Training Machine-Learned Density Functionals on Band Gaps.

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Semilocal Density Functional Theory (DFT) systematically underestimates band gaps, a fundamental challenge.
• This band gap problem hinders accurate prediction of electronic properties and studying charge transfer mechanisms due to self-interaction and delocalization errors.

Purpose of the Study:

• To develop a machine learning approach for designing density functionals that accurately predict single-particle energy levels.
• To overcome limitations of traditional DFT in electronic property prediction.

Main Methods:

• Employed Gaussian processes for machine learning density functionals, explicitly fitting single-particle energy levels.
• Introduced nonlocal features of the density matrix to capture necessary electronic information.
• Trained a machine-learned functional for exact exchange energy.

Main Results:

• The trained functional accurately predicts molecular energy gaps and reaction energies, showing excellent agreement with hybrid DFT calculations.
• The model demonstrates transferability and robustness by predicting polaron formation energies in solids, despite being trained only on molecular data.

Conclusions:

• This machine learning approach offers a promising path towards developing advanced functionals for accurate electronic property prediction in molecules and materials.
• The method can be extended to full exchange-correlation functionals, advancing DFT capabilities.