Once a good approximation to the minimum energy pathway is obtained, e.g., with the help of an interpolation algorithm such as the growing string method, local surface walking algorithms can be used to determine the exact location of the saddle point. Baker’s P-RFO method,Baker:1986 using either an approximate or an exact Hessian, has proven to be a very powerful for this purpose, but does require calculation of a full Hessian matrix.
The dimer method,Henkelman:1999 on the other hand, is a mode-following algorithm that requires only the curvature along one direction in configuration space, rather than the full Hessian, which can be accomplished using only gradient evaluations. This method is thus especially attractive for large systems where a full Hessian calculation might be prohibitively expensive, or for saddle-point searches where the initial guess is such that the eigenvector of corresponding to the smallest Hessian eigenvalue does not correspond to the desired reaction coordinate. An improved version of the original dimer methodHeyden:2005a, Heyden:2005b has been implemented in Q-Chem, which significantly reduces the influence of numerical noise and thus significantly reduces the cost of the algorithm.