Constrained numerical gradients and composite gradients: Practical tools for geometry optimization and potential...

Area of Science:

• Computational Chemistry
• Molecular Modeling
• Numerical Analysis

Background:

• Numerical gradients are crucial for molecular optimization but computationally expensive.
• Constrained systems, particularly those with rigid fragments, present unique challenges in gradient computation.
• Existing methods for rigid fragment optimization may not be universally applicable or efficient.

Purpose of the Study:

• To develop an efficient method for computing numerical gradients in constrained systems.
• To reduce the number of energy evaluations required for constrained optimization.
• To provide a practical alternative for molecular optimization when analytical gradients are unavailable or unaffordable.

Main Methods:

• Separating the coordinate space into constrained and unconstrained subspaces.
• Performing numerical differentiation exclusively within the unconstrained space.
• Testing the method on systems with multiple rigid groups or molecules.

Main Results:

• The proposed method significantly reduces energy calculations for constrained systems.
• Errors in optimization are comparable to conventional methods, within convergence criteria.
• The approach demonstrates competitiveness against existing rigid fragment optimization techniques.
• The method effectively combines numerical and analytical gradients at different theory levels.

Conclusions:

• The developed method offers a substantial decrease in computational cost for numerical gradients in constrained systems.
• It provides a practical and accurate approach for molecular optimization, especially for systems with rigid fragments.
• The flexibility to combine gradient types makes it a valuable tool when high-level analytical gradients are inaccessible.