Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Neural Network Potential with Multi-Resolution Approach Enables Accurate Prediction of Reaction Free Energies in Solution

T0 review · 3 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A trained neural network potential can replace the expensive quantum-mechanical Hamiltonian inside an explicit-solvent simulation and reproduce experimental reaction free energies within a few kJ/mol across very different chemical systems.

desk verdict A practical ML/MM workflow with real experimental grounding; the DFT-proxy caveat and two Ni misclassifications keep it from being a clean sweep, but it deserves serious referee time. read the letter →

arxiv 2411.19728 v1 pith:3X76HQY2 submitted 2024-11-29 physics.chem-ph

Felix Pultar , Moritz Thuerlemann , Igor Gordiy , Eva Doloszeski , Sereina Riniker This is my paper · ORCID
classification physics.chem-ph
keywords neuralnetworkpotentialQM/MManisotropicmessagepassingelectrostaticembeddingfreeenergyumbrellasamplingexplicitsolventreaction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper tries to establish that a neural network potential can stand in for the expensive quantum-mechanical Hamiltonian inside a QM/MM simulation without losing accuracy, so that reaction free energies in explicit solvent can be computed by sampling hundreds of nanoseconds rather than by static high-level calculations. It reports that the anisotropic message passing architecture reproduces DFT energies and forces below chemical accuracy for three demanding test beds: alanine dipeptide, nickel phosphine complexes, and charged pyridine and quinoline dimers. It then shows that free energies from ML/MM umbrella sampling agree with experimental values within a few kJ/mol, while static DFT with implicit solvent and QM/MM simulations using a semi-empirical Hamiltonian deviate by up to ten times more and can even rank the wrong species. If the central claim is correct, the result would remove the main sampling bottleneck of QM/MM for condensed-phase reactivity studies.

What carries the argument

The central object is the AMP (anisotropic message passing) neural network potential, an equivariant graph neural network that places atomic multipoles (monopole, dipole, quadrupole) on each atom and uses multipole-interaction coefficients to make the messages directionally sensitive. The model is embedded in a QM/MM-style total energy $V_{\text{total}} = V_{\text{QM}} + V_{\text{QM-MM}} + V_{\text{MM}}$, with a Coulomb monopole-monopole term inside the QM zone for interactions beyond the graph cutoff, Lennard-Jones plus multipole-electrostatic coupling to MM point charges, and an MM-charge-induced polarization term added to the QM multipoles. This machinery does two jobs at once: it keeps the description of long-range and directional electrostatics physical enough to stabilize charged and metal-containing solutes in explicit solvent, and it is cheap enough to run umbrella sampling with tens of thousands of solvent atoms for hundreds of nanoseconds.

What would settle it

Compute the dissociation free energy of one challenging dimer, such as 7f or 6l, using explicit-solvent QM/MM umbrella sampling directly at the omegaB97M-D4/def2-TZVPP level of theory without any neural network, and compare the result with the AMP/MM prediction; if the directly sampled value differs from the AMP/MM value by more than the reported few kJ/mol, the network is not faithfully replacing the QM Hamiltonian for that system.

Watch

Extended reading notes

Core claim

The central claim is that substituting a QM Hamiltonian with the AMP neural network potential in an electrostatic-embedding ML/MM scheme preserves the accuracy of the underlying DFT reference while making long enhanced-sampling molecular dynamics tractable, and that the resulting free energies match experiment. Evidence includes a two-dimensional alanine dipeptide free-energy surface whose minima match DFT and NMR-derived expectations even when the network was trained on only a narrow slice of the torsional space; dissociation free energies for nickel phosphine complexes that rank experimentally mono- and bisligated states correctly, including large complexes absent from the training set; and dissociation free energies for a series of charged pyridine and quinoline dimers with a median absolute error of 2.63 kJ/mol, with static DFT plus implicit solvent off by seven to eleven times more. The paper further shows the approach scales to systems with more than 350 solute atoms embedded in tens of thousands of solvent atoms, and that inference is fast enough to run on a single CPU for small systems.

Load-bearing premise

The central premise is that the DFT reference used for training (B2-PLYP for alanine dipeptide and omegaB97M-D4 for the nickel and pyridine systems), evaluated with fixed MM point charges, is accurate enough to stand in for the experimentally measured free energies once explicit solvent and sampling are included; if that DFT-plus-charges model carries systematic error, the trained network inherits it and so do all three benchmark predictions.

Editorial extensions

If this is right

  • For reaction free energies in solution, long enhanced-sampling MD becomes feasible at near-DFT accuracy because the neural network Hamiltonian is cheap enough to evaluate for hundreds of nanoseconds with explicit solvent.
  • The same trained model can be applied to chemically related molecules that were absent from the training set, so one training dataset can cover a family of ligands or substituted dimers without per-molecule retraining.
  • Static DFT with implicit solvent and semi-empirical QM/MM can be wrong by up to an order of magnitude in free energy and sometimes rank the wrong state; replacing the QM Hamiltonian with the trained network removes most of that error.
  • Free-energy differences between bound and unbound states can be computed with median absolute errors around 2-3 kJ/mol, at or below the usual chemical-accuracy threshold of 4.184 kJ/mol.
  • The approach extends to transition-metal complexes, charged species, and large ligands where analytical Hessian calculations become impractical, so mechanistic questions that static methods cannot address become accessible.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the central claim is right, a substantial share of the error in static QM free energies comes from missing sampling and explicit solvent rather than from the DFT functional itself, which suggests that other ML/MM potentials could inherit this accuracy improvement without architectural changes.
  • The paper hints that a globally trained foundational potential fine-tuned on a few dozen examples per target could replace per-system training; that is a natural next step the authors describe but do not demonstrate.
  • Because the solvent is represented by fixed MM point charges, the method's accuracy is ultimately capped by that point-charge description of the environment; testing a polarizable MM model or a larger QM zone would show whether remaining outliers are due to the embedding or to Lennard-Jones parameters.
  • The authors note that a larger network did not meaningfully improve free-energy predictions, which implies that for these observables the DFT label error, not network capacity, may dominate; retraining the same architecture on a different high-level functional would test that interpretation directly.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper presents an extended version of the anisotropic message passing (AMP) neural network architecture for ML/MM simulations with electrostatic embedding, and applies it to compute free energies for three systems: alanine dipeptide conformational sampling, ligation states of nickel phosphine complexes, and dissociation free energies of charged pyridine/quinoline dimers. The model is trained on DFT energies and gradients evaluated in the field of fixed MM point charges, then used as the QM Hamiltonian in umbrella-sampling MD with explicit solvent. The authors report training errors below chemical accuracy, stable trajectories in prospective simulations, and computed free energies that are compared with experimental data and with static DFT/implicit-solvent and GFN2-xTB QM/MM calculations.

