arxiv: 2604.12607 · v1 · submitted 2026-04-14 · ⚛️ physics.comp-ph · physics.chem-ph

Recognition: unknown

Hierarchical generative modeling for the design of multi-component systems

Rhyan Barrett , Robin Curth , Julia Westermayr

Authors on Pith no claims yet

Pith reviewed 2026-05-10 14:10 UTC · model grok-4.3

classification ⚛️ physics.comp-ph physics.chem-ph

keywords hierarchical generative modelingmulti-component systemscatalyst designgenetic algorithmClaisen rearrangementactivation barriertransition state

0 comments

The pith

A hierarchical generative framework couples genetic search with molecular generation to jointly optimize composition and geometry in multi-component catalytic systems.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a closed-loop method that pairs a genetic algorithm for arranging components in space with a generative model for designing their chemical identities. This joint optimization targets functional multi-component systems such as catalysts and enzymes, where the combinatorial explosion of possibilities makes brute-force search impossible and existing generative tools are limited to single molecules. By holding the central transition-state geometry fixed during search and refining only the surrounding components, the framework steers toward lower activation energies. A sympathetic reader cares because the approach supplies a general, data-driven route to engineering complex molecular environments that single-molecule methods cannot reach.

Core claim

The central claim is that a hierarchical generative optimization framework, formed by coupling a genetic algorithm for configurational search with a generative model for molecular design, enables simultaneous refinement of geometry and composition in multi-component systems. As a proof of concept, the method designs catalytic environments for the Claisen rearrangement of p-tolyl ether around a fixed reference transition-state geometry. Post-hoc Climbing-Image Nudged Elastic Band calculations confirm a 30% reduction in activation barrier, demonstrating that the closed-loop process can produce chemically valid systems with targeted functionality.

What carries the argument

The hierarchical generative optimization framework, which integrates a genetic algorithm to explore spatial configurations with a generative model to propose molecular components.

If this is right

The framework supplies a general strategy for automated, data-driven design of catalysts, enzyme active sites, and advanced materials.
Generative molecular design extends beyond isolated molecules to larger multi-component assemblies whose function depends on both identity and arrangement.
Joint optimization of composition and geometry becomes tractable even when the total number of possible systems is combinatorially large.
Post-hoc validation with methods such as Nudged Elastic Band calculations can confirm functional improvements in the designed systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same closed-loop structure could be applied to other reactions once a reference transition-state geometry is available from computation.
Replacing the current generative model with higher-fidelity architectures might increase the fraction of chemically valid proposals returned by the genetic search.
Iterative application of the framework could refine supramolecular or materials systems whose performance depends on multiple interacting components.

Load-bearing premise

A generative model trained on simpler data can, when paired with a genetic algorithm, reliably produce chemically valid components while exploring the joint space of composition and geometry around a fixed transition-state geometry.

What would settle it

Post-hoc Climbing-Image Nudged Elastic Band calculations performed on the generated catalytic environments that show no reduction in activation barrier or that reveal chemically invalid molecular structures.

Figures

Figures reproduced from arXiv: 2604.12607 by Julia Westermayr, Rhyan Barrett, Robin Curth.

