Energy randomization, intramolecular

Results of the earliest study of this system (20) showed that randomly sampled trajectories reacted through both channels at rates that were slower than expected, with a greater deviation for the C— channel. Excitation biased in favor of C—modes further retarded both C—C and C—reaction channels. These observations led to the conclusion that our classical model molecule was intrinsically non-RRKM. Intramolecular energy randomization was restricted on the time scale of dissociation. C—bonds were the worst offenders. 

Obviously the RRK theory is an over-simplification for intramolecular dynamics.However, it has been found useful in predicting unimolecular decay rates for comparison with both experimental results and other theoretical ones. Nevertheless, the observation of RRK-like decay in the present study does not demonstrate the validity for this system of any of the RRK assumptions, including the assumption of energy randomization. 

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. 

The local conformational preferences of a PE chain are described by more complicated torsion potential energy functions than those in a random walk. The simulation must not only establish the coordinates on the 2nnd lattice of every second carbon atom in the initial configurations of the PE chains, but must also describe the intramolecular short range interactions of these carbon atoms, as well as the contributions to the short-range interactions from that... 

RADIATION-SENSITIVE GROUPS. Although the absorption of radiation energy is dependent only on the electron density of the substrate and therefore occurs spatially at random on a molecular scale, the subsequent chemical changes are not random. Some chemical bonds and groups are particularly sensitive to radiation-induced reactions. They include COOH, C-Hal, -SO2-, NHz, C=C. Spatial specificity of chemical reaction may result from intramolecular or intermolecular migration of energy or of reactive species -free radicals or ions. 

The RIS model with neighbor dependence is used to calculate random-coil dimensions for the e/s-forms of PBD and PIP in the limit of large x. Comparison of calculated and experimental values of the characteristic ratio and its temperature coefficient is used to determine intramolecular energies of various conformational sequences of the chain backbone. 

Intramolecular reactions are favored by entropy. Recall that entropy is a measure of the disorder of a system. It costs energy to put order into a system—to decrease the entropy of that system. In the case of an intermolecular reaction, the nucleophile and the electrophile must first come together from their initial random positions. This requires an increase in the order of the system, an entropically unfavorable process. In the case of an intramolecular reaction, the nucleophile is held in proximity to the electrophile by the connecting carbon chain. It takes a much smaller increase in the order of the system to position the nucleophile for reaction. In other words, the nucleophile is much closer to the electrophile at all times, and attaining the proper orientation required for the reaction is much more probable. 

In order to remove the need for explicit trajectory analysis, one makes the statistical approximation. This approximation can be formulated in a number of equivalent ways. In the microcanonical ensemble, all states are equally probable. Another formulation is that the lifetime of reactant (or intermediate) is random and follows an exponential decay rate. But perhaps the simplest statement is that intramolecular vibrational energy redistribution (IVR) is faster than the reaction rate. IVR implies that if a reactant is prepared with some excited vibrational mode or modes, this excess energy will randomize into all of the vibrational modes prior to converting to product. 

Conformational synmorphism describes the situation in which different conformers of a molecule are distributed randomly throughout the crystal lattice. Such a situation usually exists when two or more conformers have similar overall molecular shapes. Thus at any particular molecular site a number of conformations may be adopted, the relative population being determined by the relative intermolecular and intramolecular energies involved, as in Fig. 5.1(d). 

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