PULSES: multi-agent AI for autonomous excited-state model building and dynamics

1. Introduction

• Direct quantum-chemical dynamics costs restrict accessible system sizes, environments, timescales and trajectory ensembles, while excited-state models face challenges from coupled surfaces and expensive, method-dependent labels.Training configurations may also cluster in dynamically important regions that equilibrium sampling alone cannot adequately cover.Source: §1 · p. 2
• Building a fit-for-purpose model requires coupled choices about the system, target process, electronic-structure level, sampling, reference data, representation, training, validation and dynamics.A coverage gap or inconsistency found later may require revising sampling, quantum-chemical calculations or the model.Source: §1 · pp. 2–3
• Scientific autonomy requires expert-approved boundaries before execution and stage-specific checks, because technically successful workflows can still produce silent scientific failures.Examples include incorrect state assignments, inadequate sampling, inconsistent units, data leakage or an unsuitable dynamics approximation.Source: §1 · pp. 3–4
• PULSES separates expert-approved planning from execution: a human expert and Planner define objectives, methods and decision boundaries before the Orchestrator coordinates specialist agents and artifact-specific assurance.The assurance agents assess artifacts before they propagate downstream.Source: §1 · p. 4
• PULSES demonstrates specialized excited-state models in perylene assemblies, solvent-dependent biphenyl relaxation and intramolecular proton transfer in 10-hydroxybenzo[h]quinoline.The biphenyl solvent dependence is qualitatively consistent with measurements on a long-chain-substituted derivative, but the different molecules limit direct quantitative comparison.Source: §1 · pp. 4–5

2.1 Expert-approved planning and assurance-gated execution

• After expert approval of a Scientific Execution Contract, PULSES delegates in-scope operations, while assurance agents evaluate artifacts and gate downstream use or recovery.Artifacts can pass, advance conditionally with a persistent warning, or fail and return for revision or escalation; the Orchestrator decides the workflow-level response.Source: Figure 1 · p. 5, §2.1 · p. 6

2.2 Traceable autonomous construction of an ethylene S1 potential

• A 25-trial hyperparameter search brought the ethylene S1 SchNet model above the predefined R² > 0.99 criterion on training, validation, and test sets.The workflow delivered the tuned model with its checkpoint, hyperparameters, and training configuration after the initial model fell short.Source: Figure 2 · p. 8, §2.2 · p. 9

2.3 General performance across excited-state-related tasks

• STCI scores ranged from 25.0 to 100.0, while VBD ranged from (2,2) for benzene single-point work to (7,6) for the complete biphenyl training–relaxation workflow.The benchmarks assess both requested task complexity and validated capability classes connected along a workflow.Source: Table 1 · p. 11, §2.3 · pp. 12–13

2.4 Autonomous construction and evaluation of a perylene exciton model

• After one expansion to 2,900 training dimers, all nine perylene Hamiltonian elements achieved test-set R² ≥ 0.990, but some distance-specific checks remained below target.The remaining failed interval checks had RMSEs below 43 meV; the Orchestrator stopped expansion after diagnostics rather than treating the strict interval criterion as satisfied.Source: §2.4 · p. 14, Figure 3 · p. 15
• On 100 unseen production-MD dimers, perylene Hamiltonian-element RMSEs ranged from 1.48 to 66.21 meV and excitation-energy RMSEs from 25.17 to 64.20 meV; spectrum MAE was 36.7 meV.The unseen-set test followed adaptive model development; the 36.7 meV MAE compares the four excited states with QC exciton-model excitation energies.Source: §2.4 · pp. 14–15, Figure 3 · p. 15

2.5 End-to-end execution of complex workflows: Biphenyl excited-state relaxation in solvents

• Across six aprotic solvents, mean biphenyl torsional-relaxation times increased broadly with viscosity, from 0.254 ps in acetonitrile to 3.519 ps in n-hexadecane.Methanol, ethanol, and 1-butanol means were 0.389, 0.233, and 0.501 ps, respectively, below the aprotic-solvent trend; the observations qualitatively paralleled experiments on a para-substituted derivative.Source: §2.5 · p. 17
• For biphenyl, Figure 4 tracks agent-trained MACE profiles, sampling, test errors, methanol trajectories, and torsional threshold-crossing times versus viscosity across nine solvents.The figure description specifies 48 methanol trajectories and test errors for 100 geometries, but the supplied passages do not state numerical outcomes.Source: Figure 4 · p. 18, §2.5 · p. 18

