Short report by Luisa Kärmer: Electron Density Prediction by Equivariant Neural Networks with Applications in Computer Aided Drug Design (March-May)

Directly using electron density is rare because it depends on quantum mechanical calculations, which usually require iterative adjustments of basis function coefficients to approximate wavefunctions and minimize system energy. This makes Density Functional Theory calculations, yielding electron densities, particularly time-consuming. To address these challenges, we explored the use of equivariant neural networks trained on ab initio data from small molecular fragments to predict electron densities for larger molecular systems. Our Electron Density Neural Network (ElektroNN) model demonstrated unbelievably good generalization abilities, predicting electron densities of drug molecules and peptides with a mean deviation of under 1% per atom across various levels of molecular complexity. To utilize this rich molecular representation, one can use existing density-derived descriptors such as Fukui functions from conceptual density functional theory, or focus gradients and Laplacians of electron density from the quantum theory of atoms in molecules (QTAIM), or design new descriptors — possibly in “basis function space” instead of “grid space”. Explicit equations relating the electron density of a protein-ligand complex to a Hellmann-Feynman interaction energy require the solution of rather complex integrals. I focused on using the density predictions of ElektroNN as input for additional models to predict DFT-SAPT interaction energies that correlate well with experimental enthalpies and can be generated as “synthetic data”.