(169s) Dipole Moment Predictions Using Machine Learning Electron Density Models

Accurate electron density information is essential for understanding chemical systems, particularly in scenarios involving dynamic processes like chemical reactions and ion transport. In materials chemistry, access to such data holds immense significance across various applications. The standard approach to predicting electron densities from quantum mechanics (QM) is limited due to high computational cost and poor scalability, constraining their application to smaller system sizes and shorter time scales for dynamics. To address this challenge, existing machine learning (ML) based electron density prediction methods, like DeepCDP (deep charge density prediction), provide a computationally efficient alternative for predicting QM-level electron densities with just the atomic coordinates as input. Useful physical properties like the dipole moment of a system can be computed just using electron density predictions. Efficient prediction of the dipole moment carries significant implications, for instance, in discerning whether proton transfer in a system follows proton-coupled electron transfer or hydrogen atom transfer. However, existing ML methods for electron density predictions face difficulties in predicting dipole moments with errors exceeding 10 Debye for some small molecules. In this study, we investigate the causes of errors in dipole moment prediction with ML models, utilizing the DeepCDP formalism. The original DeepCDP formalism employs the weighted smooth overlap of atomic positions to characterize environments on a grid-point basis and map them to electron density data generated from QM simulations. We curated a diverse selection of molecules spanning varying polarities, atomic radii, electronegativities, and types of bonds (covalent or ionic). Subsequently, we trained models for each of these systems independently and evaluated their predictions on electron densities and dipole moments. Our observations reveal that nearly all models predict electron densities with R2 values exceeding 0.99 and low mean squared errors. Models trained on nonpolar systems demonstrate better accuracy in predicting dipole moments compared to polar systems. We identify that systems containing atoms with larger nuclear charges exhibit the most significant prediction errors in dipole moments. This trend persists across both polar and nonpolar cases, with more pronounced errors observed in polar cases. Furthermore, we establish correlations between the nuclear charge in a system and the error in predicting the total number of electrons. These findings suggest that our current fingerprinting method struggles to correlate points at the center of atoms with high nuclear charge with their corresponding electron density, thus leading to errors in dipole moment prediction. We discuss avenues for parameter tuning and modifications to the atomic fingerprints to address these challenges.