Conservation-Resolved Error Decomposition: A Benchmark Axis for Electronic-Structure Methods and Machine-Learned Interatomic Potentials

<jats:p>Benchmarks rank electronic-structure methods, semiempirical methods, and machine-learned potentials by errors on single molecules, whereas thermochemical applications use balanced energy dierences. A molecular score combines error components that a stated balance removes with those it retains, and a finite reaction benchmark samples only selected stoichiometries. We propose conservation-resolved error decomposition (CRED), which projects the molecular error vector onto the subspace spanned by conserved counts. The orthogonal residual is the reaction-visible error coordinate, and its per-molecule norm defines the conservation-resolved surviving error (CRSE). CRED requires one energy per molecule and no reaction construction. CRSE is defined before reaction-set selection and, when elemental composition is conserved, is invariant to per-element reference shifts, placing fitted potentials and electronic-structure methods on a common axis. Across nested MACE-OFF23 subsets, raw error changes eightfold while the surviving isodesmic share remains 0.80 to 0.83. Composition-level CRSE is 2.36 and 2.83 kcal/mol for B3LYP-D3(BJ) and ÊB97X-V; resolving this dierence requires about 10 2 balanced reactions, versus 41 in GMTKN55. Blind predictions for eleven held-out methods calibrate against observed reaction scales at a slope of 1.08 [0.91, 1.26]. Applied to seven learned potentials, CRSE locates chemical-domain boundaries at 2.2 to 17.1 times the analytic median on each model’s element coverage. CRED therefore converts a molecular benchmark into a conservation-resolved assessment of reaction-relevant error, benchmark resolution, and fitted-model domain.</jats:p>