Significance. If the claims are validated, the approach is a significant methodological advance: it demonstrates electrostatic-embedding ML/MM simulations of explicitly solvated systems with hundreds of QM atoms over hundreds of nanoseconds, including quantitative free-energy predictions for challenging charged dimers and transition-metal complexes. The paper's strengths include independent experimental benchmarks (NMR ligation states in Ref. [102], experimental dissociation free energies in Ref. [119]) rather than validation only against training labels, explicit discussion of limitations (footnote 4 on the absence of a double-hybrid explicit-solvent ground truth; the LJ-parameter hypothesis for 5b), and releases of training data and code. The experimental agreement provides an independent grounding of the central claim, although the nickel application shows partial misclassifications that temper the 'excellent agreement' wording.

major comments (3)
  1. [Section 3.2 (Nickel complex application), Figure 7] The abstract's claim of 'excellent agreement with experimental data' is overstated for the nickel phosphine application: two of ten complexes are misclassified by the AMP models (CataCXium A in both entries, CyJohnPhos in entry 7), and the value for Pt-Bu3 is set arbitrarily to 41.84 kJ/mol because the bisligated complex dissociated in simulation. This post hoc assignment directly influences the classification success rate and should not be counted as a quantitative prediction. Please report classification accuracy and confidence intervals on ΔGdiss, treat Pt-Bu3 as a qualitative dissociation event, and either exclude it from numerical error statistics or justify why the arbitrary value is not biasing the conclusion.
  2. [Section 5.3 and footnote 4] All training labels are DFT energies evaluated in a fixed-charge QM/MM embedding (B2-PLYP/def2-QZVPP for alanine dipeptide; ωB97M-D4/def2-TZVPP for the other systems), with no explicit-solvent CCSD(T)- or double-hybrid-level reference. The experimental benchmarks therefore validate the combined pipeline (DFT reference + explicit solvent + NNP sampling), not the NNP substitution in isolation. This limitation is acknowledged in footnote 4, but the abstract's statement that the NNP has 'the same accuracy' as the QM Hamiltonian should be qualified. A small explicit-solvent high-level benchmark (e.g., a few pyridine dimers at DLPNO-CCSD(T) level) would directly quantify the systematic error of the reference labels and materially strengthen the central claim.
  3. [Section 2.3.2, Eq. (16)] The expression for the MM-induced multipoles contains a sum over all QM atoms i on the right-hand side for a quantity indexed by i on the left-hand side. As written, the equation suggests a nonlocal polarization term that redistributes multipoles across the entire QM zone, which is inconsistent with the per-atom polarizability description in the text. Please clarify the summation limits (presumably only over MM atoms j for each fixed i) or explain the intended global contribution. This is a technical description that directly affects the reproducibility of the method.
minor comments (5)
  1. [Section 3.1, Table 2] The comparison between AMP free-energy minima and static B2-PLYP minima mixes two different definitions of 'minimum': free-energy surface local minima from umbrella sampling versus optimized geometries with quasi-RRHO corrections. A direct comparison using the same state definition (e.g., same integration regions on the free-energy surface) would make the quantitative agreement for alanine dipeptide more transparent.
  2. [Section 3.2, Figure 10] The phrase 'up to ten times higher deviation' for static QM methods is an overstatement; the reported medAE values are about 5-8 times higher than the AMP medAE. Please rephrase to 'roughly five to eight times higher' or provide the maximum ratio explicitly.
  3. [Section 3.2, discussion after Eq. (19)] The arbitrary assignment of the Pt-Bu3 dissociation free energy is mentioned in a note in the text but should be highlighted in the main body of the results because it is a central caveat for interpreting the nickel classification numbers.
  4. [Section 2.3.3, Figure 2] The scaling claim O(N^1.24) is based on CPU inference steps per second, while the GPU scaling is described only qualitatively. Please report error bars or confidence intervals for the fitted scaling exponents and specify the system sizes used for each point on the GPU curve.
  5. [Throughout (Eqs. (6), (14), (15))] There are several formatting artifacts (e.g., 'bracehtipupleft' in Eq. (6), the limits in Eq. (14), and the placement of summation indices in Eq. (15)). Please ensure the equations are typeset cleanly so that the summation ranges and tensor indices are unambiguous.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the free-energy predictions are benchmarked against independent experimental datasets (NMR ligation states, experimental dissociation free energies), and the NNP's agreement with its DFT training reference is a fidelity check, not the claimed experimental validation.

full rationale

The paper's derivation chain is: train AMP to reproduce DFT energies and gradients in an electrostatic embedding, then use the trained model as a Hamiltonian in explicit-solvent enhanced-sampling MD, and compare the resulting free energies to experiment. Each leg is externally grounded: the DFT labels are fixed references (B2-PLYP or omegaB97M-D4), not derived from the experimental targets; the free-energy predictions for nickel set 4 and for pyridine/quinoline dimers are checked against independent NMR and thermodynamic data rather than against training labels; and the dissociation free energies are emergent from umbrella-sampling reweighting, not fitted parameters. The main self-citations (AMP architecture, Ref. 14, and prior ML/MM work, Refs. 66-67) are descriptive: the present paper re-implements, modifies, and independently tests the architecture, so no load-bearing claim reduces to a self-citation. The acknowledged limitations (Section 2.2's presupposition that a QM-reference-trained model recovers experiment, and footnote 4's lack of an explicit-solvent double-hybrid ground truth) are accuracy caveats about the DFT proxy, not circular steps. The alanine-dipeptide comparison to B2-PLYP static minima is a consistency check at the training level of theory, but it is supplemented by experimental and literature comparison, so it does not make the central claim circular.

