Path Integral Calculation of Quantum Nonadiabatic Rates in Model Condensed Phase Reactions

1996 ◽  
Vol 100 (11) ◽  
pp. 4430-4436 ◽  
Author(s):  
Maria Topaler ◽  
Nancy Makri
Keyword(s):  
Path Integral ◽  
Condensed Phase ◽  
Condensed Phase Reactions

Chemical Reactions In Condensed Phases

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Chemical Reactions ◽  
Condensed Phase ◽  
Chemical Change ◽  
Classical Mechanics ◽  
Chemical System ◽  
Condensed Phases ◽  
Molecular Configuration ◽  
Middle Stage ◽  
Condensed Phase Reactions ◽  
Energy Surfaces

Understanding chemical reactions in condensed phases is essentially the understanding of solvent effects on chemical processes. Such effects appear in many ways. Some stem from equilibrium properties, for example, solvation energies and free energy surfaces. Others result from dynamical phenomena: solvent effect on diffusion of reactants toward each other, dynamical cage effects, solvent-induced energy accumulation and relaxation, and suppression of dynamical change in molecular configuration by solvent induced friction. In attempting to sort out these different effects it is useful to note that a chemical reaction proceeds by two principal dynamical processes that appear in three stages. In the first and last stages the reactants are brought together and products are separated from each other. In the middle stage the assembled chemical system undergoes the structural/chemical change. In a condensed phase the first and last stages involve diffusion, sometimes (e.g. when the species involved are charged) in a force field. The middle stage often involves the crossing of a potential barrier. When the barrier is high the latter process is rate-determining. In unimolecular reactions the species that undergoes the chemical change is already assembled and only the barrier crossing process is relevant. On the other hand, in bi-molecular reactions with low barrier (of order kBT or less), the rate may be dominated by the diffusion process that brings the reactants together. It is therefore meaningful to discuss these two ingredients of chemical rate processes separately. Most of the discussion in this chapter is based on a classical mechanics description of chemical reactions. Such classical pictures are relevant to many condensed phase reactions at and above room temperature and, as we shall see, can be generalized when needed to take into account the discrete nature of molecular states. In some situations quantum effects dominate and need to be treated explicitly. This is the case, for example, when tunneling is a rate determining process. Another important class is nonadiabatic reactions, where the rate determining process is hopping (curve crossing) between two electronic states. Such reactions are discussed in Chapter 16.

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