Constrained Structure Minimizations on Hyperspheres for Minimum Energy Path Following

In this work, a reliable and robust trust region method for restricted minimizations on hyperspheres is developed. The working equations of this new methodology are presented, together with their validation. The performance and characteristics of this new algorithm are discussed by a constrained minimization on a sphere using a two-dimensional Quapp model surface. The obtained results show that the proposed method for minimizations on hyperspheres guarantees convergence to constrained minima. Its enhanced numerical stability permits tight convergence criteria for constrained minimizations. The application of the new restricted minimizer in the framework of the hierarchical transition state finder and for the calculation of intrinsic reaction coordinates for 38 chemical reactions demonstrates its robustness and efficiency.