Pith. sign in

REVIEW 3 major objections 4 minor 143 references

Performance of Tkatchenko-Scheffler Dispersion Method with Updated van der Waals Radii: Importance for Alkali-Containing Systems

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read A polarizability-based update to van der Waals radii fixes the systematic alkali overbinding in the Tkatchenko-Scheffler dispersion method, matching many-body accuracy for alkali halides and lead halide perovskites.

desk verdict A solid, careful benchmark showing that updated TS radii fix the alkali overbinding; the qualitative conclusion holds, but the quantitative edge over MBD NL depends on reference-volume construction that still contains thermal expansion. read the letter →

arxiv 2608.01501 v1 pith:6EBPFL6R submitted 2026-08-02 cond-mat.mtrl-sci

Aaron M. Schankler , Ruyi Song , Sampreeti Bhattacharya , Ela Lucas , Lee Hampton III , Alexandre Tkatchenko , Yosuke Kanai , Volker Blum This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords Tkatchenko-SchefflerdispersionvanderWaalsradiialkalihalideshalideperovskitesdensityfunctionaltheorylatticeconstantsmany-bodyzero-pointcorrection
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 seeks to establish that the large overbinding error of the 2009 Tkatchenko-Scheffler pairwise dispersion correction in alkali-containing materials comes from underestimated free-atom van der Waals radii for alkali elements, and that the 2018 revision of those radii fixes it. Using alkali dimers, nineteen alkali halides, twenty-five non-alkali binary semiconductors, and three CsPbX3 perovskites, it shows that PBE+TS 2018 and the narrower PBE+TS alkali variant cut the mean absolute alkali-halide volume error from about 20% to roughly 3-4%, matching the much more expensive many-body dispersion method. For the perovskites, the updated pairwise methods avoid the artificial symmetry breaking and exaggerated lattice anisotropy of TS 2009, although the many-body method still gives the smallest low-temperature volume errors. This matters because the cheap pairwise correction can then be used with confidence for alkali-containing systems such as hybrid halide perovskites.

What carries the argument

The load-bearing object is the polarizability-based van der Waals radius relation $R_0^A = C(\alpha_A^{\mathrm{eff}})^{1/7}$ ($C=2.54$ a.u.), introduced in the 2018 revision and paired with a revised heteronuclear distance $R_{AB}^0 = 2C((\alpha_A+\alpha_B)/2)^{1/7}$. It replaces the density-contour radii of the 2009 method. Because alkali atoms have large polarizabilities, the relation substantially increases their radii, which controls the onset of the damping function in the pairwise $E_{\mathrm{vdW}} = -\frac12\sum f_{\mathrm{damp}} C_6/R^6$ energy; the later onset removes the spurious extra binding. The Hirshfeld-volume scaling of $C_6$ and $\alpha$ is unchanged, so the whole correction

What would settle it

An anharmonic phonon calculation of the zero-point equilibrium volumes of CsPbCl3, CsPbBr3, and CsPbI3 would settle the ranking: if the true 0 K references differ from the Appendix B values by more than about 1.5%, the reported ordering among TS 2018, TS alkali, and MBD NL in the perovskite benchmarks changes.

Watch

Extended reading notes

Core claim

The central claim is that TS 2009's alkali overbinding stems from underestimated free-atom van der Waals radii, and that replacing them with polarizability-derived radii removes the error. The 2018 revision uses $R_0^A = C(\alpha_A^{\mathrm{eff}})^{1/7}$ with $C=2.54$ a.u., giving much larger radii for alkali atoms and a later damping onset for the $-C_6/R^6$ term. The paper shows that PBE+TS 2018 and PBE+TS alkali match RPA@PBE dimer curves within about 0.1 eV, cut alkali-halide volume error from 20% to about 3.4-4.0% (close to PBE+MBD NL's 2.6%), and preserve correct Pnma symmetry and better $b/a$ and $\beta$ anisotropies in CsPbCl3, CsPbBr3, and CsPbI3, where TS 2009 artificially breaks s

Load-bearing premise

The benchmark conclusions rest on the zero-point-corrected experimental reference volumes used in Appendix B; if that phonon-based correction is biased for any material class, the reported volume errors could shift by about 1.5%, enough to reorder the perovskite results.

Editorial extensions

If this is right

  • For alkali halides, PBE+TS 2018 and PBE+TS alkali lower the mean absolute cell-volume error from about 20% with TS 2009 to about 3.4-4.0%, closely matching PBE+MBD NL's 2.6%.
  • For non-alkali binary semiconductors, TS 2018 keeps errors around 3.0%, essentially unchanged from TS 2009's 2.3%, so the alkali fix does not hurt other materials.
  • For CsPbCl3, CsPbBr3, and CsPbI3, the updated methods remove TS 2009's artificial symmetry lowering and exaggerated b/a and beta distortions; MBD NL still wins on low-temperature volume but overshoots the beta angle.
  • TS alkali is exactly TS 2009 in alkali-free systems, so existing TS 2009-based workflows can be extended to alkali-containing systems without changing results elsewhere.
  • The cheap pairwise TS method becomes a practical option for hybrid organic-inorganic perovskites and other alkali-containing insulators.

