RS-CIDER: A non-local machine learning model for approximating screened hybrid functionals

Abstract

Screened hybrid functionals such as HSE06 improve the description of band gaps, charge localization, and redox energetics relative to semilocal approximations, but their explicit Hartree-Fock exchange term is computationally costly for large, periodic systems, especially in plane-wave basis set calculations. Here we present RS-CIDER, a machine-learned non-local exchange functional that approximates the short-range Hartree-Fock exchange term in HSE06 by explicitly fitting both ground-state energies and single-particle energy levels. RS-CIDER combines scale-invariant semilocal and non-local density descriptors and can be evaluated self-consistently without explicitly applying the short-range Hartree-Fock exchange operator. RS-CIDER shows close agreement with HSE06 for molecular reaction energies and solid-state band gaps. Further tests across distinct materials show agreement between RS-CIDER and HSE06 for local magnetism, Cu-O phase competition, polaron localization, and neutral-defect energetics. For an Fe olivine, chemistry-specific fine-tuning recovers the HSE06 Li intercalation voltage. A timing benchmark shows that RS-CIDER reduces the measured per-SCF-step wall time by more than an order of magnitude relative to HSE06. Together, these molecular and solid-state results establish RS-CIDER as an efficient self-consistent machine-learned surrogate for HSE06.