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 partitioned rational function optimization (P-RFO) method, which utilizes an approximate or exact Hessian, has proven to be a very powerful method for this purpose.

The dimer method [436] on the other hand, is a mode following algorithm that utilizes only the curvature along one direction in configuration space (rather than the full Hessian) and requires only gradient evaluations. It is therefore especially applicable for large systems where a full Hessian calculation is very time consuming, or for saddle point searches where the eigenvector of the lowest Hessian eigenvalue of the starting configuration does not correspond to the reaction coordinate. A recent modification of this method has been developed [437, 438] to significantly reduce the influence of numerical noise, as it is common in quantum chemical methods, on the performance of the dimer algorithm, and to significantly reduce its computational cost. This improved dimer method has recently been implemented within Q-Chem.