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Impact of the damping function in dispersion-corrected density functional theory on the properties of liquid water

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Zero-damping, not BJ-damping, makes dispersion-corrected DFT reproduce liquid-water structure, diffusion, and density.

desk verdict Damping-function choice matters for liquid water—zero-damping's repulsive short-range force is a plausible mechanism that improves GGA water across TS and D3—but the abstract overclaims on clusters and the MD results rest on HDNNPs that are never validated against direct DFT for the damping-specific signal. read the letter →

arxiv 2506.20371 v1 pith:RNPBVKT5 submitted 2025-06-25 physics.chem-ph

K. Nikolas Lausch , Redouan El Haouari , Daniel Trzewik , Jörg Behler This is my paper
classification physics.chem-ph
keywords liquidwaterdispersioncorrectiondampingfunctionzero-dampingBecke-JohnsonDFT-D3Tkatchenko-Schefflermodelhigh-dimensionalneuralnetworkpotentials
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

This paper argues that the damping function used in a dispersion correction is not a minor technical detail: for liquid water, it can decide whether a density-functional simulation matches experiment. Comparing the two standard damping schemes, zero-damping and Becke-Johnson (BJ) damping, across two exchange-correlation functionals (PBE and RPBE) and two dispersion models (DFT-D3 and Tkatchenko-Scheffler), the authors find that zero-damping consistently produces softer structure, faster self-diffusion, higher density, and a density maximum closer to experiment. The reason, they argue, is that zero-damping produces repulsive short-range forces that artificially weaken water's tetrahedral hydrogen-bonding network, which compensates for the known tendency of generalized-gradient-approximation functionals to over-structure the liquid; BJ-damping is strictly attractive and instead strengthens the network, causing double counting. Because both dampings perform equally well on static water-cluster benchmarks, the paper concludes that dispersion models cannot be validated on interaction energies alone and that the role of the damping function needs to be re-evaluated generally.

What carries the argument

The load-bearing object is the damping function that multiplies the pairwise London-type dispersion potential. Zero-damping, the Fermi-type function in the TS model and the zero-damping form in DFT-D3, switches the correction off at short interatomic distances, creating a region of repulsive dispersion force; BJ-damping, a rational function that approaches a finite constant at short range, keeps the correction attractive at all distances. The sign of the short-range gradient is the mechanism the paper uses to explain every observed property difference. To make the comparison in the liquid, the authors train high-dimensional neural network potentials on dispersion-corrected DFT reference data, enabling nanosecond molecular dynamics of 512 to 1024 water molecules; the damping effect is then tracked through radial distribution functions, system-size-extrapolated self-diffusion coefficients, density isobars, and a Stillinger-cluster analysis of interstitial-site occupation.

What would settle it

Compute the dispersion force difference between zero- and BJ-damping at the oxygen-oxygen distances that dominate the first solvation shell (about 2.6 to 3.4 Å); if that difference is comparable to or smaller than the 25 to 54 meV/au force root-mean-square errors of the neural-network potentials, the MD ordering of structures and diffusion cannot be confidently attributed to the damping function. The claim would be directly settled by reproducing the key RPBE-D3(0) versus RPBE-D3(BJ) comparison with a much more accurate potential or with short direct ab initio MD trajectories: if the structural ordering flips, the mechanism is an artifact of the learned potentials.

Watch

Extended reading notes

Core claim

The central claim is that the short-range behavior of the damping function, not the dispersion model or the exchange-correlation functional, controls how well dispersion-corrected DFT describes liquid water. For the PBE and RPBE functionals combined with either DFT-D3 or the Tkatchenko-Scheffler (TS) model, the authors show that damping to zero at short distances, a functional form that produces a repulsive gradient, yields radial distribution functions closer to coupled-cluster molecular dynamics reference data, larger self-diffusion coefficients, higher equilibrium densities, and density maxima at lower temperatures than BJ-damping, which remains attractive at all distances. The repulsive short-range forces of zero-damping weaken the tetrahedral hydrogen-bonding network that generalized-gradient-approximation functionals tend to over-stabilize; this compensation is absent for BJ-damping, whose extra attraction at short range leads to double counting with the functional and an over-structured liquid. The same ordering is found for both dispersion models, and the paper shows that DFT-D4, which uses BJ-damping exclusively, cannot reproduce the zero-damping improvement. The implied conclusion is that much of what has been attributed to including dispersion in simulations of water may in fact be an effect of the damping form.

Load-bearing premise

The whole comparison rests on the neural-network potentials reproducing the dispersion-corrected DFT forces accurately enough to preserve the small differences between damping models; the RPBE-TS(F)(S22) potential has roughly twice the force error of the others, and the damping-induced changes in the radial distribution functions are modest, so a subtle fitting bias could change the ordering.

Editorial extensions

If this is right

  • Static interaction-energy benchmarks cannot validate a dispersion correction for condensed-phase use: zero- and BJ-damping are indistinguishable on S22, S66, and water-cluster data yet differ in every simulated liquid property.
  • If the mechanism is general, the accuracy of zero-damped GGA water simulations is partly an error compensation between repulsive damping forces and the functional's over-structuring, so experimental agreement with such models should not be read as evidence that the underlying functional is accurate.
  • Dispersion corrections that use BJ-damping exclusively, such as DFT-D4 and XDM, cannot obtain the improved water description reported here without some other compensating change.
  • For the Tkatchenko-Scheffler model, the benchmark set used for damping parametrization (S22 versus S66) can reverse the sign of the effect for RPBE, so published water results should be checked against which benchmark the damping parameters came from.

Reading between the lines

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

  • If the mechanism transfers beyond water, the damping-function choice could matter equally for other hydrogen-bonded or network-forming condensed systems, such as ices, clathrate hydrates, and aqueous interfaces, where the same GGA over-structuring is common; the paper only demonstrates the effect for liquid water.
  • The supplementary finding that the two BJ-damping parameters are nearly linearly related suggests that a single-parameter BJ form could be re-optimized for condensed-phase targets, potentially recovering part of zero-damping's beneficial compensation without introducing repulsive forces; this is a testable route the authors leave open.
  • The paper attributes the density difference to interstitial-site occupation rather than to stronger dispersion attraction, an explanation that could be tested directly by computing per-molecule coordination numbers at matched densities for both damping forms.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. The paper investigates whether the choice of damping function (zero/Fermi-type versus Becke-Johnson) in dispersion-corrected DFT significantly affects the simulated properties of liquid water. The authors parametrize Tkatchenko-Scheffler (TS) dispersion corrections with both damping forms for PBE and RPBE using the S22 and S66 benchmark sets, compare with DFT-D3(0) and DFT-D3(BJ), and test the resulting models on water-cluster interaction energies. They then train high-dimensional neural network potentials (HDNNPs) on bulk water reference data for 14 different functional/dispersion combinations and use them in molecular dynamics simulations to compute radial distribution functions, self-diffusion coefficients, and density isobars. The central claim is that zero-damping outperforms BJ-damping for liquid water because its repulsive short-range gradient weakens the tetrahedral hydrogen-bond network, compensating for known GGA deficiencies, whereas the strictly attractive BJ form leads to stronger over-structuring and slower diffusion.

