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arxiv: 2412.03831 · v2 · submitted 2024-12-05 · 💻 cs.LG · cs.AI· physics.atm-clus· physics.chem-ph· physics.comp-ph

A large language model-type architecture for high-dimensional molecular potential energy surfaces

Xiao Zhu , Srinivasan S. Iyengar This is my paper

Pith reviewed 2026-05-23 08:15 UTC · model grok-4.3

classification 💻 cs.LG cs.AIphysics.atm-clusphysics.chem-phphysics.comp-ph
keywords potential energy surfacesgraph neural networkshigh-dimensional molecular systemsCCSD accuracywater clusterssubsystem decompositionneural network architectures
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The pith

Graph-based neural networks trained on molecular subsystems scale to predict accurate 186-dimensional potential energy surfaces.

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

The paper introduces an algorithm that represents molecules as graphs containing nodes, edges, and faces to capture subsystem interactions. A family of neural networks is trained on these lower-dimensional subsystems to build potential energy surfaces, first for a 51-nuclear-dimension system and then extended to 186 dimensions. This approach achieves sub-kcal/mol accuracy at CCSD level for the protonated 21-water cluster. A reader would care because direct computation of such high-dimensional surfaces is a major barrier to predicting reaction rates in chemistry.

Core claim

We represent a molecular system as a graph which contains a set of nodes, edges, faces, etc. Interactions between these sets, which represent molecular subsystems, are used to construct the potential energy surface for a 51 nuclear dimensional system using a family of neural networks. We then show that this same family of lower-dimensional graph-based neural networks can be transformed to provide accurate predictions for a 186-dimensional potential energy surface with sub-kcal/mol accuracy, yielding the first efforts towards a full-dimensional potential energy surface for the protonated 21-water cluster at CCSD level accuracy.

What carries the argument

Graph-theoretically obtained subsystem neural networks that are transformed to predict full-dimensional potential energy surfaces from lower-dimensional components.

If this is right

  • The method delivers sub-kcal/mol accuracy on the higher-dimensional potential energy surface problem.
  • It produces the first full-dimensional potential energy surface for the protonated 21-water cluster at CCSD level accuracy.
  • Lower-dimensional subsystem networks can be transformed to handle systems up to 186 nuclear dimensions.
  • The graph representation of molecular interactions enables construction of surfaces for reasonably sized chemical systems.

Where Pith is reading between the lines

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

  • The same subsystem decomposition might reduce computational cost for other many-atom systems where direct high-dimensional training is prohibitive.
  • This could allow mapping of reaction pathways in larger solvated clusters without requiring full ab initio calculations at every point.
  • The graph structure may generalize to non-water molecular systems if subsystem interactions follow similar patterns.

Load-bearing premise

The family of lower-dimensional graph-based neural networks trained on subsystems can be transformed or combined to yield accurate predictions for the full 186-dimensional surface without significant loss of fidelity or introduction of systematic errors from the decomposition.

What would settle it

Direct computation of CCSD energies for multiple configurations of the protonated 21-water cluster and comparison against the model's output would falsify the claim if the errors consistently exceed sub-kcal/mol levels.

Figures

Figures reproduced from arXiv: 2412.03831 by Srinivasan S. Iyengar, Xiao Zhu.

Figure 1
Figure 1. Figure 1: FIG. 1. The density of gray edges represents the number [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Visual illustration of neural networks used to com [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Visual illustration of neural networks used to com [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The common constructs of graph based depiction [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. General flow of data to generate a family of NNs [PITH_FULL_IMAGE:figures/full_fig_p003_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The graphical complexity for the two systems. [PITH_FULL_IMAGE:figures/full_fig_p004_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. The protonated 21 water cluster absolute errors from [PITH_FULL_IMAGE:figures/full_fig_p004_8.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The solvated zundel potential energy absolute errors. [PITH_FULL_IMAGE:figures/full_fig_p004_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. The protonated 21 water cluster potential energy [PITH_FULL_IMAGE:figures/full_fig_p004_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. The protonated 21-water cluster MAE if the trans [PITH_FULL_IMAGE:figures/full_fig_p005_11.png] view at source ↗
read the original abstract

