Toward Orbital-Free Density Functional Theory with Small Data Sets and Deep Learning.

Area of Science:

• Computational physics
• Quantum chemistry
• Materials science

Background:

• Density functional theory (DFT) is crucial for electronic structure calculations.
• Accurate prediction of electron kinetic energy is computationally demanding.
• Machine learning offers potential for accelerating DFT calculations.

Purpose of the Study:

• To develop and apply voxel deep neural networks for predicting kinetic energy densities and functional derivatives.
• To investigate the direct prediction of ground-state electron density for graphene.
• To explore machine learning-accelerated DFT methods for electronic structure calculations.

Main Methods:

• Utilized voxel deep neural networks (DNNs) for kinetic energy predictions.
• Trained DNNs on Thomas-Fermi model and Kohn-Sham DFT calculations.
• Developed a functional derivative-free Monte Carlo-based orbital-free DFT algorithm.

Main Results:

• Successfully predicted electron kinetic energy densities and functional derivatives.
• Achieved direct minimization of ground-state electron density for graphene using DNNs.
• Predicted graphene lattice kinetic energy within chemical accuracy using limited DFT data.
• Identified a sampling issue in Kohn-Sham DFT calculations.
• Demonstrated an accurate two-electron density calculation using a machine-learned functional.

Conclusions:

• Voxel DNNs are effective for predicting electronic properties in DFT.
• Machine learning can significantly reduce computational cost in DFT.
• Identified challenges in current DFT sampling methods requiring further investigation.