Significance. If the central claim holds, the work has substantial significance: it challenges the common assumption that the damping function is a minor technical detail in dispersion-corrected DFT, and it would have direct implications for methods that exclusively use BJ-damping, such as DFT-D4 and XDM. The paper is systematic and broad: it covers two xc functionals, two dispersion models, two parametrization sets, and fourteen potentials; it uses system-size-extrapolated diffusion coefficients with confidence intervals, long NVT and NpT trajectories, and an internal consistency analysis based on interstitial-site populations. These are genuine strengths. The main weakness is that the dynamic conclusions are delivered entirely through HDNNPs, and the manuscript does not directly demonstrate that the learned potentials preserve the small, damping-specific force differences that are claimed to drive the observed ordering. Because the worst-fitting potential is also the behavioral outlier, the central dynamic claim carries a validation risk that needs to be addressed before the conclusions can be considered fully established.

major comments (4)
  1. [Section III C, Table I, and Section IV C] The central dynamic claim depends on HDNNPs resolving damping-induced differences in the DFT potential energy surface, but this is never directly validated. Table I reports force-component RMSEs of about 25 to 55 meV/a0 for the 14 potentials, while the discriminating signal shown in Fig. 1, the repulsive short-range gradient of zero-damping versus the attractive BJ profile, contributes only a few meV per Å per pair. A global force RMSE dominated by covalent and hydrogen-bond contributions cannot certify that the networks learned the systematic inter-model force differences that produce the reported RDF, diffusion, and density ordering. I recommend adding a direct comparison of HDNNP forces and energies against the underlying dispersion-corrected DFT for representative liquid-water configurations for each model, and ideally a targeted test such as comparing the damping-model force difference with the per-model HDNNP force error. This is a load-bearing validation step for the paper's main conclusion.
  2. [Abstract and Section IV B, Table IV] The abstract states that 'regardless of the dispersion model, both types of damping perform equally well for interaction energies of water clusters,' but the data in Table IV do not support this for RPBE. For example, RPBE-TS(BJ)(S66) has MAE_rel = 1.83 meV and RPBE-TS(BJ)(S22) has 4.45 meV, whereas RPBE-TS(F)(S66) has 9.52 meV and RPBE-TS(F)(S22) has 16.48 meV; RPBE-D3(BJ) also outperforms RPBE-D3(0). The main text itself describes the RPBE-TS(BJ) models as 'outstandingly' good. The 'equally well' claim should be revised to reflect the functional and model dependence, or the water-cluster analysis should be reframed so that the static benchmarks are not presented as uniformly damping-insensitive.
  3. [Section IV C 2, Table V, and Fig. S14] The general claim that zero-damping yields faster self-diffusion than BJ-damping is not resolved for PBE at 300 K. The supplementary figure S14 shows that the PBE 300 K diffusion coefficients overlap within their uncertainties for the different damping models, and the main text acknowledges that additional simulations would be needed to separate the methods at this temperature. The diffusion ordering is therefore carried by the PBE 400 K data and the RPBE 300 K data. The abstract and conclusions state the self-diffusion result without this temperature caveat. Please either qualify the claim to the conditions under which the ordering is statistically resolved, or provide additional 300 K PBE sampling that resolves the models.
  4. [Section III C, Table I, and Sections IV C 1 and IV C 3] The RPBE-TS(F)(S22) potential is simultaneously the worst-fitting HDNNP (force RMSE about 54 meV/a0, roughly twice the other models) and the behavioral outlier (most over-structured RDF, lowest diffusion, Tmax = 355 K). The paper interprets this outlier as a physical double-counting effect, but the confounding explanation—that the learned potential is simply less accurate—is not addressed. Because this potential is used to support the threshold argument in Section IV C 1 and the double-counting interpretation, the authors should show that its anomalous behavior persists with a better-fitted potential or with direct DFT MD for this model, rather than only with the single HDNNP fit reported in Table I.
minor comments (6)
  1. [Introduction] There is a typo in the first paragraph: 'consensus' is written as 'concensus'.
  2. [Section IV B] The text refers to the 'BEGDG set'; the correct acronym is BEGDB, as used elsewhere.
  3. [Equation (18)] In the sentence following Eq. (18), 'EH2O, iis' should be 'EH2O,i is'.
  4. [Figure 5 caption] The caption contains 'N V Ediffusion coefficients'; this should read 'NVE diffusion coefficients'.
  5. [Table V] The column header rHB,max OO appears to be a typo; based on the text it should refer to the OH RDF, i.e., rHB,max OH.
  6. [Section IV C 3] The definition of the Stillinger radius and the choice of 3.3 Å for PBE and 3.4 Å for RPBE could be stated more explicitly in the main text, since the neighbor-count analysis in Fig. 6b depends on this choice.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: damping parameters are fitted to S22/S66 and transferred to water; liquid-water results are emergent HDNNP dynamics, not fitted inputs.

full rationale

The central comparisons are genuine transfer tests, not fits renamed as predictions. The TS damping parameters (sr,6 for Fermi damping; a1,a2 for BJ damping) are optimized only against CCSD(T) interaction energies in the S22 and S66 benchmark sets (Sec. IV A, Tables II-III) and then transferred to BEGDB water clusters and bulk-water MD. No liquid-water property (RDF, diffusion coefficient, density) enters the parameter fit, so those results cannot be forced by construction. The DFT-D3 models use Grimme's independent parameters, external to this work. The HDNNPs are trained only on DFT energies and forces for bulk-water configurations; the reported RDFs, self-diffusion coefficients, and density isobars are emergent outcomes of MD, not training targets. The mechanistic explanation (zero-damping's repulsive short-range gradient weakens the tetrahedral H-bond network) is inferred from Fig. 1 and from observed RDF peak changes, coordination-number histograms, diffusion ordering, and Tmax; it is not a definitional identity, since the damping function's algebraic form does not fix those observables. The only self-citations are the CCMD benchmark data of Daru et al. (Ref. 9) and Stolte et al. (Ref. 101), sharing the senior author; these are external high-level references used for comparison, not inputs to the fits, so they are not load-bearing. Main risks are accuracy limitations: the HDNNPs are not directly validated against DFT-MD trajectories, the force RMSEs (25-55 meV/a0, Table I) are comparable to the subtle damping-induced force differences, and Sec. SIV B concedes PBE self-diffusion at 300 K is not fully resolved. These are validation concerns, not circularity.