2.6 End-to-end execution of complex workflows: Gas-phase excited-state proton transfer in HBQ

• HBQ modeling defined a proton-transfer coordinate and sampled both tautomeric basins and the intervening region, labelling 1,000 geometries across enol-like, intermediate, and keto-like configurations.The Orchestrator verified the tautomeric identity of the starting geometry; the MD Agent used GFN-xTB dynamics with well-tempered metadynamics, and separate MACE potentials were trained for S0 and S1.Source: §2.6 · p. 19
• S0/S1 force-component R² values were 0.9962/0.9905 and RMSEs were 0.077/0.123 eV Å⁻¹; corrected test energy MAEs were 0.0246/0.0241 eV.The test partition was excluded from fitting but consulted during S1 refinement and final acceptance, so the reported S1 test metrics do not represent an unseen final test set.Source: §2.6 · p. 19, Figure 5 · p. 21
• 75/100 HBQ trajectories crossed within 100 fs; the fast subset averaged 58.25 fs, while ensemble-averaged coordinate crossing was 67.47 fs, recovering an ultrafast enol-to-keto pathway.Proton transfer was defined as the first crossing of the coordinate from negative to nonnegative values.Source: §2.6 · p. 20, Figure 5 · p. 21
• PULSES completed HBQ preparation, reactive sampling, QC labelling, S0/S1 training, and 100-trajectory simulation in 17.2 h, but its less accurate potentials make it a first-pass screen before expert refinement.The workflow recovered the expected enol-to-keto pathway and ultrafast regime; direct on-the-fly dynamics for the same integration steps would require approximately 2.2 million energy-and-gradient evaluations.Source: §2.6 · p. 20, Figure 5 · p. 21

3. Discussion

• PULSES coordinated data generation, electronic-structure calculations, model construction, and simulation across perylene, biphenyl, and gas-phase HBQ applications.The applications addressed collective excitonic states, nonreactive solvent-dependent torsional relaxation, and reactive proton transfer, respectively.Source: §3 · p. 22
• Scientific Assurance Agents make artifact validation and unresolved uncertainty explicit before outputs propagate downstream, but correlated reasoning errors remain possible.Domain Agents and paired assurance agents may share the same underlying language model.Source: §3 · p. 22
• The study lacks an ablation of the assurance layer and calls for measuring error detection, silent-failure escape rates, and recovery costs.It also proposes examining heterogeneous language models and deterministic validators.Source: §3 · p. 23
• The current implementation models dynamics on separately modeled adiabatic surfaces; nonadiabatic couplings and surface-hopping dynamics remain future extensions.Such extensions would require coordinated learning and validation of energies, gradients, couplings, state tracking, and phase consistency near degeneracies.Source: §3 · p. 23
• Controlled comparisons across models, repeated executions, and matched budgets are needed to distinguish model effects from architectural effects.The authors position PULSES as traceable, checked execution infrastructure for expert-approved strategies, not a substitute for scientific expertise.Source: §3 · p. 23

4.1 PULSES architecture and execution

• The planner and orchestrator coordinate domain agents and Scientific Assurance Agents, with shared artifacts, workflow records, and scheduler continuations supporting execution and traceability.The expert and planner approve an OMWAB contract before the orchestrator receives a frozen, hash-identified plan; changes to objectives, methods, or acceptance criteria require approval unless pre-authorized.Source: §4.1 · pp. 23–24, §4.2 · pp. 24–25

4.3 Scientific validation and revision

• Scientific Assurance Agents assess physical plausibility, methodological consistency, and limitations; PASS permits scoped advancement, INCONCLUSIVE withholds acceptance, and FAIL blocks dependent downstream use.A preliminary pilot entry supports reuse in a high-throughput workflow but does not certify individual production results.Source: §4.3 · p. 25