Computing high-dimensional potential energy surfaces for molecular systems and materials is considered to be a great challenge in computational chemistry with potential impact in a range of areas including the fundamental prediction of reaction rates. In this paper, we design and discuss an algorithm that has similarities to large language models in generative AI and natural language processing. Specifically, we represent a molecular system as a graph which contains a set of nodes, edges, faces, etc. Interactions between these sets, which represent molecular subsystems in our case, are used to construct the potential energy surface for a reasonably sized chemical system with 51 nuclear dimensions. For this purpose, a family of neural networks that pertain to the graph-theoretically obtained subsystems get the job done for this 51 nuclear dimensional system. We then ask if this same family of lower-dimensional graph-based neural networks can be transformed to provide accurate predictions for a 186-dimensional potential energy surface. We find that our algorithm does provide accurate results for this larger-dimensional problem with sub-kcal/mol accuracy for the higher-dimensional potential energy surface problem. Indeed, as a result of these developments, here we produce the first efforts towards a full-dimensional potential energy surface for the protonated 21-water cluster (186 nuclear dimensions) at CCSD level accuracy.

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.

Referee Report

2 major / 0 minor

Summary. The manuscript proposes a graph-based neural network architecture inspired by large language models for constructing high-dimensional molecular potential energy surfaces (PES). It first applies a family of such networks to subsystems yielding a 51-nuclear-dimensional PES, then claims that the same family can be transformed to deliver sub-kcal/mol accuracy on the full 186-dimensional PES of the protonated 21-water cluster at CCSD level, presenting this as the first such full-dimensional effort.

Significance. If the central extrapolation claim holds with rigorous validation, the work could offer a scalable route to full-dimensional PES for large clusters, with potential impact on reaction-rate predictions in computational chemistry. The absence of training protocols, error metrics, baselines, and the explicit transformation rule in the provided text, however, prevents assessment of whether the result is reproducible or generalizable.

major comments (2)
  1. [Abstract] Abstract: The central claim that lower-dimensional (51D) graph-based networks 'can be transformed' to yield sub-kcal/mol accuracy on the 186D surface is unsupported by any description of the transformation procedure, error decomposition, or direct numerical comparison against independent CCSD reference values on the full system. This step is load-bearing for the paper's primary result.
  2. [Abstract] Abstract: No training details, validation metrics, error bars, baseline comparisons, or data sources are supplied for either the 51D or 186D cases, making it impossible to evaluate the asserted sub-kcal/mol accuracy or the CCSD-level fidelity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful review and constructive feedback. The comments correctly identify that key supporting details are missing from the current manuscript text, which we will address through revision to improve clarity and reproducibility.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that lower-dimensional (51D) graph-based networks 'can be transformed' to yield sub-kcal/mol accuracy on the 186D surface is unsupported by any description of the transformation procedure, error decomposition, or direct numerical comparison against independent CCSD reference values on the full system. This step is load-bearing for the paper's primary result.

    Authors: We agree that the transformation procedure, error decomposition, and direct numerical comparisons are not described in sufficient detail in the current text. In the revised manuscript we will add an explicit description of the transformation rule applied to the family of networks, an error decomposition analysis, and tabulated direct comparisons of the 186D predictions against independent CCSD reference values on the full protonated 21-water cluster. revision: yes

  2. Referee: [Abstract] Abstract: No training details, validation metrics, error bars, baseline comparisons, or data sources are supplied for either the 51D or 186D cases, making it impossible to evaluate the asserted sub-kcal/mol accuracy or the CCSD-level fidelity.

    Authors: We concur that these elements are required for proper evaluation. The revised manuscript will include the training protocols, validation metrics with error bars, baseline comparisons against other methods, and data sources for both the 51D subsystem and 186D full-system cases. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical performance claims rest on external CCSD benchmarks rather than definitional reduction.

full rationale

The paper trains graph-based networks on 51D subsystems then claims a transformation yields sub-kcal/mol accuracy on the 186D protonated 21-water cluster at CCSD level. No equations, fitted parameters, or self-citations are shown that make the 186D result identical to the 51D inputs by construction. The central step is an empirical extrapolation whose validity is asserted via numerical agreement with independent reference data, not by renaming or re-using the training loss. This is a standard non-circular modeling claim; absence of explicit transformation details is a clarity issue, not a circularity reduction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides insufficient technical detail to enumerate free parameters, axioms, or invented entities; all arrays left empty pending full text review.

