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.