Assumptions & free parameters 6 free parameters · 4 assumptions · 1 invented entities

The central claim rests on no new physical particles or forces. The load-bearing ingredients are the DFT ground-truth labels, the xTB-generated training distribution, classical LJ parameters, and the reweighting protocol. Several cutoffs and loss weights are hand-chosen and influence the results, so they are listed as free parameters.

free parameters (6)
  • QM graph cutoff r_cutoff = 5.0 A
    Chosen hyperparameter controlling graph neighborhood; affects which interactions are learned versus treated by the explicit Coulomb term. Table 5.
  • QM/MM polarization cutoff = 9.0 A (600k) / 10.0 A (2.7M)
    Defines the range over which MM charges induce multipoles in the QM zone; hand-set in Table 5.
  • QM/MM electrostatics cutoff = 14.0 A
    Cutoff for multipole-monopole interactions between QM and MM particles; hand-set and suspected as a possible source of nickel free-energy offset.
  • Multipole channels = 32 (600k) / 64 (2.7M)
    Architecture capacity choice; the paper reports that the larger model changes error magnitudes, so results depend on this hand-chosen setting.
  • Loss balancing prefactors = alpha=0.99, beta=100, gamma=100
    Hand-set weights in Eq. 18 that balance energies, forces, and multipole predictions in the training objective.
  • Nickel Lennard-Jones parameters = epsilon=23.6 kJ/mol, sigma=2.27 A
    Taken from the literature (Ref. 138) and used directly in VLJ,QMMM; the authors list LJ parameters as a possible cause of the nickel misclassifications.
assumptions (4)
  • domain assumption DFT reference energies are an adequate proxy for experimental free energies in solution.
    All training labels are B2-PLYP/def2-QZVPP or omegaB97M-D4/def2-TZVPP energies with fixed MM point charges (Section 5.3); no explicit-solvent CCSD(T)-level validation is provided (footnote 4).
  • domain assumption GFN2-xTB biased trajectories cover the configuration space visited by prospective ML/MM sampling.
    Training snapshots originate only from xTB QM/MM runs at elevated temperatures and electronic temperature (Section 5.3); extrapolation to AMP/MM sampling is assumed.
  • domain assumption Classical fixed-charge MM and LJ parameters accurately describe MM and QM-MM non-electrostatic interactions.
    VLJ,QMMM uses unmodified force-field parameters (Eq. 12, Section 5.2); the authors explicitly name LJ parameters as a possible error source for nickel complexes.
  • domain assumption WHAM/MBAR reweighting and the chosen bound/unbound definitions give unbiased free energies.
    Data analysis in Section 5.5; no volume correction is applied, and for very high nickel DeltaGdiss values the well depth is used instead of the formal quotient.
invented entities (1)
  • Learned per-atom polarizability alpha_i and MM-induced multipoles M^k_{i,QM-MM}
    purpose: Models polarization of the QM zone by MM point charges through Eq. 16.
    These are internal machine-learned degrees of freedom with no external falsifiable handle beyond the model's own energies and forces; they are not proposed as physical observables.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Neural Network Potential with Multi-Resolution Approach Enables Accurate Prediction of Reaction Free Energies in Solution." pith.science (2026). https://pith.science/paper/3X76HQY2

@misc{pith2026241119728,
  author       = {Pith},
  title        = {Pith review of: Neural Network Potential with Multi-Resolution Approach Enables Accurate Prediction of Reaction Free Energies in Solution},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3X76HQY2}},
  note         = {Machine review of arXiv:2411.19728}
}
read the original abstract

We present design and implementation of a novel neural network potential (NNP) and its combination with an electrostatic embedding scheme, commonly used within the context of hybrid quantum-mechanical/molecular-mechanical (QM/MM) simulations. Substitution of a computationally expensive QM Hamiltonian by a NNP with the same accuracy largely reduces the computational cost and enables efficient sampling in prospective MD simulations, the main limitation faced by traditional QM/MM set-ups. The model relies on the recently introduced anisotropic message passing (AMP) formalism to compute atomic interactions and encode symmetries found in QM systems. AMP is shown to be highly efficient in terms of both data and computational costs, and can be readily scaled to sample systems involving more than 350 solute and 40'000 solvent atoms for hundreds of nanoseconds using umbrella sampling. The performance and broad applicability of our approach are showcased by calculating the free-energy surface of alanine dipeptide, the preferred ligation states of nickel phosphine complexes, and dissociation free energies of charged pyridine and quinoline dimers. Results with this ML/MM approach show excellent agreement with experimental data. In contrast, free energies calculated with static high-level QM calculations paired with implicit solvent models or QM/MM MD simulations using cheaper semi-empirical methods show up to ten times higher deviation from the experimental ground truth and sometimes even fail to reproduce qualitative trends.

Figures

Figures reproduced from arXiv: 2411.19728 by the authors.

Figure 1
Figure 1. Schematic illustration of the trade-offs between system size and sampling approach when [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Number of inference steps per second (left axis) and estimated inference speed (right axis, [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. (A): Correlation of predicted QM gradients and reference QM gradients using AMP trained on 80’000 data points from the entire ϕ/ψ space of alanine dipeptide (entry 1 in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: Free-energy landscape and local minima (white dots) calculated via umbrella sampling [ [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: Schematic representation of nickel η 2 carbonyl phosphine complexes from Ref. [102] and the dissociation process investigated alongside ligand structures. As for the alanine dipeptide system, initial investigations focused on the amount of training data required to rep…
Figure 6
Figure 6. Figure 6: (A): Correlation of predicted QM gradients and reference QM gradients using AMP (entry 7 in [PITH_FULL_IMAGE:figures/full_fig_p015_6.png]
Figure 7
Figure 7. Figure 7: Free-energy calculation and ligand state assignment of ten nickel phosphine complexes with [PITH_FULL_IMAGE:figures/full_fig_p016_7.png]
Figure 8
Figure 8. Figure 8: Schematic representation of pyridine and quinoline structures from Ref. [ [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: (A): Correlation of predicted QM gradients and reference QM gradients using AMP (entry 7 in [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]
Figure 10
Figure 10. Figure 10: Correlation of experimental and theoretical dissociation free energies computed for a subset [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. NepoIP/MM: Towards Accurate Biomolecular Simulation with a Machine Learning/Molecular Mechanics Model Incorporating Polarization Effects

    physics.chem-ph 2025-02 conditional novelty 6.0 of 10

    A machine-learning force field that takes the surrounding electrostatic potential as input reproduces QM/MM-quality peptide dynamics and transfers across water and protein environments.