**Figure 2.** Figure 2: FIG. 2. Transition-state test system and environment parameterization. The transition-state geometry [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. a) Progress of the genetic algorithms. Solid lines represent the mean interaction energy of all [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Development of a) the atom type distribution and b) the functional group distribution of the sets of [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. a) Transition state of the Claisen rearrangement of p-tolyl ether with surrounding vectors charac [PITH_FULL_IMAGE:figures/full_fig_p015_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. This figure shows the distribution of a) the number of heavy atoms and b) the atom type distribution [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. (a) Histogram of RMSDs between transition-state region structures obtained from MACE-OFF [PITH_FULL_IMAGE:figures/full_fig_p023_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Reference energies of the test set versus predicted energies of the finetuned MACE-OFF23 medium [PITH_FULL_IMAGE:figures/full_fig_p025_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. Distributions of a) C-C, b) C-N, and c) C-O bonds as well as d) C-C-C, e) C-C-N, and f) C-C-O [PITH_FULL_IMAGE:figures/full_fig_p026_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. UMAP projections of the initial molecule dataset sampled from SPICE and the datasets generated during the different iterations of our workflow for each of the five local positions. XII. CLAISEN REARRANGEMENT REACTION LEWIS STRUCTURES FIG. 11. Lewis structures of reactant and product structures in the studied reaction [PITH_FULL_IMAGE:figures/full_fig_p027_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. Lewis structures of reactant and product structures in the studied reaction [PITH_FULL_IMAGE:figures/full_fig_p027_11.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12. Progress of the genetic algorithms. Solid lines represent the mean interaction energy of all [PITH_FULL_IMAGE:figures/full_fig_p028_12.png] view at source ↗

read the original abstract

The functionality of catalysts, enzymes, and supramolecular assemblies emerges not from individual molecules alone, but from the subtle interplay between multiple components arranged in complex systems. Designing such systems is a grand challenge, the combinatorial explosion of possible chemical compositions and spatial arrangements makes brute-force exploration infeasible, while many current generative approaches remain limited to isolated molecules. In this work, we introduce a hierarchical generative optimization framework that overcomes this barrier by coupling a genetic algorithm for configurational search with a generative model for molecular design. This closed-loop approach enables simultaneous refinement of geometry and composition, efficiently steering discovery toward systems with targeted functionality. As a proof of concept, we design catalytic environments for the Claisen rearrangement of p-tolyl ether by optimizing surrounding components around a fixed reference transition-state geometry. Despite this constraint during the search phase, post-hoc validation via Climbing-Image Nudged Elastic Band calculations confirm a 30% reduction in activation barrier. Beyond this example, our framework provides a general strategy for data-driven discovery of functional multi-component systems, opening the door to automated design of catalysts, enzyme active sites, and advanced materials. Scientific contribution. The study presents a closed loop generative framework that enables joint optimization of molecular components and their spatial organization in multi-component systems. The method moves generative molecular design beyond single molecules toward larger and more complex systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper's hierarchical GA plus generative model loop for joint composition and geometry optimization in multi-component systems is a practical step past single-molecule tools, but the fixed central TS geometry in the Claisen example makes the 30% barrier reduction claim need clearer NEB validation details to hold up.

read the letter

The main takeaway is that this work couples a genetic algorithm for arranging components in space with a generative model that designs the molecules themselves, running them in a closed loop to optimize multi-component setups like catalytic environments. They demonstrate it on the Claisen rearrangement of p-tolyl ether by building around a fixed reference transition state and report a 30% lower activation barrier confirmed by post-hoc climbing-image NEB calculations. This moves generative approaches beyond isolated molecules toward systems where both what the pieces are and how they fit together matter at once. The framing of the combinatorial explosion problem is direct, and the choice of an external validation method like NEB keeps the result from depending only on the optimizer's internal scores. The concrete number from the example gives readers something specific to evaluate rather than just a method sketch. The soft spot sits with the fixed central TS geometry during the search phase. The stress-test concern lands because if the later NEB does not initialize from or converge near that same geometry and reaction coordinate, the reported drop could reflect a shifted or alternative path instead of improved catalysis on the intended one. The abstract gives no information on NEB image setup, whether central atoms relax, or how the baseline barrier was computed under matching conditions, so the full paper needs those specifics to make the claim reliable. Training data for the generative model, GA hyperparameters, and convergence checks are also thin in the summary, which is common in early work but limits immediate reproducibility. This is aimed at computational chemists and materials researchers already using generative models or evolutionary algorithms who want to extend them to interacting multi-component problems. A reader looking for algorithmic ideas to adapt for catalyst or enzyme design would find the framework and the proof-of-concept numbers useful to build from. It deserves a serious referee because the core coupling targets a real gap with a measurable outcome, even though revisions will need to tighten the validation procedure and add baseline comparisons. I would send it for peer review with requests focused on the NEB details and controls.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces a hierarchical generative optimization framework that couples a genetic algorithm for configurational search with a generative model for molecular design, enabling joint optimization of composition and geometry in multi-component chemical systems. As a proof-of-concept, the authors optimize surrounding components around a fixed reference transition-state geometry for the Claisen rearrangement of p-tolyl ether and report a 30% reduction in activation barrier, validated post-hoc by Climbing-Image Nudged Elastic Band (CI-NEB) calculations.

