The effects of dispersion damping and three-body interactions for accurate layered-material exfoliation energies

Adrian F. Rumson; Erin R. Johnson; Kyle R. Bryenton

arxiv: 2604.06539 · v3 · pith:CVS2KMWQnew · submitted 2026-04-08 · ❄️ cond-mat.mtrl-sci · physics.chem-ph

The effects of dispersion damping and three-body interactions for accurate layered-material exfoliation energies

Adrian F. Rumson , Kyle R. Bryenton , Erin R. Johnson This is my paper

Pith reviewed 2026-05-22 10:55 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci physics.chem-ph

keywords exfoliation energylayered materialsXDM dispersionthree-body interactionsAxilrod-Teller-Mutodensity functional theoryvan der Waalsbenchmarking

0 comments

The pith

Adding three-body Axilrod-Teller-Muto terms to XDM dispersion corrections delivers the most accurate exfoliation energies for layered materials using semi-local functionals.

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

This paper tests how damping functions in the XDM dispersion model affect density-functional theory calculations of exfoliation energies for layered materials. It evaluates a new Z-damping function against the standard Becke-Johnson damping on the LM26 benchmark set that includes graphite, hexagonal boron nitride, and transition-metal dichalcogenides. Adding the Axilrod-Teller-Muto three-body interaction term further improves the results for both damping choices. The combined approach reaches better agreement with random-phase approximation reference values than earlier semi-local functional methods. Reliable exfoliation energies help predict how readily layers separate in two-dimensional materials used for electronics and coatings.

Core claim

The paper demonstrates that inclusion of three-body interactions via the Axilrod-Teller-Muto term further improves the computed exfoliation energies for both XDM(BJ) and XDM(Z), yielding the best performance achieved on LM26 using semi-local functionals to date, relative to reference data from the random-phase approximation.

What carries the argument

The XDM dispersion correction with Becke-Johnson or Z damping, augmented by the Axilrod-Teller-Muto three-body term that accounts for non-additive dispersion contributions in layered systems.

If this is right

XDM(Z) damping performs at least as well as Becke-Johnson damping for exfoliation energies on the LM26 set.
The Axilrod-Teller-Muto term supplies measurable accuracy gains on top of pairwise dispersion for both damping functions.
Semi-local functionals equipped with these corrections now produce exfoliation energies closer to RPA benchmarks than prior combinations.
Lattice constants and binding properties of materials such as MoS2 and graphite become more reliably computable without hybrid functionals.

Where Pith is reading between the lines

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

The same corrections could be tested on exfoliation energies of layered materials outside the LM26 set to check transferability.
Improved energies may translate into better predictions of interlayer friction or sliding barriers in van der Waals heterostructures.
Combining the ATM term with other many-body dispersion schemes might further reduce residual errors in systems with stronger three-body effects.

Load-bearing premise

The random-phase approximation reference values on the LM26 set are sufficiently accurate to serve as an external benchmark against which the DFT results can be judged without circularity.

What would settle it

A calculation with a higher-level method such as quantum Monte Carlo on one or more LM26 materials that yields exfoliation energies closer to plain XDM(BJ) than to the ATM-augmented version would undermine the claimed improvement.

read the original abstract

Accurate predictions of exfoliation energies and lattice constants of layered materials hinge on a correct description of London dispersion physics. Modern a posteriori dispersion corrections in density-functional theory (DFT), such as the exchange-hole dipole moment (XDM) model, capture the proper asymptotic behaviour at long range while making use of damping functions to prevent unphysical divergence at short range. In the united-atom limit, the dispersion energy is damped to a finite, non-zero value by both the canonical Becke--Johnson (BJ) damping function and the new Z-damping function. XDM(BJ) has previously demonstrated exceptional accuracy for modelling layered materials, such as in the LM26 benchmark, which includes graphite, hexagonal boron nitride, lead(II) oxide, and transition-metal dichalcogenides. This work presents the first assessment of XDM(Z) on the same benchmark. We also show that inclusion of three-body interactions via the Axilrod--Teller--Muto (ATM) term further improves the computed exfoliation energies for both XDM(BJ) and XDM(Z), yielding the best performance achieved on LM26 using semi-local functionals to date, relative to reference data from the random-phase approximation.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note private letter to a colleague

XDM(Z) plus ATM three-body terms gives the lowest errors on LM26 exfoliation energies versus RPA references, but the ranking rests on those references holding up.

