High-Throughput Condensed-Phase Hybrid Density Functional Theory for Large-Scale Finite-Gap Systems: The SeAApproach

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the PWSCFmodule of Quantum ESPRESSO(QE). The resulting SeAapproach (SeA= SCDM + exx+ ACE) combines and seamlessly integrates: (i) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), (ii) a recently extended version of exx(a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank V^xxoperator), and (iii) adaptively compressed exchange (ACE, a low-rank V^xxapproximation). In doing so, SeAharnesses three levels of computational savings: pair selectionand domain truncationfrom SCDM + exx(which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rankV^xxapproximationfrom ACE (which reduces the number of calls to SCDM + exxduring the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H2O)64configurations (with densities spanning 0.4–1.7 g/cm3), SeAprovides a 1−2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8−26× compared to the convolution-based PWSCF(ACE)implementation in QEand ≈78−247× compared to the conventional PWSCF(Full)approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using SeAvia an actively learned data set with ≈8,700 (H2O)64configurations. Using an out-of-sample set of (H2O)512configurations (at nonambient conditions), we confirmed the accuracy of this SeA-trained potential and showcased the capabilities of SeAby computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.