Finding transition states using reduced potential-energy surfaces

We propose a method to locate saddle points that is based on the interplay between the driving coordinate and the restricted quasi-Newton algorithm, The method locates the transition state using a reduced potential-energy surface. The reduced potential-energy surface is characterized by the set of driving coordinates. The proposed algorithm starts at a point on the surface that is slightly perturbed from either reactant or product and, in principle, converges to the transition state. Finally we give a special type of update Hessian matrix formula that should be applied in optimizations carried out on reduced potential-energy surfaces.