Significance. If the central claim holds, the work provides a general closed-loop strategy for data-driven design of functional multi-component systems such as catalysts and enzyme active sites, extending generative modeling beyond isolated molecules. The external validation via independent NEB calculations is a strength that supports the algorithmic procedure.

major comments (2)

[Abstract and Validation/Results section] The post-hoc CI-NEB validation is load-bearing for the 30% barrier reduction claim (abstract and results). The manuscript must specify whether NEB images were initialized from the fixed reference TS geometry used in the search, whether central transition-state atoms were permitted to relax, and how the baseline barrier (without optimized components) was computed under identical conditions; without this, it is unclear if the reported lowering corresponds to the intended reaction coordinate or an alternative path.
[Abstract and Methods] The abstract and methods provide no information on the training data for the generative model, search hyperparameters, convergence criteria, or controls for false positives in the optimization loop. These details are required to assess whether the framework reliably explores the joint composition-geometry space while producing chemically valid systems.

minor comments (1)

[Abstract] The abstract states that CI-NEB calculations 'confirm a 30% reduction' but does not report the actual barrier values, error estimates, or number of independent runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which have helped us identify areas where the manuscript requires greater clarity. We address each major comment below and will incorporate the necessary revisions in the updated version of the manuscript.

read point-by-point responses

Referee: [Abstract and Validation/Results section] The post-hoc CI-NEB validation is load-bearing for the 30% barrier reduction claim (abstract and results). The manuscript must specify whether NEB images were initialized from the fixed reference TS geometry used in the search, whether central transition-state atoms were permitted to relax, and how the baseline barrier (without optimized components) was computed under identical conditions; without this, it is unclear if the reported lowering corresponds to the intended reaction coordinate or an alternative path.

Authors: We agree that the current description of the post-hoc CI-NEB validation lacks the requested specificity, which is important for interpreting the 30% barrier reduction. In the revised manuscript we will add explicit statements in the Validation/Results section clarifying that (i) all NEB images were initialized from the fixed reference transition-state geometry employed during the generative search, (ii) the central transition-state atoms were permitted to relax during the climbing-image NEB optimization while the surrounding components remained at their optimized positions, and (iii) the baseline barrier was obtained by performing an identical CI-NEB calculation on the reference TS geometry in the absence of the optimized surrounding components, using the same level of theory, convergence thresholds, and computational settings. These additions will confirm that the reported lowering corresponds to the intended reaction coordinate. revision: yes
Referee: [Abstract and Methods] The abstract and methods provide no information on the training data for the generative model, search hyperparameters, convergence criteria, or controls for false positives in the optimization loop. These details are required to assess whether the framework reliably explores the joint composition-geometry space while producing chemically valid systems.

