KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Orbital-free density functional theory (OF-DFT) offers a computationally inexpensive method for calculating molecular properties.
• A major limitation of OF-DFT is the difficulty in accurately determining the kinetic energy as a direct functional of the electron density.
• Existing methods struggle with the expressivity, spatial context, and data requirements for learning accurate kinetic energy functionals.

Purpose of the Study:

• To develop a novel deep learning approach for learning the kinetic energy functional in OF-DFT.
• To address the challenges of model expressivity, spatial context, and training data generation for accurate kinetic energy functional prediction.
• To achieve chemical accuracy in predicting molecular properties using the learned kinetic energy functional.

Main Methods:

• Introduced KineticNet, an equivariant deep neural network utilizing point convolutions for predicting quantities on molecular quadrature grids.
• Designed convolution filters with high spatial resolution near nuclear cusps and an atom-centric architecture for information propagation.
• Developed a data generation strategy involving random external potential perturbations to create diverse training datasets.

Main Results:

• KineticNet successfully learned kinetic energy functionals with chemical accuracy for various input densities and geometries of small molecules.
• Demonstrated the capability of OF-DFT density optimization with chemical accuracy for two-electron systems using the learned functionals.
• Achieved efficient computation on GPUs due to a limited memory footprint.

Conclusions:

• KineticNet represents a significant advancement in OF-DFT, enabling accurate kinetic energy functional prediction.
• The developed AI model overcomes key limitations in OF-DFT, paving the way for more efficient and accurate computational chemistry.
• This work demonstrates the potential of deep learning to solve fundamental challenges in electronic structure theory.