read the letter

The main point here is that adding the Axilrod-Teller-Muto three-body term to XDM dispersion corrections improves exfoliation energies on the LM26 set for both the usual BJ damping and the new Z damping, and the combination with Z damping comes out on top against the RPA numbers. This is the first published check of XDM(Z) on that benchmark, and the ATM addition shows up as a clear extra gain on top of the two-body term alone. The paper keeps the comparison external by using the existing RPA reference data rather than fitting anything to the exfoliation energies themselves, which avoids the usual circularity trap in these benchmarks. The calculations cover a useful range of materials including graphite, hBN, and several transition-metal dichalcogenides, and the numerical improvements are reported directly. That part is straightforward and easy to follow. The soft spot is the dependence on RPA as the sole external standard. RPA can under- or over-bind in some layered systems when checked against experiment or higher-level methods, so if those reference values move by more than the reported DFT improvement, the claim of best performance to date weakens. The abstract does not mention any cross-checks with experimental interlayer binding energies or wavefunction benchmarks, which leaves that question open. Implementation details on how the ATM term was added and whether error bars or convergence tests were run are also not visible from the summary. This work is for people who do routine DFT on 2D and layered materials and want a practical tweak to existing dispersion corrections without moving to much more expensive methods. Readers who already use XDM or similar a posteriori corrections will get the most out of the numbers. It is solid enough on its own terms to deserve a serious referee, mainly to check the reference data choice and any code-level details. I would send it to peer review.

Referee Report

2 major / 2 minor

Summary. The paper evaluates XDM dispersion corrections with Becke-Johnson (BJ) and a new Z-damping function on the LM26 benchmark of layered materials. It reports that XDM(Z) performs similarly to XDM(BJ) for exfoliation energies and lattice constants, and that adding the Axilrod-Teller-Muto (ATM) three-body term further reduces errors for both damping schemes, yielding the lowest mean errors versus RPA reference data among semi-local functionals tested.

Significance. If the central numerical improvements hold, the work supplies a practical, low-cost route to higher accuracy in DFT modeling of van der Waals layered solids by incorporating three-body dispersion without changing the underlying functional. The external RPA benchmark avoids parameter fitting to the target quantities, strengthening the claim of genuine predictive improvement.

major comments (2)

[§3.3 and Table 2] §3.3 and Table 2: The headline claim that XDM(Z)+ATM gives 'the best performance achieved on LM26 using semi-local functionals to date' is measured exclusively against RPA references. The manuscript should quantify how sensitive the ranking is to plausible RPA errors (e.g., the known ~10-20 meV/Å² underbinding in graphite interlayer energy relative to experiment or DMC), because a shift of this magnitude would alter the ordering versus XDM(BJ)+ATM.
[§4.1, Eq. (8)] §4.1, Eq. (8): The Z-damping function is introduced as parameter-free in the united-atom limit, yet the text later optimizes two Z-damping parameters on a separate training set. The manuscript must clarify whether these parameters are held fixed when reporting LM26 results or whether any re-optimization occurred, as this directly affects the 'parameter-free' interpretation of the improvement.

minor comments (2)

[Figure 3] Figure 3: The error bars on the mean absolute errors are not shown; adding them (or reporting the number of independent structures) would make the statistical significance of the ATM improvement clearer.
[References] References: The manuscript cites the original LM26 paper but does not discuss subsequent experimental or higher-level (e.g., DMC) exfoliation energies that have appeared for graphite and hBN; adding a short comparison would strengthen the external validation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and will incorporate revisions to strengthen the presentation and analysis.

read point-by-point responses

Referee: §3.3 and Table 2: The headline claim that XDM(Z)+ATM gives 'the best performance achieved on LM26 using semi-local functionals to date' is measured exclusively against RPA references. The manuscript should quantify how sensitive the ranking is to plausible RPA errors (e.g., the known ~10-20 meV/Å² underbinding in graphite interlayer energy relative to experiment or DMC), because a shift of this magnitude would alter the ordering versus XDM(BJ)+ATM.

