Minimum energy path chain reactions

With the DFTB parameters that we recently developed, direct calculations on nano-scale models can be driven with great efficiency. The minimum energy paths (MEP) of the benzene hydrogenation reactions can be calculated by the nudged elastic band method. As an example, the minimum energy path of the elementary reaction (CeHe + H = CeH ) on a two-fold site of the 1.9 nm MCNP is shown in Fig. 16.12. There are 19 intermediate images on the chain-of-states of the reaction. The corresponding reactant state, transition state (TS), and the product state are presented in Fig. 16.13. 

The procedure and methods for the MEP determination by the NEB and parallel path optimizer methods have been explained in detail elsewhere [25, 27], Briefly, these methods are types of chain of states methods [20, 21, 25, 26, 30, 31]. In these methods the path is represented by a discrete number of images which are optimized to the MEP simultaneously. This parallel optimization is possible since any point on the MEP is a minimum in all directions except for the reaction coordinate, and thus the energy gradient for any point is parallel to the local tangent of the reaction path. 

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