Assumptions & free parameters 8 free parameters · 5 assumptions · 0 invented entities

The central claim rests on fitted damping parameters (8 entries) and on standard domain assumptions about the validity of dispersion corrections, transferability from gas-phase dimers to bulk water, the adequacy of classical MD, the fidelity of machine-learned potentials, and the accuracy of CCSD(T)/CCMD references. No new physical entities are introduced.

free parameters (8)
  • sr,6 for PBE-TS(F) (S22) = 0.94
    Fitted by minimizing MAE on the S22 benchmark set; controls the range of Fermi-type (zero) damping.
  • sr,6 for PBE-TS(F) (S66) = 0.99
    Fitted on the S66 benchmark set.
  • sr,6 for RPBE-TS(F) (S22) = 0.60
    Fitted on the S22 benchmark set.
  • sr,6 for RPBE-TS(F) (S66) = 0.65
    Fitted on the S66 benchmark set.
  • a1, a2 for PBE-TS(BJ) (S22) = a1=0.00, a2=5.90 a0
    Fitted on S22; a1=0 makes the damping independent of environment and element pair.
  • a1, a2 for PBE-TS(BJ) (S66) = a1=0.00, a2=6.27 a0
    Fitted on S66.
  • a1, a2 for RPBE-TS(BJ) (S22) = a1=0.16, a2=2.95 a0
    Fitted on S22.
  • a1, a2 for RPBE-TS(BJ) (S66) = a1=0.67, a2=0.01 a0
    Fitted on S66.
assumptions (5)
  • domain assumption Pairwise additive London-type dispersion corrections with empirical damping are a valid correction scheme for GGA DFT.
    The entire study operates within this framework (Section II A), inherited from Grimme and Tkatchenko-Scheffler; no independent justification is provided beyond prior literature.
  • domain assumption Damping function parameters fitted on gas-phase dimers (S22/S66) transfer to condensed liquid water.
    The TS parameters are fitted to molecular interaction energies and then applied to bulk-water MD (Sections IV A to IV C); transferability is assumed and is part of the paper's implied critique.
  • domain assumption Classical MD without nuclear quantum effects adequately captures damping-dependent differences in liquid water structure and dynamics.
    The authors compare classical MD RDFs to CCMD including NQEs and rely on prior claims that NQEs have small effects (Section IV C 1).
  • domain assumption The HDNNP functional form (ACSF plus neural network) can represent the dispersion-corrected PES to the required accuracy for the sampled liquid configurations.
    Neural network potentials are trained on reference data and used to propagate MD (Section III C, Table I); this is an approximation beyond the dispersion model itself.
  • domain assumption Standard quantum-chemistry reference data (CCSD(T) interaction energies, CCMD liquid water) are accurate enough to serve as benchmarks.
    CCSD(T) for S22/S66/BEGDB and coupled-cluster MD for RDF and diffusion are treated as ground truth (Sections IV A, IV C).

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Cite this review

Pith. "Pith review of Impact of the damping function in dispersion-corrected density functional theory on the properties of liquid water." pith.science (2026). https://pith.science/paper/RNPBVKT5

@misc{pith2026250620371,
  author       = {Pith},
  title        = {Pith review of: Impact of the damping function in dispersion-corrected density functional theory on the properties of liquid water},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RNPBVKT5}},
  note         = {Machine review of arXiv:2506.20371}
}
read the original abstract

Accounting for dispersion interactions is essential in approximate density functional theory (DFT). Often, a correction potential based on the London formula is added, which is damped at short distances to avoid divergence and double counting of interactions treated locally by the exchange-correlation functional. Most commonly, two forms of damping, known as zero- and Becke-Johnson (BJ)-damping, are employed and it is generally assumed that the choice has only a minor impact on performance even though the resulting correction potentials differ quite dramatically. Recent studies have cast doubt on this assumption pointing to a significant effect of damping for liquid water, but the underlying reasons have not yet been investigated. Here, we analyze this effect in detail for the widely used Tkatchenko-Scheffler and DFT-D3 dispersion models. We demonstrate that, regardless of the dispersion model, both types of damping perform equally well for interaction energies of water clusters, but find that for the two investigated functionals zero-damping outperforms BJ-damping in dynamic simulations of liquid water. Compared to BJ-damping, zero-damping provides, e.g., an improved structural description, self-diffusion, and density of liquid water. This can be explained by the repulsive gradient at small distances resulting from damping to zero that artificially destabilizes water's tetrahedral hydrogen-bonding network. Therefore, zero-damping can compensate for deficiencies often observed for generalized gradient functionals, which is not possible for strictly attractive BJ-damping. Consequently, the improvement that can be achieved by applying a dispersion correction strongly depends on the employed damping function suggesting that the role of damping in dispersion-corrected DFT needs to be generally reevaluated.

Figures

Figures reproduced from arXiv: 2506.20371 by the authors.

Figure 1
Figure 1. FIG. 1: Dispersion energy [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Approximate dispersion energies [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: Results for the BEGDB water cluster benchmark set [PITH_FULL_IMAGE:figures/full_fig_p013_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4: OO (a) and OH (b) RDFs produced by the PBE and RPBE functionals in HDNNP-driven MD simulations [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: System-size specific diffusion coefficients [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: (a) Density isobars of liquid water obtained from HDNNP-driven MD simulations employing the PBE and [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]

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Reference graph

Works this paper leans on

109 extracted references · 38 canonical work pages · cited by 1 Pith paper

  1. [1]

    Mallamace , author C

    author author F. Mallamace , author C. Branca , author M. Broccio , author C. Corsaro , author C.-Y. \ Mou , \ and\ author S.-H. \ Chen ,\ 10.1073/pnas.0706504104 journal journal PNAS \ volume 104 ,\ pages 18387 ( year 2007 ) NoStop

    work page doi:10.1073/pnas.0706504104 2007

  2. [2]

    author author L. G. M. \ Pettersson , author R. H. \ Henchman , \ and\ author A. Nilsson ,\ 10.1021/acs.chemrev.6b00363 journal journal Chem. Rev. \ volume 116 ,\ pages 7459 ( year 2016 ) NoStop

    doi:10.1021/acs.chemrev.6b00363 2016

  3. [3]