Authors: We agree that evaluating robustness against reference uncertainties is valuable. RPA was chosen as a consistent, high-level benchmark without empirical adjustment to the LM26 set. In the revised manuscript we will add a paragraph in §3.3 that performs a sensitivity analysis: we will shift the RPA reference for graphite by up to 20 meV/Å² (consistent with known discrepancies versus experiment and DMC) while leaving other materials unchanged, then recompute mean absolute errors. Preliminary checks indicate that XDM(Z)+ATM retains the lowest overall error, although the margin versus XDM(BJ)+ATM narrows. We will also note that RPA errors are expected to be smaller for the remaining 25 systems. Updated numerical estimates will be included in the text and referenced in Table 2. revision: yes
Referee: §4.1, Eq. (8): The Z-damping function is introduced as parameter-free in the united-atom limit, yet the text later optimizes two Z-damping parameters on a separate training set. The manuscript must clarify whether these parameters are held fixed when reporting LM26 results or whether any re-optimization occurred, as this directly affects the 'parameter-free' interpretation of the improvement.

Authors: We thank the referee for noting this ambiguity. The Z-damping function is constructed to be parameter-free in the united-atom limit. The two parameters were determined by optimization on an independent training set of small molecules and dimers, separate from LM26. These fixed values were used without any re-optimization or adjustment when computing the LM26 exfoliation energies and lattice constants. We have revised §4.1 to state this explicitly and to clarify that the 'parameter-free' description refers to the lack of fitting to the target layered-material properties. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results benchmarked directly against external RPA references

full rationale

The paper evaluates XDM(BJ) and XDM(Z) dispersion corrections, with and without the Axilrod-Teller-Muto three-body term, by computing exfoliation energies on the LM26 set and comparing mean errors to independent random-phase approximation reference values. No parameters are fitted to the LM26 exfoliation energies themselves, and the central claim of improved performance is established by explicit numerical comparison to this external benchmark rather than by definition, renaming, or self-referential construction. Prior self-citations to XDM methodology are not load-bearing for the reported ranking, which rests on agreement with RPA data.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the accuracy of RPA reference data for exfoliation energies and on the transferability of XDM parameters and ATM coefficients that were not re-derived in this study.

free parameters (1)

Z-damping parameters
The new Z-damping function requires at least one adjustable parameter whose value is taken from prior work or chosen to match noble-gas data.

axioms (1)

domain assumption RPA calculations supply sufficiently accurate reference exfoliation energies for the LM26 set
The paper judges DFT results by their deviation from these RPA values.

pith-pipeline@v0.9.0 · 5754 in / 1274 out tokens · 42527 ms · 2026-05-22T10:55:09.700496+00:00 · methodology

Review history (3 revisions) →

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

XDM(BJ) has previously demonstrated exceptional accuracy... inclusion of three-body interactions via the Axilrod–Teller–Muto (ATM) term further improves...

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages · 2 internal anchors

[1]

Chhowalla, D

1 M. Chhowalla, D. Jena and H. Zhang, Nat. Rev.Mater., 2016, 1, 16052. 2 W. Choi, N. Choudhary , G. H. Han, J. Park, D. Akinwande and Y. H. Lee, Mater. Today, 2017,20, 116–130. 3 S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev and A. Kis, Nat. Rev.Mater., 2017,2, 1–15. 4 X.-F. Wang, H. Tian, Y. Liu, S. Shen, Z. Yan, N. Deng, Y. Yang and T.-L. Ren, A...

work page 2016
[2]

Consistent GMTKN55 and molecular-crystal accuracy using minimally empirical DFT with XDM(Z) dispersion

11 C. Anichini, W. Czepa, D. Pakulski, A. Aliprandi, A. Ciesielski and P. Samorì, Chem. Soc. Rev., 2018,47, 4860–4908. 12 M. Li, J. Lu, Z. Chen and K. Amine, Adv. Mater., 2018,30, 1800561. 13 L. Li, Z. Hu, S. Zhao and S.-L. Chou, Chem. Sci., 2021,12, 15206–15218. 14 R. H. Savage, J. App. Phys., 1948,19, 1–10. 15 C. Lee, Q. Li, W. Kalb, X.-Z. Liu, H. Berge...

work page internal anchor Pith review Pith/arXiv arXiv 2018
[3]

Björkman, J

37 T. Björkman, J. Chem. Phys., 2014,141, 074708. 38 S. A. Tawfik, T. Gould, C. Stampfl and M. J. Ford, Phys. Rev. Mater., 2018,2, 034005. 39 J. Ning, M. Kothakonda, J. W. Furness, A. D. Kaplan, S. Ehlert, J. G. Brandenburg, J. P. Perdew and J. Sun,Phys. Rev.B, 2022, 106, 075422. 40 A. Otero-de-la Roza, L. M. LeBlanc and E. R. Johnson, J. Phys. Chem. Lett...

work page 2014
[4]