4.4 Benchmark design and evaluation

• The benchmark compared agent outputs with manual or literature references; 12 tasks ran three times, while three costly workflows ran once without establishing repeatability.Repeated-run tasks were assessed for protocol adherence, completion, artifact validity, and agreement with reference outcomes; scalar outputs used MAE.Source: §4.4 · p. 26

4.5 Ethylene excitation-energy prediction

• The ethylene SchNet model met the R² > 0.99 acceptance criterion on validation and test partitions, achieving test-set R² of 0.9963 and RMSE of 10.1 meV.It was trained from scratch on 800 training, 100 validation, and 100 test conformers to predict S₁ excitation energies.Source: §4.5 · pp. 26–27

4.6 Perylene exciton Hamiltonian learning

• For perylene, an ensemble learned four diabatic energies and five couplings; failed acceptance checks prompted expansion to 2,900 dimers and monomer-swap augmentation to 5,800 examples.Candidate dimers came from controlled configurations and heating trajectories, with an additional unseen-data evaluation described.Source: §4.6 · p. 27

4.7 Biphenyl torsional relaxation in solution

• Separate S₀ and S₁ MACE potentials modeled biphenyl in nine explicit solvents, with 48 vertical-switch trajectories per solvent used to estimate torsional relaxation.Trajectories ran for 100 ps at 298 K and 1 bar; solvent-level mean crossing times were compared across external viscosity values.Source: §4.7 · p. 28

4.8 Excited-state proton transfer in HBQ

• For gas-phase HBQ proton transfer, separate force-weighted MACE potentials were trained on 1,000 geometries, but the original test partition was consulted during S₁ refinement.One hundred coordinate–velocity pairs initialized S₁ switches, each followed by 1 ps of unbiased dynamics; transfer was the first negative-to-nonnegative coordinate crossing.Source: §4.8 · pp. 28–29

4.9 Predictive accuracy and statistical analysis

• Prediction errors were evaluated against retained QC labels with state, Hamiltonian-element, and distance-bin results kept separate; reproducibility records linked configurations, seeds, and artifacts.HBQ serial-equivalent QC timing estimates were distinguished from recorded ML dynamics timings and calendar wall time; complete historical token usage, monetary cost, and human intervention totals were not established.Source: §4.9 · pp. 29–30, §4.10 · p. 30

Supplementary Note 1. Benchmarking Framework

• The 15-task benchmark distinguishes requested task complexity (STCI), demonstrated scientific capability (VBD), and accuracy relative to validated references.Related tasks may be represented as separate cases when their requested workflow scope or stopping point differs.Source: Supplementary Note 1. Benchmarking… · p. 35

1.1 Scientific Task Complexity Index (STCI)

• STCI quantifies each task’s scientific demands using five components defined in Supplementary Table 1, with scores reflecting the fixed task specification independently of execution outcome.Source: §1.1 · p. 35, Table 1 · p. 35

1.2 Verified Breadth-Depth (VBD)

• VBD reports breadth and depth as (B, D), scoring capability classes from validated execution evidence and counting each class at most once toward breadth.Depth measures connected capabilities.Source: §1.2 · p. 35, Table 2 · p. 36, Table 3 · p. 36

1.3 Accuracy and reproducibility

• For scalar-output tasks, accuracy is the three-run mean absolute error against a validated manual reference, not physical accuracy against experiment.Development runs were excluded, and prompts were fixed during evaluation.Source: §1.3 · p. 36
• A repeated workflow passes only when all three executions meet scope-specific criteria without human intervention; expensive demonstrations are instead reported as Validated (n = 1).Multistage criteria include protocol adherence, completion, artifact validity, and agreement with reference outcomes.Source: §1.3 · pp. 36–37

1.4 Scoring summary

• Supplementary Table 4 summarizes STCI component values, verified capability indicators, and resulting STCI and VBD scores across 15 tasks.The supplied passage describes the table's contents but does not provide its task-level values.Source: §1.4 · p. 37, Table 4 · p. 37

1.5 Task-specific acceptance criteria

• Acceptance criteria depend on each task’s stopping scope, while anthracene scan checks include calculation settings, geometry integrity, and extracted exciton outputs.The three recorded anthracene runs document repeated completion with their specified grid protocols.Source: §1.5 · p. 38, §1.6 · p. 38