    Morawietz , author A

    author author T. Morawietz , author A. Singraber , author C. Dellago , \ and\ author J. Behler ,\ 10.1073/pnas.1602375113 journal journal PNAS \ volume 113 ,\ pages 8368 ( year 2016 ) NoStop

    doi:10.1073/pnas.1602375113 2016

  4. [4]

    Chen , author H.-Y

    author author M. Chen , author H.-Y. \ Ko , author R. C. \ Remsing , author M. F. \ Calegari Andrade , author B. Santra , author Z. Sun , author A. Selloni , author R. Car , author M. L. \ Klein , author J. P. \ Perdew , \ and\ author X. Wu ,\ 10.1073/pnas.1712499114 journal journal PNAS \ volume 114 ,\ pages 10846 ( year 2017 ) NoStop

    doi:10.1073/pnas.1712499114

  5. [5]

    Omranpour , author P

    author author A. Omranpour , author P. Montero De Hijes , author J. Behler , \ and\ author C. Dellago ,\ 10.1063/5.0201241 journal journal J. Chem. Phys. \ volume 160 ,\ pages 170901 ( year 2024 ) NoStop

    doi:10.1063/5.0201241 2024

  6. [6]

    Del Ben , author J

    author author M. Del Ben , author J. Hutter , \ and\ author J. VandeVondele ,\ 10.1063/1.4927325 journal journal J. Chem. Phys. \ volume 143 ,\ pages 054506 ( year 2015 ) NoStop

    work page doi:10.1063/1.4927325 2015

  7. [7]

    author author M. J. \ Gillan , author D. Alfè , \ and\ author A. Michaelides ,\ 10.1063/1.4944633 journal journal J. Chem. Phys. \ volume 144 ,\ pages 130901 ( year 2016 ) NoStop

    doi:10.1063/1.4944633 2016

  8. [8]

    Del Ben , author M

    author author M. Del Ben , author M. Schönherr , author J. Hutter , \ and\ author J. VandeVondele ,\ 10.1021/jz401931f journal journal J. Phys. Chem. Lett. \ volume 4 ,\ pages 3753 ( year 2013 ) NoStop

    doi:10.1021/jz401931f 2013

Show all 109 references
  1. [9]

    Daru , author H

    author author J. Daru , author H. Forbert , author J. Behler , \ and\ author D. Marx ,\ 10.1103/PhysRevLett.129.226001 journal journal Phys. Rev. Lett. \ volume 129 ,\ pages 226001 ( year 2022 ) NoStop

    2022 doi

  2. [10]

    Yu , author C

    author author Q. Yu , author C. Qu , author P. L. \ Houston , author R. Conte , author A. Nandi , \ and\ author J. M. \ Bowman ,\ 10.1021/acs.jpclett.2c00966 journal journal J. Phys. Chem. Lett. \ volume 13 ,\ pages 5068 ( year 2022 ) NoStop

    doi

  3. [11]

    author author M. S. \ Chen , author J. Lee , author H.-Z. \ Ye , author T. C. \ Berkelbach , author D. R. \ Reichman , \ and\ author T. E. \ Markland ,\ 10.1021/acs.jctc.2c01203 journal journal J. Chem. Theory Comput. \ volume 19 ,\ pages 4510 ( year 2023 ) NoStop

    doi

  4. [12]

    Burke ,\ 10.1063/1.4704546 journal journal J

    author author K. Burke ,\ 10.1063/1.4704546 journal journal J. Chem. Phys. \ volume 136 ,\ pages 150901 ( year 2012 ) NoStop

    2012 doi

  5. [13]

    author author A. D. \ Becke ,\ 10.1063/1.4869598 journal journal J. Chem. Phys. \ volume 140 ,\ pages 18A301 ( year 2014 ) NoStop

    2014 doi

  6. [14]

    Groß \ and\ author S

    author author A. Groß \ and\ author S. Sakong ,\ 10.1021/acs.chemrev.1c00679 journal journal Chem. Rev. \ volume 122 ,\ pages 10746 ( year 2022 ) NoStop

    2022 doi

  7. [15]

    Montero de Hijes , author C

    author author P. Montero de Hijes , author C. Dellago , author R. Jinnouchi , \ and\ author G. Kresse ,\ 10.1063/5.0227514 journal journal J. Chem. Phys. \ volume 161 ,\ pages 131102 ( year 2024 ) NoStop

    2024 doi

  8. [16]

    author author A. A. \ Hassanali , author J. Cuny , author V. Verdolino , \ and\ author M. Parrinello ,\ 10.1098/rsta.2012.0482 journal journal Philos. Trans. R. Soc. A \ volume 372 ,\ pages 20120482 ( year 2014 ) NoStop

    2012

  9. [17]

    Wang , author G

    author author J. Wang , author G. Román-Pérez , author J. M. \ Soler , author E. Artacho , \ and\ author M.-V. \ Fernández-Serra ,\ 10.1063/1.3521268 journal journal J. Chem. Phys. \ volume 134 ,\ pages 024516 ( year 2011 ) NoStop

    2011 doi

  10. [18]

    author author T. D. \ K \"u hne , author M. Krack , \ and\ author M. Parrinello ,\ 10.1021/ct800417q journal journal J. Chem. Theory Comput. \ volume 5 ,\ pages 235 ( year 2009 ) NoStop

    2009 doi

  11. [19]

    Sprik , author J

    author author M. Sprik , author J. Hutter , \ and\ author M. Parrinello ,\ 10.1063/1.471957 journal journal J. Chem. Phys. \ volume 105 ,\ pages 1142 ( year 1996 ) NoStop

    1996 doi

  12. [20]

    Tonigold \ and\ author A

    author author K. Tonigold \ and\ author A. Groß ,\ 10.1002/jcc.22900 journal journal J. Comput. Chem. \ volume 33 ,\ pages 695 ( year 2012 ) NoStop

    2012 doi

  13. [21]

    Grimme , author A

    author author S. Grimme , author A. Hansen , author J. G. \ Brandenburg , \ and\ author C. Bannwarth ,\ 10.1021/acs.chemrev.5b00533 journal journal Chem. Rev. \ volume 116 ,\ pages 5105 ( year 2016 ) NoStop

    2016 doi

  14. [22]

    Todorova , author A

    author author T. Todorova , author A. P. \ Seitsonen , author J. Hutter , author I.-F. W. \ Kuo , \ and\ author C. J. \ Mundy ,\ 10.1021/jp055127v journal journal J. Phys. Chem. B \ volume 110 ,\ pages 3685 ( year 2006 ) NoStop

    2006 doi

  15. [23]

