Gradient Projection Method for Constraint Optimization and Relaxed Energy Paths on Conical Intersection Spaces and...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Geometry optimization is crucial for understanding molecular behavior.
• Optimizing conical intersection geometries presents unique challenges.
• Existing methods may require defining specific reaction coordinates.

Purpose of the Study:

• To present a generalized gradient projection algorithm for constrained geometry optimization.
• To enable optimization on potential energy surfaces (PES) and conical intersection (CI) seams.
• To develop a method for determining relaxed energy paths (REP) without a predefined reaction coordinate.

Main Methods:

• Gradient projection algorithm with generalized constraints.
• Singular value decomposition (SVD) for orthogonalizing constraint gradients.
• Optimization of minimum energy structures and REPs.

Main Results:

• The algorithm successfully applies multiple constraints during optimization.
• Constraints, including those for maintaining CI, are transformed using SVD.
• The method converges to geometries satisfying all constraints.
• Demonstrated optimization of minimum energy structures and REPs in CI space and on PES.

Conclusions:

• The presented algorithm offers a robust approach for constrained geometry optimization.
• It provides a flexible way to explore PES and CI spaces.
• The method simplifies the determination of reaction pathways and relevant molecular structures.