1.6 Run-level evaluation records

• Run records distinguish the detailed demonstrations from benchmark executions and document planning approval, clarifications, and post-approval autonomy.Clarifications resolved open choices; after approval, no further user input was given.Source: §1.6 · p. 38, §1.7 · pp. 38–39

2.1–2.4 Benzene calculation prompts

• Benzene prompts specify single-point energy, ionization potential, electron affinity, and range-separated-functional tuning calculations with their inputs and requested outputs.The electron-affinity prompt compares def2-svp and def2-svpd; the tuning prompt scans and refines omega.Source: §2.1 · p. 40, §2.2 · p. 40, §2.3 · p. 40

2.5–2.6 Spectroscopy and molecular dynamics

• The perylene spectroscopy prompt requests gas-phase and acetonitrile TDDFT spectra, while the biphenyl prompt specifies solvated GPU molecular dynamics and dihedral analysis.The spectroscopy prompt requests ten excited states and Gaussian broadening; the MD prompt specifies a 5 ns production run.Source: §2.5 · p. 42, §2.6 · p. 43

2.7–2.8 Benzene p-stacking

• Benzene p-stacking prompts distinguish a submission-only 121-geometry scan from a completed interaction-energy surface with a heatmap.The surface prompt defines interaction energy as E_int = E_dimer - 2 * E_monomer and requires all jobs to complete.Source: §2.7 · p. 44, §2.8 · p. 45

2.9 Anthracene exciton-model scan

• The anthracene prompt requests a TeraChem exciton-model scan of dimer energy and coupling surfaces using wPBEh/6-31g* and specified RESP/ESP settings.Source: §2.9 · p. 46

2.10–2.11 Ethylene workflows

• Ethylene prompts cover either a sampling-only handoff or an end-to-end MD-QC-ML workflow, with different stopping scopes and explicit gas-phase NVT conditions.The end-to-end request includes QC for 1,000 conformations, SchNet training, and fallback planning if tuning leaves severe underperformance.Source: §2.10 · p. 47, §2.11 · pp. 47–48

2.12 Perylene dimer excitation-energy scan

• The perylene dimer scan requests exciton-model and supermolecular TDDFT S1–S5 energies across stacking distances, with LE and CT states included and TT states excluded.Source: §2.12 · p. 48

2.13 Perylene exciton model training

• The perylene model-training mission targets the 4×4 Frenkel exciton Hamiltonian’s matrix elements, broad distance coverage, held-out evaluation, and targeted resampling when regions underperform.The prompt specifies bounded QC batches, tuning records before data expansion, and overall and per-distance-bin R² targets of at least 0.95.Source: §2.13 · pp. 48–50

2.14 HBQ ESIPT

• Sample at least 1,000 different conformations spanning the enol-to-TS-to-keto pathway, including the rare TS region, for good training coverage; they need not come from one long trajectory.Use GFN-xTB with PLUMED metadynamics biased along delta_PT = d(O-H) - d(N-H) for sampling. Label each conformation with wb97xd3/6-31G* ground-state S0 and TDA excited-state S1 gradient calculations.Source: §2.14 · p. 51
• Train separate S₀ and S₁ MACE models on labeled energies and forces; if accuracy is inadequate, use ensemble uncertainty to guide additional sampling and retraining.The protocol gives force accuracy R² > 0.99 as a target for a good model.Source: §2.14 · p. 51
• For HBQ dynamics, sample an optimized enol structure at 300 K in the gas phase, vertically switch each of 100 snapshots to S₁, and run 1 ps of unbiased NVE dynamics.The protocol estimates transfer time from when the proton-transfer coordinate crosses zero, averaging crossing times across trajectories.Source: §2.14 · p. 51

2.15 Biphenyl excited-state relaxation in solvents

• For biphenyl, the workflow studies S₁ torsional relaxation after a vertical S₀-to-S₁ switch across nine explicit solvents and compares timescales with documented viscosities.The requested comparison concerns plain biphenyl, not an exact reproduction of substituted-biphenyl Figure 7 or its fluorescence τ2 measurement.Source: §2.15 · pp. 52–53
• For biphenyl, analyze torsional relaxation curves and uncertainty by solvent, testing timescale identifiability and model sensitivity before reporting any viscosity trend.The workflow calls for trajectory-level bootstrap uncertainty and comparison of reasonable relaxation models.Source: §2.15 · p. 53