    Guidon , author F

    author author M. Guidon , author F. Schiffmann , author J. Hutter , \ and\ author J. VandeVondele ,\ 10.1063/1.2931945 journal journal J. Chem. Phys. \ volume 128 ,\ pages 214104 ( year 2008 ) NoStop

    2008 doi

  16. [24]

    \ Lin , author A

    author author I.-C. \ Lin , author A. P. \ Seitsonen , author M. D. \ Coutinho-Neto , author I. Tavernelli , \ and\ author U. Rothlisberger ,\ 10.1021/jp806376e journal journal J. Phys. Chem. B \ volume 113 ,\ pages 1127 ( year 2009 ) NoStop

    doi

  17. [25]

    Yoo \ and\ author S

    author author S. Yoo \ and\ author S. S. \ Xantheas ,\ 10.1063/1.3573375 journal journal J. Chem. Phys. \ volume 134 ,\ pages 121105 ( year 2011 ) NoStop

    2011 doi

  18. [26]

    Bankura , author A

    author author A. Bankura , author A. Karmakar , author V. Carnevale , author A. Chandra , \ and\ author M. L. \ Klein ,\ 10.1021/jp506120t journal journal J. Phys. Chem. C \ volume 118 ,\ pages 29401 ( year 2014 ) NoStop

    2014 doi

  19. [27]

    author author R. A. \ DiStasio , Jr. , author B. Santra , author Z. Li , author X. Wu , \ and\ author R. Car ,\ 10.1063/1.4893377 journal journal J. Chem. Phys. \ volume 141 ,\ pages 084502 ( year 2014 ) NoStop

    2014 doi

  20. [28]

    Marsalek \ and\ author T

    author author O. Marsalek \ and\ author T. E. \ Markland ,\ 10.1021/acs.jpclett.7b00391 journal journal J. Phys. Chem. Lett. \ volume 8 ,\ pages 1545 ( year 2017 ) NoStop

    2017 doi

  21. [29]

    Hermann , author R

    author author J. Hermann , author R. A. J. \ DiStasio , \ and\ author A. Tkatchenko ,\ 10.1021/acs.chemrev.6b00446 journal journal Chem. Rev. \ volume 117 ,\ pages 4714 ( year 2017 ) NoStop

    2017 doi

  22. [30]

    Dion , author H

    author author M. Dion , author H. Rydberg , author E. Schröder , author D. C. \ Langreth , \ and\ author B. I. \ Lundqvist ,\ 10.1103/PhysRevLett.92.246401 journal journal Phys. Rev. Lett. \ volume 92 ,\ pages 246401 ( year 2004 ) NoStop

    doi

  23. [31]

    Klimeš , author D

    author author J. Klimeš , author D. R. \ Bowler , \ and\ author A. Michaelides ,\ 10.1088/0953-8984/22/2/022201 journal journal J. Phys.: Condens. Matter \ volume 22 ,\ pages 022201 ( year 2009 ) NoStop

    2009 doi

  24. [32]

    author author O. A. \ Vydrov \ and\ author T. Van Voorhis ,\ 10.1063/1.3521275 journal journal J. Chem. Phys. \ volume 133 ,\ pages 244103 ( year 2010 ) NoStop

    2010 doi

  25. [33]

    author author O. A. \ von Lilienfeld , author I. Tavernelli , author U. Rothlisberger , \ and\ author D. Sebastiani ,\ 10.1103/PhysRevLett.93.153004 journal journal Phys. Rev. Lett. \ volume 93 ,\ pages 153004 ( year 2004 ) NoStop

    2004 doi

  26. [34]

    Eisenschitz \ and\ author F

    author author R. Eisenschitz \ and\ author F. London ,\ 10.1007/BF01341258 journal journal Z. Physik \ volume 60 ,\ pages 491 ( year 1930 ) NoStop

    1930 doi

  27. [35]

    Grimme ,\ 10.1002/jcc.20078 journal journal J

    author author S. Grimme ,\ 10.1002/jcc.20078 journal journal J. Comput. Chem. \ volume 25 ,\ pages 1463 ( year 2004 ) NoStop

    2004 doi

  28. [36]

    Grimme ,\ 10.1002/jcc.20495 journal journal J

    author author S. Grimme ,\ 10.1002/jcc.20495 journal journal J. Comput. Chem. \ volume 27 ,\ pages 1787 ( year 2006 ) NoStop

    2006 doi

  29. [37]

    Grimme , author J

    author author S. Grimme , author J. Antony , author S. Ehrlich , \ and\ author H. Krieg ,\ 10.1063/1.3382344 journal journal J. Chem. Phys. \ volume 132 ,\ pages 154104 ( year 2010 ) NoStop

    2010 doi

  30. [38]

    Grimme , author S

    author author S. Grimme , author S. Ehrlich , \ and\ author L. Goerigk ,\ 10.1002/jcc.21759 journal journal J. Comput. Chem. \ volume 32 ,\ pages 1456 ( year 2011 ) NoStop

    2011 doi

  31. [39]

    Caldeweyher , author S

    author author E. Caldeweyher , author S. Ehlert , author A. Hansen , author H. Neugebauer , author S. Spicher , author C. Bannwarth , \ and\ author S. Grimme ,\ 10.1063/1.5090222 journal journal J. Chem. Phys. \ volume 150 ,\ pages 154122 ( year 2019 ) NoStop

    doi

  32. [40]

    Tkatchenko \ and\ author M

    author author A. Tkatchenko \ and\ author M. Scheffler ,\ 10.1103/PhysRevLett.102.073005 journal journal Phys. Rev. Lett. \ volume 102 ,\ pages 073005 ( year 2009 ) NoStop

    2009 doi

  33. [41]

    author author A. D. \ Becke \ and\ author E. R. \ Johnson ,\ 10.1063/1.1884601 journal journal J. Chem. Phys. \ volume 122 ,\ pages 154104 ( year 2005 a ) NoStop

    2005 doi

  34. [42]

    author author A. D. \ Becke \ and\ author E. R. \ Johnson ,\ 10.1063/1.2795701 journal journal J. Chem. Phys. \ volume 127 ,\ pages 154108 ( year 2007 ) NoStop

    2007 doi

  35. [43]

    Hermann \ and\ author A

    author author J. Hermann \ and\ author A. Tkatchenko ,\ 10.1021/acs.jctc.7b01172 journal journal J. Chem. Theory Comput. \ volume 14 ,\ pages 1361 ( year 2018 ) NoStop

    2018 doi

  36. [44]

    Koide ,\ 10.1088/0022-3700/9/18/009 journal journal J

    author author A. Koide ,\ 10.1088/0022-3700/9/18/009 journal journal J. Phys. B: At. Mol. Phys. \ volume 9 ,\ pages 3173 ( year 1976 ) NoStop

