Adaptive Vibrational Coordinates via Symmetry-Aware Normalizing Flows.

Area of Science:

• Computational chemistry
• Quantum mechanics
• Molecular spectroscopy

Background:

• Normalizing flows offer a data-driven approach to learn optimal vibrational coordinates.
• Learned coordinates improve accuracy in vibrational spectral calculations and molecular behavior analysis.
• Incorporating molecular symmetry is crucial for accurate and efficient quantum chemical calculations.

Purpose of the Study:

• To extend normalizing flows for learning optimal vibrational coordinates that incorporate molecular symmetry.
• To develop a novel G-equivariant invertible residual network architecture for symmetry-aware coordinate learning.
• To demonstrate the utility of symmetry-aware normalizing flows for accurate vibrational spectral calculations.

Main Methods:

• Introduction of a novel G-equivariant invertible residual network architecture.
• Enforcement of exact equivariance with respect to discrete molecular symmetry groups.
• Combination with symmetry-adapted basis sets to preserve Hamiltonian block-diagonal structure.
• Optimization of coordinates for states spanning single or multiple irreducible representations.

Main Results:

• The G-equivariant architecture ensures learned coordinate transformations respect imposed molecular symmetry.
• Symmetry-aware optimization preserves the block-diagonal structure of the Hamiltonian.
• Optimizing coordinates across different irreducible representations yields comparable results.
• Demonstrated utility for formaldehyde (H2CO) and ammonia (NH3) molecules.

Conclusions:

• Symmetry-aware normalizing flows effectively learn optimal vibrational coordinates that respect molecular symmetry.
• Learned optimal coordinates are shared across irreducible representations, accelerating basis convergence.
• This framework enhances the accuracy and efficiency of vibrational spectral calculations.