• Role-specific prompts, registered tools, and domain skills guide agents through scientific software and workflow tasks.Tools have defined input schemas and support molecular preparation, simulation, quantum chemistry, analysis, and reporting.Source: Supplementary Note 3. PULSES… · p. 55
• A Planner develops plans while an Orchestrator coordinates five specialist agents covering molecular preparation, dynamics, quantum chemistry, machine learning, and reporting.Additional agents support workflow design and evaluation, and a separate reviewer can assess scientific evidence when needed.Source: Supplementary Note 3. PULSES… · p. 55
• Shared records and artifact schemas connect plans, runtime settings, scheduler continuations, audits, QC batches, and results through identifiers and checksums.Saved conversation state supports restoration and continuation of planning sessions after long-running jobs.Source: Supplementary Note 3. PULSES… · p. 55
• The application uses Python-based orchestration and scientific software, supports Docker, and can run locally or through Slurm with configured concurrency limits.Development runs used a shared Conda/Mamba environment on the Pascal cluster.Source: Supplementary Note 3. PULSES… · p. 55
• Run archives preserve snapshots, configurations, checksums, job identifiers, and logs; per-call ledgers track model use, but no task-wide token or monetary budget is enforced.Scheduler continuations allow long-running calculations to proceed without continuous agent monitoring.Source: Supplementary Note 3. PULSES… · p. 55

• The contract expresses objectives, approved methods, workflow structure, acceptance criteria, and resource and decision boundaries across three plan sections rather than five mandatory schema fields.The approval record stores the plan, approval status, content hash, snapshot path, and authorization mode.Source: Supplementary Note 4. Expert-approved… · p. 56
• The Planner keeps missing inputs and unresolved scientific choices visible as questions or assumptions for user review.Scientific questions are resolved through Planner–user review, not an independent approval-routine check.Source: Supplementary Note 4. Expert-approved… · p. 56
• The user authorizes execution after review; the application freezes the matching plan version, while changes to scientific scope or requirements need further approval.Approved plans are stored as SHA-256-identified snapshots, and changed drafts do not automatically replace the approved version.Source: Supplementary Note 4. Expert-approved… · p. 56
• Workflow-specific final contracts document the agreed requirements, accepted assumptions, and conditions requiring further approval.The original task prompts are provided in Supplementary Note 2.Source: Supplementary Note 4. Expert-approved… · p. 56

• Deterministic validators check protocol-specific inputs, execution evidence, and outputs, but successful execution alone does not establish scientific acceptance.Checks can cover data integrity, physical quantities, duration, thermodynamic or sampling criteria, workflow execution, and molecular integrity.Source: Supplementary Note 5. Scientific… · p. 57
• Model-based scientific reviewers assess evidence separately from the producing agent, but review pathways differ by domain and equivalent independent reviewers are not established everywhere.The MD reviewer receives a review packet without file-access or modification tools; the QC evaluator can inspect and test files.Source: Supplementary Note 5. Scientific… · p. 57
• PASS accepts only the evaluated stage and permitted downstream use; INCONCLUSIVE withholds acceptance, while FAIL denotes a demonstrated violation.In the MD pathway, blocking deterministic failures cannot be overridden by a favorable model review.Source: Supplementary Note 5. Scientific… · p. 57
• Warnings and limitations persist through handoffs and assessments, while recovery is scope-bounded and lacks a unified budget for repairs, resampling, relabelling, retraining, or total expenditure.Unchanged MD validation requests and repeated executions have separate attempt limits.Source: Supplementary Note 5. Scientific… · pp. 57–58
• After 24 hyperparameter trials, the selected ethylene SchNet model achieved validation R² 0.99861 and test R² 0.99630, following an initial model below the 0.99 target.A GPU-resource failure was handled by retaining 276 valid calculations and rerunning the remaining 724 entries to complete labels for all 1,000 geometries.Source: Supplementary Note 5. Scientific… · p. 58