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Works this paper leans on

82 extracted references · 82 canonical work pages · 1 internal anchor

  1. [1]

    Molecular Potential Energy Functions; Wiley, New York, 1984

    Murrell, J.; Carter, S.; Farantos, S.; Huxley, P.; Varan- das, A. Molecular Potential Energy Functions; Wiley, New York, 1984

    work page 1984

  2. [2]

    J.; Bowman, J

    Braams, B. J.; Bowman, J. M. Permutationally invari- ant potential energy surfaces in high dimensionality. Int. Revs. Phys. Chem. 2009, 28, 577

    work page 2009

  3. [3]

    Xie, Z.; Bowman, J. M. Permutationally Invariant Poly- nomial Basis for Molecular Energy Surface Fitting Via Monomial Symmetrization. J. Chem. Theory and Com- put. 2010, 6, 26

    work page 2010

  4. [4]

    F.; Rabitz, H

    Alı¸ s,¨O. F.; Rabitz, H. Efficient implementation of high dimensional model representations. J. Math. Chem. 2001, 29, 127–142

    work page 2001

  5. [5]

    Product representation of po- tential energy surfaces

    J¨ ackle, A.; Meyer, H.-D. Product representation of po- tential energy surfaces. J. Chem. Phys.1996, 104, 7974– 7984

    work page 1996

  6. [6]

    The multigrid POTFIT (MGPF) method: Grid representations of potentials for quantum dynamics of large systems

    Pel´ aez, D.; Meyer, H.-D. The multigrid POTFIT (MGPF) method: Grid representations of potentials for quantum dynamics of large systems. J. Chem. Phys. 2013, 138, 014108

    work page 2013

  7. [7]

    Calculating vibrational spec- tra with sum of product basis functions without stor- ing full-dimensional vectors or matrices

    Leclerc, A.; Carrington, T. Calculating vibrational spec- tra with sum of product basis functions without stor- ing full-dimensional vectors or matrices. The Journal of Chemical Physics 2014, 140, 174111

    work page 2014

  8. [8]

    L.; Bowman, J

    Qu, C.; Conte, R.; Houston, P. L.; Bowman, J. M. Full-dimensional potential energy surface for acetylace- tone and tunneling splittings. Phys. Chem. Chem. Phys. 2021, 23, 7758–7767

    work page 2021

  9. [9]

    Position Paper on Materials Design – A Modern Ap- proach

    Grossmann, W.; Eilermann, S.; Rensmeyer, T.; Liebert, A.; Hohmann, M.; Wittke, C.; Niggemann, O. Position Paper on Materials Design – A Modern Ap- proach. 2023; https://arxiv.org/abs/2312.10996

    work page arXiv 2023

  10. [10]

    Vasudevan, R.; Pilania, G.; Balachandran, P. V. Ma- chine learning for materials design and discovery. Jour- nal of Applied Physics 2021, 129, 070401

    work page 2021

  11. [11]

    P.; G´ omez-Bombarelli, R

    Axelrod, S.; Schwalbe-Koda, D.; Mohapatra, S.; Dame- wood, J.; Greenman, K. P.; G´ omez-Bombarelli, R. Learning Matter: Materials Design with Machine Learn- ing and Atomistic Simulations. Accounts of Materials Research 2022, 3, 343–357

    work page 2022

  12. [12]

    S.; Van der Ven, A.; Ceder, G

    Persson, K.; Hinuma, Y.; Meng, Y. S.; Van der Ven, A.; Ceder, G. Thermodynamic and Kinetic Properties of the Li-Graphite System from First-Principles Calculations. Phys. Rev. B 2010, 82, 125416

    work page 2010

  13. [13]

    Scal- able Fragment-Based 3D Molecular Design with Rein- forcement Learning

    Flam-Shepherd, D.; Zhigalin, A.; Aspuru-Guzik, A. Scal- able Fragment-Based 3D Molecular Design with Rein- forcement Learning. 2022

    work page 2022

  14. [14]

    Feynman, R. P. Simulating physics with computers. In- ternational Journal of Theoretical Physics 1982, 21, 467–488

    work page 1982

  15. [15]

    P.; Hey, J.; Allen, R

    Feynman, R. P.; Hey, J.; Allen, R. W. Feynman Lectures on Computation; Addison-Wesley Longman Publishing Co., Inc., 1998

    work page 1998

  16. [16]

    P.; Hibbs, A

    Feynman, R. P.; Hibbs, A. R. Quantum Mechanics and Path Integrals; McGraw-Hill Book Company: New York, 1965

    work page 1965

  17. [17]

