Accurate and scalable exchange-correlation with deep learning

Density Functional Theory (DFT) is the most widely used electronic structure method for predicting the properties of molecules and materials. Although DFT is, in principle, an exact reformulation of the Schrödinger equation, practical applications rely on approximations to the unknown exchange-correlation (XC) functional. Most existing XC functionals are constructed using a limited set of increasingly complex, hand-crafted features that improve accuracy at the expense of computational efficiency. Yet, no current approximation achieves the accuracy and generality for predictive modeling of laboratory experiments at chemical accuracy -- typically defined as errors below 1 kcal/mol. In this work, we present Skala, a modern deep learning-based XC functional that bypasses expensive hand-designed features by learning representations directly from data. Skala achieves chemical accuracy for atomization energies of small molecules while retaining the computational efficiency typical of semi-local DFT. This performance is enabled by training on an unprecedented volume of high-accuracy reference data generated using computationally intensive wavefunction-based methods. Notably, Skala systematically improves with additional training data covering diverse chemistry. By incorporating a modest amount of additional high-accuracy data tailored to chemistry beyond atomization energies, Skala achieves accuracy competitive with the best-performing hybrid functionals across general main group chemistry, at the cost of semi-local DFT. As the training dataset continues to expand, Skala is poised to further enhance the predictive power of first-principles simulations.

@article{luise2025_2506.14665,
  title={ Accurate and scalable exchange-correlation with deep learning },
  author={ Giulia Luise and Chin-Wei Huang and Thijs Vogels and Derk P. Kooi and Sebastian Ehlert and Stephanie Lanius and Klaas J. H. Giesbertz and Amir Karton and Deniz Gunceler and Megan Stanley and Wessel P. Bruinsma and Lin Huang and Xinran Wei and José Garrido Torres and Abylay Katbashev and Bálint Máté and Sékou-Oumar Kaba and Roberto Sordillo and Yingrong Chen and David B. Williams-Young and Christopher M. Bishop and Jan Hermann and Rianne van den Berg and Paola Gori-Giorgi },
  journal={arXiv preprint arXiv:2506.14665},
  year={ 2025 }
}