Dataset and target

• The model predicted the vertical S₁ excitation energy, ΔE₁(R) = Eₛ₁(R) − Eₛ₀(R), from ethylene geometries sampled at 400 K.The 1,000 geometries were labelled with TeraChem at B3LYP/6-31G* within the Tamm–Dancoff approximation.Source: Supplementary Note 6. Ethylene… · p. 59

Training and model selection

• The 1,000 geometries were split into 800 training, 100 validation, and 100 test examples; SchNet was trained from scratch and tuned over 24 additional trials.Trial tune_trial_016 was selected by validation RMSE, and the retained checkpoint was epoch 685 of 700.Source: Supplementary Note 6. Ethylene… · p. 59

Results

• Validation and test RMSEs were 0.007197 and 0.010152 eV, respectively, with R² values of 0.99861 and 0.99630.All partitions came from the same 400 K sampling campaign, so these metrics describe prediction within that sampled ensemble.Source: Supplementary Note 6. Ethylene… · p. 59

7.1 Model definition and scientific scope

• The four-state Hamiltonian represented two local-excitation and two charge-transfer states with nine learned elements; the oppositely directed CT-state coupling was fixed at zero.Phase correction established consistent signs for coupling targets before separate three-member neural-network ensembles were fitted to each element.Source: §7.1 · p. 60

7.2 Candidate generation and dataset allocation

• The 13,000-dimer candidate pool combined controlled rigid-body configurations and MD-derived structures, with candidates grouped by closest intermolecular C–C distance.The initial allocation included 1,600 training, 400 validation, 1,000 test, 1,300 uncertainty, and 8,700 reserve dimers; distance intervals did not capture all orientational or intramolecular variation.Source: §7.2 · p. 60

7.3 Accuracy checks and one round of label expansion

• After 218 of 338 interval checks failed, 1,300 reserve dimers were labelled and added, producing a final training set of 2,900 unique dimers.The single expansion used existing reserve geometries from the fixed pool, not a new MD trajectory or uncertainty-ranked acquisition.Source: §7.3 · p. 61

7.4 Final performance and the stopping decision

• All nine Hamiltonian elements achieved overall test R² ≥ 0.990 with RMSEs of 0.484–13.8 meV, but 87 of 338 interval checks remained below the R² target.The Orchestrator stopped further expansion while recording that the strict interval criterion remained unmet.Source: §7.4 · pp. 61–62
• The four diagonalized excitation energies had test R² values of 0.991–0.998 and RMSEs of 2.50–13.7 meV; all four passed every test interval.Two excitation-energy interval failures occurred in validation, while 85 Hamiltonian-element checks remained failed.Source: §7.4 · pp. 61–62

7.5 Evaluation provenance

• Test geometries were excluded from fitting but their diagnostics informed expansion and stopping; a separate evaluation used 100 previously unseen dimers from one production trajectory.In that evaluation, predictive R² was below 0.95 for ELE1, ELE2, VLE1_CT2, and VLE2_CT1.Source: §7.5 · pp. 62–63

7.6 Selected spectra and their reference calculations

• Diagonalized Hamiltonians yielded excitation energies and eigenvectors, which combined QC diabatic transition dipoles to calculate oscillator strengths and broadened spectra.For 100 production dimers, the dimer excitation-energy MAE and RMSE were 36.7 and 49.1 meV relative to QC exciton-model energies.Source: §7.6 · p. 63

7.7 Reference for the exciton-model framework

• The cited exciton-model framework is Ren, Chen and Liu’s 2025 size-transferable prediction model for excited-state properties of molecular assemblies.The perylene Hamiltonian used that framework as its basis.Source: §7.1 · p. 60, §7.7 · p. 63

Training configurations and QC labels

• Paired S₀/S₁ energies and gradients were calculated for 1,000 torsion-stratified biphenyl geometries, and separate ScaleShiftMACE models were trained for the two states.Test force-component RMSEs were 0.0243 and 0.1295 eV Å⁻¹ for S₀ and S₁, respectively.Source: Supplementary Note 8. Biphenyl… · p. 64

Explicit-solvent dynamics

• The models replaced intramolecular solute interactions during 432 explicit-solvent S₁ trajectories across nine solvents, each propagated for 100 ps.Each vertical switch preserved coordinates, velocities, and box vectors; solvent and solute–solvent interactions remained classical.Source: Supplementary Note 8. Biphenyl… · p. 64