Reference graph

Works this paper leans on

172 extracted references · 69 canonical work pages · cited by 1 Pith paper

  1. [102]

    S. H. Newman-Stonebraker, S. R. Smith, J. E. Borowski, E. Peters, T. Gensch, H. C. Johnson, M. S. Sigman, A. G. Doyle,Science 2021, 374, 301–308

    work page 2021

  2. [119]

    Pollice, M

    R. Pollice, M. Bot, I. J. Kobylianskii, I. Shenderovich, P. Chen,J. Am. Chem. Soc. 2017, 139, 13126–13140

    work page 2017

  3. [1]

    Vennelakanti, A

    V. Vennelakanti, A. Nazemi, R. Mehmood, A. H. Steeves, H. J. Kulik,Curr. Opin. Struct. Biol. 2022, 72, 9–17

    2022

  4. [2]

    Bursch, J

    M. Bursch, J. Mewes, A. Hansen, S. Grimme,Angew. Chem. Int. Ed. 2022, 61, e202205735

    2022

  5. [3]

    Seritan, C

    S. Seritan, C. Bannwarth, B. S. Fales, E. G. Hohenstein, C. M. Isborn, S. I. L. Kokkila-Schumacher, X. Li, F. Liu, N. Luehr, J. W. Snyder, C. Song, A. V. Titov, I. S. Ufimtsev, L. Wang, T. J. Martínez, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2020, 11, e1523

    2020

  6. [4]

    Kussmann, H

    J. Kussmann, H. Laqua, C. Ochsenfeld,J. Chem. Theory Comput. 2021, 17, 1512–1521

    2021

  7. [5]

    Neese, F

    F. Neese, F. Wennmohs, U. Becker, C. Riplinger,J. Chem. Phys. 2020, 152, 224108

    2020

  8. [6]

    Neese, Wiley Interdiscip

    F. Neese, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2022, 12, e1606

    2022

Show all 172 references
  1. [7]

    J. A. Keith, V. Vassilev-Galindo, B. Cheng, S. Chmiela, M. Gastegger, K.-R. Müller, A. Tkatchenko, Chem. Rev. 2021, 121, 9816–9872

    2021

  2. [8]

    O. T. Unke, S. Chmiela, H. E. Sauceda, M. Gastegger, I. Poltavsky, K. T. Schütt, A. Tkatchenko, K.-R. Müller, Chem. Rev. 2021, 121, 10142–10186

    2021

  3. [9]

    Warshel, M

    A. Warshel, M. Karplus, J. Am. Chem. Soc. 1972, 94, 5612–5625

    1972

  4. [10]

    Warshel, M

    A. Warshel, M. Levitt, J. Mol. Biol. 1976, 103, 227–249

    1976

  5. [11]

    U. C. Singh, P. A. Kollman,J. Comput. Chem. 1986, 7, 718–730

    1986

  6. [12]

    H. M. Senn, W. Thiel, Angew. Chem. Int. Ed. 2009, 48, 1198–1229

    2009

  7. [13]

    Brunk, U

    E. Brunk, U. Rothlisberger, Chem. Rev. 2015, 115, 6217–6263

    2015

  8. [14]

    Thürlemann, S

    M. Thürlemann, S. Riniker,The Eleventh International Conference on Learning Representations 2023

    2023

  9. [15]

    Bannwarth, S

    C. Bannwarth, S. Ehlert, S. Grimme,J. Chem. Theory Comput. 2019, 15, 1652–1671

    2019

  10. [16]

    Bannwarth, E

    C. Bannwarth, E. Caldeweyher, S. Ehlert, A. Hansen, P. Pracht, J. Seibert, S. Spicher, S. Grimme, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2021, 11, e1493

    2021

  11. [17]

    W. Kohn, L. J. Sham, Phys. Rev. 1965, 140, A1133–A1138

    1965

  12. [18]

    Møller, M

    C. Møller, M. S. Plesset, Phys. Rev. 1934, 46, 618–622

    1934

  13. [19]

    Riniker, J

    S. Riniker, J. Chem. Inf. Model. 2018, 58, 565–578

    2018

  14. [20]

    W. F. van Gunsteren, H. J. C. Berendsen,Angew. Chem. Int. Ed. 1990, 29, 992–1023

    1990

  15. [21]

    Gelpi, A

    J. Gelpi, A. Hospital, R. Goñi, M. Orozco,Adv. Appl. Bioinform. Chem. 2015, 37–47

    2015

  16. [22]

    W. F. van Gunsteren, C. Oostenbrink,J. Chem. Inf. Model. 2024, 64, 6281–6304

    2024

  17. [23]

    L. Hu, U. Ryde, J. Chem. Theory Comput. 2011, 7, 2452–2463

    2011

  18. [24]

    Šebesta, V

    F. Šebesta, V. Sláma, J. Melcr, Z. Futera, J. V. Burda,J. Chem. Theory Comput. 2016, 12, 3681–3688

    2016

  19. [25]

    A. C. T. van Duin, S. Dasgupta, F. Lorant, W. A. Goddard,J. Phys. Chem. A 2001, 105, 9396–9409

    2001

  20. [26]

    Y. Guo, C. Riplinger, U. Becker, D. G. Liakos, Y. Minenkov, L. Cavallo, F. Neese,J. Chem. Phys. 2018, 148, 011101

    2018

  21. [27]

    J. J. P. Stewart, J. Mol. Model. 2012, 19, 1–32

    2012

  22. [28]

    M. Gaus, Q. Cui, M. Elstner,J. Chem. Theory Comput. 2011, 7, 931–948. 26

    2011

  23. [29]

    Schmid, A

    N. Schmid, A. P. Eichenberger, A. Choutko, S. Riniker, M. Winger, A. E. Mark, W. F. van Gunsteren, Eur. Biophys. J. 2011, 40, 843–856

    2011

  24. [30]

    Boothroyd, P

    S. Boothroyd, P. K. Behara, O. C. Madin, D. F. Hahn, H. Jang, V. Gapsys, J. R. Wagner, J. T. Horton, D. L. Dotson, M. W. Thompson, J. Maat, T. Gokey, L.-P. Wang, D. J. Cole, M. K. Gilson, J. D. Chodera, C. I. Bayly, M. R. Shirts, D. L. Mobley,J. Chem. Theory Comput. 2023, 19, ...

