Barnes Update Applied in the Gauss-Newton Method: An Improved Algorithm to Locate Bond Breaking Points

Area of Science:

• Computational Chemistry
• Mechanochemistry
• Chemical Physics

Background:

• Mechanochemical reactions are initiated by mechanical energy, often modeled as perturbations to potential energy surfaces (PES).
• Optimal bond breaking points (BBPs) are critical on the PES, where the Hessian matrix's zero eigenvector aligns with the gradient, indicating optimal force application.

Purpose of the Study:

• To develop a novel, efficient algorithm for locating optimal bond breaking points (BBPs) in molecular systems.
• To improve upon existing methods for identifying critical points in mechanochemical reactions.

Main Methods:

• The proposed algorithm combines the Gauss-Newton method with the Barnes update for handling nonsymmetric Jacobian matrices.
• This approach is presented as an improvement over the Broyden update for BBP localization.

Main Results:

• The new algorithm's efficiency is demonstrated on a multidimensional model potential energy surface (PES).
• The method's effectiveness is further validated using two medium-sized molecular systems relevant to enzymatic catalysis and mechanochemistry.

Conclusions:

• The developed Gauss-Newton-based algorithm provides an efficient means to locate optimal bond breaking points (BBPs).
• This method facilitates the understanding and harnessing of tensile forces for inducing mechanochemical reactions, transforming them into barrierless processes.