Bowl breakout, escaping the positive region when searching for saddle   points
  We present a scheme improving the minimum-mode following method for finding first order saddle points by confining the displacements of atoms to the subset of those subject to the largest force. By doing so it is ensured that the displacement remains of a local character within regions where all eigenvalues of the Hessian matrix are positive. However, as soon as a region is entered where an eigenvalue turns negative all atoms are released to maintain the ability of determining concerted moves. Applying the proposed scheme reduces the required number of force calls for the determination of connected saddle points by a factor two or more compared to a free search. Furthermore, a wider distribution of the relevant low barrier saddle points is obtained. Finally, the dependency on the initial distortion and the applied maximal step size is reduced making minimum-mode guided searches both more robust and applicable. 
Andreas Pedersen and Mathieu Luiser
cond-mat.mtrl-sci physics.comp-ph