Sparse Linear Surrogates Match Neural Network Potentials on the SPICE Biomolecular Benchmark with Three Orders of Magnitude Smaller Training Sets

Abstract

We introduce the orbital cluster expansion (OCE), a linear regression on physics-motivated local features derived from atomic orbital eigenenergies, and benchmark it against the SPICE 2.0 biomolecular data set at the ωB97M-D3BJ/def2-TZVPPD level. With regression of formation energies on 677 dipeptides spanning the natural amino acids, ridge regression on 414 OCE features attains a parent-stratified test root-mean-square error of 30 meV per atom with Spearman ρ = 0.97 and R 2 = 0.95 against a target spread of only 0.13 eV per atom, matching MACE-OFF23(L) and ANI-2x trained with 104–106 conformations but with ∼103 fewer training points. Comparable accuracy holds on 500 PubChem drug-like molecules and 500 DES370K dimers. We characterize a fundamental dual regime: intermolecular ranking is preserved across chemistries, while intraconformer ranking is random because the basis cannot resolve geometry-only variation within a fixed connectivity. OCE is a transparent, physically interpretable surrogate for intermolecular biomolecular screening.