A generalized recipe to construct elementary or multi-step reaction paths via a stochastic formulation: Application to the conformational change in noble gas clusters

Highlights: • We demonstrate a general strategy to map out reaction paths irrespective of the number of kinetic steps involved. • The objective function proposed does not need the information of gradient norm and eigenvalue of Hessian matrix explicitly. • A stochastic optimizer Simulated Annealing is used in searching reaction path. • The strategy is applied in mapping out the path for conformational changes in pure Ar clusters and Ar_NXe mixed clusters. - abstract: In this paper we demonstrate a general strategy to map out reaction paths irrespective of the number of kinetic steps required to bring about the change. i.e., whether the transformation takes place in a single step or in multiple steps with the appearance of intermediates. The objective function proposed is unique and works equally well for a concerted or a multiple step pathway. As the objective function proposed does not explicitly involves the calculation of the gradient of the potential energy function or the eigenvalues of the Hessian Matrix during the iterative process, the calculation is computationally economical. To map out the reaction path, we cast the entire problem as one of optimization and the solution is done with the use of the stochastic optimizer Simulated Annealing. The formalism is tested on Argon clusters (Ar_N) and Argon clusters singly doped with Xenon (Ar_N-1Xe). The size of the systems for which the method is applied ranges from N=7-25, where N is the total number of atoms in the cluster. We also test the results obtained by us by comparing with an established gradient only method. Moreover to demonstrate that our strategy can overcome the standard problems of drag method, we apply our strategy to a two dimensional LEPS + harmonic oscillator Potential to locate the TS, in which standard drag method has been seen to encounter problems