A method for finding the ridge between saddle points applied to rare event rate estimates

Area of Science:

• Materials Science
• Computational Chemistry
• Surface Science

Background:

• Atomic scale systems exhibit complex energy surfaces governing material properties and reactions.
• Understanding atomic rearrangement mechanisms is crucial for catalysis, diffusion, and material design.
• The harmonic approximation to transition state theory (TST) is widely used but has limitations.

Purpose of the Study:

• To develop a novel method for identifying the ridge between first-order saddle points on multidimensional energy surfaces.
• To assess the validity of the harmonic approximation in transition state theory.
• To discover new atomic transition mechanisms and minima along reaction pathways.

Main Methods:

• A string method using discretised points along a path between saddle points.
• Iterative optimization requiring only atomic forces.
• Inversion of forces along unstable eigenmodes perpendicular to the path.
• Application to Al adatom diffusion on Al(100) surface.

Main Results:

• Successfully identified ridges between various concerted displacement and hop mechanisms for Al adatom diffusion.
• Provided a means to test the harmonic approximation by analyzing saddle point heights along the ridge.
• Discovered new minima along the ridge, indicating additional transition mechanisms.
• Estimated corrections to the harmonic approximation of TST.

Conclusions:

• The developed method effectively characterizes ridges between saddle points, crucial for understanding atomic rearrangements.
• This technique enhances the reliability of transition state theory by providing a way to validate its approximations.
• The identification of new minima opens avenues for discovering previously unknown reaction pathways in atomic systems.