The Energy Gap as a Universal Reaction Coordinate for the Simulation of Chemical Reactions

The selection of a proper reaction coordinate is a major bottleneck in simulations of chemical reactions in complex systems. Increasing the number of variables that are used to bias the reaction largely affects the convergence and leads to an unbearable increase in computational price. This problem can be overcome by employing a complex reaction coordinate that depends on many geometrical variables of the system, such as the energy gap (EGAP) in the empirical valence bond (EVB) method. EGAP depends on all of the coordinates of the system, and its robustness has been demonstrated for a variety of enzymatic reactions. In this work, we demonstrate that EGAP, derived from a classical representation, can be used as a reaction coordinate in systems described with any quantum chemistry Hamiltonian. Benefits of using EGAP as a reaction coordinate as compared to a traditional geometrical variable are illustrated in the case of a symmetric nucleophilic substitution reaction in water solution. EGAP is shown to provide a significantly more efficient sampling and allows a better localization of the transition state as compared to a geometrical reaction coordinate.