Extreme-Scale Linear-Scaling Kohn-Sham DFT at 100 Million Atoms: Bridging Quantum Simulations and Experiments

Abstract

Kohn-Sham density functional theory (DFT) remains the workhorse of ab initio materials simulation, yet cubic computational and quadratic memory scaling have confined calculations to a few hundred to thousands of atoms, spanning only nanometers, far below experimentally relevant length scales. We introduce XLSDFT, a linear-scaling DFT framework based on divide-and-conquer decomposition of the one-particle density matrix and Chebyshev-filtered subspace iteration, achieving linear computational and memory scaling while retaining DFT accuracy. Deployed on the LineShine exascale supercomputer, XLSDFT reduces computational complexity by orders of magnitude, enabling unprecedented DFT scale: a 200-million-atom silicon crystal, twentyfold beyond the prior record. Our implementation achieves 96.6% weak-scaling efficiency and sustained 157.9 Pflop/s (FP64) for a 100-million-atom scaling study. We further simulate an 11-million-atom all-solid-state battery interface of unprecedented complexity, 1,000 times beyond prior DFT for such systems, revealing how lithium metal reacts with the solid electrolyte at atomic resolution, in quantitative agreement with spectroscopy experiments.