Authors: We concur that these implementation details are essential for reproducibility and for evaluating the robustness of the closed-loop procedure. The revised manuscript will include a new subsection in the Methods section that reports (i) the composition and size of the training dataset used to train the generative model, (ii) the full set of genetic-algorithm hyperparameters (population size, mutation and crossover rates, number of generations), (iii) the convergence criteria applied to the optimization loop, and (iv) the controls implemented to mitigate false positives, including chemical-validity filters, duplicate-structure removal, and independent energy evaluations of candidate systems. revision: yes

Circularity Check

0 steps flagged

No circularity: algorithmic framework with independent post-hoc validation

full rationale

The paper presents a hierarchical generative optimization framework that couples a genetic algorithm for configurational search with a generative model for molecular design. The central result—a 30% activation-barrier reduction for the Claisen rearrangement—is obtained by post-hoc Climbing-Image Nudged Elastic Band calculations performed after the generative+GA search. No equations, fitted parameters, or self-citations are invoked that reduce this empirical outcome to a tautological re-expression of the search inputs or model training data. The method is a closed-loop algorithmic procedure whose reported improvement rests on external, independent quantum-chemical validation rather than any self-definitional or fitted-input construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract provides no explicit free parameters, invented entities, or detailed axioms; the framework implicitly rests on standard assumptions of generative models and evolutionary algorithms being able to produce valid chemistry.

axioms (2)

domain assumption Generative models trained on molecular data can produce chemically reasonable components suitable for multi-component assemblies.
Invoked by the use of a generative model for molecular design in the hierarchical framework.
domain assumption Genetic algorithms can efficiently search the combined space of composition and geometry for functional systems.
Central to the closed-loop optimization described.

pith-pipeline@v0.9.0 · 5539 in / 1402 out tokens · 62809 ms · 2026-05-10T14:10:33.980412+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

68 extracted references · 5 canonical work pages

[1]

Therefore, after each generative phase converged, molecules that lead to the highest stabilization energy increase are collected

Chemical insights and design principles Finally, to gain a better understanding of what influences the reaction rate, chemical analysis of the molecules that lead to a stabilized transition state is performed. Therefore, after each generative phase converged, molecules that lead to the highest stabilization energy increase are collected. As these molecule...
[2]

Environment Construction and Parameterization The first step in the genetic optimization phase is to construct a population of local chemical environments around a given reaction under investigation. In this work, we chose the environment to be five molecules that could be attached to, e.g., enzyme active sites, and position them along a set of predefined...
[3]

For each environment, a molecule is randomly selected for each vectorj, and its correspond- ing parameters(x j, θj, ϕj)are generated randomly within their respective domains

Initial Population and Evaluation An initial population of candidate environments is generated by repeating the above processn times. For each environment, a molecule is randomly selected for each vectorj, and its correspond- ing parameters(x j, θj, ϕj)are generated randomly within their respective domains. This stochastic initialization ensures diversity...
[4]

These selected individuals form the basis for the crossover (or overlap) phase, which is designed to combine favorable traits from different environments (see Figure 5c)

Overlap Phase (Crossover) Following evaluation, the GA proceeds by selecting the top-performing half of the population based on the defined score. These selected individuals form the basis for the crossover (or overlap) phase, which is designed to combine favorable traits from different environments (see Figure 5c). For each vectorj, consider two parent e...
[5]

MPD 2-Router largely recovers this region, leaving residual errors sparse rather than spatially clustered

Mutation Phase Toavoidprematureconvergencetolocaloptima, amutationstepisincorporatedintotheGA(see Figure 5d). During this phase, each parameter of the child environment is subjected to mutation with a fixed probabilityγ. The mutation introduces random changes, thereby allowing exploration of new regions in the parameter space. Mathematically, for any give...

work page doi:10.6084/m9
[6]

P. G. Polishchuk, T. I. Madzhidov, and A. Varnek, Estimation of the size of drug-like chemical space based on gdb-17 data, J. Comput. Aided Mol. Des.27, 675 (2013)

2013
[7]

Reymond, Chemical space as a unifying theme for chemistry, J

J.-L. Reymond, Chemical space as a unifying theme for chemistry, J. Cheminform.17, 6 (2025)

2025
[8]

O. A. von Lilienfeld, K.-R. Müller, and A. Tkatchenko, Exploring chemical compound space with quantum-based machine learning, Nat. Rev. Chem.4, 347 (2020)

2020
[9]

