Correcting the Liquid Densities of Universal Machine-Learning Interatomic Potentials Using Local-Number-Density Repulsion

Universal machine-learning interatomic potentials (MLIPs) such as UMA, trained on reference data from meta-generalized gradient approximation or hybrid functionals that incorporate dispersion interactions, often overestimate molecular-liquid densities, thereby placing every property computed at constant pressure at the wrong state point. This study proposes a correction that adds to the MLIP a repulsive energy quadratic in the local number density of each atom, with two coefficients fitted only to the equations of state of water and ethanol; the forces and stresses follow analytically, so neither electronic-structure calculations nor retraining is required. For UMA, the correction reduces the density mean absolute error (MAE) of 22 liquids from 10.8% to 2.5%, lowering the error for every liquid and bringing 20 of them within ±5% of experiment, while improving the bulk modulus (MAE from 71.6% to 22.1%), heat of vaporization, and second hydration shell of water, none of which was calibrated. Applied to SevenNet-Omni without recalibration, the same coefficients reduce the density MAE from 8.2% to 1.8%, with 21 of 22 liquids within ±5% of experiment.