anharmonic vibrations such as intramolecular hindered rotations (torsional motion) have been treated more realistically [56,110,138]. However, in many... 

In liquids and dense gases where collisions, intramolecular molecular motions and energy relaxation occur on the picosecond timescales, spectroscopic lineshape studies in the frequency domain were for a long time the principle source of dynamical information on the equilibrium state of manybody systems. These interpretations were based on the scattering of incident radiation as a consequence of molecular motion such as vibration, rotation and translation. Spectroscopic lineshape analyses were intepreted through arguments based on the fluctuation-dissipation theorem and linear response theory (9,10). In generating details of the dynamics of molecules, this approach relies on FT techniques, but the statistical physics depends on the fact that the radiation probe is only weakly coupled to the system. If the pertubation does not disturb the system from its equilibrium properties, then linear response theory allows one to evaluate the response in terms of the time correlation functions (TCF) of the equilibrium state. Since each spectroscopic technique probes the expectation value... 

---