How Accurate Are DFT Forces? Unexpectedly Large Uncertainties in Molecular Datasets

TL;DR

Net forces in datasets including SPICE, Transition1x, ANI-1x, ANI-1xbb, AIMNet2, QCML, and OMol25 are considered, finding significant discrepancies in force components averaging from 1.7 meV/{\AA} in the SPICE dataset to 33.2 meV/{\AA} in the ANI-1x dataset.

Abstract

Training of general-purpose machine learning interatomic potentials (MLIPs) relies on large datasets with properties usually computed with density functional theory (DFT). A pre-requisite for accurate MLIPs is that the DFT data are well converged to minimize numerical errors. A possible symptom of errors in DFT force components is nonzero net force. Here, we consider net forces in datasets including SPICE, Transition1x, ANI-1x, ANI-1xbb, AIMNet2, QCML, and OMol25. Several of these datasets suffer from significant nonzero DFT net forces. We also quantify individual force component errors by comparison to recomputed forces using more reliable DFT settings at the same level of theory, and we find significant discrepancies in force components averaging from 1.7 meV/Å in the SPICE dataset to 33.2 meV/Å in the ANI-1x dataset. These findings underscore the importance of well converged DFT data as increasingly accurate MLIP architectures become available.

Figures (4)

• Figure 1: Distributions of net force per atom in the ANI-1xbb, QCML, ANI-1x, AIMNet2, Transition1x, and SPICE datasets. The 1 meV/Å/atom threshold is indicated by a vertical dashed line in each plot. On the top left of each of panels A-F, the fraction of the dataset with net forces below the threshold is indicated. The red bar at the top of each panel highlights net forces above 1 meV/Å/atom which indicate significant errors in individual force components. In the region between $10^{-3}$ and 1 meV/Å, indicated with an amber bar, significant DFT force errors often appear but do not result in large net forces. Negligible net forces below $10^{-3}$ meV/Å are in the region indicated with the green bar.
• Figure 2: Absolute discrepancies in atomic Cartesian force components between original literature values and values recomputed using ORCA 6.0.1 with our chosen settings in randomly selected structures from the ANI-1x (large basis set data), Transition1x, AIMNet2, and SPICE datasets, with their force root mean square deviation (RMSD) values, shown in panels A, B, C, and D, respectively. Each data point represents the difference in a single Cartesian force component (x, y, or z) for one atom in meV/Å. The histograms depict the distribution of these per-component discrepancies, and the RMSD values are calculated with the component-wise discrepancies. For the SPICE dataset in panel D, we also provide force discrepancies for all configurations whose original Psi4 net forces are greater than 50 meV/Å. Panel E compares original Psi4 and recomputed ORCA force components. Note that the scale in panel E has data in units of eV/Å, while other panels report data in meV/Å.
• Figure 3: Force RMSDs, in meV/Å, on the random samples containing 1000 configurations each shown in \ref{['fig:force_diff']}. Each RMSD value is shown next to an arrow connecting two boxes, and the boxes represent computational settings either shown on the left hand-side in the same shade of grey, or written explicitly in the box. For Transition1x, we also show the effect of retaining outliers on the force RMSD. For SPICE, we show the single outlier which alone is responsible for changing the RMSD from 1.34 to 30.1 meV/Å.
• Figure 4: Distribution of per atom net forces in the 1000 K NVT subset of OMAT24. 65% of the configurations exceed 1 meV/Å/atom net force threshold, with thousands even exceeding 100 meV/Å/atom. The red bar on top indicates the region above the 1 meV/Å/atom threshold. The green bar indicates negligible net forces below $10^{-3}$ meV/Å/atom and the amber bar indicates net forces of intermediate size.