Classical Optimal Control for Energy Minimization Based On Diffeomorphic Modulation under...

Area of Science:

• Computational Chemistry
• Chemical Physics
• Optimization Algorithms

Background:

• Global energy minimization is crucial for understanding molecular systems and optimizing parameters in various applications.
• Existing methods face challenges in resolving near-degenerate states and navigating complex potential energy surfaces.

Purpose of the Study:

• To introduce and validate the Classical Optimal Control Optimization (COCO) method for efficient global energy minimization.
• To demonstrate COCO's capability in locating global energy minima in challenging potential landscapes.

Main Methods:

• Implementation of the diffeomorphic modulation under observable-response-preserving homotopy (DMORPH) gradient algorithm.
• Classical evolution of a probe particle on a potential energy surface coupled to an electric field.
• Optimization of control parameters (mass, dipole, electric field) using energy gradients.

Main Results:

• The COCO method successfully resolved near-degenerate states separated by large energy barriers.
• COCO accurately located global energy minima for golf potentials on diverse surfaces.
• Preliminary results showed successful energy minimization for multidimensional Lennard-Jones clusters.

Conclusions:

• The COCO algorithm provides a robust and effective approach for global energy minimization.
• COCO is anticipated to be valuable for general minimization problems, including machine learning and molecular structure determination.