title: Tracing the minimum-energy path on the free-energy surface.
abstract: The free-energy profile of a reaction can be estimated in a molecular-dynamics approach by imposing a mechanical constraint along a reaction coordinate (RC). Many recent studies have shown that the temperature can greatly influence the path followed by the reactants. Here, we propose a practical way to construct the minimum-energy path directly on the free-energy surface at a given temperature. First, we follow the blue-moon ensemble method to derive the expression of the free-energy gradient for a given RC. These derivatives are then used to find the actual minimum-energy reaction path at finite temperature, in a way similar to the intrinsic reaction path of Fukui on the potential-energy surface. [K. Fukui, J. Phys. Chem. 74, 4161 (1970)]. Once the path is known, one can calculate the free-energy profile using thermodynamic integration. We also show that the mass-metric correction cancels for many types of constraints, making the procedure easy to use. Finally, the minimum-free-energy path at 300 K for the addition of CCl2 to ethylene is compared with a path based on a simple one-dimensional reaction coordinate. A comparison is also given with the reaction path at 0 K.
authors.affiliation: Laboratoire de Chimie, UMR CNRS 5182, Ecole Normale Supérieure de Lyon, Lyon Cedex 07, France. paul.fleurat-lessard@ens-lyon.fr
authors.forename: Paul
authors.initials: P
authors.lastname: Fleurat-Lessard
authors.forename: Tom
authors.initials: T
authors.lastname: Ziegler
mesh_terms: D000465:Algorithms; D002627:Chemistry, Physical / Q000379:methods*; D003198:Computer Simulation; D003521:Cyclopropanes / Q000737:chemistry; D008956:Models, Chemical; D015233:Models, Statistical; D008962:Models, Theoretical; D008968:Molecular Conformation; D016011:Normal Distribution; D012984:Software; D013696:Temperature; D013816:Thermodynamics
chemical_list: D003521:Cyclopropanes; C030797:cyclopropane