Potential barriers, chemical reaction dynamics

Theory may play two particularly important roles in rationalizing and predicting chemical reaction dynamics. As noted in the last section, the first step to understanding the dynamical behavior of a complex chemical system is breaking down the overall system into its constituent elementary processes. From a theoretical standpoint, the likely importance of various processes may be qualitatively assessed from the potential energy surfaces of putative reactions. Reactions with very high barriers will be less likely to play an important role, while low-barrier reactions will be more likely to do so. 

GH Theory was originally developed to describe chemical reactions in solution involving a classical nuclear solute reactive coordinate x. The identity of x will depend of course on the reaction type, i.e., it will be a separation coordinate in an SnI unimolecular ionization and an asymmetric stretch in anSN2 displacement reaction. To begin our considerations, we can picture a reaction free energy profile in the solute reactive coordinate x calculated via the potential of mean force Geq(x) -the system free energy when the system is equilibrated at each fixed value of x, which would be the output of e.g. equilibrium Monte Carlo or Molecular Dynamics calculations [25] or equilibrium integral equation methods [26], Attention then focusses on the barrier top in this profile, located at x. ... 

The knowledge of the two-minima energy surface is sufficient theoretically to determine the microscopic and static rate of reaction of a charge transfer in relation to a geometric variation of the molecule. In practice, the experimental study of the charge-transfer reactions in solution leads to a macroscopic reaction rate that characterizes the dynamics of the intramolecular motion of the solute molecule within the environment of the solvent molecules. Stochastic chemical reaction models restricted to the one-dimensional case are commonly used to establish the dynamical description. Therefore, it is of importance to recall (1) the fundamental properties of the stochastic processes under the Markov assumption that found the analysis of the unimolecular reaction dynamics and the Langevin-Fokker-Planck method, (2) the conditions of validity of the well-known Kramers results and their extension to the non-Markovian effects, and (3) the situation of a reaction in the absence of a potential barrier. 

If the metadynamics method is applied to the simulation of chemical reactions in conjunction with Car-Parrinello molecular dynamics [36,40,49], the history dependent potential has to force the system to cross barriers of several tenths of kcal/mol in a very short time, usually a few picoseconds. This implies that a lot of energy is injected in the degrees of freedom associated with the collective variables. This might lead to a significant dishomogeneity in the temperature distribution of the system, and possibly to instabilities in the dynamics. 

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