Net force analysis of the B3LYP-D3BJ/DZVP subset of the SPICE dataset: A diagnostic tool for machine learning force...

The SPICE dataset is widely used to train and benchmark machine learning force fields, yet the numerical consistency of its underlying density functional theory (DFT) force calculations has received limited systematic evaluation. We present a large-scale analysis of molecular net forces in the B3LYP-D3BJ/DZVP subset of SPICE 1 OpenFF, comprising 16,560 molecules and approximately one million conformations. For isolated systems, fully converged DFT calculations are expected to satisfy translational invariance, yielding near-zero molecular net forces within numerical precision. We observed a mean molecular net force of 0.0001166 Hartree/Bohr (5.99 meV/Å), with 98% of molecules exceeding 0.000038 Hartree/Bohr (1.95 meV/Å). Molecular net force increased with molecular size (r = 0.59) and conformational energy spread (r = 0.61). Multivariable, bootstrap, and robust regression analyses consistently identified molecular size, conformational energy spread, mean atomic force norm, and molecular charge as independent predictors of net force (adjusted R² = 0.45). Monte Carlo simulations showed that the observed size dependence is substantially more consistent with stochastic accumulation of small force imbalances than with fully systematic directional bias. Filtering molecules by net force reduced baseline prediction error primarily because smaller molecules were preferentially retained, rather than through improved force consistency after accounting for molecular size. Molecular net force therefore provides a complementary diagnostic of force consistency but should not be interpreted as a direct measure of atomic-force accuracy. The proposed framework is readily applicable to quality assessment of DFT datasets used for machine learning.