Hamilton–Jacobi equation, reaction action surface and the emergence of the force concept in chemical reaction dynamics

A combination of Hamilton–Jacobi equation and fast marching algorithm can be used to study reaction dynamics by converting the potential energy surface to a reaction action surface. The reaction action surface has been found to be an important tool in theoretical chemistry, allowing us to provide a different force-based perspective of chemical reactions. Several properties such as reaction force, reaction force surface, reaction path force and reaction path force constant have been defined and calculated by using the reaction action surface. This paper investigates these newly defined properties in order to understand the role they play in chemical reaction with reference to a model 4-well potential energy surface.