Transferable machine learning of excited-state dynamics with extremal pooling
Cesare Malosso, Wei Bin How, Gonzalo Díaz Mirón, Ali Hassanali, Michele Ceriotti
Abstract
Photochemical processes govern phenomena ranging from solar energy conversion and atmospheric chemistry to vision and photosynthesis. Accurate simulation of these processes requires modeling excited-state potential energy surfaces, often involving chemical reactions, tasks that remain computationally prohibitive for extended systems and long timescales using traditional \textit{ab initio} methods. Machine learning interatomic potentials have revolutionized ground-state simulations, but their extension to excited states faces fundamental challenges: standard architectures assume energy extensivity, an assumption that fails for excited states. Here, we present a size-intensive machine-learning framework for excited-state dynamics based on \textit{extremal pooling} of predicted atomic HOMO and LUMO contributions. Trained exclusively on excitations energies and forces, the architecture learns interpretable atomic-level contributions that encode physical information on the extent of electron localization. We demonstrate this framework on the photoexcited solvated electron in liquid water, a paradigmatic problem in radiation chemistry leading to competing pathways involving both hydrogen-atom dissociation and proton-coupled electron transfer. The model not only reproduces the relevant chain of reactions and product species that form during excitation, but also allows one to explicitly study the dynamics of the solvated electron in quantitative agreement with previously reported Restricted Open-Shell Kohn-Sham calculations, while enabling excited-state simulations of periodic systems at length and time scales inaccessible to the reference electronic-structure method. This work establishes a general strategy for machine learning-driven excited-state dynamics applicable to diverse photochemical systems, from molecular chromophores in solution to extended condensed-phase systems.
AI Impact Assessments
(1 models)Scientific Impact Assessment
1. Core Contribution
This paper addresses a fundamental architectural limitation in machine learning interatomic potentials (MLIPs): standard architectures decompose energy as a sum of local atomic contributions (extensive), but electronic excitation energies are *intensive* properties that should not scale with system size. The authors propose extremal pooling — using SmoothMax/SmoothMin (log-sum-exp) operations to aggregate per-atom HOMO and LUMO contributions predicted by a graph neural network, rather than summing them. The excitation energy gap is then computed as E_LUMO − E_HOMO, which is intensive by construction. This is coupled with a standard extensive ground-state MLIP to yield the full excited-state energy surface for dynamics.
The key insight is elegant: frontier orbital energies are determined by extremal (best/worst) local environments, not averages over all atoms. This maps naturally onto SmoothMax/SmoothMin operations, providing both physical motivation and size-transferability. The approach is architecture-agnostic — any atom-centered ML backbone producing per-atom scalars can be used.
2. Methodological Rigor
The framework is demonstrated on photoexcited liquid water, specifically the competing HAT (hydrogen atom transfer) and PCET (proton-coupled electron transfer) pathways following UV excitation. The validation is multi-layered:
However, some methodological choices warrant scrutiny. The pooling parameter α = 20 eV⁻¹ is fixed rather than learned, which imposes a global localization scale. The authors acknowledge this and suggest learnable attention as future work. The classification of HAT vs. PCET trajectories using a 1 eV threshold on the LUMO distribution gap (Δ) is somewhat heuristic, though it achieves 98% agreement with spin-density-based classification on ROKS trajectories. The absence of long-range electrostatics is a noted limitation that could affect quantitative accuracy for charge-separated states.
3. Potential Impact
The impact potential is substantial across several dimensions:
Methodological: The extremal pooling concept is broadly applicable beyond excited states. Any intensive, locally-determined quantity in an extensive system — polaron binding energies, defect formation energies, band edges — could benefit from this architecture. This addresses a genuine gap in the MLIP toolkit.
Application domain: Enabling excited-state MD at 512 molecules over picoseconds (vs. 64 molecules over sub-picoseconds for ROKS) represents roughly a 100× expansion in accessible phase space. The finite-size analysis reveals systematic effects: HAT lifetimes increase from ~33 fs to ~52 fs going from 64 to 512 molecules, and the longest PCET trajectories extend from 1.2 ps to 3.4 ps. These are genuinely new physical insights that would be inaccessible without size-transferable ML models.
Interpretability: The emergent chemical interpretability of learned atomic HOMO/LUMO contributions — without explicit training on orbital information — is a notable strength. Different chemical species (O atoms, bulk H, OH• radicals, cavity protons) naturally separate in the (h_HOMO, h_LUMO) plane, enabling trajectory classification and electron tracking without wavefunction analysis.
4. Timeliness & Relevance
This work arrives at an opportune moment. MLIPs have matured for ground-state simulations, and extending them to excited states is widely recognized as a frontier challenge. Several concurrent efforts (SpaiNN, x-MACE for excited states, reactive ML potentials for proton transfer) address related problems but typically for isolated molecules without size transferability. The extensivity/intensivity distinction is a well-known conceptual issue that has lacked a clean architectural solution for condensed-phase excited-state dynamics.
The specific application to solvated electrons is also timely given recent experimental advances in ultrafast spectroscopy of ionized water and renewed theoretical interest in aqueous radiation chemistry.
5. Strengths & Limitations
Strengths:
Limitations:
6. Additional Observations
The modular design (separate ground-state and gap models combined at inference) is pragmatic but introduces error accumulation. The relatively modest dataset size (~3600 configurations) is enabled by the focused active learning strategy. Reproducibility prospects are good given the planned code/data release and the use of existing software (metatrain, PET-MAD).
