DeMiR: Density-Matrix-Informed Representations for Molecular Property Prediction

The Hohenberg–Kohn theorem, which states that all physical quantities in the ground state are functionals of the electron density, suggests that much of a molecule's behavior is encoded in its electronic structure. This study proposes DeMiR, a model that treats electron density matrix prediction as a pretraining task. DeMiR reconstructs cc-pVDZ/B3LYP density matrices for molecules ranging in size from QM9-scale molecules to drug-like molecules with up to 146 atoms, achieving median NMAE values of 1.0% and 2.16%, respectively. At the atomic level, the model's embeddings contain electronic structure information: per-atom electronic observables are predicted with an $R^2$ of 0.94 by a linear probe, whereas Uni-Mol reaches 0.84 and a randomly initialized model of the same architecture only 0.63. The embeddings also remove 44.9% of the residual error left by a geometry-based descriptor, showing that this information is not linearly accessible from an explicit geometric descriptor. At the molecular level, transfer depends on the label type. Where electronic structure directly determines the property, transfer holds: on an external experimental pKa test set, fine-tuned DeMiR achieves an MAE of 1.143, significantly outperforming a randomly initialized control with the same architecture and training budget (1.397), and performing on par with or better than chemical foundation models pretrained on far larger datasets. In contrast, for labels such as pIC50 and ADMET, DeMiR shows no consistent advantage over existing general-purpose foundation models, as two-dimensional substructures and physicochemical descriptors have already saturated predictive performance. This study presents the scope within which a connection between electron density prediction capability and molecular property prediction capability holds, along with its boundaries.