Bowl breakout, escaping the positive region when searching for saddle points

TL;DR

This paper introduces an improved minimum-mode following method that confines atomic displacements to enhance saddle point searches, reducing force calls and increasing robustness in finding connected saddle points.

Contribution

The proposed scheme confines atomic displacements to the largest force subset, improving efficiency and robustness of saddle point searches compared to traditional methods.

Findings

Reduces force calls by a factor of two or more.

Obtains a wider distribution of low barrier saddle points.

Enhances robustness and reduces dependency on initial conditions.

Abstract

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.