    Meyer, H.-D.; Manthe, U.; Cederbaum, L. S. The multi-configurational time-dependent Hartree approach. Chem. Phys. Lett. 1990, 165, 73–78

    work page 1990

  18. [18]

    A.; Chuang, I

    Nielsen, M. A.; Chuang, I. L. Quantum computation and quantum information; Cambridge University Press, Cambridge, 2000

    work page 2000

  19. [19]

    Rabitz, H.; Alı¸ s,¨O. F. General foundations of high di- mensional model representations. J. Math. Chem. 1999, 25, 197–233

    work page 1999

  20. [20]

    Using neural networks, optimized coordinates, and high-dimensional model rep- resentations to obtain a vinyl bromide potential surface

    Manzhos, S.; Carrington Jr, T. Using neural networks, optimized coordinates, and high-dimensional model rep- resentations to obtain a vinyl bromide potential surface. J. Chem. Phys. 2008, 129, 224104

    work page 2008

  21. [21]

    Multi-layer Potfit: An accurate potential repre- sentation for efficient high-dimensional quantum dynam- ics

    Otto, F. Multi-layer Potfit: An accurate potential repre- sentation for efficient high-dimensional quantum dynam- ics. J. Chem. Phys. 2014, 140, 014106

    work page 2014

  22. [22]

    Sumner, I.; Iyengar, S. S. Quantum Wavepacket Ab Ini- tio Molecular Dynamics: An Approach for Comput- ing Dynamically Averaged Vibrational Spectra Includ- ing Critical Nuclear Quantum Effects. J. Phys. Chem. A 2007, 111, 10313

    work page 2007

  23. [23]

    DeGregorio, N.; Iyengar, S. S. Efficient and Adaptive Methods for Computing Accurate Potential Surfaces for Quantum Nuclear Effects: Applications to Hydrogen- Transfer Reactions. J. Chem. Theory Comput.2018, 14, 30–47

    work page 2018

  24. [24]

    Transferability of ma- chine learning potentials: Protonated water neural net- work potential applied to the protonated water hexamer

    Schran, C.; Brieuc, F.; Marx, D. Transferability of ma- chine learning potentials: Protonated water neural net- work potential applied to the protonated water hexamer. J. Chem. Phys. 2021, 154

    work page 2021

  25. [27]

    Accurate Global Potential En- ergy Surfaces for the H + CH 3OH Reaction by Neural Network Fitting with Permutation Invariance

    Lu, D.; Behler, J.; Li, J. Accurate Global Potential En- ergy Surfaces for the H + CH 3OH Reaction by Neural Network Fitting with Permutation Invariance. J. Phys. Chem. A 2020, 124, 5737–5745

    work page 2020

  26. [28]

    Mode specific dynamics in the H 2 + SH− →H + H 2S reaction

    Lu, D.; Qi, J.; Yang, M.; Behler, J.; Song, H.; Li, J. Mode specific dynamics in the H 2 + SH− →H + H 2S reaction. Phys. Chem. Chem. Phys. 2016, 18, 29113–29121

    work page 2016

  27. [29]

    A critical comparison of neu- ral network potentials for molecular reaction dynamics with exact permutation symmetry

    Li, J.; Song, K.; Behler, J. A critical comparison of neu- ral network potentials for molecular reaction dynamics with exact permutation symmetry. Phys. Chem. Chem. Phys. 2019, 21, 9672–9682

    work page 2019

  28. [30]

    S.; Nebgen, B

    Smith, J. S.; Nebgen, B. T.; Zubatyuk, R.; Lubbers, N.; Devereux, C.; Barros, K.; Tretiak, S.; Isayev, O.; Roit- berg, A. E. Approaching coupled cluster accuracy with a general-purpose neural network potential through trans- fer learning. Nat Commun 2019, 10, 2903

    work page 2019

  29. [31]

    A nine-dimensional ab initio global po- tential energy surface for the H 2O+ + H2− →H3O+ + H reaction

    Li, A.; Guo, H. A nine-dimensional ab initio global po- tential energy surface for the H 2O+ + H2− →H3O+ + H reaction. J. Chem. Phys. 2014, 140, 224313

    work page 2014

  30. [32]

    J.; Finney, J

    Lu, F.; Cheng, L.; DiRisio, R. J.; Finney, J. M.; Boyer, M. A.; Moonkaen, P.; Sun, J.; Lee, S. J. R.; Deustua, J. E.; Miller, T. F., III; McCoy, A. B. Fast 9 Near Ab Initio Potential Energy Surfaces Using Machine Learning. J. Phys. Chem. A 2022, 126, 4013–4024

    work page 2022

  31. [33]