Relaxation observable

• Relaxation time was the first sampled crossing of a threshold derived from each trajectory’s starting and late-time inter-ring angles, averaged across 48 trajectories per solvent.The threshold statistic did not require fitting an exponential decay.Source: Supplementary Note 8. Biphenyl… · p. 64

Error and solvent analyses

• Figure 4c’s bootstrap bands describe within-bin resampling variability, not confidence intervals or variation among independently trained models.The Figure 4e linear fit used only six aprotic solvents, with no uncertainty bars or regression weighting.Source: Supplementary Note 8. Biphenyl… · p. 65

Dataset and models

• The QC-labelled dataset comprised 1,000 geometries selected across enol, intermediate, and keto proton-coordinate regions, with paired S₀/S₁ energies and gradients.Separate ScaleShiftMACE models exceeded force-component R² = 0.99 on validation and test partitions, although S₁ refinement consulted test performance.Source: Supplementary Note 9. Excited-state… · p. 66

Dynamics protocol

• One hundred coordinate–velocity states from a continuous 1 ns S₀ trajectory initialized 1 ps vertical-switch S₁ trajectories.Each trajectory used unbiased NVE dynamics with a 0.5 fs timestep.Source: Supplementary Note 9. Excited-state… · p. 66

First-passage results

• All 100 S₁ trajectories crossed δPT = 0 within 1 ps; the 75 trajectories crossing before 100 fs had a conditional mean of 58.25 fs.Across all 100 trajectories, the mean individual first-passage time was 125.55 fs and the median was 70.69 fs.Source: Supplementary Note 9. Excited-state… · p. 66

Ensemble statistic

• The first zero crossing of the ensemble-mean coordinate occurred at 67.47 fs, distinct from the mean of individual crossing times.The cumulative first-passage distribution counts the fraction of trajectories whose individual crossing time is at or before t.Source: Supplementary Note 9. Excited-state… · p. 67

Supplementary Note 10. Cross-workflow reproducibility and resources

• Metrics are computed per target and partition; force scores pool Cartesian components, while ensemble dispersion is not a confidence interval for predictive performance.Perylene Figure 3d reports per-target RMSE over production dimers without distance-bin averaging or offset correction; biphenyl Figure 4c reports bootstrapped within-bin energy RMSE summaries.Source: Supplementary Note 10. Cross-workflow… · p. 68
• Perylene validation and test errors informed expansion and stopping, so the final test reflects an adaptively developed campaign; the separate 100-dimer production cohort had no further fitting or selection.The production cohort used the same selected ensembles and is reported separately from the original 1,000-dimer development-consulted test partition.Source: Supplementary Note 10. Cross-workflow… · p. 68
• Biphenyl S₀ trajectories used deterministic solvent-dependent velocity seeds, but inspected propagation scripts did not explicitly set Langevin integrator seeds.S₁ trajectories inherited saved S₀ positions, velocities, and box vectors; recorded seeds and disjoint dataset identities do not guarantee statistical independence or bitwise reproducibility.Source: Supplementary Note 10. Cross-workflow… · p. 68
• HBQ model refinement consulted test performance, and its inspected driver did not explicitly seed PyTorch thermostat noise.The shared S0/S1 split was stratified by proton-transfer coordinate and region; selected models used separate training seeds.Source: Supplementary Note 10. Cross-workflow… · pp. 68–69
• 5,486.60 h is the direct-QC serial-equivalent estimate; HBQ's 22.750 h partial sum includes overlapping tasks and excludes several costs.The direct-QC extrapolation assumes one gradient evaluation per molecular step; the HBQ sum excludes unaccounted sampling, failed attempts, queue waiting, analysis, and model-service costs.Source: Supplementary Note 10. Cross-workflow… · p. 69
• Provenance manifests distinguish selected results from intermediate candidates, retries, and earlier campaigns; workflow records also identify enabled components and stage-specific software and hardware.Anthracene runtime profiles record planning, multiple agents, skills, excited-state guidance, and an independent evaluator; software and hardware are associated with individual stages.Source: Supplementary Note 10. Cross-workflow… · p. 69