Exact constraints and appropriate norms in machine-learned exchange-correlation functionals.

Area of Science:

• Computational chemistry
• Materials science
• Quantum mechanics

Background:

• Density functional approximations are crucial for electronic structure calculations.
• Traditional methods rely on human-designed functionals adhering to exact constraints.
• Machine learning offers a novel approach to developing these approximations.

Purpose of the Study:

• To integrate machine learning with exact-constraint satisfaction for density functional approximations.
• To develop a deep neural network that de-orbitalizes the Strongly Constrained and Appropriately Normed (SCAN) functional.
• To replicate the SCAN functional using only electron density and local derivative information.

Main Methods:

• Designed a deep neural network architecture.
• Trained the network to mimic the SCAN functional.
• Utilized electron density and local derivative inputs, excluding orbital-dependent kinetic energy density.
• Tested performance on molecular and periodic systems.

Main Results:

• Successfully trained a deep neural network to approximate the SCAN functional.
• The machine-learned functional avoids the need for orbital-dependent kinetic energy density.
• Demonstrated good performance and transferability across different system types.

Conclusions:

• The integrated approach of machine learning and exact constraints is effective.
• De-orbitalized SCAN functional approximations can be achieved using neural networks.
• This method shows promise for developing accurate and transferable density functionals.