T. A. d. Oliveira, M. P. d. Silva, E. H. B. Maia, A. M. d. Silva, and A. G. Taranto, Virtual screening algorithms in drug discovery: a review focused on machine and deep learning methods, Drugs and Drug Candidates2, 311 (2023)

2023
[10]

Gorgulla, Recent developments in ultralarge and structure-based virtual screening approaches, Annu

C. Gorgulla, Recent developments in ultralarge and structure-based virtual screening approaches, Annu. Rev. Biomed. Data Sci.6, 229 (2023)

2023
[11]

Sci.12, 7866 (2021)

D.E.Graff, E.I.Shakhnovich,andC.W.Coley,Acceleratinghigh-throughputvirtualscreeningthrough molecular pool-based active learning, Chem. Sci.12, 7866 (2021)

2021
[12]

K. Yang, K. Swanson, W. Jin, C. Coley, P. Eiden, H. Gao, A. Guzman-Perez, T. Hopper, B. Kelley, M. Mathea,et al., Analyzing learned molecular representations for property prediction, J. Chem. Inf. Model.59, 3370 (2019)

2019
[13]

Vamathevan, D

J. Vamathevan, D. Clark, P. Czodrowski, I. Dunham, E. Ferran, G. Lee, B. Li, A. Madabhushi, P. Shah, M. Spitzer,et al., Applications of machine learning in drug discovery and development, Nat. Rev. Drug Discov.18, 463 (2019)

2019
[14]

Gómez-Bombarelli, J

R. Gómez-Bombarelli, J. N. Wei, D. Duvenaud, J. M. Hernández-Lobato, B. Sánchez-Lengeling, D. She- berla, J. Aguilera-Iparraguirre, T. D. Hirzel, R. P. Adams, and A. Aspuru-Guzik, Automatic chemical design using a data-driven continuous representation of molecules, ACS Cent. Sci.4, 268 (2018)

2018
[15]

H. H. Loeffler, J. He, A. Tibo, J. P. Janet, A. Voronov, L. H. Mervin, and O. Engkvist, Reinvent 4: Modern ai–driven generative molecule design, J. Cheminform.16, 20 (2024)

2024
[16]

Gao and C

W. Gao and C. W. Coley, The synthesizability of molecules proposed by generative models, J. Chem. Inf. Model.60, 5714 (2020)

2020
[17]

Sanchez-Lengeling and A

B. Sanchez-Lengeling and A. Aspuru-Guzik, Inverse molecular design using machine learning: Gener- ative models for matter engineering, Science361, 360 (2018)

2018
[18]

M. H. Segler, T. Kogej, C. Tyrchan, and M. P. Waller, Generating focused molecule libraries for drug discovery with recurrent neural networks, ACS Cent. Sci.4, 120 (2018)

2018
[19]

W. Jin, R. Barzilay, and T. Jaakkola, Junction tree variational autoencoder for molecular graph gen- eration, inInternational conference on machine learning(PMLR, 2018) pp. 2323–2332

2018
[20]

Brown, M

N. Brown, M. Fiscato, M. H. Segler, and A. C. Vaucher, Guacamol: benchmarking models for de novo molecular design, J. Chem. Inf. Model.59, 1096 (2019). 30

2019
[21]

Gebauer, M

N. Gebauer, M. Gastegger, and K. Schütt, Symmetry-adapted generation of 3d point sets for the targeted discovery of molecules, Adv. Neural Inf. Process. Syst.32(2019)

2019
[22]

N. W. Gebauer, M. Gastegger, S. S. Hessmann, K.-R. Müller, and K. T. Schütt, Inverse design of 3d molecular structures with conditional generative neural networks, Nat. Commun.13, 973 (2022)

2022
[23]

Diffdock: Diffusion steps, twists, and turns for molecular docking.arXiv preprint arXiv:2210.01776, 2022

