A Quadratically-Converging Nudged Elastic Band Optimizer.

Area of Science:

• Computational Chemistry
• Materials Science
• Chemical Physics

Background:

• The nudged elastic band (NEB) method is a standard technique for determining minimum energy pathways in configuration space.
• Current NEB algorithms often exhibit slow convergence, limiting their practical application.

Purpose of the Study:

• To enhance the convergence speed of the NEB method.
• To introduce a more efficient optimization strategy for locating minimum energy paths.

Main Methods:

• Derivation of the analytic derivative of the NEB force.
• Implementation of a full Newton-Raphson optimization incorporating the analytic derivative.
• Development of an efficient algorithm to remove translational and rotational components for molecular systems.
• Inclusion of a strategy to reverse Newton-Raphson steps that increase the NEB force.

Main Results:

• Achieved quadratic convergence for the NEB optimization.
• Demonstrated the effectiveness of the new method on analytic two-dimensional potentials.
• Validated the approach on a system of Lennard-Jones particles.

Conclusions:

• The developed analytic derivative and Newton-Raphson optimization significantly accelerate NEB calculations.
• This improved method offers a more efficient way to find minimum energy paths, particularly for molecular systems.
• The findings pave the way for faster exploration of reaction mechanisms and material phase transitions.