Nuclear Gradients from Auxiliary-Field Quantum Monte Carlo and Their Applications in ML-Driven Geometry Optimization...

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Accurate calculation of nuclear forces is crucial for predicting molecular properties and reaction pathways.
• Existing methods can be computationally expensive, limiting their application to large systems or complex dynamics.
• Phaseless auxiliary-field quantum Monte Carlo (AFQMC) offers a promising quantum mechanical approach but requires efficient force computation.

Purpose of the Study:

• To develop and validate a method for computing nuclear forces within the AFQMC framework.
• To integrate machine learning (ML) strategies for handling noisy AFQMC data.
• To demonstrate the application of ML-derived potentials for molecular structure and reaction path calculations.

Main Methods:

• Leveraging automatic differentiation of the energy functional to compute nuclear gradients.
• Validating the accuracy of computed forces against finite difference calculations.
• Employing machine learning models to learn from noisy AFQMC energy data.
• Performing geometry optimizations and nudged elastic band (NEB) calculations using ML potentials.

Main Results:

• Achieved computational cost for nuclear forces comparable to energy evaluation.
• Demonstrated excellent agreement between AFQMC-derived forces and finite difference results.
• Successfully identified the transition state for formamide-formimidic acid tautomerization using ML potentials.
• Obtained transition-state geometries and barrier heights in close agreement with high-level coupled-cluster reference values.

Conclusions:

• The developed method enables accurate and scalable nuclear force calculations within AFQMC.
• ML potentials trained on AFQMC data can reliably predict molecular structures and reaction pathways.
• This work facilitates highly accurate geometry optimizations, molecular dynamics, and reaction path calculations.