Machine learning of electronic structure and atomistic properties from the external potential

Area of Science:

• Computational chemistry
• Machine learning
• Quantum mechanics

Background:

• Electronic structure calculations are computationally expensive, hindering atomistic simulations.
• Current machine learning (ML) approaches often map molecular geometries to properties or approximate electronic structure quantities.
• Existing methods face challenges in efficiently describing nonlocal effects and deriving multiple molecular observables simultaneously.

Purpose of the Study:

• To develop a novel operator-centric machine learning framework for electronic structure calculations.
• To leverage the external potential as a direct input for ML models.
• To create a scalable and efficient method for modeling molecular properties and Fock matrices.

Main Methods:

• An operator-centric framework using the external potential (in an atomic orbital basis) as input.
• Construction of hierarchical, body-ordered representations mirroring atom-centered descriptors.
• Utilizing the matrix-valued external potential for equivariant message-passing neural networks.
• Employing successive products of the external potential for scalable equivariant message passing.

Main Results:

• Demonstrated the ability to model molecular properties like energies and dipole moments directly from the external potential.
• Successfully learned effective operator-to-operator maps, including mappings to the Fock matrix.
• Showcased an efficient description of nonlocal effects through the proposed method.
• Enabled simultaneous derivation of multiple molecular observables from the learned Fock matrix.

Conclusions:

• The proposed operator-centric framework offers a scalable and efficient alternative for electronic structure calculations using machine learning.
• This approach provides a direct link between the external potential and molecular properties, simplifying complex computations.
• The method facilitates the simultaneous prediction of various molecular observables by learning operator-to-operator mappings, advancing computational chemistry.