Applying Large Graph Neural Networks to Predict Transition Metal Complex Energies Using the tmQM_wB97MV Data Set
Aaron G. Garrison, Javier Heras-Domingo, John R. Kitchin, Gabriel dos Passos Gomes, Zachary W. Ulissi and Samuel M. Blau, “Applying Large Graph Neural Networks to Predict Transition Metal Complex Energies Using the tmQMwB97MV Data Set”, Journal of Chemical Information and Modeling 63(24), 7642-7654 (2023). https://doi.org/10.1021/acs.jcim.3c01226
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Question
Large, diverse training sets such as OC20 and OC22 have made general machine learning surrogates possible for heterogeneous catalysis, but homogeneous catalysis has had far less data. The tmQM set (86,665 single-metal transition metal complexes from the Cambridge Structural Database, xTB geometries, TPSSh/def2-SVP energies) was the obvious starting point. The paper asks whether graph neural networks developed for OC20 can learn the total electronic energies of these complexes, why they fail on part of tmQM, and whether better reference data and pretraining on heterogeneous catalysis data help (Garrison et al. 2023).
Approach
Four graph neural networks from the Open Catalyst Project code, SchNet, SpinConv, PaiNN and GemNet-T, were trained from scratch on atomic numbers and coordinates (metal translated to the origin) with mean absolute error (MAE) loss. Targets were reference-corrected energies: per-element energies from a linear regression over the data were subtracted to give a formation-energy-like quantity. Because the models carry no total charge input, each data set was also used in a neutral-only form. Metrics were test MAE (meV/atom), the fraction of structures within 1 kcal/mol of DFT (energy within threshold, EwT), parity plots, and tSNE maps of SOAP descriptors colored by residual.
After seeing systematic failures on tmQM, the authors built tmQMwB97MV: they removed 155 structures with missing (implicit) hydrogens, found with a heuristic that flags carbons with only one neighbor within 3 Å, and recomputed single-point energies at the ωB97M-V/def2-SVPD level in Q-Chem through a high-throughput workflow with on-the-fly error handling. Only three structures failed to converge, leaving 86,507 complexes (71,042 neutral). Models were trained with 80/10/10, 60/20/20, 40/30/30 and 20/40/40 random splits on both the full and neutral sets (32 models). GemNet-T was also fine-tuned from public OC20 checkpoints with a learning rate ten times smaller than for training from scratch.
Key findings
On tmQM, SchNet, SpinConv and GemNet-T all showed a cluster of strongly underpredicted energies even on the training set (for one model, 370 of 69,333 training structures had errors above 0.1 Ha). PaiNN fit the training set but showed the same region on the test set, a sign of overfitting. The cluster persisted after removing charged structures and was essentially unchanged when the 155 hydrogen-deficient structures were excluded. The residual maps traced it mainly to the iron-group metals Fe, Ru and Os. The authors read this as an inconsistency in the TPSSh/def2-SVP data that nothing in the DFT output itself revealed, so the ML models served as a diagnostic of data quality.
On tmQMwB97MV the underpredicted region disappeared, no metal stood out in the residual maps, and MAE and R² improved for every model except PaiNN. The ranking was GemNet-T > PaiNN ≈ SpinConv > SchNet, roughly following model complexity and OC20 performance; training time ran SchNet < PaiNN < GemNet-T < SpinConv. Test EwT on the full set rose with training fraction, from 3.2 to 4.9% for SchNet and from 5.6% (20% training) to 11.9% (60%) and 11.6% (80%) for GemNet-T. Neutral-only models were much more accurate, but their learning curves flattened and sometimes rose at the largest size, whereas models trained with charged species kept improving at a nearly constant rate (PaiNN and GemNet-T). No model reached the 0.5 meV/atom accuracy that other work has called excellent.
Fine-tuning from OC20 reduced GemNet-T test MAE by 35.8% on the full set (4.85 versus 7.54 meV/atom, R² 0.97 versus 0.93, EwT 17.05 versus 11.65%) and by 14.2% on the neutral subset (3.26 versus 3.80 meV/atom, EwT 23.47 versus 25.24%, so EwT dropped slightly).
Significance
The paper releases a cleaner, higher-level energy set for transition metal complexes, with splits, checkpoints and configurations on GitHub, and shows that the choice of exchange-correlation functional and basis set in reference data can decide whether a model looks learnable at all. The transfer from OC20 suggests that heterogeneous catalysis data can improve models for molecular catalysts. The authors note the data set still lacks open-shell complexes and reactive intermediates, and that models need explicit charge and spin to treat the redox chemistry central to homogeneous catalysis.