Transition path ensemble kinetics

Finally, in Sect. 7.6, we have discussed how various free energy calculation methods can be applied to determine free energies of ensembles of pathways rather than ensembles of trajectories. In the transition path sampling framework such path free energies are related to the time correlation function from which rate constants can be extracted. Thus, free energy methods can be used to study the kinetics of rare transitions between stable states such as chemical reactions, phase transitions of condensed materials or biomolecular isomerizations. 

In analogy with the results of theoretical calculations on the dissociation path of CO on rhodium by De Koster and Van Santen [53], we visualize the rupture of the N-O bond as sketched in Fig. 5.12. Starting from a threefold position, the adsorbed NO molecule bends across a rhodium atom to the next threefold site. By stretching over the central rhodium atom, the antibonding NO orbitals have a strong interaction with the Rh d-orbitals, and the N-O bond is efficiently weakened. The picture implies that NO requires an ensemble of at least five atoms on the (111) surface of an fee transition metal in order to dissociate. This is in fair agreement with kinetic modelling, which indicates that three to four NO adsorption sites must be invoked to obtain realistic kinetic parameters [52]. 

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