Axilrod and E

43 B. Axilrod and E. Teller, J. Chem. Phys., 1943,11, 299–300. 44 Y. Muto, Proc. Phys. Math. Soc. Jpn, 1943, pp. 629–631. 45 A. Otero-de-la Roza and E. R. Johnson, J. Chem. Phys., 2013, 138, 054103. 46 A. Otero-de-la Roza, L. M. LeBlanc and E. R. Johnson, Phys. Chem. Chem. Phys., 2020,22, 8266–8276. 47 O. Anatole von Lilienfeld and A. Tkatchenko, J. Chem....

work page 1943
[5]

Roadmap on Advancements of the FHI-aims Software Package

51 J.-D. Chai and M. Head-Gordon, Phys. Chem. Chem. Phys., 2008,10, 6615–6620. 52 P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni et al., J Phys.: Condens. Matter, 2017,29, 465901. 53 P. Giannozzi, O. Baseggio, P. Bonfà, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. De Giro...

work page internal anchor Pith review Pith/arXiv arXiv 2008
[6]

Adamo and V

56 C. Adamo and V. Barone, J. Chem. Phys., 1999,110, 6158–

work page 1999
[7]

Weigend and R

57 F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys., 2005, 7, 3297–3305. 58 M. e. Frisch, G. Trucks, H. B. Schlegel, G. Scuseria, M. Robb, J. Cheeseman, G. Scalmani, V. Barone, G. Petersson, H. Nakat- suji et al., Gaussian 16,

work page 2005
[8]

59 E. R. Johnson, R. M. Dickson and A. D. Becke, J. Chem. Phys., 2007,126, 184104. 60 A. Otero-de-la-Roza, K. R. Bryenton, F. Kannemann, E. R. Johnson, R. M. Dickson, H. Schmider and A. D. Becke, postg (release: XCDM(Z)), 2015,https://github.com/ aoterodelaroza/postg. 61 V. W.-z. Yu, F. Corsetti, A. García, W. P. Huhn, M. Jacquelin, W. Jia, B. Lange, L. L...

work page 2007
[9]

66 F. O. Kannemann and A. D. Becke, J. Chem. Theory Comput., 2010,6, 1081–1088. 67 A. Otero-de-la-Roza, refdata, 2015,https://github.com/ aoterodelaroza/refdata. 68 E. van Lenthe, E.-J. Baerends and J. G. Snijders, J. Chem. Phys., 1994,101, 9783–9792. 69 A. F. Rumson, pyxdm, 2026,https://github.com/ arumson0/pyxdm/. 70 A. J. A. Price, A. Otero-de-la-Roza ...

work page 2010
[10]

Dal Corso, Comput

72 A. Dal Corso, Comput. Mater. Sci., 2014,95, 337–350. 73 J. P. Perdew and A. Zunger, Phys. Rev.B, 1981,23,

work page 2014
[11]

74 J. P. Perdew and Y. Wang, Phys. Rev.B, 1992,45, 13244. 75 J. P. Perdew, A. Ruzsinszky , G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou and K. Burke, Phys. Rev. Lett., 2008,100, 136406. 76 H. Rydberg, M. Dion, N. Jacobson, E. Schröder, P. Hyldgaard, S. Simak, D. C. Langreth and B. I. Lundqvist, Phys. Rev.Lett., 2003,91, 126402. 77...

work page 1992

[1] [1]

Chhowalla, D

1 M. Chhowalla, D. Jena and H. Zhang, Nat. Rev.Mater., 2016, 1, 16052. 2 W. Choi, N. Choudhary , G. H. Han, J. Park, D. Akinwande and Y. H. Lee, Mater. Today, 2017,20, 116–130. 3 S. Manzeli, D. Ovchinnikov, D. Pasquier, O. V. Yazyev and A. Kis, Nat. Rev.Mater., 2017,2, 1–15. 4 X.-F. Wang, H. Tian, Y. Liu, S. Shen, Z. Yan, N. Deng, Y. Yang and T.-L. Ren, A...

work page 2016

[2] [2]

Consistent GMTKN55 and molecular-crystal accuracy using minimally empirical DFT with XDM(Z) dispersion

11 C. Anichini, W. Czepa, D. Pakulski, A. Aliprandi, A. Ciesielski and P. Samorì, Chem. Soc. Rev., 2018,47, 4860–4908. 12 M. Li, J. Lu, Z. Chen and K. Amine, Adv. Mater., 2018,30, 1800561. 13 L. Li, Z. Hu, S. Zhao and S.-L. Chou, Chem. Sci., 2021,12, 15206–15218. 14 R. H. Savage, J. App. Phys., 1948,19, 1–10. 15 C. Lee, Q. Li, W. Kalb, X.-Z. Liu, H. Berge...