    1976 doi

  37. [45]

    author author A. D. \ Becke \ and\ author E. R. \ Johnson ,\ 10.1063/1.2065267 journal journal J. Chem. Phys. \ volume 123 ,\ pages 154101 ( year 2005 b ) NoStop

    2005 doi

  38. [46]

    author author E. R. \ Johnson \ and\ author A. D. \ Becke ,\ 10.1063/1.1949201 journal journal J. Chem. Phys. \ volume 123 ,\ pages 024101 ( year 2005 ) NoStop

    2005 doi

  39. [47]

    author author E. R. \ Johnson \ and\ author A. D. \ Becke ,\ 10.1063/1.2190220 journal journal J. Chem. Phys. \ volume 124 ,\ pages 174104 ( year 2006 ) NoStop

    2006 doi

  40. [48]

    Sakong , author K

    author author S. Sakong , author K. Forster-Tonigold , \ and\ author A. Groß ,\ 10.1063/1.4948638 journal journal J. Chem. Phys. \ volume 144 ,\ pages 194701 ( year 2016 ) NoStop

    2016 doi

  41. [49]

    Dodia , author T

    author author M. Dodia , author T. Ohto , author S. Imoto , \ and\ author Y. Nagata ,\ 10.1021/acs.jctc.9b00253 journal journal J. Chem. Theory Comput. \ volume 15 ,\ pages 3836 ( year 2019 ) NoStop

    2019 doi

  42. [50]

    author author J. P. \ Perdew , author K. Burke , \ and\ author M. Ernzerhof ,\ 10.1103/PhysRevLett.77.3865 journal journal Phys. Rev. Lett. \ volume 77 ,\ pages 3865 ( year 1996 ) NoStop

    1996 doi

  43. [51]

    Hammer , author L

    author author B. Hammer , author L. B. \ Hansen , \ and\ author J. K. \ Nørskov ,\ 10.1103/PhysRevB.59.7413 journal journal Phys. Rev. B \ volume 59 ,\ pages 7413 ( year 1999 ) NoStop

    1999 doi

  44. [52]

    Schröder , author A

    author author H. Schröder , author A. Creon , \ and\ author T. Schwabe ,\ 10.1021/acs.jctc.5b00400 journal journal J. Chem. Theory Comput. \ volume 11 ,\ pages 3163 ( year 2015 ) NoStop

    2015 doi

  45. [53]

    author author M. A. \ Caro ,\ 10.48550/arXiv.1704.00761 title Parametrization of the Tkatchenko - Scheffler dispersion correction scheme for popular exchange-correlation density functionals: effect on the description of liquid water , \ ( year 2017 ),\ note arXiv:1704.00761 [c...

    doi arXiv

  46. [54]

    Jurečka , author J

    author author P. Jurečka , author J. Šponer , author J. Černý , \ and\ author P. Hobza ,\ 10.1039/B600027D journal journal Phys. Chem. Chem. Phys. \ volume 8 ,\ pages 1985 ( year 2006 ) NoStop

    1985 doi

  47. [55]

    Řezáč , author K

    author author J. Řezáč , author K. E. \ Riley , \ and\ author P. Hobza ,\ 10.1021/ct2002946 journal journal J. Chem. Theory Comput. \ volume 7 ,\ pages 2427 ( year 2011 ) NoStop

    2011 doi

  48. [56]

    Řezáč , author K

    author author J. Řezáč , author K. E. \ Riley , \ and\ author P. Hobza ,\ 10.1021/ct5000692 journal journal J. Chem. Theory Comput. \ volume 10 ,\ pages 1359 ( year 2014 ) NoStop

    2014 doi

  49. [57]

    Řezáč , author P

    author author J. Řezáč , author P. Jurečka , author K. E. \ Riley , author J. Černý , author H. Valdes , author K. Pluháčková , author K. Berka , author T. Řezáč , author M. Pitoňák , author J. Vondrášek , \ and\ author P. Hobza ,\ 10.1135/cccc20081261 journal journal Collect....

    doi

  50. [58]

    Temelso , author K

    author author B. Temelso , author K. A. \ Archer , \ and\ author G. C. \ Shields ,\ 10.1021/jp2069489 journal journal J. Phys. Chem. A \ volume 115 ,\ pages 12034 ( year 2011 ) NoStop

    2011 doi

  51. [59]

    Behler \ and\ author M

    author author J. Behler \ and\ author M. Parrinello ,\ 10.1103/PhysRevLett.98.146401 journal journal Phys. Rev. Lett. \ volume 98 ,\ pages 146401 ( year 2007 ) NoStop

    2007 doi

  52. [60]

    Behler ,\ 10.1002/qua.24890 journal journal Int

    author author J. Behler ,\ 10.1002/qua.24890 journal journal Int. J. Quantum Chem. \ volume 115 ,\ pages 1032 ( year 2015 ) NoStop

    2015 doi

  53. [61]

    Behler ,\ 10.1002/anie.201703114 journal journal Angew

    author author J. Behler ,\ 10.1002/anie.201703114 journal journal Angew. Chem. Int. Ed. \ volume 56 ,\ pages 12828 ( year 2017 ) NoStop

    2017 doi

  54. [62]

    Behler ,\ 10.1021/acs.chemrev.0c00868 journal journal Chem

    author author J. Behler ,\ 10.1021/acs.chemrev.0c00868 journal journal Chem. Rev. \ volume 121 ,\ pages 10037 ( year 2021 ) NoStop

    2021 doi

  55. [63]

    Bučko , author S

    author author T. Bučko , author S. Lebègue , author J. Hafner , \ and\ author J. G. \ Ángyán ,\ 10.1103/PhysRevB.87.064110 journal journal Phys. Rev. B \ volume 87 ,\ pages 064110 ( year 2013 ) NoStop

    2013 doi

  56. [64]

    author author H. B. G. \ Casimir \ and\ author D. Polder ,\ 10.1103/PhysRev.73.360 journal journal Phys. Rev. \ volume 73 ,\ pages 360 ( year 1948 ) NoStop

    1948 doi

  57. [65]

    Otero-de-la Roza \ and\ author E

    author author A. Otero-de-la Roza \ and\ author E. R. \ Johnson ,\ 10.1063/5.0015133 journal journal J. Chem. Phys. \ volume 153 ,\ pages 054121 ( year 2020 ) NoStop

    2020 doi

  58. [66]

