Machine learning intermolecular transfer integrals with compact atomic cluster representations

TL;DR

This work develops a symmetry-aware machine learning surrogate for intermolecular transfer integrals $J_{ab}$ in organic semiconductors by extending the Atomic Cluster Expansion (ACE) to model transfer with a linear, locality-based representation. It introduces two molecular representations—heavy-atom and Bead coarse-grained—within ACE and demonstrates data-efficient performance on ethylene, thiophene, and naphthalene dimers, achieving sub-μeV to meV accuracy with modest training sets. The results show heavy-atom representations outperform Bead for small to medium conjugated dimers, with naphthalene achieving robust predictions under both schemes, underscoring ACE’s potential for high-throughput charge-transfer simulations. The approach provides a principled, symmetry-respecting framework for rapid prediction of electronic couplings, enabling scalable modeling of organic electronic materials and guiding material design.

Abstract

Calculating intermolecular charge transfer integrals in organic semiconductors requires substantial computer resource for each individual calculation. We might alternatively construct a machine learning model for transfer integrals, which model the full six-degrees of freedom for the relative position of dimer pairs, trained on representative calculations for the molecules of interest. Recent developments have produced effective machine learning force fields, which model the total energy of atomic assemblies. We extend the Atomic Cluster Expansion (ACE) with the correct symmetries for transfer (kinetic-energy) integrals. Combined with a spherical harmonic basis makes, this forms a strong inductive bias and makes for a data efficient model. We introduce coarse-grained and heavy-atom representations, and assess the methodology on representative conjugated semiconductors: ethylene, thiophene, and naphthalene.

Figures (8)

• Figure 1: Schematic representation of charge transfer in organic semiconductors. The active layer features a hybrid donor/acceptor shape situated between the anode and cathode electrodes. A magnified perspective illustrates the electronic coupling between two $\pi$-conjugated molecules (Mol $a$ and Mol $b$), defined by their respective centre-of-mass displacement $(x_{ab}, y_{ab}, z_{ab})$ and relative rotational orientations $(\theta_x, \theta_y, \theta_z)$. The transfer integral $J_{ab}$, which dictates the charge transfer rate between molecules, depends on their relative coordinates.
• Figure 2: Illustration of the Heavy-atom representations used for ACE descriptor construction for (left) ethylene and (right) thiophene dimers. (a) The ethylene dimer is represented using only carbon atoms (yellow and green dots for Mol $a$ and Mol $b$, respectively). Panels (b) and (c) illustrate variations of the Heavy-atom representation: (b) includes only carbon atoms, while (c) incorporates both carbon and sulphur atoms as distinct elements.
• Figure 3: Illustration of two types of molecular representations used for constructing ACE descriptors. The central diagram shows a dimer of Naphthalene (Mol $a$ and Mol $b$). The left pathway depicts the Bead (coarse-grained) representation, in which each aromatic ring is represented by a single Bead. The right pathway illustrates the Heavy-atom Representation, where only heavy (Heavy-atom) atoms are included.
• Figure 4: Heatmaps shows the 2-dimensional transfer integrals of ethylene (a), thiophene (b), and naphthalene (c).
• Figure 5: Analysis of ethylene (upper), thiophene (middle), and naphthalene (lower) dimer RDFs for the ACE descriptor construction for the Heavy-atom representation.