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How Well Does Kohn-Sham Regularizer Work for Weakly Correlated Systems?

Bhupalee Kalita1, Ryan Pederson2, Jielun Chen2

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We developed spin-adapted Kohn-Sham regularizer (sKSR), a machine learning method for electronic structure calculations. sKSR accurately predicts ground-state energies for diverse molecules, outperforming existing methods.

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Area of Science:

  • Computational chemistry
  • Materials science
  • Machine learning

Background:

  • Kohn-Sham density functional theory (DFT) is crucial for electronic structure calculations.
  • Existing methods struggle with strongly correlated systems.
  • Differentiable machine learning offers a new approach to developing exchange-correlation functionals.

Purpose of the Study:

  • To test the Kohn-Sham regularizer (KSR) on weakly correlated systems.
  • To develop a spin-adapted KSR (sKSR) for improved accuracy.
  • To assess the generalizability of sKSR from atoms to molecules.

Main Methods:

  • Proposed spin-adapted KSR (sKSR) with trainable local, semilocal, and nonlocal approximations.
  • Minimized density and total energy loss for functional training.
  • Trained on 1D atomic systems (H, He, Li, Be, Be2+) and tested on molecular systems.

Main Results:

  • sKSR demonstrated good generalization from atoms to molecules.
  • The semilocal approximation showed comparable errors to other differentiable methods.
  • The nonlocal sKSR functional significantly outperformed existing machine learning functionals.

Conclusions:

  • sKSR is a promising machine learning approach for electronic structure calculations.
  • The nonlocal sKSR functional achieves high accuracy for ground-state energies.
  • This method advances the development of accurate exchange-correlation functionals in DFT.