    Klimeš \ and\ author A

    author author J. Klimeš \ and\ author A. Michaelides ,\ 10.1063/1.4754130 journal journal J. Chem. Phys. \ volume 137 ( year 2012 ),\ 10.1063/1.4754130 NoStop

    2012 doi

  59. [67]

    author author B. M. \ Axilrod \ and\ author E. Teller ,\ 10.1063/1.1723844 journal journal J. Chem. Phys. \ volume 11 ,\ pages 299 ( year 1943 ) NoStop

    1943 doi

  60. [68]

    Pyykkö \ and\ author M

    author author P. Pyykkö \ and\ author M. Atsumi ,\ 10.1002/chem.200800987 journal journal Chem. Eur. J. \ volume 15 ,\ pages 186 ( year 2009 ) NoStop

    2009 doi

  61. [69]

    author author K. J. \ Miller ,\ 10.1021/ja00179a044 journal journal J. Am. Chem. Soc. \ volume 112 ,\ pages 8533 ( year 1990 ) NoStop

    1990 doi

  62. [70]

    Brinck , author J

    author author T. Brinck , author J. S. \ Murray , \ and\ author P. Politzer ,\ 10.1063/1.465038 journal journal J. Chem. Phys. \ volume 98 ,\ pages 4305 ( year 1993 ) NoStop

    1993 doi

  63. [71]

    author author F. L. \ Hirshfeld ,\ 10.1007/BF00549096 journal journal Theoret. Chim. Acta \ volume 44 ,\ pages 129 ( year 1977 ) NoStop

    1977 doi

  64. [72]

    Chu \ and\ author A

    author author X. Chu \ and\ author A. Dalgarno ,\ 10.1063/1.1779576 journal journal J. Chem. Phys. \ volume 121 ,\ pages 4083 ( year 2004 ) NoStop

    2004 doi

  65. [73]

    \ Chai \ and\ author M

    author author J.-D. \ Chai \ and\ author M. Head-Gordon ,\ 10.1039/B810189B journal journal Phys. Chem. Chem. Phys. \ volume 10 ,\ pages 6615 ( year 2008 ) NoStop

    2008 doi

  66. [74]

    Wu \ and\ author W

    author author Q. Wu \ and\ author W. Yang ,\ 10.1063/1.1424928 journal journal J. Chem. Phys. \ volume 116 ,\ pages 515 ( year 2002 ) NoStop

    2002 doi

  67. [75]

    Behler ,\ 10.1063/1.4966192 journal journal J

    author author J. Behler ,\ 10.1063/1.4966192 journal journal J. Chem. Phys. \ volume 145 ,\ pages 170901 ( year 2016 ) NoStop

    2016 doi

  68. [76]

    No\'e , author A

    author author F. No\'e , author A. Tkatchenko , author K.-R. \ M \"u ller , \ and\ author C. Clementi ,\ 10.1146/annurev-physchem-042018-052331 journal journal Ann. Rev. Phys. Chem. \ volume 71 ,\ pages 361 ( year 2020 ) NoStop

    2020 doi

  69. [77]

    u tt , author A. Tkatchenko , \ and\ author K.-R. \ M \

    author author O. T. \ Unke , author S. Chmiela , author H. E. \ Sauceda , author M. Gastegger , author I. Poltavsky , author K. T. \ Sch \"u tt , author A. Tkatchenko , \ and\ author K.-R. \ M \"u ller ,\ 10.1021/acs.chemrev.0c01111 journal journal Chem. Rev. \ volume 121 ,\ p...

    doi

  70. [78]

    Friederich , author F

    author author P. Friederich , author F. H \"a se , author J. Proppe , \ and\ author A. Aspuru-Guzik ,\ 10.1038/s41563-020-0777-6 journal journal Nat. Mater \ volume 20 ,\ pages 750 ( year 2021 ) NoStop

    2021 doi

  71. [79]

    Behler \ and\ author G

    author author J. Behler \ and\ author G. Cs\' a nyi ,\ 0.1140/epjb/s10051-021-00156-1 journal journal Eur. Phys. J. B \ volume 94 ,\ pages 142 ( year 2021 ) NoStop

    2021

  72. [80]

    Behler ,\ 10.1063/1.3553717 journal journal J

    author author J. Behler ,\ 10.1063/1.3553717 journal journal J. Chem. Phys. \ volume 134 ,\ pages 074106 ( year 2011 ) NoStop

    2011 doi

  73. [81]

    author author A. M. \ Tokita \ and\ author J. Behler ,\ 10.1063/5.0160326 journal journal J. Chem. Phys. \ volume 159 ,\ pages 121501 ( year 2023 ) NoStop

    2023 doi

  74. [82]

    Blum , author R

    author author V. Blum , author R. Gehrke , author F. Hanke , author P. Havu , author V. Havu , author X. Ren , author K. Reuter , \ and\ author M. Scheffler ,\ 10.1016/j.cpc.2009.06.022 journal journal Comput. Phys. Commun. \ volume 180 ,\ pages 2175 ( year 2009 ) NoStop

    2009 doi

  75. [83]

    Boys \ and\ author F

    author author S. Boys \ and\ author F. Bernardi ,\ 10.1080/00268977000101561 journal journal Mol. Phys. \ volume 19 ,\ pages 553 ( year 1970 ) NoStop

    1970 doi

  76. [84]

    author author B. H. \ Wells \ and\ author S. Wilson ,\ 10.1016/0009-2614(83)87508-3 journal journal Chem. Phys. Lett. \ volume 101 ,\ pages 429 ( year 1983 ) NoStop

    1983 doi

  77. [85]

    Hermann , author M

    author author J. Hermann , author M. Stöhr , author S. Góger , author S. Chaudhuri , author B. Aradi , author R. J. \ Maurer , \ and\ author A. Tkatchenko ,\ 10.1063/5.0170972 journal journal J. Chem. Phys. \ volume 159 ,\ pages 174802 ( year 2023 ) NoStop

    doi

  78. [86]

    Eckhoff \ and\ author J

    author author M. Eckhoff \ and\ author J. Behler ,\ 10.1063/5.0073449 journal journal J. Chem. Phys. \ volume 155 ,\ pages 244703 ( year 2021 a ) NoStop

    2021 doi

  79. [87]

    Eckhoff \ and\ author J

    author author M. Eckhoff \ and\ author J. Behler ,\ 10.1021/acs.jctc.8b01288 journal journal J. Chem. Theory Comput. \ volume 15 ,\ pages 3793 ( year 2019 ) NoStop

    2019 doi

  80. [88]

    Eckhoff \ and\ author J

    author author M. Eckhoff \ and\ author J. Behler ,\ 10.1038/s41524-021-00636-z journal journal npj Comput. Mater. \ volume 7 ,\ pages 1 ( year 2021 b ) NoStop

    2021 doi

  81. [89]

    Plimpton ,\ 10.1006/jcph.1995.1039 journal journal J

    author author S. Plimpton ,\ 10.1006/jcph.1995.1039 journal journal J. Comput. Phys. \ volume 117 ,\ pages 1 ( year 1995 ) NoStop

    1995

  82. [90]

    author author A. P. \ Thompson , author H. M. \ Aktulga , author R. Berger , author D. S. \ Bolintineanu , author W. M. \ Brown , author P. S. \ Crozier , author P. J. \ in 't Veld , author A. Kohlmeyer , author S. G. \ Moore , author T. D. \ Nguyen , author R. Shan , author M...

