Spring pair method of finding saddle points using the minimum energy path as a compass.

Area of Science:

• Computational chemistry
• Materials science
• Statistical mechanics

Background:

• Locating index-1 saddle points is essential for understanding chemical reaction pathways and phase transitions.
• Traditional methods often rely on Hessian matrix calculations, which can be computationally expensive and prone to failure.

Purpose of the Study:

• To introduce a novel, efficient, and Hessian-independent method for accurately locating index-1 saddle points.
• To provide a reliable alternative to existing saddle point finding algorithms.

Main Methods:

• The proposed spring pair method (SPM) uses a pair of spring-coupled particles on an energy surface.
• It employs gradient decomposition to design complementary drifting and climbing dynamics.
• The method evolves the particle pair without requiring Hessian information.

Main Results:

• The spring pair converges to the minimum energy path (MEP) and aligns with its tangent.
• SPM provides a reliable ascent direction for efficient saddle point convergence.
• The method was validated on various systems, including Lennard-Jones and Morse clusters, water clusters, and the Landau energy functional.

Conclusions:

• The spring pair method (SPM) is a simple, efficient, and robust approach for finding saddle points.
• SPM offers significant advantages over traditional Hessian-dependent methods, particularly in avoiding convergence failures.
• The method's applicability is demonstrated across diverse chemical and physical systems.