G. Corso, H. Stärk, B. Jing, R. Barzilay, and T. Jaakkola, Diffdock: Diffusion steps, twists, and turns for molecular docking, arXiv preprint arXiv:2210.01776 (2022)

work page arXiv 2022
[24]

B. Jing, G. Corso, J. Chang, R. Barzilay, and T. Jaakkola, Torsional diffusion for molecular conformer generation, Advances in neural information processing systems35, 24240 (2022)

2022
[25]

Westermayr, J

J. Westermayr, J. Gilkes, R. Barrett, and R. J. Maurer, High-throughput property-driven generative design of functional organic molecules, Nat. Comput. Sci.3, 139 (2023)

2023
[26]

Therrien, E

F. Therrien, E. H. Sargent, and O. Voznyy, Using gnn property predictors as molecule generators, Nature Communications16, 4301 (2025)

2025
[27]

Zhavoronkov, Y

A. Zhavoronkov, Y. A. Ivanenkov, A. Aliper, M. S. Veselov, V. A. Aladinskiy, A. V. Aladinskaya, V. A. Terentiev, D. A. Polykovskiy, M. D. Kuznetsov, A. Asadulaev,et al., Deep learning enables rapid identification of potent ddr1 kinase inhibitors, Nat. Biotechnol.37, 1038 (2019)

2019
[28]

Popova, O

M. Popova, O. Isayev, and A. Tropsha, Deep reinforcement learning for de novo drug design, Science advances4, eaap7885 (2018)

2018
[29]

Blaschke, J

T. Blaschke, J. Arús-Pous, H. Chen, C. Margreitter, C. Tyrchan, O. Engkvist, K. Papadopoulos, and A. Patronov, Reinvent 2.0: an ai tool for de novo drug design, J. Chem. Inf. Model.60, 5918 (2020)

2020
[30]

Wei and J

H. Wei and J. A. McCammon, Structure and dynamics in drug discovery, npj Drug Discov.1, 1 (2024)

2024
[31]

C. J. Cramer and D. G. Truhlar, A universal approach to solvation modeling, Acc. Chem. Res.41, 760 (2008)

2008
[32]

Pakdel, A

S. Pakdel, A. Rasmussen, A. Taghizadeh, M. Kruse, T. Olsen, and K. S. Thygesen, High-throughput computational stacking reveals emergent properties in natural van der waals bilayers, Nat. Commun. 15, 932 (2024)

2024
[33]

M. Korn, C. Ehrt, F. Ruggiu, M. Gastreich, and M. Rarey, Navigating large chemical spaces in early- phase drug discovery, Curr. Opin. Struct. Biol.80, 102578 (2023)

2023
[34]

Y. Liu, X. Huang, X. Yan, T. Zhang, J. Sun, and Y. Liu, Performance optimization engineering of multicomponent absorbing materials based on machine learning, ACS Appl. Mater. Interfaces15, 27056 (2023)

2023
[35]

Zhang, W

Z. Zhang, W. X. Shen, Q. Liu, and M. Zitnik, Efficient generation of protein pockets with pocketgen, Nat. Mach. Intell.6, 1382 (2024)

2024
[36]

S. Wen, W. Zheng, U. T. Bornscheuer, and S. Wu, Generative artificial intelligence for enzyme design: Recent advances in models and applications, Curr. Opin. Green Sustain. Chem.52, 101010 (2025)

2025
[37]

G. Kiss, N. Çelebi-Ölçüm, R. Moretti, D. Baker, and K. Houk, Computational enzyme design, Angew. Chem. Int. Ed.52, 5700 (2013). 31

2013
[38]

W. G. Poole, M. L. Samways, D. Branduardi, R. D. Taylor, M. L. Verdonk, and J. W. Essex, Acceler- ating fragment-based drug discovery using grand canonical nonequilibrium candidate monte carlo, Nat. Commun.16, 6198 (2025)

2025
[39]

