Short-Range Δ‑Machine Learning: A Cost-Efficient Strategy to Transfer Chemical Accuracy to Condensed Phase Systems

DFT-based machine-learning potentials (MLPs) are now routinely trained for condensed-phase systems, but surpassing DFT accuracy remains challenging due to the cost or unavailability of periodic reference calculations. Our previous work (Phys. Rev. Lett. 2022, 129, 226001) demonstrated that high-accuracy periodic MLPs can be trained within the CCMD framework using extended yet finite reference calculations. Here, we introduce short-range Δ-Machine Learning (srΔML), a method that starts from a baseline MLP trained on low-level periodic data and adds a Δ-MLP correction based on high-level cluster calculations at the CC level. Applied to liquid water, srΔML reduces the required cluster size from (H2O)64 to (H2O)15 and significantly lowers the number of clusters needed, resulting in a 50–200× reduction in computational cost. The resulting potential closely reproduces the target CC potential and accurately captures both two- and three-body structural descriptors.