    A.; Pablo- Garc´ ıa, S.; Leong, S

    Aldossary, A.; Campos-Gonzalez-Angulo, J. A.; Pablo- Garc´ ıa, S.; Leong, S. X.; Rajaonson, E. M.; Thiede, L.; Tom, G.; Wang, A.; Avagliano, D.; Aspuru-Guzik, A. In Silico Chemical Experiments in the Age of AI: From Quantum Chemistry to Machine Learning and Back. Ad- vanced Materials 2024, 36, 2402369

    work page 2024

  32. [34]

    Generalized neural-network representation of high-dimensional potential-energy sur- faces

    Behler, J.; Parrinello, M. Generalized neural-network representation of high-dimensional potential-energy sur- faces. Phys. Rev. Lett. 2007, 98

    work page 2007

  33. [35]

    Four Generations of High-Dimensional Neu- ral Network Potentials

    Behler, J. Four Generations of High-Dimensional Neu- ral Network Potentials. Chem. Rev. 2021, 121, 10037– 10072

    work page 2021

  34. [36]

    A.; Wolke, C

    Fournier, J. A.; Wolke, C. T.; Johnson, M. A.; Odbadrakh, T. T.; Jordan, K. D.; Kathmann, S. M.; Xantheas, S. S. Snapshots of Proton Accommodation at a Microscopic Water Surface: Understanding the Vi- brational Spectral Signatures of the Charge Defect in Cryogenically Cooled H(H2O)+ n =2–28 Clusters. J. Phys. Chem. A 2015, 119, 37

    work page 2015

  35. [37]

    I.; Diken, E

    Shin, J.-W.; Hammer, N. I.; Diken, E. G.; John- son, M. A.; Walters, R. S.; Jaeger, T. D.; Duncan, M. A.; Christie, R. A.; Jordan, K. D. Infrared Signature of Structures Associated with the H +(H2O)n (N = 6 to

    work page

  36. [38]

    Science 2004, 304, 1137

    Clusters. Science 2004, 304, 1137

    work page 2004

  37. [39]

    S.; Petersen, M

    Iyengar, S. S.; Petersen, M. K.; Day, T. J. F.; Burn- ham, C. J.; Teige, V. E.; Voth, G. A. The Properties of Ion-Water Clusters. I. the Protonated 21-Water Cluster. J. Chem. Phys. 2005, 123, 084309

    work page 2005

  38. [40]

    Iyengar, S. S. Further Analysis of the Dynamically Aver- aged Vibrational Spectrum for the “magic” Protonated 21-Water Cluster. J. Chem. Phys. 2007, 126, 216101

    work page 2007

  39. [41]

    I.; Diken, E

    Hammer, N. I.; Diken, E. G.; Roscioli, J. R.; John- son, M. A.; Myshakin, E. M.; Jordan, K. D.; McCoy, A. B.; Huang, X.; Bowman, J. M.; Carter, S. The Vibrational Predissociation Spectra of the H 5O+ 2·RGn(RG = Ar,Ne) clusters: Correlation of the solvent perturbations in the free OH and shared pro- ton transitions of the Zundel ion. J. Chem. Phys. 2005, 1...

    work page 2005

  40. [42]

    M.; Diken, E

    Headrick, J. M.; Diken, E. G.; Walters, R. S.; Ham- mer, N. I.; Christie, R. A.; Cui, J.; Myshakin, E. M.; Duncan, M. A.; Johnson, M. A.; Jordan, K. Spectral Sig- natures of Hydrated Proton Vibrations in Water Clus- ters. Science 2005, 308, 1765

    work page 2005

  41. [43]

    M.; Iyengar, S

    Dietrick, S. M.; Iyengar, S. S. Constructing Periodic Phase Space Orbits from Ab Initio Molecular Dynam- ics Trajectories to Analyze Vibrational Spectra: Case Study of the Zundel (H 5O+ 2 ) Cation. J. Chem. Theory and Comp. 2012, 8, 4876

    work page 2012

  42. [44]

    R.; Pivonka, N

    Asmis, K. R.; Pivonka, N. L.; Santambrogio, G.; Br¨ ummer, M.; Kaposta, C.; Neumark, D. M.; W¨ oste, L. Gas-Phase Infrared Spectrum of the Protonated Water Dimer. Science 2003, 299, 1375

    work page 2003

  43. [45]

