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,^{46} 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,^{365} 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
method^{376, 375} has been implemented in Q-Chem, which
significantly reduces the influence of numerical noise and thus significantly
reduces the cost of the algorithm.