Single-Probe Operator-Defect Control of ACE Reuse in Plane-Wave Hybrid DFT

Abstract Hybrid density functional theory is limited by the repeated cost of exact exchange (EXX). Adaptively compressed exchange (ACE) reduces this cost, but repeated ACE use still requires a decision on when the compressed operator should be reconstructed. We introduce adaptiveEXX, an a posteriori controller for gamma-point plane-wave hybrid DFT that uses one Rademacher probe in the occupied subspace to monitor an EXX operator-defect indicator. The cached ACE operator is rebuilt when the monitored defect exceeds a prescribed threshold, while a deterministic five-call safety horizon limits the maximum reuse age. The one-probe indicator gives the same threshold classification as the full occupied-space defect at all 69 calibration points, and an independent random seed gives the same 69 classifications. For Si (8 atoms) and MgO (2 atoms), increasing the monitor from one to three or five probes increases stochastic work without changing SCF evaluation or ACE action counts. Across five PBE0 benchmarks, the geometric-mean occupied-ACE to adaptiveEXX wall-time ratio is 1.15, and the Si size series reaches 1.67 for the 16-atom cell. HSE06 calculations confirm numerical compatibility with screened exchange but do not show an acceleration relative to that of occupied-subspace ACE. The method is therefore an online operator-quality control layer for bounded ACE reuse rather than a replacement for a fixed rebuild period that is already known to be favorable.