QM9 thermochemistry benchmark

The QM9 dataset contains optimized geometries, harmonic frequencies, and thermochemical properties for 133,885 neutral CHONF molecules. The associated Scientific Data paper reports that the calculations used B3LYP/6-31G(2df,p) and provides U0, U, H, G, and Cv at 298.15 K.

Run the benchmark from a source checkout:

python scripts/validate_qm9.py

The command downloads the original 86 MB archive, verifies its MD5 checksum, and streams the dataset without extracting it. It checks the linear/nonlinear classification of all 133,885 geometries and recomputes thermochemistry for a pinned 1,000-molecule sample. The sample contains the first 100 molecules, record 14,564, 450 evenly spaced records, and a seeded random remainder.

Method

QM9 stores the zero-point energy and internal energy at 0 K, so the electronic energy is reconstructed as U0 - ZPVE. ThermoScreening then recomputes all thermal quantities from the published geometry and frequencies.

The XYZ records do not store the rotational symmetry number used by Gaussian. The pinned source settings use sigma=2 for records 3, 4, and 23 and sigma=1 for the other sampled records. This avoids treating a symmetry metadata difference as a thermochemistry error.

Reference result

Energy differences are reported in microhartree. The source energies are printed to six decimal places and Cv to three decimal places.

Property	Mean absolute error	Maximum absolute error
U0	0.243309 microhartree	0.499333 microhartree
U	0.399690 microhartree	1.389329 microhartree
H	0.394658 microhartree	1.382253 microhartree
G	1.612468 microhartree	3.207543 microhartree
Cv	0.000259 cal/(mol K)	0.000575 cal/(mol K)

The maximum Gibbs-energy difference is approximately 0.0020 kcal/mol. The benchmark therefore reproduces the published quantities to the precision available from QM9’s rounded coordinates, frequencies, and energies.

Near-linear geometry

QM9 records 25 and 14,564 are slightly bent geometries with six and eighteen vibrational modes, respectively. Their smallest-to-largest principal-moment ratios are about 9.7e-8 and 2.9e-9. Looser linearity tolerances treated them as exactly linear and expected an extra vibrational mode. The regression tests require both geometries to be handled as nonlinear. The benchmark also checks the mode count for every QM9 geometry, including 433 records whose frequency rows contain two complete mode sets.

Interpretation

This is an independent numerical validation of the ideal-gas rigid-rotor harmonic-oscillator implementation over varied molecular sizes and structures. It does not measure the predictive accuracy of B3LYP or compare computed thermochemistry with experiment.