Cartesian equivariant representations for learning and understanding molecular orbitals.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Machine Learning

Background:

• Orbital properties are crucial for understanding chemical reactivity and excited-state behavior.
• Current deep learning models lack robust representations for molecular orbitals compared to geometries and Hamiltonians.

Purpose of the Study:

• To develop and apply advanced equivariant deep learning architectures for molecular orbital representation.
• To assign global labels to orbitals, including energies and characterizations, from computational chemistry data.

Main Methods:

• Applied state-of-the-art equivariant deep learning architectures.
• Developed the Cartesian Equivariant Orbital Network (CEONET) to featurize molecular orbital coefficients.
• Utilized graph-based machine learning with equivariant node features.

Main Results:

• CEONET accurately predicts quantitative orbital labels like orbital energy and entropy.
• The CEONET representation provides an interpretable latent space for qualitative orbital character (e.g., bonding/antibonding).
• Demonstrated the model's ability to infer multireference character via orbital entropy.

Conclusions:

• CEONET offers a powerful new representation for integrating deep learning with electronic structure theory.
• The network facilitates automation and interpretation of advanced electronic structure methods.
• CEONET's capabilities pave the way for machine-learned active space selection in computational chemistry.