Data-driven prediction of total ionization cross sections for small molecules using graph neural networks

Abstract

Abstract Total ionization cross sections (TICS) for electron impact on molecules are essential inputs for plasma modeling and electron-transport simulations. The semi-empirical Binary-Encounter-Bethe (BEB) method provides reliable single-ionization TICS, but every molecule requires a separate quantum-chemical calculation to obtain the orbital binding and kinetic energies that enter the formula. Although an individual calculation is inexpensive, this per-molecule quantum-chemical step becomes the practical bottleneck as datasets grow and as one moves toward larger molecules, where the quantum-chemical cost itself rises steeply. Here we introduce a data-driven surrogate that predicts BEB-level TICS directly from molecular structure, bypassing these calculations. Using about 134,000 small molecules (H, C, N, O, and F) from the QM9 database, we represent each molecule as a graph of atoms and bonds and train a graph neural network (GNN)—a model that learns directly from this atomic graph—to predict the full TICS curve over a wide energy range (10–10,000 eV) in a single step. Comparing three ways of encoding structure across four GNN architectures, we find that distance-based representations, which are invariant to translation and rotation, consistently give the most accurate predictions—indicating that the choice of structural representation matters more than the network architecture. The best models reproduce the reference curves with a root-mean-square error of about 0.05 (in units of 10⁻¹⁶ cm²), offering a fast route to generating large-scale TICS datasets for plasma modeling and electron–molecule collision databases, while bypassing the per-molecule orbital-energy calculations otherwise required by BEB.