Dynamical bottlenecks, potential energy

The existence of the polyad number as a bottleneck to energy flow on short time scales is potentially important for efforts to control molecnlar reactivity rising advanced laser techniqnes, discussed below in section Al.2.20. Efforts at control seek to intervene in the molecnlar dynamics to prevent the effects of widespread vibrational energy flow, the presence of which is one of the key assumptions of Rice-Ramsperger-Kassel-Marcns (RRKM) and other theories of reaction dynamics [6]. 

A different strategy to approach such problems is to search for the dynamical bottlenecks through which the system passes during a transition between metastable states. If the dynamics of the system is dominated by energetic effects (as opposed to entropic effects), such bottlenecks can be identified with saddle points in the potential energy surface. In this case, saddle points are transition states, activated states from which the system can access different stable states through small fluctuations. Comparing stable states with transition states one can often infer the mechanism of the reaction. Reaction rate constants, which are very important because they are directly comparable to... 

Calculations of reaction rates with variationally determined dynamical bottlenecks and realistic treatments of tunneling require knowledge of an appreciable, but still manageably localized, region of the potential energy surface [33[. In this chapter we assume that such potentials are available or can be modeled or calculated by direct dynamics, and we focus attention on the dynamical methods. 

The value of the transmission coefficient kt is shown for each feature in Table 2. (The value of kt for the last feature is greater than 1 because it includes contributions from higher energy transition states that have not been included in the fit.) Many of the values of the transmission coefficients are very close to unity, suggesting that these features correspond to quantized transition states that are nearly ideal dynamical bottlenecks to the reactive flux. Several of the values of kt deviate from unity this could be the result of the assumption of parabolic effective potential barriers or from recrossing or other multidimensional effects. 

Figure 1.1. Prototypical potential energy surface of a simple system (a) and of a complex system (b). In a simple, low-dimensional system, dynamical bottlenecks for transitions between long-lived stable states most often coincide with saddle points on the potential energy surface. Locating these stationary points reveals the reaction mechanism. In a typical complex system, the potential energy surface is rugged and has countless local minima and saddle points. Nevertheless, there can be well-defined long-lived stable states and rare transitions between them. Such transitions can occur via a multitude of different transition pathways.

The advent of parallel processing raises other interesting possibilities in the dynamics of Van der Waals clusters. In particular, the multidimensional integration bottleneck alluded to in the introduction comprises largely of evaluation of the potential energy at a very large number of... 

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