Paying attention to long-range electron correlation: a size-independent deep-learning approach to predicting molecules' electronic energies from one- and two-electron integrals

TL;DR

A descriptor for molecular electronic structure is proposed that is based solely on the one- and two-electron integrals but is translationally, rotationally, and unitarily invariant, and training on few-electron systems can guide predictions for systems with more electrons.

Abstract

We propose a descriptor for molecular electronic structure that is based solely on the one- and two-electron integrals but is translationally, rotationally, and unitarily invariant. Then, directly exploiting size consistency, we train and fine tune a neural network to predict the energies of strongly-correlated systems, specifically hydrogen clusters. We use an attention mechanism to formulate a size-independent approach that uses and preserves size-consistency. Therefore, training on few-electron systems can guide predictions for systems with more electrons. Our results are more accurate than alternative geometry-based machine-learning models.

Figures (5)

• Figure 1: MAE on the test set vs amount of training data
• Figure 2: Predicted and FCI energies for the dissociation of the linear H_6 chain, computed with the STO-6G basis set. The MAE for predicted energies is 0.053 Hartree.
• Figure 3: Energy prediction of the dissociation curve for linear chain of ten hydrogen atoms using different methods
• Figure 4: Architecture of the physics-informed Attention mechanism, featuring an asymptotic gate ($\omega$) to enforce physically valid dissociation limits
• Figure 5: Predicted and FCI energies for the dissociation of the linear H_8 chain, computed with the STO-6G basis set