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Foundations of Chemical Kinetics Lecture 15: Variational - - PowerPoint PPT Presentation
Foundations of Chemical Kinetics Lecture 15: Variational - - PowerPoint PPT Presentation
Foundations of Chemical Kinetics Lecture 15: Variational transition-state theory and the fate of the products Marc R. Roussel Department of Chemistry and Biochemistry Transition-state dividing surface (TSDS) Recrossing trajectories R BC R AB
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Recrossing trajectories
BC
RAB R
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The transmission coefficient
Suppose that, in the vicinity of the transition state, typical trajectories that cross the TSDS at least once in the reactant to product direction have the following qualitative appearance and frequencies [Truhlar and Garrett, Acc. Chem. Res. 13, 440 (1980)]:
40% 20% 20% 10% 10% TSDS
◮ Standard TST counts all the
reactant-to-product (circled) crossings.
◮ Only the crossings circled in green
should count.
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The transmission coefficient (continued)
40% 20% 20% 10% 10% TSDS
Transmission coefficient = 0.4+ 1 2(0.1) = 0.45
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Variational transition-state theory
◮ There is nothing sacrosanct about the TSDS through and
perpendicular to the saddle point.
◮ We could equally well pick other dividing surfaces.
Basic idea of variational transition-state theory: Vary the TSDS in
- rder to minimize the computed rate constant.
Calculation machinery: Very similar to normal transition-state theory, except that we evaluate the partition function at points other than the saddle point.
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Variational transition-state theory
A possible result
Variational Saddle 5% 20% 75% TSDS TSDS
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Where does the energy accumulated to get to the transition state go?
◮ Since the transition state is higher in energy than either the
reactants or products, the products are not typically in thermal equilibrium when first formed, i.e. they carry excess energy.
◮ Where does this energy go? ◮ Possibilities:
Electronic energy: Only in reactions where the products have low-lying excited states, especially if there is an avoided crossing Translational kinetic energy Rotational kinetic energy Vibrational energy: This possibility can be predicted from the shape of the PES.
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How vibrationally excited products can arise
BC
RAB R
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