  83. [91]

    Singraber , author J

    author author A. Singraber , author J. Behler , \ and\ author C. Dellago ,\ 10.1021/acs.jctc.8b00770 journal journal J. Chem. Theory Comput. \ volume 15 ,\ pages 1827 ( year 2019 ) NoStop

    2019 doi

  84. [92]

    Nosé ,\ 10.1080/00268978400101201 journal journal Mol

    author author S. Nosé ,\ 10.1080/00268978400101201 journal journal Mol. Phys. \ volume 52 ,\ pages 255 ( year 1984 ) NoStop

    1984 doi

  85. [93]

    author author W. G. \ Hoover ,\ 10.1103/PhysRevA.31.1695 journal journal Phys. Rev. A \ volume 31 ,\ pages 1695 ( year 1985 ) NoStop

    1985 doi

  86. [94]

    Frenkel \ and\ author B

    author author D. Frenkel \ and\ author B. Smit ,\ @noop title Understanding Molecular Simulation ,\ edition 2nd \ ed.\ ( publisher Academic Press ,\ address San Diego ,\ year 2002 ) NoStop

    2002

  87. [95]

    Schmitz \ and\ author C

    author author G. Schmitz \ and\ author C. Hättig ,\ 10.1021/acs.jctc.7b00180 journal journal J. Chem. Theory Comput. \ volume 13 ,\ pages 2623 ( year 2017 ) NoStop

    2017 doi

  88. [96]

    Takatani , author E

    author author T. Takatani , author E. G. \ Hohenstein , author M. Malagoli , author M. S. \ Marshall , \ and\ author C. D. \ Sherrill ,\ 10.1063/1.3378024 journal journal J. Chem. Phys. \ volume 132 ,\ pages 144104 ( year 2010 ) NoStop

    doi

  89. [97]

    Manna , author M

    author author D. Manna , author M. K. \ Kesharwani , author N. Sylvetsky , \ and\ author J. M. L. \ Martin ,\ 10.1021/acs.jctc.6b01046 journal journal J. Chem. Theory Comput. \ volume 13 ,\ pages 3136 ( year 2017 ) NoStop

    2017 doi

  90. [98]

    Morawietz \ and\ author J

    author author T. Morawietz \ and\ author J. Behler ,\ 10.1021/jp401225b journal journal J. Phys. Chem. A \ volume 117 ,\ pages 7356 ( year 2013 ) NoStop

    2013 doi

  91. [99]

    Cheng , author E

    author author B. Cheng , author E. A. \ Engel , author J. Behler , author C. Dellago , \ and\ author M. Ceriotti ,\ 10.1073/pnas.1815117116 journal journal PNAS \ volume 116 ,\ pages 1110 ( year 2019 ) NoStop

    2019 doi

  92. [100]

    Torres , author L

    author author A. Torres , author L. S. \ Pedroza , author M. Fernandez-Serra , \ and\ author A. R. \ Rocha ,\ 10.1021/acs.jpcb.1c04372 journal journal J. Phys. Chem. B \ volume 125 ,\ pages 10772 ( year 2021 ) NoStop

    2021 doi

  93. [101]

    Stolte , author J

    author author N. Stolte , author J. Daru , author H. Forbert , author J. Behler , \ and\ author D. Marx ,\ 10.1021/acs.jpclett.4c02925 journal journal J. Phys. Chem. Lett. \ volume 15 ,\ pages 12144 ( year 2024 ) NoStop

    2024 doi

  94. [102]

    Gomez , author Z

    author author A. Gomez , author Z. A. \ Piskulich , author W. H. \ Thompson , \ and\ author D. Laage ,\ 10.1021/acs.jpclett.2c00825 journal journal J. Phys. Chem. Lett. \ volume 13 ,\ pages 4660 ( year 2022 ) NoStop

    2022 doi

  95. [103]

    author author J. C. \ Grossman , author E. Schwegler , author E. W. \ Draeger , author F. Gygi , \ and\ author G. Galli ,\ 10.1063/1.1630560 journal journal J. Chem. Phys. \ volume 120 ,\ pages 300 ( year 2004 ) NoStop

    2004 doi

  96. [104]

    Schwegler , author J

    author author E. Schwegler , author J. C. \ Grossman , author F. Gygi , \ and\ author G. Galli ,\ 10.1063/1.1782074 journal journal J. Chem. Phys. \ volume 121 ,\ pages 5400 ( year 2004 ) NoStop

    2004 doi

  97. [105]

    Jedlovszky , author M

    author author P. Jedlovszky , author M. Mezei , \ and\ author R. Vallauri ,\ 10.1016/S0009-2614(00)00002-6 journal journal Chem. Phys. Lett. \ volume 318 ,\ pages 155 ( year 2000 ) NoStop

    doi

  98. [106]

    author author F. H. \ Stillinger , Jr. ,\ 10.1063/1.1776907 journal journal J. Chem. Phys. \ volume 38 ,\ pages 1486 ( year 1963 ) NoStop

    1963 doi

  99. [107]

    Wedekind \ and\ author D

    author author J. Wedekind \ and\ author D. Reguera ,\ 10.1063/1.2786457 journal journal J. Chem. Phys. \ volume 127 ,\ pages 154516 ( year 2007 ) NoStop

    2007 doi

  100. [108]

    Tkatchenko , author R

    author author A. Tkatchenko , author R. A. \ DiStasio , author R. Car , \ and\ author M. Scheffler ,\ 10.1103/PhysRevLett.108.236402 journal journal Phys. Rev. Lett. \ volume 108 ,\ pages 236402 ( year 2012 ) NoStop

    2012 doi

  101. [109]

    author author N. R. \ Kestner \ and\ author J. E. \ Combariza ,\ https://doi.org/10.1002/9780470125908.ch2 journal journal Rev. Comput. Chem. \ volume 13 ,\ pages 99 ( year 1999 ) NoStop

    1999 doi

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