Chandraghatgi, H.-F

R. Chandraghatgi, H.-F. Ji, G. L. Rosen, and B. A. Sokhansanj, Streamlining computational fragment- based drug discovery through evolutionary optimization informed by ligand-based virtual prescreening, J. Chem. Inf. Model.64, 3826 (2024)

2024
[40]

C. W. Murray and D. C. Rees, The rise of fragment-based drug discovery, Nat. Chem.1, 187 (2009)

2009
[41]

Elijošius, F

R. Elijošius, F. Zills, I. Batatia, S. W. Norwood, D. P. Kovács, C. Holm, and G. Csányi, Zero shot molecular generation via similarity kernels, Nat. Commun.16, 5991 (2025)

2025
[42]

Irani, M

M. Irani, M. Haqgu, A. Talebi, and M. Gholami, A joint experimental and theoretical study of kinetic and mechanism of rearrangement of allyl p-tolyl ether, J. Mol. Struct. THEOCHEM893, 73 (2009)

2009
[43]

D. P. Kovács, J. H. Moore, N. J. Browning, I. Batatia, J. T. Horton, Y. Pu, V. Kapil, W. C. Witt, I.-B. Magdău, D. J. Cole, and G. Csányi, MACE-OFF: Transferable Short Range Machine Learning Force Fields for Organic Molecules, arXiv (2025), arXiv:2312.15211 [physics]

work page arXiv 2025
[44]

Mardirossian and M

N. Mardirossian and M. Head-Gordon,ωb97m-v: A combinatorially optimized, range-separated hybrid, meta-gga density functional with vv10 nonlocal correlation, J. Chem. Phys.144(2016)

2016
[45]

Grimme, S

S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem.32, 1456 (2011)

2011
[46]

Eastman, P

P. Eastman, P. K. Behara, D. L. Dotson, R. Galvelis, J. E. Herr, J. T. Horton, Y. Mao, J. D. Chodera, B. P. Pritchard, Y. Wang, G. De Fabritiis, and T. E. Markland, SPICE, A Dataset of Drug-like Molecules and Peptides for Training Machine Learning Potentials, Sci. Data10, 11 (2023)

2023
[47]

D. P. Kovács, J. H. Moore, N. J. Browning, I. Batatia, J. T. Horton, Y. Pu, V. Kapil, W. C. Witt, I.-B. Magdau, D. J. Cole,et al., Mace-off: Short-range transferable machine learning force fields for organic molecules, J. Am. Chem. Soc.147, 17598 (2025)

2025
[48]

Henkelman, B

G. Henkelman, B. P. Uberuaga, and H. Jónsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, The Journal of chemical physics113, 9901 (2000)

2000
[49]

A. P. Bartók, R. Kondor, and G. Csányi, On representing chemical environments, Phys. Rev. B87, 184115 (2013)

2013
[50]

McInnes, J

L. McInnes, J. Healy, and J. Melville, Umap: Uniform manifold approximation and projection for dimension reduction, arXiv (2018)

2018
[51]

C. W. Coley, L. Rogers, W. H. Green, and K. F. Jensen, Scscore: Synthetic complexity learned from a reaction corpus, J. Chem. Inf. Model.58, 252 (2018)

2018
[52]

Jeziorski, R

B. Jeziorski, R. Moszynski, and K. Szalewicz, Perturbation theory approach to intermolecular potential energy surfaces of van der waals complexes, Chem. Rev.94, 1887 (1994)

1994
[53]

Adamo and V

C. Adamo and V. Barone, Toward reliable density functional methods without adjustable parameters: The pbe0 model, J. Chem. Phys.110, 6158 (1999). 32

1999
[54]

Uyeda and E

C. Uyeda and E. N. Jacobsen, Enantioselective claisen rearrangements with a hydrogen-bond donor catalyst, J. Am. Chem. Soc.130, 9228 (2008)

2008
[55]

