Experimentally Accurate Graph Neural Network Predictions of Core-Electron Binding Energies

TL;DR

This paper presents a graph neural network model for predicting core-electron binding energies in organic molecules, demonstrating good accuracy, size transferability, and interpretability through architectural choices and case studies.

Contribution

The authors develop an interpretable GNN model trained on high-level theory data, achieving accurate experimental predictions and analyzing environment effects beyond nearest neighbors.

Findings

Achieves 0.33 eV mean absolute error against experimental data.

Two node features effectively encode molecule-specific information.

Model outperforms invariant models on non-equilibrium geometries.

Abstract

Graph neural network architectures are advantageous for predicting core-electron binding energies which depend on local bond environment effects, as the number of message passing layers defines the topological (bond) radius of the model's receptive field. This provides an interpretable connection between the model's architecture and the definition of locality in the considered environment. Here we present a graph neural network model for predicting carbon 1s core-electron binding energies in organic molecules. The model is trained with multiconfiguration pair-density functional theory on 8637 carbon atoms in 2116 molecules with 4-16 atoms and evaluated against 570 experimental values in 113 different molecules containing 3-45 atoms. Previous work benchmarked a mean absolute error of 0.27 eV to experiment for the training data level of theory [J. Phys. Chem. A 2025, 129, 36, 8419-8431] and the present model demonstrates an experimental evaluation error of 0.33 eV with good size transferability to larger systems. By examining the effect of the number of message passing layers on the performance, we show that two chemically informed node features, the atomic binding energy and environment electronegativity, encode molecule-specific information when normalized across the graph and capture beyond nearest-neighbor environment effects outside the receptive field. A case study on the 45 atom avobenzone tautomers demonstrates the model's ability for instant and precise analysis of complex molecules. Finally, the model's E(3)-equivariance is shown to out-perform an invariant model on non-equilibrium geometries from a methanol C-O bond stretch. The software and data are provided by the open-source AugerNet package at https://doi.org/10.5281/zenodo.19689244.