    Dynamics and Infrared Spectroscopy of the Protonated Water Dimer

    Vendrell, O.; Gatti, F.; Meyer, H.-D. Dynamics and Infrared Spectroscopy of the Protonated Water Dimer. Ang. Chem. Intl. Ed. 2007, 46, 6918

    work page 2007

  44. [46]

    G.; Headrick, J

    Diken, E. G.; Headrick, J. M.; Roscioli, J. R.; Bopp, J. C.; Johnson, M. A.; McCoy, A. B. Fundamen- tal Excitations of the Shared Proton in the H 3O− 2 and H5O+ 2 Complexes. J. Phys. Chem. A 2005, 109, 1487

    work page 2005

  45. [47]

    H.; Diken, E

    Robertson, W. H.; Diken, E. G.; Price, E. A.; Shin, J.- W.; Johnson, M. A. Spectroscopic Determination of the OH- Solvation Shell in the OH−(H2O)n Clusters. Science 2003, 299, 1367

    work page 2003

  46. [57]

    Kumar, A.; DeGregorio, N.; Iyengar, S. S. Graph- Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Di- mensions. J. Chem. Theory Comput. 2021, 17, 6671– 6690

    work page 2021

  47. [59]

    Zhu, X.; Iyengar, S. S. Graph Theoretic Molecular Frag- mentation for Multidimensional Potential Energy Sur- faces Yield an Adaptive and General Transfer Machine Learning Protocol. J. Chem. Theory Comput. 2022, 18, 10 5125–5144

    work page 2022

  48. [62]

    S.; Saha, D.; Dwivedi, A.; Lopez-Ruiz, M

    Iyengar, S. S.; Saha, D.; Dwivedi, A.; Lopez-Ruiz, M. A.; Kumar, A.; Zhang, J. H.; Ricard, T. C.; Richerme, P.; Sabry, A. Quantum Algorithms for the Study of Elec- tronic Structure and Molecular Dynamics: Novel Com- putational Protocols. In Comprehensive Computational Chemistry; Elsevier, 2023

    work page 2023

  49. [65]

    Parallel dis- tributed processing model with local space-invariant in- terconnections and its optical architecture

    Zhang, W.; Itoh, K.; Tanida, J.; Ichioka, Y. Parallel dis- tributed processing model with local space-invariant in- terconnections and its optical architecture. Appl. Opt. 1990, 29, 4790–4797

    work page 1990

  50. [66]

    K.; Maclaurin, D.; Iparraguirre, J.; Bom- barell, R.; Hirzel, T.; Aspuru-Guzik, A.; Adams, R

    Duvenaud, D. K.; Maclaurin, D.; Iparraguirre, J.; Bom- barell, R.; Hirzel, T.; Aspuru-Guzik, A.; Adams, R. P. Convolutional networks on graphs for learning molecular fingerprints. Advances in neural information processing systems. 2015; pp 2224–2232

    work page 2015

  51. [67]

    A large language model-type architecture for high-dimensional molecular potential energy surfaces

    Vaswani, A.; Shazeer, N.; Parmar, N.; Uszkoreit, J.; Jones, L.; Gomez, A. N.; Kaiser, L. u.; Polosukhin, I. Attention is All you Need. Advances in Neural Infor- mation Processing Systems. Guyon, I., Luxburg, U. V., Bengio, S., Wallach, H., Fergus, R., Vishwanathan, S., Garnett, R., Eds.; Curran Associates, Inc., 2017; Vol. 30. SUPPORTING INFORMATION A lar...

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  52. [68]

    In Figure S3, the large blue axis refers to the axis of the major moment of inertia, that is smallest inertia value

    We first rotate the fragment geometry coordinates into center of mass coordinates and mass moment of inertia frame of reference. In Figure S3, the large blue axis refers to the axis of the major moment of inertia, that is smallest inertia value

    work page

  53. [69]

    (b) For cases where the major axis projected value is identical, the second major axis pro- jection value is used to resolve the order of atoms

    Following this the atoms are ordered in increasing order of atomic weights, and then (a) increasing order of coordinate projection along the major moment of inertia axis. (b) For cases where the major axis projected value is identical, the second major axis pro- jection value is used to resolve the order of atoms

    work page

  54. [70]

