A constrained reduced-dimensionality search algorithm to follow chemical reactions on potential energy surfaces

A constrained reduced-dimensionality algorithm can be used to efficiently locate transition states and products in reactions involving conformational changes. The search path (SP) is constructed stepwise from linear combinations of a small set of manually chosen internal coordinates, namely the predictors. The majority of the internal coordinates, the correctors, are optimized at every step of the SP to minimize the total energy of the system so that the path becomes a minimum energy path connecting products and transition states with the reactants. Problems arise when the set of predictors needs to include weak coordinates, for example, dihedral angles, as well as strong ones such as bond distances. Two principal constraining methods for the weak coordinates are proposed to mend this situation: static and dynamic constraints. Dynamic constraints are automatically activated and revoked depending on the state of the weak coordinates among the predictors, while static ones require preset control factors and act permanently. All these methods enable the successful application (4 reactions are presented involving cyclohexane, alanine dipeptide, trimethylsulfonium chloride, and azafulvene) of the reduced dimensionality method to reactions where the reaction path covers large conformational changes in addition to the formation/breaking of chemical bonds. Dynamic constraints are found to be the most efficient method as they require neither additional information about the geometry of the transition state nor fine tuning of control parameters.