    2023

  25. [31]

    Behler, J

    J. Behler, J. Chem. Phys 2011, 134, 074106

    2011

  26. [32]

    Gilmer, S

    J. Gilmer, S. S. Schoenholz, P. F. Riley, O. Vinyals, G. E. Dahl,Proceedings of the 34th International Conference on Machine Learning 2017, 1263–1272

    2017

  27. [33]

    A. P. Bartók, S. De, C. Poelking, N. Bernstein, J. R. Kermode, G. Csányi, M. Ceriotti,Sci. Adv. 2017, 3, e1701816

    2017

  28. [34]

    Chmiela, A

    S. Chmiela, A. Tkatchenko, H. E. Sauceda, I. Poltavsky, K. T. Schütt, K.-R. Müller, Sci. Adv. 2017, 3, e1603015

    2017

  29. [35]

    K. T. Schütt, H. E. Sauceda, P.-J. Kindermans, A. Tkatchenko, K.-R. Müller, J. Chem. Phys. 2018, 148, 241722

    2018

  30. [36]

    K. T. Schütt, O. T. Unke, M. Gastegger,Proceedings of the 38th International Conference on Machine Learning 2021, 9377–9388

    2021

  31. [37]

    O. T. Unke, S. Chmiela, M. Gastegger, K. T. Schütt, H. E. Sauceda, K.-R. Müller, Nat. Commun. 2021, 12, 7273

    2021

  32. [38]

    Batzner, A

    S. Batzner, A. Musaelian, L. Sun, M. Geiger, J. P. Mailoa, M. Kornbluth, N. Molinari, T. E. Smidt, B. Kozinsky, Nat. Commun. 2022, 13, 2453

    2022

  33. [39]

    Musaelian, S

    A. Musaelian, S. Batzner, A. Johansson, L. Sun, C. J. Owen, M. Kornbluth, B. Kozinsky,arXiv 2022, arXiv:2204.05249

    2022 arXiv

  34. [40]

    Batatia, D

    I. Batatia, D. P. Kovács, G. N. Simm, C. Ortner, G. Csányi,arXiv 2022, arXiv:2206.07697

    2022 arXiv

  35. [41]

    S. N. Pozdnyakov, M. Ceriotti,arXiv 2022, arXiv:2201.07136

    2022 arXiv

  36. [42]

    T. S. Cohen, M. Welling,Proceedings of The 33rd International Conference on Machine Learning 2016, 2990–2999

    2016

  37. [43]

    Weiler, M

    M. Weiler, M. Geiger, M. Welling, W. Boomsma, T. S. Cohen,Adv. Neural Inf. Process Syst. 2018, 31

    2018

  38. [44]

    V. G. Satorras, E. Hoogeboom, M. Welling,2021, 9323–9332

    2021

  39. [45]

    Grisafi, D

    A. Grisafi, D. M. Wilkins, M. J. Willatt, M. Ceriotti,Atomic-Scale Representation and Statistical Learning of Tensorial Properties , Chapter 1, pp. 1–21

  40. [46]

    Thürlemann, L

    M. Thürlemann, L. Böselt, S. Riniker,J. Chem. Theory Comput. 2022, 18, 1701–1710

    2022

  41. [47]

    J. A. Rackers, L. Tecot, M. Geiger, T. E. Smidt,Mach. Learn.: Sci. Technol. 2023, 4, 015027

    2023

  42. [48]

    B. K. Miller, M. Geiger, T. E. Smidt, F. Noé,arXiv 2020, arXiv:2008.08461

    2020 arXiv

  43. [49]

    Batatia, S

    I. Batatia, S. Batzner, D. P. Kovács, A. Musaelian, G. N. Simm, R. Drautz, C. Ortner, B. Kozinsky, G. Csányi, arXiv 2022, arXiv:2205.06643

    2022 arXiv

  44. [50]

    W. F. van Gunsteren, A. E. Mark,J. Chem. Phys. 1998, 108, 6109–6116

    1998

  45. [51]

    Roßbach, C

    S. Roßbach, C. Ochsenfeld, J. Chem. Theory Comput. 2017, 13, 1102–1107

    2017

  46. [52]

    U. Ryde, J. Chem. Theory Comput. 2017, 13, 5745–5752

    2017

  47. [53]

    X. Fu, Z. Wu, W. Wang, T. Xie, S. Keten, R. Gomez-Bombarelli, T. S. Jaakkola,Transact. Mach. Learn. Res. 2023

    2023

  48. [54]

    D. P. Kovács, J. H. Moore, N. J. Browning, I. Batatia, J. T. Horton, V. Kapil, W. C. Witt, I.-B. Magdău, D. J. Cole, G. Csányi,arXiv 2023, arXiv:2312.15211. 27

    2023 arXiv

  49. [55]

    K. T. Schütt, S. S. P. Hessmann, N. W. A. Gebauer, J. Lederer, M. Gastegger,J. Chem. Phys. 2023, 158

    2023

  50. [56]

    R. P. Pelaez, G. Simeon, R. Galvelis, A. Mirarchi, P. Eastman, S. Doerr, P. Thölke, T. E. Markland, G. De Fabritiis,J. Chem. Theory Comput. 2024, 20, 4076–4087

    2024

  51. [57]

    J. S. Smith, O. Isayev, A. E. Roitberg,Chem. Sci. 2017, 8, 3192–3203

    2017

  52. [58]

    Devereux, J

    C. Devereux, J. S. Smith, K. K. Huddleston, K. Barros, R. Zubatyuk, O. Isayev, A. E. Roitberg, J. Chem. Theory Comput. 2020, 16, 4192–4202

    2020

  53. [59]

    I. G. Tironi, R. Sperb, P. E. Smith, W. F. van Gunsteren,J. Chem. Phys. 1995, 102, 5451–5459

    1995

  54. [60]

    Eastman, B

    P. Eastman, B. P. Pritchard, J. D. Chodera, T. E. Markland,arXiv 2024, arXiv:2406.13112

    2024 arXiv

  55. [61]

    B. A. C. Horta, P. T. Merz, P. F. J. Fuchs, J. Dolenc, S. Riniker, P. H. Hünenberger,J. Chem. Theory Comput. 2016, 12, 3825–3850

    2016

  56. [62]

    O. T. Unke, M. Meuwly, J. Chem. Theory Comput. 2019, 15, 3678–3693

    2019

  57. [63]

    Bereau, R

    T. Bereau, R. A. DiStasio, A. Tkatchenko, O. A. von Lilienfeld,J. Chem. Phys. 2018, 148, 241706

    2018

  58. [64]

    Thürlemann, L

    M. Thürlemann, L. Böselt, S. Riniker,J. Chem. Theory Comput. 2023, 19, 562–579

    2023

  59. [65]

    Thürlemann, S

    M. Thürlemann, S. Riniker, Chem. Sci. 2023, 14, 12661–12675

    2023

  60. [66]