    We then arrive at an ordered list of atoms for any given fragment that consistently represents the chemical environment that the specific atom re- sides within

    work page

  55. [71]

    OH distance 1

    After permuting all atoms based on the relative po- sitions along the fragment moment of inertia axis, the distance matrix is computed and reshaped into a vector to define the fragment descriptor. S3. THE CHALLENGE OF TRANSFERRING FRAGMENT NEURAL NETWORKS ACROSS MOLECULAR SYSTEMS Our goal in this section is to lay the ground work to transfer the neural ne...

    work page

  56. [72]

    Zhu, X.; Iyengar, S. S. Graph Theoretic Molecular Frag- mentation for Multidimensional Potential Energy Sur- faces Yield an Adaptive and General Transfer Machine Learning Protocol. J. Chem. Theory Comput. 2022, 18, 5125–5144

    work page 2022

  57. [73]

    C.; Zhu, X.; Iyengar, S

    Ricard, T. C.; Zhu, X.; Iyengar, S. S. Capturing weak interactions in surface adsorbate systems at coupled clus- ter accuracy: a graph-theoretic molecular fragmentation approach improved through machine learning. J. Chem. Theory Comput. 2023, 19, 8541

    work page 2023

  58. [74]

    Automated Fitting of Neural Network Potentials at Coupled Cluster Accuracy: Protonated Water Clusters as Testing Ground

    Schran, C.; Behler, J.; Marx, D. Automated Fitting of Neural Network Potentials at Coupled Cluster Accuracy: Protonated Water Clusters as Testing Ground. J. Chem. Theory Comput. 2020, 16, 88–99

    work page 2020

  59. [75]

    T.; Szekely, E.; Imbalzano, G.; Behler, J.; Csanyi, G.; Ceriotti, M.; Goetz, A

    Nguyen, T. T.; Szekely, E.; Imbalzano, G.; Behler, J.; Csanyi, G.; Ceriotti, M.; Goetz, A. W.; Paesani, F. Com- parison of permutationally invariant polynomials, neural networks, and Gaussian approximation potentials in rep- resenting water interactions through many-body expan- sions. J. Chem. Phys. 2018, 148

    work page 2018

  60. [76]

    J.; Finney, J

    Lu, F.; Cheng, L.; DiRisio, R. J.; Finney, J. M.; Boyer, M. A.; Moonkaen, P.; Sun, J.; Lee, S. J. R.; Deustua, J. E.; Miller, T. F., III; McCoy, A. B. Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning. J. Phys. Chem. A 2022, 126, 4013–4024

    work page 2022

  61. [77]

    M.; Fraser-Smith, J

    Law, M. M.; Fraser-Smith, J. T.; Perotto, C. U. The potential energy surface of isomerising disilyne. PHYS- ICAL CHEMISTRY CHEMICAL PHYSICS 2012, 14, 6922–6936

    work page 2012

  62. [78]

    F.; Carrington, T., Jr

    Castro, E.; Avila, G.; Manzhos, S.; Agarwal, J.; Schae- fer, H. F.; Carrington, T., Jr. Applying a Smolyak col- location method to Cl 2CO. MOLECULAR PHYSICS 2017, 115, 1775–1785

    work page 2017

  63. [79]

    S.; Ricard, T

    Iyengar, S. S.; Ricard, T. C.; Zhu, X. A reformulation of all ONIOM-type molecular fragmentation approaches using graph theory-based projection operators: Applica- tions to dynamics, molecular potential surfaces, and ma- chine learning and quantum computing. J. Phys. Chem. A 2024, 128, 466

    work page 2024

  64. [80]

    Set Partition- ing via Inclusion Exclusion

    Bj¨ orklund, A.; Husfeldt, T.; Koivisto, M. Set Partition- ing via Inclusion Exclusion. SIAM J. Comput. 2009, 39, 546

    work page 2009

  65. [81]

    H.; Iyengar, S

    Zhang, J. H.; Iyengar, S. S. Graph- |Q⟩⟨C|: A Graph- based Quantum-classical algorithm for efficient elec- tronic structure on hybrid quantum/classical hardware systems: Improved quantum circuit depth performance. J. Chem. Theory Comput. 2022, 18, 2885

    work page 2022

  66. [82]

    S.; Zhang, J

    Iyengar, S. S.; Zhang, J. H.; Saha, D.; Ricard, T. C. Graph-|Q⟩⟨C|: A Quantum Algorithm with Reduced Quantum Circuit Depth for Electronic Structure. J. Phys. Chem. A 2023, 127, 9334

    work page 2023

  67. [83]

