Neural Mulliken Analysis: Molecular Graphs from Density Matrices for QSPR on Raw Quantum-Chemical Data

Here, molecular graphs derived from the one-electron density matrix are introduced within a more general effort to explore whether incorporating electronic structure awareness allows a single model to both better generalize from small data and better learn molecular encodings. Diagonal density matrix blocks serve as atomic node embeddings, while off-diagonal blocks provide embeddings for "link" nodes related to atomic pairs. In a minimal basis, these embeddings have dimensions of only 45 and 81, yet no information is lost and the original density matrix can be fully reconstructed. Blocks from the basis set overlap matrix are used as edge embeddings to encode structural information and as weights for message aggregation operations. Additionally, element-wise multiplication performed during aggregation may provide access to electronic charges, analogous to Mulliken population analysis. The proposed concept was evaluated using data from the First and Second Solubility Challenges (Llinàs et al. J.Chem. Inf. Model. 2008, 48, 1289-1303; Llinàs and Avdeef J. Chem. Inf. Model. 2019, 59, 3036-3040). A graph neural network (GNN) trained on sets of 94 and 1000 drug-like molecules achieved improved solubility prediction accuracy (RMSE 0.63, R² 0.79 in SC-1 and RMSE of 0.83 and 0.92, R² of 0.57 and 0.79 on the "tight" and "loose" SC-2 test sets, respectively). If combined with existing techniques for predicting electron density from molecular structures, this approach is promising for addressing a range of chemical machine-learning problems.