The finite-size analysis (Table I, Figure 7) represents the paper's most novel scientific finding beyond the methodology: systematic lengthening of both HAT and PCET lifetimes with system size challenges the assumption that these are purely local processes.
Generated Jun 16, 2026
Comparison History (20)
Paper 2 addresses a broader challenge—extending ML potentials to excited-state dynamics—with a novel architecture (extremal pooling) that solves the fundamental extensivity problem. Its transferability to condensed-phase systems at scales inaccessible to ab initio methods gives it wide applicability across photochemistry, materials science, and biochemistry. While Paper 1 makes an important theoretical advance extending GW to strongly correlated systems, its immediate impact is narrower, primarily benefiting the electronic structure theory community. Paper 2's practical scalability and cross-disciplinary relevance (solar energy, atmospheric chemistry, biology) suggest broader scientific impact.
Paper 2 addresses a fundamental, 150-year-old question regarding the origin of biological homochirality. By providing a physical mechanism for enantiomeric selection via the CISS effect, its findings have profound interdisciplinary implications across astrobiology, chemistry, and physics. While Paper 1 presents a highly valuable methodological advancement in computational chemistry with strong practical applications, Paper 2 offers a paradigm-shifting explanation for a universal property of life, granting it broader fundamental scientific impact.
Paper 1 addresses a fundamental limitation in simulating excited-state dynamics using a novel machine-learning approach. By overcoming the energy extensivity assumption, it allows for scalable simulations of photochemical processes. This enables broad applications in solar energy, atmospheric chemistry, and biology. In contrast, Paper 2 offers a valuable but highly specialized algorithmic efficiency improvement for quantum-chemical calculations involving magnetic fields. Consequently, Paper 1 has significantly broader interdisciplinary relevance, timeliness, and transformative potential.
Paper 2 introduces a fundamentally novel architectural innovation (extremal pooling) that addresses a key limitation in ML potentials for excited states—the breakdown of energy extensivity. This opens an entirely new domain of ML-driven photochemistry simulations across diverse systems. While Paper 1 is a rigorous and important benchmarking study that resolves discrepancies in DFT water simulations, it is primarily methodological validation rather than a new capability. Paper 2's broader applicability to photochemistry, solar energy, atmospheric chemistry, and biology, combined with its conceptual novelty, gives it higher potential for cross-disciplinary impact.
Paper 1 introduces a fundamentally novel machine learning architecture (extremal pooling) that addresses a core physical challenge in excited-state dynamics—the breakdown of energy extensivity. It enables simulations at previously inaccessible scales for photochemistry, with broad applications across solar energy, atmospheric chemistry, and biology. Paper 2 provides useful but incremental benchmarking insights on initialization strategies for a specific quantum computing ansatz, finding that results are largely insensitive to initialization choice. While practically relevant for quantum computing workflows, its scope and transformative potential are narrower compared to Paper 1's general framework for excited-state dynamics.
Paper 1 addresses a fundamental limitation in machine learning potentials for excited-state dynamics, enabling large-scale simulations of photochemical processes previously inaccessible to ab initio methods. Its novel 'extremal pooling' approach and broad applicability across materials science, chemistry, and biology suggest a highly transformative impact. In contrast, Paper 2 provides a valuable but more narrowly focused methodological improvement for calculating ionization potentials within quantum chemistry, which is less likely to drive widespread interdisciplinary breakthroughs.
Paper 2 addresses a fundamental limitation in machine learning interatomic potentials by introducing a size-intensive framework for excited-state dynamics. This conceptual breakthrough enables the simulation of complex photochemical processes at unprecedented scales, opening entirely new domains in chemistry and materials science to MLIPs. While Paper 1 provides a valuable computational efficiency improvement for long-range interactions, Paper 2's methodological innovation solves a critical physical constraint (energy extensivity failure) and has broader potential for transformative applications across diverse scientific fields.
Paper 1 addresses a fundamental limitation in ML potentials—extending them to excited states with correct size-intensive behavior via extremal pooling. This opens an entirely new domain (photochemistry, radiation chemistry, condensed-phase excited-state dynamics) to ML-driven simulation, representing a conceptual breakthrough. Paper 2, while technically impressive in pushing the accuracy-efficiency Pareto frontier for ground-state potentials, is an incremental architectural improvement in a crowded field. Paper 1's novelty, broader scientific applicability across photochemistry, and the introduction of a physically motivated framework for a previously unsolved problem give it greater long-term impact.
Paper 1 presents a fundamental methodological breakthrough in machine learning for excited-state dynamics, overcoming the energy extensivity limitation using extremal pooling. This innovation enables simulations of complex photochemical processes at previously inaccessible length and time scales. Its broad applicability to solar energy, atmospheric chemistry, and biological processes gives it a significantly wider interdisciplinary impact compared to Paper 2, which offers valuable but more specialized fundamental physics insights into hydrogen chemisorption and topological surface states on a specific material class.
Paper 2 addresses a broader and more impactful problem: enabling excited-state molecular dynamics at scales inaccessible to ab initio methods via a novel ML architecture with extremal pooling. It tackles the fundamental challenge of size-intensivity in excited states, demonstrates transferability on the solvated electron (a paradigmatic condensed-phase problem), and opens doors to simulating photochemistry in extended systems. While Paper 1 makes important advances in variational excited-state electronic structure for small molecules, Paper 2's framework has wider applicability across photochemistry, materials science, and atmospheric chemistry, with greater potential for transformative real-world impact.