Self-consistent electron density with shell structure using neural network-based Pauli potential.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Orbital-free density functional theory (OF-DFT) offers near-linear scaling for electronic structure calculations.
• A key challenge in OF-DFT is the accurate representation of the non-interacting kinetic energy functional.
• The Pauli kinetic energy functional and its corresponding potential remain significant hurdles.

Purpose of the Study:

• To develop a feed-forward neural network (NN) model for representing the Pauli potential.
• To improve the accuracy of OF-DFT calculations by providing a robust Pauli potential approximation.
• To enable more efficient quantum mechanical calculations for atomic systems.

Main Methods:

• A feed-forward neural network was trained to predict the Pauli potential using electron density grids as input.
• The NN-based Pauli potential was integrated with the Hohenberg-Kohn variational principle.
• Non-interacting kinetic energy was computed by combining NN-derived Pauli kinetic energy and von Weizsäcker kinetic energy.

Main Results:

• The NN approach successfully generated self-consistent radial densities with accurate atomic shell structures.
• High accuracy was observed for smaller atoms, with some deviations noted for larger atoms.
• The method efficiently calculates Pauli potential and kinetic energy without requiring functional derivatives.

Conclusions:

• Neural networks offer a powerful tool for approximating complex functionals in OF-DFT.
• This work represents a significant advancement in applying machine learning to enhance OF-DFT accuracy and efficiency.
• The developed method provides a practical pathway for improved quantum mechanical calculations in atomic systems.