Constant advance replicas method for locating minimum energy paths and transition states

Area of Science:

• Computational Chemistry
• Chemical Physics
• Reaction Mechanism Studies

Background:

• Locating minimum energy paths (MEPs) and transition states is crucial for understanding chemical reactions.
• Existing methods like the string method (SM) face challenges with complex conformational changes.

Purpose of the Study:

• Introduce and validate the chain-of-states (CoS) constant advance replicas (CAR) method and its climbing image variant (CI-CAR).
• To provide a robust and numerically precise algorithm for identifying MEPs and transition states.

Main Methods:

• The CAR algorithm utilizes Lagrange multipliers for holonomic constraints on replicas to maintain consistent distances.
• Two contextual regularization schemes enhance convergence and numerical stability.
• Tested on Müller potential, alanine dipeptide isomerization, peptide helix unwinding, and Baker reactions.

Main Results:

• CAR method achieves high numerical precision, solving constrained reaction paths within approximately 5 Lagrange multiplier updates.
• Demonstrated efficacy across diverse analytical, classical, and quantum mechanical systems.
• Adaptive momentum (AdaM) optimizers explored for complex conformational changes.

Conclusions:

• The CAR approach offers a significant advancement in reaction path finding within the two-ended CoS framework.
• CAR methods provide a robust and precise alternative to existing algorithms like RPCons and SM.
• The study highlights the potential for improved computational efficiency in chemical dynamics simulations.