Toward universal excited-state machine-learned potentials: a local excitation Hamiltonian for size consistency and transferability
Abstract
Universal machine-learned interatomic potentials could make excited-state simulations across chemical space routine, but excitation energies, unlike ground-state energies, are not sums of atomic contributions. The excited states of noninteracting molecules are the union of their states, which pooled multistate readouts reproduce at best for the lowest state. We introduce LEH-MACE, whose excitation energies are the eigenvalues of a local excitation Hamiltonian assembled from atom-centred blocks, so this union holds exactly. We generated TD-DFT energies and forces for about 300,000 equilibrium, thermal, and excited-state geometries of over 100,000 molecules. LEH-MACE's advantage over direct readouts grew with the distance from the training data and was largest above $S_1$, with about half their $S_2$ and $S_3$ errors for long conjugated oligomers. For molecule pairs, only LEH-MACE kept its single-molecule accuracy, while a softmin readout remained superior for $S_1$ dynamics of larger chromophores. Exact size consistency is thus one step toward such potentials.
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Research summary
The paper introduces LEH-MACE, a machine-learned potential that uses a local excitation Hamiltonian to achieve exact size consistency for excited-state simulations, significantly improving transferability and accuracy for higher excited states compared to direct regression methods. This architectural innovation addresses a fundamental limitation in current MLIPs, enabling more reliable simulations of non-interacting systems and higher-energy states, with a large-scale open dataset and codebase supporting the field's progress toward universal excited-state potentials.
Methodology
The paper introduces LEH-MACE, a machine-learned interatomic potential (MLIP) specifically designed for excited states. The core methodological innovation is the "Local Excitation Hamiltonian" (LEH). Unlike standard MLIPs that predict scalar energy values directly, LEH-MACE constructs a local Hamiltonian matrix from atom-centered blocks. The excitation energies are derived as the eigenvalues of this matrix. This architectural choice enforces exact size consistency for non-interacting systems, a property that direct regression of excitation energies fails to satisfy because excited states of non-interacting molecules are the union of their individual states, not a sum. The model is built upon the MACE (Message Passing Atomic Cluster Expansion) framework, leveraging its equivariant message passing capabilities. The training data consists of TD-DFT (Time-Dependent Density Functional Theory) energies and forces for a massive dataset of ~300,000 geometries across >100,000 molecules, covering equilibrium, thermal, and excited-state configurations.
Results & evaluation
The experimental evaluation is extensive and rigorous. The authors generated a large-scale dataset (300k geometries, 100k molecules) using TD-DFT, which is computationally expensive and demonstrates significant resource investment. They benchmark LEH-MACE against direct readout baselines (likely standard MACE or similar architectures predicting energies directly). Key results show that LEH-MACE's advantage grows with distance from training data and is most pronounced for higher excited states ($S_2, S_3$), where it achieves roughly half the error of direct readouts for long conjugated oligomers. Crucially, they test size consistency on molecule pairs, showing that only LEH-MACE maintains single-molecule accuracy, validating the theoretical motivation. However, they acknowledge that a "softmin readout" remains superior for $S_1$ dynamics of larger chromophores, indicating LEH-MACE is not a universal replacement but a specialized tool for transferability and higher states.
Reproducibility
Reproducibility is high. The authors provide a Zenodo DOI for the dataset (geometries, energies, forces, splits) and a GitHub repository (MIT license) containing the implementation, checkpoints, training configurations, and analysis scripts. The use of standard TD-DFT references and open-source code (MACE-based) further enhances reproducibility. The data is licensed under CC BY 4.0.
Limitations
The primary limitation is the reliance on TD-DFT as the ground truth, which has known issues with double excitations and charge-transfer states. The model is specifically tuned for singlet states ($S_1-S_3$) and may not generalize to triplet states or other spin multiplicities without further adaptation. The paper notes that for $S_1$ dynamics of large chromophores, a different readout (softmin) is better, suggesting LEH-MACE might be less effective for the most common use case (lowest excited state dynamics) compared to specialized alternatives, though it excels in transferability and higher states. The computational cost of constructing the local Hamiltonian and computing eigenvalues at inference time may be higher than scalar regression.
Broader impact
This work is significant for the field of computational chemistry and scientific ML. Excited-state simulations are critical for understanding photophysics, photochemistry, and materials science (e.g., organic photovoltaics, LEDs). The lack of size consistency in previous MLIPs has been a major barrier to simulating large systems or mixtures. By solving this via the LEH architecture, the paper enables more accurate and transferable simulations of excited states across chemical space. The large-scale dataset and open-source code will likely become a standard benchmark and tool for the community. It represents a step toward "universal" MLIPs for excited states. The paper introduces LEH-MACE, a machine-learned potential that uses a local excitation Hamiltonian to achieve exact size consistency for excited-state simulations, significantly improving transferability and accuracy for higher excited states compared to direct regression methods. This architectural innovation addresses a fundamental limitation in current MLIPs, enabling more reliable simulations of non-interacting systems and higher-energy states, with a large-scale open dataset and codebase supporting the field's progress toward universal excited-state potentials.
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