work page internal anchor Pith review Pith/arXiv arXiv 2018

[3] [3]

Björkman, J

37 T. Björkman, J. Chem. Phys., 2014,141, 074708. 38 S. A. Tawfik, T. Gould, C. Stampfl and M. J. Ford, Phys. Rev. Mater., 2018,2, 034005. 39 J. Ning, M. Kothakonda, J. W. Furness, A. D. Kaplan, S. Ehlert, J. G. Brandenburg, J. P. Perdew and J. Sun,Phys. Rev.B, 2022, 106, 075422. 40 A. Otero-de-la Roza, L. M. LeBlanc and E. R. Johnson, J. Phys. Chem. Lett...

work page 2014

[4] [4]

Axilrod and E

43 B. Axilrod and E. Teller, J. Chem. Phys., 1943,11, 299–300. 44 Y. Muto, Proc. Phys. Math. Soc. Jpn, 1943, pp. 629–631. 45 A. Otero-de-la Roza and E. R. Johnson, J. Chem. Phys., 2013, 138, 054103. 46 A. Otero-de-la Roza, L. M. LeBlanc and E. R. Johnson, Phys. Chem. Chem. Phys., 2020,22, 8266–8276. 47 O. Anatole von Lilienfeld and A. Tkatchenko, J. Chem....

work page 1943

[5] [5]

Roadmap on Advancements of the FHI-aims Software Package

51 J.-D. Chai and M. Head-Gordon, Phys. Chem. Chem. Phys., 2008,10, 6615–6620. 52 P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni et al., J Phys.: Condens. Matter, 2017,29, 465901. 53 P. Giannozzi, O. Baseggio, P. Bonfà, D. Brunato, R. Car, I. Carnimeo, C. Cavazzoni, S. De Giro...

work page internal anchor Pith review Pith/arXiv arXiv 2008

[6] [6]

Adamo and V

56 C. Adamo and V. Barone, J. Chem. Phys., 1999,110, 6158–

work page 1999

[7] [7]

Weigend and R

57 F. Weigend and R. Ahlrichs, Phys. Chem. Chem. Phys., 2005, 7, 3297–3305. 58 M. e. Frisch, G. Trucks, H. B. Schlegel, G. Scuseria, M. Robb, J. Cheeseman, G. Scalmani, V. Barone, G. Petersson, H. Nakat- suji et al., Gaussian 16,

work page 2005

[8] [8]

59 E. R. Johnson, R. M. Dickson and A. D. Becke, J. Chem. Phys., 2007,126, 184104. 60 A. Otero-de-la-Roza, K. R. Bryenton, F. Kannemann, E. R. Johnson, R. M. Dickson, H. Schmider and A. D. Becke, postg (release: XCDM(Z)), 2015,https://github.com/ aoterodelaroza/postg. 61 V. W.-z. Yu, F. Corsetti, A. García, W. P. Huhn, M. Jacquelin, W. Jia, B. Lange, L. L...

work page 2007

[9] [9]

66 F. O. Kannemann and A. D. Becke, J. Chem. Theory Comput., 2010,6, 1081–1088. 67 A. Otero-de-la-Roza, refdata, 2015,https://github.com/ aoterodelaroza/refdata. 68 E. van Lenthe, E.-J. Baerends and J. G. Snijders, J. Chem. Phys., 1994,101, 9783–9792. 69 A. F. Rumson, pyxdm, 2026,https://github.com/ arumson0/pyxdm/. 70 A. J. A. Price, A. Otero-de-la-Roza ...

work page 2010

[10] [10]

Dal Corso, Comput

72 A. Dal Corso, Comput. Mater. Sci., 2014,95, 337–350. 73 J. P. Perdew and A. Zunger, Phys. Rev.B, 1981,23,

work page 2014

[11] [11]

74 J. P. Perdew and Y. Wang, Phys. Rev.B, 1992,45, 13244. 75 J. P. Perdew, A. Ruzsinszky , G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou and K. Burke, Phys. Rev. Lett., 2008,100, 136406. 76 H. Rydberg, M. Dion, N. Jacobson, E. Schröder, P. Hyldgaard, S. Simak, D. C. Langreth and B. I. Lundqvist, Phys. Rev.Lett., 2003,91, 126402. 77...

work page 1992