    Böselt, M

    L. Böselt, M. Thürlemann, S. Riniker,J. Chem. Theory Comput. 2021, 17, 2641–2658

    2021

  61. [67]

    Hofstetter, L

    A. Hofstetter, L. Böselt, S. Riniker,Phys. Chem. Chem. Phys. 2022, 24, 22497–22512

    2022

  62. [68]

    Csizi, M

    K.-S. Csizi, M. Reiher, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2022, e1656

    2022

  63. [69]

    L. W. Chung, W. M. C. Sameera, R. Ramozzi, A. J. Page, M. Hatanaka, G. P. Petrova, T. V. Harris, X. Li, Z. Ke, F. Liu, H.-B. Li, L. Ding, K. Morokuma,Chem. Rev. 2015, 115, 5678–5796

    2015

  64. [70]

    S.-L. J. Lahey, C. N. Rowley,Chem. Sci. 2020, 11, 2362–2368

    2020

  65. [71]

    Galvelis, A

    R. Galvelis, A. Varela-Rial, S. Doerr, R. Fino, P. Eastman, T. E. Markland, J. D. Chodera, G. De Fabritiis, J. Chem. Inf. Model. 2023, 63, 5701–5708

    2023

  66. [72]

    K. Song, S. Käser, K. Töpfer, L. I. Vazquez-Salazar, M. Meuwly,J. Chem. Phys. 2023, 159, 024125

    2023

  67. [73]

    Ramakrishnan, P

    R. Ramakrishnan, P. O. Dral, M. Rupp, O. A. von Lilienfeld,J. Chem. Theory Comput. 2015, 11, 2087–2096

    2015

  68. [74]

    P. W. Battaglia, J. B. Hamrick, V. Bapst, A. Sanchez-Gonzalez, V. F. Zambaldi, M. Malinowski, A. Tacchetti, D. Raposo, A. Santoro, R. Faulkner, Ç. Gülçehre, H. F. Song, A. J. Ballard, J. Gilmer, G. E. Dahl, A. Vaswani, K. R. Allen, C. Nash, V. Langston, C. Dyer, N. Heess, D. W...

    2018 arXiv

  69. [75]

    Klicpera, J

    J. Klicpera, J. Groß, S. Günnemann,arXiv 2020, arXiv:2003.03123

    2020 arXiv

  70. [76]

    C. J. Burnham, N. J. English,Int. J. Mol. Sci. 2020, 21, 277

    2020

  71. [77]

    D. Lin, J. Chem. Phys. 2015, 143, 114115

    2015

  72. [78]

    Guenot, P

    J. Guenot, P. A. Kollman,J. Comp. Chem. 1993, 14, 295–311

    1993

  73. [79]

    Head-Gordon, M

    T. Head-Gordon, M. Head-Gordon, M. J. Frisch, C. Brooks, J. Pople,Int. J. Quantum Chem. 2009, 36, 311–322

    2009

  74. [80]

    Torrie, J

    G. Torrie, J. Valleau, J. Comput. Phys. 1977, 23, 187–199

    1977

  75. [81]

    Kästner, Wiley Interdiscip

    J. Kästner, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2011, 1, 932–942

    2011

  76. [82]

    Weigend, R

    F. Weigend, R. Ahlrichs, Phys. Chem. Chem. Phys. 2005, 7, 3297–3305

    2005

  77. [83]

    Grimme, J

    S. Grimme, J. Chem. Phys. 2006, 124, 034108

    2006

  78. [84]

    Grimme, J

    S. Grimme, J. Antony, S. Ehrlich, H. Krieg,J. Chem. Phys. 2010, 132, 154104. 28

    2010

  79. [85]

    Grimme, S

    S. Grimme, S. Ehrlich, L. Goerigk,J. Comput. Chem. 2011, 32, 1456–1465

    2011

  80. [86]

    Rubner, C

    Y. Rubner, C. Tomasi, L. Guibas,Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271) 1998

    1998

  81. [87]

    M. R. Shirts, J. D. Chodera,J. Chem. Phys. 2008, 129, 124105

    2008

  82. [88]

    Grdadolnik, S

    J. Grdadolnik, S. Golič Grdadolnik, F. Avbelj,J. Phys. Chem. B 2008, 112, 2712–2718

    2008

  83. [89]

    Parchaňský, J

    V. Parchaňský, J. Kapitán, J. Kaminský, J. Šebestík, P. Bouř,J. Phys. Chem. Lett. 2013, 4, 2763–2768

    2013

  84. [90]

    Schweitzer-Stenner, Phys

    R. Schweitzer-Stenner, Phys. Chem. Chem. Phys. 2023, 25, 11908–11933

    2023

  85. [91]

    S. C. Lovell, I. W. Davis, W. B. Arendall, P. I. W. de Bakker, J. M. Word, M. G. Prisant, J. S. Richardson, D. C. Richardson,Proteins: Struct. Funct. Bioinf. 2003, 50, 437–450

    2003

  86. [92]

    G. d. M. Seabra, R. C. Walker, M. Elstner, D. A. Case, A. E. Roitberg,J. Phys. Chem. A 2007, 111, 5655–5664

    2007

  87. [93]

    Mironov, Y

    V. Mironov, Y. Alexeev, V. K. Mulligan, D. G. Fedorov,J. Comput. Chem. 2018, 40, 297–309

    2018

  88. [94]

    Barone, M

    V. Barone, M. Cossi, J. Phys. Chem. A 1998, 102, 1995–2001

    1998

  89. [95]

    Grimme, Chem

    S. Grimme, Chem. Eur. J. 2012, 18, 9955–9964

    2012

  90. [96]

    GitHub Issue on the Treatment of External Point Charges by xtb, https://github.com/grimme- lab/xtb/issues/820

  91. [97]

    Kumar, P

    A. Kumar, P. R. Arantes, A. Saha, G. Palermo, B. M. Wong,Molecules 2023, 28, 1277

    2023

  92. [98]

    Kubař, K

    T. Kubař, K. Welke, G. Groenhof,J. Comput. Chem. 2015, 36, 1978–1989

    2015

  93. [99]

    de Meijere, F

    A. de Meijere, F. Diederich, Metal-Catalyzed Cross-Coupling Reactions , Wiley, 2004

    2004

  94. [100]

    J. F. Hartwig, Organotransition Metal Chemistry , University Science Books,2010

    2010

  95. [101]

