Simulation techniques reaction path methods

Classical simulations often lack the crucial insight into the problem, because one cannot simply use the force to characterize all the possible interactions. Fortunately, with decades of development, theoretical calculations have become quite sophisticated for crystals and molecules, although not yet for realistic nanometer-sized materials. For solids, the pseudopotential as well as the full-potential linearized augmented plane-wave (FLAPW) method within the density functional theory are well developed. Modern quantum chemical techniques (Gaussian98 [5] and MOLPRO [6]) are quite efficient to compute the potential surfaces for a given molecule. In order to illustrate those possibilities, we show some of our own results in simulating the reaction path for a segment of the retinal molecule in rhodopsin [7]. 

The Sj 2 reaction, X + RY XR + Y", has been simulated with MC equilibrium calculations by Jorgensen and coworkers [81, 82]. The procedure used by these authors involves three steps i) the lowest energy reaction path is determined for the in vacuo system by using ab initio molecular orbital calculations ii) inter-molecular potential functions are obtained to describe the interactions between the substrate and a solvent molecule these potentials depend on the internal structure of the substrate iii) MC simulations are carried out to determine the free energy profile for the reaction in solution. This is a difficult computational task since importance sampling methods are required to explore all the values of the reaction coordinate. A similar technique was used by Madura and Jorgensen [83] in simulating the nucleophilic addition of hydroxide ion to formaldehyde in the gas phase and in aqueous solution. 

In atomic scale simulations, there is often a clear separation of timescales. The rate of rare events, e.g., chemical reactions, in a system coupled to a heat bath can be estimated by evaluating the free energy barriers for the transitions. Transition State Theory (TST) [9] is the foundation for this approach. Due to the large difference in time scale between atomic vibrations and typical thermally induced processes such as chemical reactions or diffusion, this would require immense computational power to directly simulate dynamical trajectories for a sufficient period of time to include these rare events. Identification of transition states is often the critical step in assessing rates of chemical reactions and path techniques like the nudged elastic band method is often used to identify these states [10-12,109]. 

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