Exploring Potential Energy Surface with Mathematica: An Algorithmic Demonstration of Minimum Energy Path, Stationary Points and Transition State

The reaction profile (energy profile) is a widely used conceptual tool in chemical kinetics to represent the progress of a chemical reaction. Quantitatively, a reaction profile can be viewed as a minimum energy path (MEP) on the potential energy surface (PES), which connects the reactants and products through one or more transition states or intermediates. In this article, we used Mathematica program to demonstrate a generic method for finding reaction profile on a Müller-Brown PES by applying steepest descent algorithm. The properties of the MEP and stationary points were discussed in detail. The general characteristics of the transition state (TS), and imaginary mode were illustrated with a vibrational analysis of hydrogen exchange reaction, H2+H → H+H2.