    C. C. C. Johansson Seechurn, M. O. Kitching, T. J. Colacot, V. Snieckus,Angew. Chem. Int. Ed. 2012, 51, 5062–5085

    2012

  96. [103]

    Z. L. Niemeyer, A. Milo, D. P. Hickey, M. S. Sigman,Nat. Chem. 2016, 8, 610–617

    2016

  97. [104]

    J. E. Borowski, S. H. Newman-Stonebraker, A. G. Doyle,ACS Catal. 2023, 13, 7966–7977

    2023

  98. [105]

    K. D. Vogiatzis, M. V. Polynski, J. K. Kirkland, J. Townsend, A. Hashemi, C. Liu, E. A. Pidko, Chem. Rev. 2018, 119, 2453–2523

    2018

  99. [106]

    Nandy, C

    A. Nandy, C. Duan, M. G. Taylor, F. Liu, A. H. Steeves, H. J. Kulik,Chem. Rev. 2021, 121, 9927–10000

    2021

  100. [107]

    Bursch, A

    M. Bursch, A. Hansen, P. Pracht, J. T. Kohn, S. Grimme,Phys. Chem. Chem. Phys. 2021, 23, 287–299

    2021

  101. [108]

    T. J. Giese, J. Zeng, L. Lerew, E. McCarthy, Y. Tao, c. Ekesan, D. M. York,J. Phys. Chem. B 2024, 128, 6257–6271

    2024

  102. [109]

    D. G. Brown, J. Boström, J. Med. Chem. 2015, 59, 4443–4458

    2015

  103. [110]

    Mardirossian, M

    N. Mardirossian, M. Head-Gordon, J. Chem. Phys. 2016, 144, 214110

    2016

  104. [111]

    Najibi, L

    A. Najibi, L. Goerigk, J. Comput. Chem. 2020, 41, 2562–2572

    2020

  105. [112]

    Caldeweyher, C

    E. Caldeweyher, C. Bannwarth, S. Grimme,J. Chem. Phys. 2017, 147, 034112

    2017

  106. [113]

    Caldeweyher, S

    E. Caldeweyher, S. Ehlert, A. Hansen, H. Neugebauer, S. Spicher, C. Bannwarth, S. Grimme,J. Chem. Phys. 2019, 150, 154122

    2019

  107. [114]

    Santra, J

    G. Santra, J. M. L. Martin,AIP Conference Proceedings 2019, 2186, 030004

    2019

  108. [115]

    Grimme, Angew

    S. Grimme, Angew. Chem. Int. Ed. 2013, 52, 6306–6312. 29

    2013

  109. [116]

    A. V. Marenich, C. J. Cramer, D. G. Truhlar,J. Phys. Chem. B 2009, 113, 6378–6396

    2009

  110. [117]

    Peverati, D

    R. Peverati, D. G. Truhlar,J. Phys. Chem. Lett. 2012, 3, 117–124

    2012

  111. [118]

    M. A. Iron, T. Janes, J. Phys. Chem. A 2019, 123, 3761–3781

    2019

  112. [120]

    J. S. Hub, B. L. de Groot, H. Grubmüller, G. Groenhof,J. Chem. Theory Comput. 2014, 10, 381–390

    2014

  113. [121]

    Klamt, Wiley Interdiscip

    A. Klamt, Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2011, 1, 699–709

    2011

  114. [122]

    Y. Zhao, D. G. Truhlar,Theor. Chem. Acc. 2008, 120, 215–241

    2008

  115. [123]

    Katzberger, S

    P. Katzberger, S. Riniker, Chem. Sci. 2024, 15, 10794–10802

    2024

  116. [124]

    Paszke, S

    A. Paszke, S. Gross, F. Massa, A. Lerer, J. Bradbury, G. Chanan, T. Killeen, Z. Lin, N. Gimelshein, L. Antiga, A. Desmaison, A. Köpf, E. Yang, Z. DeVito, M. Raison, A. Tejani, S. Chilamkurthy, B. Steiner, L. Fang, J. Bai, S. Chintala,arXiv 2019, arXiv:1912.01703

    2019 arXiv

  117. [125]

    K. He, X. Zhang, S. Ren, J. Sun,2015 IEEE International Conference on Computer Vision (ICCV) 2015, 1026–1034

    2015

  118. [126]

    Ramachandran, B

    P. Ramachandran, B. Zoph, Q. V. Le,arXiv 2017, arXiv:1710.05941

    2017 arXiv

  119. [127]

    D. P. Kingma, J. Ba,arXiv 2017, arXiv:1412.6980

    2017 arXiv

  120. [128]

    Pascanu, T

    R. Pascanu, T. Mikolov, Y. Bengio,arXiv 2013, arXiv:1211.5063

    2013 arXiv

  121. [129]

    Schmid, C

    N. Schmid, C. D. Christ, M. Christen, A. P. Eichenberger, W. F. Van Gunsteren,Comput. Phys. Commun. 2012, 183, 890–903

    2012

  122. [130]

    Meier, N

    K. Meier, N. Schmid, W. F. Van Gunsteren,J. Comput. Chem. 2012, 33, 2108–2117

    2012

  123. [131]

    Poliak, P

    P. Poliak, P. Bleiziffer, F. Pultar, S. Riniker, C. Oostenbrink,J. Comput. Chem. 2024, accepted

    2024

  124. [132]

    Landrum, P

    G. Landrum, P. Tosco, B. Kelley, Ric, D. Cosgrove, sriniker, gedeck, R. Vianello, NadineSchneider, E. Kawashima, D. N, G. Jones, A. Dalke, B. Cole, M. Swain, S. Turk, AlexanderSavelyev, A. Vaucher, M. Wójcikowski, I. Take, D. Probst, K. Ujihara, V. F. Scalfani, guillaume godin...

