Predicting electronic screening for fast Koopmans spectral functional calculations
Abstract
Koopmans spectral functionals are a powerful extension of Kohn-Sham density-functional theory (DFT) that enable the prediction of spectral properties with state-of-the-art accuracy. The success of these functionals relies on capturing the effects of electronic screening through scalar, orbital-dependent parameters. These parameters have to be computed for every calculation, making Koopmans spectral functionals more expensive than their DFT counterparts. In this work, we present a machine-learning model that -- with minimal training -- can predict these screening parameters directly from orbital densities calculated at the DFT level. We show on two prototypical use cases that using the screening parameters predicted by this model, instead of those calculated from linear response, leads to orbital energies that differ by less than 20 meV on average. Since this approach dramatically reduces run-times with minimal loss of accuracy, it will enable the application of Koopmans spectral functionals to classes of problems that previously would have been prohibitively expensive, such as the prediction of temperature-dependent spectral properties. More broadly, this work demonstrates that measuring violations of piecewise linearity (i.e. curvature in total energies with respect to occupancies) can be done efficiently by combining frozen-orbital approximations and machine learning.
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Research Focus: The study focuses on developing a machine-learning model to predict electronic screening parameters for Koopmans spectral functionals, aimed at improving computational efficiency while maintaining accuracy in spectral property predictions.
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Methodology: A machine-learning framework is introduced, which uses ridge regression based on translationally- and rotationally-invariant power spectrum descriptors derived from orbital densities to predict the screening parameters required for Koopmans spectral functional calculations.
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Results: The model demonstrated high accuracy in predicting screening parameters and corresponding eigenenergies, achieving a mean absolute error of less than 25 meV for predicted eigenenergies after training with just a few snapshots, outperforming simpler benchmark models.
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Key Contribution(s): This work enables significant reductions in computational time for Koopmans spectral functional calculations by replacing the computationally expensive ab initio screening parameter calculations with predictions from a machine-learning model.
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Significance: The findings indicate that machine learning can effectively bridge the gap between accuracy and computational cost in quantum mechanical calculations, making advanced spectral functional methods more accessible for a wider range of scientific problems.
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Broader Applications: The developed machine-learning approach could potentially be adapted for other quantum mechanical methods related to Koopmans functionals, including localized orbital scaling corrections and various energy curvature calculations, thereby broadening its impact in computational materials science and quantum chemistry.