Hammett-Inspired Product Baseline for Data-efficient $Δ$-ML in Chemical Space

Abstract: Data-hungry machine learning methods have become a new standard to efficiently navigate chemical compound space for molecular and materials design and discovery. Due to the severe scarcity and cost of high-quality experimental or synthetic simulated training data, however, data-acquisition costs can be considerable. Relying on reasonably accurate approximate legacy baseline labels with low computational complexity represents one of the most effective strategies to curb data-needs, e.g.~through $\Delta$-, transfer-, or multi-fidelity learning. A surprisingly effective and data-efficient baseline model is presented in the form of a generic coarse-graining Hammett-Inspired Product (HIP) {\em Ansatz}, generalizing the empirical Hammett equation towards arbitrary systems and properties. Numerical evidence for the applicability of HIP includes solvation free energies of molecules, formation energies of quaternary elpasolite crystals, carbon adsorption energies on heterogeneous catalytic surfaces, HOMO-LUMO gaps of metallorganic complexes, activation energies for S$_\text{N}$2 reactions, and catalyst-substrate binding energies in cross-coupling reactions. After calibration on the same training sets, HIP yields an effective baseline for improved $\Delta$-machine learning models with superior data-efficiency when compared to previously introduced specialised domain-specific models.