Potential energy surfaces statistical kinetic models

A simplified approach is statistical rate theory (transition state theory) with the help of which the overall rate constant k(T) may be obtained from potential energy surface (PES) in a single jump averaging out all of the intermediate details. It is generally not possible to extract microscopic details such as energy-dependent cross sections from conventional kinetics experiments. The preferable approach is to calculate microscopic quantities from some model and then perform the downward averaging for comparison with measured quantities. 

Statistical models are widely exploited in kinetic studies and their usefulness certainly does not need any further proof. Nevertheless, the good agreement between average quantum mechanical and statistical rates, calculated for real molecules, as opposed to model systems, and for the same potential energy surfaces, found in the studies over the past decade may convince even the few non-believers. 

Simultaneously with the development of the Kinetic Model, the appKcation of statistical mechanics provided the basis for the Statistical Mechanics Model. Here a chemical reaction was viewed as the motion of a point in phase space, the co-ordinates of which were the distances between the molecules and their momentum. The expression for reaction rate was thus obtained from the passage of systems through the col point of the potential energy surface. 

Additional work needs to be done to develop a theoretical model to represent the trimethylene kinetics. The dynamics in the trimethylene region of the potential energy surface is neither statistical nor direct, and instead contains both these elements. Future work on the kinetics of cyclopropane stereomutation will include developing a theoretical model for trimethylene s dynamics, assessing the accuracy of assuming RRKM dynamics for cyclopropane, and determining a more accurate PES for trimethylene. 

Many desorption experiments have now shown v values which are well away from the kT/h value. The desorption of CO from Ru 001 [341] gave i 1015s-1. This prompted Ibach et al. [342] to investigate the CO/Ni lll system and they pointed out that a value of 1013 s-1 can only be expected if the adsorbate is mobile and has free rotation or has states of low excitation energy. The model they used to elucidate the kinetics was a modification of an earlier theoretical treatment derived by Landau and Lifshitz [343]. It is to be expected that the chemical potentials of gas phase and adsorbed species will be equal (/ua = pg). From Fermi statistics, the probability of site occupation on the surface is... 

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