B. M. Wood, M. Dzamba, X. Fu, M. Gao, M. Shuaibi, L. Barroso-Luque, K. Abdelmaqsoud, V. Gharakhanyan, J. R. Kitchin, D. S. Levine, K. Michel, A. Sriram, T. Cohen, A. Das, A. Rizvi, S. J. Sahoo, Z. W. Ulissi, and C. L. Zitnick, UMA: A Family of Universal Models for Atoms, arXiv (2025), 2506.23971

work page arXiv 2025
[56]

D. S. Levine, M. Shuaibi, E. W. C. Spotte-Smith, M. G. Taylor, M. R. Hasyim, K. Michel, I. Batatia, G. Csányi, M. Dzamba, P. Eastman, N. C. Frey, X. Fu, V. Gharakhanyan, A. S. Krishnapriyan, J. A. Rackers, S. Raja, A. Rizvi, A. S. Rosen, Z. Ulissi, S. Vargas, C. L. Zitnick, S. M. Blau, and B. M. Wood, The Open Molecules 2025 (OMol25) Dataset, Evaluations,...

work page arXiv 2025
[57]

Drautz, Atomic cluster expansion for accurate and transferable interatomic potentials, Phys

R. Drautz, Atomic cluster expansion for accurate and transferable interatomic potentials, Phys. Rev. B99, 014104 (2019)

2019
[58]

Batatia, D

I. Batatia, D. P. Kovacs, G. Simm, C. Ortner, and G. Csányi, Mace: Higher order equivariant message passing neural networks for fast and accurate force fields, Adv. Neural Inf. Process. Syst.35, 11423 (2022)

2022
[59]

W. C. Witt, C. van der Oord, E. Gelžinyt˙ e, T. Järvinen, A. Ross, J. P. Darby, C. H. Ho, W. J. Baldwin, M. Sachs, J. Kermode,et al., Acepotentials. jl: A julia implementation of the atomic cluster expansion, J. Chem. Phys.159(2023)

2023
[60]

R. M. Parrish, L. A. Burns, D. G. Smith, A. C. Simmonett, A. E. DePrince III, E. G. Hohenstein, U. Bozkaya, A. Y. Sokolov, R. Di Remigio, R. M. Richard,et al., Psi4 1.1: An open-source electronic structure program emphasizing automation, advanced libraries, and interoperability, J. Chem. Theory Comput.13, 3185 (2017)

2017
[61]

A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dułak, J. Friis, M. N. Groves, B. Hammer, C. Hargus,et al., The atomic simulation environment—a python library for working with atoms, J. Phys.: Condens. Matter29, 273002 (2017)

2017
[62]

Neese, Software update: The orca program system—version 6.0, Wiley Interdiscip

F. Neese, Software update: The orca program system—version 6.0, Wiley Interdiscip. Rev.: Comput. Mol. Sci.15, e70019 (2025)

2025
[63]

Bannwarth, S

C. Bannwarth, S. Ehlert, and S. Grimme, Gfn2-xtb—an accurate and broadly parametrized self- consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions, J. Chem. Theory Comput.15, 1652 (2019)

2019
[64]

Dai, Convergence properties of the bfgs algoritm, SIAM J

Y.-H. Dai, Convergence properties of the bfgs algoritm, SIAM J. Optim.13, 693 (2002)

2002
[65]

J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett.77, 3865 (1996)

1996
[66]

Landrum, Rdkit documentation, Release1, 4 (2013)

G. Landrum, Rdkit documentation, Release1, 4 (2013)

2013
[67]

Himanen, M

L. Himanen, M. O. J. Jäger, E. V. Morooka, F. Federici Canova, Y. S. Ranawat, D. Z. Gao, P. Rinke, and A. S. Foster, DScribe: Library of descriptors for machine learning in materials science, Comput. Phys. Commun.247, 106949 (2020). 33

2020
[68]

McInnes, J

L. McInnes, J. Healy, N. Saul, and L. Grossberger, Umap: Uniform manifold approximation and projection, J. Open Source Softw.3, 861 (2018)

2018