Computational simulation to determine the optimal energy requirement in a process using the improved and simplified string method

In this work we determined computationally the optimal energy requirement to carry a bimolecular substitution nucleophilic reaction (Sn2) from chloromethane to fluoromethane in gas phase and in aqueous solution (implicit solvent by means of a dielectric constant) using the simplified and improved string method [1]. This numerical method allows the determination of the minimum energy path, using a string to link two states separated by a transition or barrier. The string is discretized in a certain number of points (images) and is optimized using a differential equation integration method, the fourth order Runge Kutta, in order for the total force along the string or curve to be minimized, subject to the restriction that the images need to be spaced evenly along the curve. This restriction is enforced by carrying continuously a cubic spline interpolation in order to distribute the images uniformly around the new curve or string obtained. The forces and energies along the string in each image were obtained with the Gaussian 09 software by means of constructing a FORTRAN 90-Gaussian 09 [2] interface, in order to solve a multidimensional constrained optimization problem. By obtaining the minimum energy path in complex dynamical process, it is possible to determine the optimal energy requirements, with industrial applications, in order to produce purer compounds, eliminating secondary products, at lower cost, and the reduction of contaminants and wastes, designing cleaner processes and fostering the implementation of green technologies. The minimum energy paths obtained in this work compared favorably with those published in the literature employing computationally costly QM/MM techniques [3].