    K.; Shah, N

    Dey, T. K.; Shah, N. R. On the number of simplicial complexes in Rd. Comput. Geom. 1997, 8, 267

    work page 1997

  68. [84]

    C.; Franzosa, R

    Adams, C. C.; Franzosa, R. D. Introduction to topology: pure and applied; 2008

    work page 2008

  69. [85]

    Affine spaces

    Berger, M.; Pansu, P.; Berry, J.-P.; Saint-Raymond, X. Affine spaces. In Problems in Geometry; Springer, 1984; p 11

    work page 1984

  70. [86]

    Li, J.; Iyengar, S. S. Ab initio Molecular Dynamics using Recursive, Spatially Separated, Overlapping Model Sub- systems Mixed Within an ONIOM Based Fragmentation Energy Extrapolation Technique. J. Chem. Theory Com- put. 2015, 11, 3978–3991

    work page 2015

  71. [87]

    Li, J.; Haycraft, C.; Iyengar, S. S. Hybrid, Extended La- grangian – Born-Oppenheimer Ab Initio Molecular Dy- namics using Fragment-Based Electronic Structure. J. Chem. Theory Comput. 2016, 12, 2493

    work page 2016

  72. [88]

    On-the-fly

    Haycraft, C.; Li, J.; Iyengar, S. S. Efficient, “On-the-fly” Born–Oppenheimer and Car–Parrinello–type Dynamics with coupled cluster accuracy through Fragment Based Electronic Structure. J. Chem. Theory Comput. 2017, 13, 21887

    work page 2017

  73. [89]

    C.; Haycraft, C.; Iyengar, S

    Ricard, T. C.; Haycraft, C.; Iyengar, S. S. Adaptive, geometric networks for efficient coarse-grained ab initio molecular dynamics with post-Hartree-Fock accuracy. J. Chem. Theory Comput. 2018, 14, 2852

    work page 2018

  74. [90]

    on-the-fly

    Ricard, T. C.; Iyengar, S. S. Efficiently capturing weak interactions in ab initio molecular dynamics through “on-the-fly” basis set extrapolation. J. Chem. Theory Comput. 2018, 14, 5535

    work page 2018

  75. [91]

    Kumar, A.; Iyengar, S. S. Fragment-based electronic structure for potential energy surfaces using a super- position of fragmentation topologies. J. Chem. Theory Comput. 2019, 15, 5769

    work page 2019

  76. [92]

    C.; Iyengar, S

    Ricard, T. C.; Iyengar, S. S. An efficient and accurate ap- proach to estimate hybrid functional and large basis set contributions to condensed phase systems and molecule- surface interactions. J. Chem. Theory Comput. 2020, 16, 4790

    work page 2020

  77. [93]

    C.; Kumar, A.; Iyengar, S

    Ricard, T. C.; Kumar, A.; Iyengar, S. S. Embedded, graph-theoretically defined many-body approximations for wavefunction-in-DFT and DFT-in-DFT: Applica- tions to gas- and condensed-phase ab initio molecular dynamics, and potential surfaces for quantum nuclear effects. Int. J. Quantum Chem. 2020, 120, e26244

    work page 2020

  78. [94]

    Kumar, A.; DeGregorio, N.; Iyengar, S. S. Graph- Theory-Based Molecular Fragmentation for Efficient and Accurate Potential Surface Calculations in Multiple Di- mensions. J. Chem. Theory Comput. 2021, 17, 6671– 6690. 15

    work page 2021

  79. [95]

    H.; Ricard, T

    Zhang, J. H.; Ricard, T. C.; Haycraft, C.; Iyen- gar, S. S. Weighted-Graph-Theoretic Methods for Many- Body Corrections within ONIOM: Smooth AIMD and the Role of High-Order Many-Body Terms. J. Chem. Theory Comput. 2021, 17, 2672–2690

    work page 2021

  80. [96]

    Kumar, A.; DeGregorio, N.; Ricard, T.; Iyengar, S. S. Graph-Theoretic Molecular Fragmentation for Potential Surfaces Leads Naturally to a Tensor Network Form and Allows Accurate and Efficient Quantum Nuclear Dynam- ics. J. Chem. Theory Comput. 2022, 18, 7243

    work page 2022

Showing first 80 references.