Ridge method for finding saddle points on potential energy surfaces

A new method is proposed for locating saddle points on potential energy surfaces. The method involves walking on the ridge separating reactants' and products' valleys toward its minimum, which is a saddle point in coordinate space. Of particular advantage for ab initio calculations, the ridge method does not require evaluation of second derivatives of the potential energy. Another important feature of the method is that no assumptions about the transition state geometry are needed, and it is easy to impose linear constraints on the molecular structure. The ridge method is supplemented by a heuristic detour algorithm, which enables one to deal with unfortunate choices of reactants' and products' coordinates. Both algorithms are illustrated by several examples where the complexity of the potential energy surface ranges from a simple analytical formula to a numerical many-body ab initio potential.