    2023

  125. [133]

    Riniker, G

    S. Riniker, G. A. Landrum, J. Chem. Inf. Model. 2015, 55, 2562–2574

    2015

  126. [134]

    S. Wang, J. Witek, G. A. Landrum, S. Riniker,J. Chem. Inf. Model. 2020, 60, 2044–2058

    2020

  127. [135]

    Chemcraft - Graphical Software for Visualization of Quantum Chemistry Computations , version 1.8, build 682

  128. [136]

    A. K. Malde, L. Zuo, M. Breeze, M. Stroet, D. Poger, P. C. Nair, C. Oostenbrink, A. E. Mark,J. Chem. Theory Comput. 2011, 7, 4026–4037

    2011

  129. [137]

    K. B. Koziara, M. Stroet, A. K. Malde, A. E. Mark,J. Comput. Aided Mol. Des. 2014, 28, 221–233

    2014

  130. [138]

    Heinz, R

    H. Heinz, R. A. Vaia, B. L. Farmer, R. R. Naik,J. Phys. Chem. C 2008, 112, 17281–17290

    2008

  131. [139]

    S. Nosé, J. Chem. Phys. 1984, 81, 511–519

    1984

  132. [140]

    W. G. Hoover, Phys. Rev. A 1985, 31, 1695–1697

    1985

  133. [141]

    H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, A. DiNola, J. R. Haak,J. Chem. Phys. 1984, 81, 3684–3690

    1984

  134. [142]

    Rumble, T

    J. Rumble, T. Bruno, M. Doa,CRC Handbook of Chemistry and Physics , CRC Press,2023

    2023

  135. [143]

    Ryckaert, G

    J.-P. Ryckaert, G. Ciccotti, H. J. Berendsen,J. Comput. Phys. 1977, 23, 327–341

    1977

  136. [144]

    Bakowies, W

    D. Bakowies, W. Thiel, J. Phys. Chem. 1996, 100, 10580–10594

    1996

  137. [145]

    H. J. C. Berendsen, J. P. M. Postma, W. F. van Gunsteren, J. Hermans inIntermolecular Forces, Springer Netherlands, 1981, pp. 331–342. 30

    1981

  138. [146]

    N. D. Mermin, Phys. Rev. 1965, 137, A1441–A1443

    1965

  139. [147]

    Feyereisen, G

    M. Feyereisen, G. Fitzgerald, A. Komornicki,Chem. Phys. Lett. 1993, 208, 359–363

    1993

  140. [148]

    Neese, F

    F. Neese, F. Wennmohs, A. Hansen, U. Becker,Chem. Phys. 2009, 356, 98–109

    2009

  141. [149]

    Weigend, Phys

    F. Weigend, Phys. Chem. Chem. Phys. 2006, 8, 1057

    2006

  142. [150]

    A. D. Becke, J. Chem. Phys. 1993, 98, 5648–5652

    1993

  143. [151]

    W. Kohn, A. D. Becke, R. G. Parr,J. Phys. Chem. 1996, 100, 12974–12980

    1996

  144. [152]

    C. Lee, W. Yang, R. G. Parr,Phys. Rev. B 1988, 37, 785–789

    1988

  145. [153]

    Ditchfield, W

    R. Ditchfield, W. J. Hehre, J. A. Pople,J. Chem. Phys. 1971, 54, 724–728

    1971

  146. [154]

    P. C. Hariharan, J. A. Pople,Theor. Chim. Acta 1973, 28, 213–222

    1973

  147. [155]

    M. M. Francl, W. J. Pietro, W. J. Hehre, J. S. Binkley, M. S. Gordon, D. J. DeFrees, J. A. Pople, J. Chem. Phys. 1982, 77, 3654–3665

    1982

  148. [156]

    W. J. Hehre, R. Ditchfield, J. A. Pople,J. Chem. Phys. 1972, 56, 2257–2261

    1972

  149. [157]

    M. Dolg, U. Wedig, H. Stoll, H. Preuss,J. Chem. Phys. 1987, 86, 866–872

    1987

  150. [158]

    J. M. L. Martin, A. Sundermann,J. Chem. Phys. 2001, 114, 3408–3420

    2001

  151. [159]

    B. P. Pritchard, D. Altarawy, B. Didier, T. D. Gibson, T. L. Windus,J. Chem. Inf. Model. 2019, 59, 4814–4820

    2019

  152. [160]

    Feller, J

    D. Feller, J. Comput. Chem. 1996, 17, 1571–1586

    1996

  153. [161]

    K. L. Schuchardt, B. T. Didier, T. Elsethagen, L. Sun, V. Gurumoorthi, J. Chase, J. Li, T. L. Windus, J. Chem. Inf. Model. 2007, 47, 1045–1052

    2007

  154. [162]

    A. P. Eichenberger, J. R. Allison, J. Dolenc, D. P. Geerke, B. A. C. Horta, K. Meier, C. Oostenbrink, N. Schmid, D. Steiner, D. Wang, W. F. van Gunsteren,J. Chem. Theory Comput. 2011, 7, 3379–3390

    2011

  155. [163]

    Kumar, J

    S. Kumar, J. M. Rosenberg, D. Bouzida, R. H. Swendsen, P. A. Kollman,J. Comput. Chem. 1992, 13, 1011–1021

    1992

  156. [164]

    Grossfield, WHAM: The Weighted Histogram Analysis Method , version 2.0.11

    A. Grossfield, WHAM: The Weighted Histogram Analysis Method , version 2.0.11

  157. [165]

    Efron in Breakthroughs in Statistics , Springer New York,1992, pp

    B. Efron in Breakthroughs in Statistics , Springer New York,1992, pp. 569–593

    1992

  158. [166]

    D. R. Herschbach, H. S. Johnston, D. Rapp,J. Chem. Phys. 1959, 31, 1652–1661

    1959

  159. [167]

    Boresch, F

    S. Boresch, F. Tettinger, M. Leitgeb, M. Karplus,J. Phys. Chem. B 2003, 107, 9535–9551

    2003

  160. [168]

    M. R. Shirts, D. L. Mobley, S. P. Brown inDrug Design, Cambridge University Press,2010, pp. 61–86

    2010

  161. [169]

    Y. Deng, B. Roux, J. Phys. Chem. B 2009, 113, 2234–2246

    2009

  162. [170]

    I. J. General, J. Chem. Theory Comput. 2010, 6, 2520–2524

    2010

  163. [171]

    Flamary, N

    R. Flamary, N. Courty, A. Gramfort, M. Z. Alaya, A. Boisbunon, S. Chambon, L. Chapel, A. Corenflos, K. Fatras, N. Fournier, L. Gautheron, N. T. Gayraud, H. Janati, A. Rakotomamonjy, I. Redko, A. Rolet, A. Schutz, V. Seguy, D. J. Sutherland, R. Tavenard, A. Tong, T. Vayer,J. Ma...

    2021

  164. [172]

    van der Walt, J

    S. van der Walt, J. L. Schönberger, J. Nunez-Iglesias, F. Boulogne, J. D. Warner, N. Yager, E. Gouillart, T. Yu, the scikit-image contributors,PeerJ 2014, 2, e453. 31

    2014

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.