Reading between the lines

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

  • Because the 2018 revision also changes radii substantially for lanthanides and actinides, the same fix may remove analogous overbinding in compounds of those elements; the paper sets those aside because of multireference complexity.
  • Other pairwise dispersion corrections that use element-dependent radii could harbor the same alkali error; transferring the polarizability-based radius update to those schemes is a natural test.
  • The better room-temperature lattice parameters reported for TS 2018 and TS alkali, despite being Born-Oppenheimer results, suggest error cancellation with missing thermal expansion; explicit finite-temperature phonon calculations could separate the two.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper benchmarks the Tkatchenko-Scheffler dispersion method with updated van der Waals radii (TS_2018), a more targeted alkali-only variant (TS_alkali), the original TS_2009, and the nonlocal many-body dispersion method (MBD NL) for structural predictions. The benchmark set comprises five alkali dimers against RPA@PBE reference curves, 45 inorganic solids against experimental volumes, and three CsPbX3 halide perovskites against low-temperature experimental structures. The central claim is that TS_2018 and TS_alkali correct the large alkali-related overbinding of TS_2009, reach accuracy comparable to PBE+MBD NL for alkali halides and binary semiconductors, and give better lattice anisotropies than TS_2009 for CsPbCl3, CsPbBr3, and CsPbI3.

Significance. If the conclusions hold, the paper provides a practical result: a simple pairwise dispersion correction with updated radii can replace a more expensive many-body method for alkali-containing solids, and the TS_alkali variant offers backward compatibility for non-alkali systems. The work is careful in several respects: RPA@PBE dimer references use counterpoise corrections and carefully converged basis sets; solid-state volumes are obtained from equation-of-state fits; and the reference volumes are corrected for zero-point motion. The data and implementations are promised to be publicly available, which strengthens reproducibility. However, the quantitative ranking among methods is sensitive to how the experimental reference volumes are defined, and the paper does not currently provide uncertainty estimates for its headline error statistics.

major comments (3)
  1. [Appendix B, Tables 2 and 4] The reference volumes for alkali halides are not Born-Oppenheimer equilibrium volumes. Table 2 states that lattice constants and elastic moduli are room-temperature data, and Appendix B subtracts only the zero-point volume correction Δv. Thermal expansion from 0 K to 300 K is therefore left in the reference. For LiF the zero-point correction alone is ~4.4% of v0, and thermal expansion adds ~1–2% for typical alkali halides. Since Table 1 separates the methods by less than one percentage point (e.g., 2.63% for MBD NL vs 3.40% for TS_2018), the central claim that TS_2018/TS_alkali are 'comparable' to MBD NL is not robust until the thermal contribution is either subtracted using low-temperature lattice constants or explicitly estimated and propagated.
  2. [Cs-containing 3D Metal Halide Perovskites, Table 6] The perovskite volume errors are evaluated against 90–100 K experimental data without any zero-point correction, while the computational volumes are at the Born-Oppenheimer surface. The paper itself notes a ~1.5% zero-point contraction for a related perovskite. For TS_2018 the reported volume overestimates (+3.1%, +3.8%, +4.5% for Cl, Br, I) would increase by roughly that amount if the reference were corrected, making MBD NL's volume advantage larger than shown in Fig. 6c. The anisotropy claims are less affected, but the section should report corrected reference volumes or a sensitivity analysis for the volume comparison.
  3. [Table 1] The aggregate errors ⟨R.E.⟩ and ⟨|R.E.|⟩ are reported without uncertainty estimates. The difference between the best-performing method (PBE+MBD NL, 2.63%) and PBE+TS_2018 (3.40%) for alkali halides is comparable to plausible systematic shifts in the experimental references (thermal expansion, Debye-model approximation). Without standard errors, bootstrap intervals, or per-material scatter, the 'comparable accuracy' conclusion is not quantitatively supported. Please add uncertainty measures and, if possible, a table of per-material errors.
minor comments (4)
  1. [Section 2.2, Eq. (6)] Eq. (6) writes R0_A = C (α_eff_A)^{1/7} using the effective polarizability defined in Eq. (3), but Eq. (7) and the TS_2018 method as described use free-atom polarizabilities. This is confusing; clarify whether the updated radii are free-atom constants or environment-dependent.
  2. [Data availability] The GitHub URL 'https://github.com/aschankler/ts18benchmark data' contains a space and is not clickable. Fix the link.
  3. [Throughout] Several typographical errors: 'the the' in the abstract, 'compatability' near the TS_alkali definition, and 'calculated calculated' in the caption of Fig. 2. Please proofread.
  4. [Section 3.1, Fig. 3] The statement that 'four methods ... perform similarly' at intermediate distances is based on visual inspection of <0.1 eV differences. A quantitative table of errors at the equilibrium distance or a measure of mean absolute deviation would make the claim more precise.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: method parameters are imported from prior work and tested against independent references.

full rationale

The paper benchmarks externally fixed parametrizations. The TS_2018 vdW radii come from Fedorov et al. (Ref. 23), with the constant C = 2.54 fitted to noble-gas vdW radii (Eq. 6) and the heteronuclear distance rule of Eq. 7 also taken from that prior work; TS_alkali is defined as TS_2009 with only alkali radii updated. None of these parameters are fitted to the alkali-dimer RPA curves, the 45 experimental solid-state volumes, or the CsPbX3 perovskite lattice parameters used as benchmarks. The paper's central claims are therefore testable consequences rather than re-statements of inputs. The only significant caveat is the construction of zero-point-corrected reference volumes in Appendix B using a Debye/Dugdale-MacDonald model with experimental B0, B1, and ΘD; this is an external reference-model uncertainty, not a circular reduction of the predicted volumes to a fitted target. Self-citations to Tkatchenko-Scheffler 2009, Fedorov et al. 2018, and MBD NL are normal method attribution and are not used to replace independent evidence; the benchmarks in this paper constitute the load-bearing verification.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The benchmark rests on the TS dispersion model, on external references (RPA curves and zero-point-corrected experiments), and on the Fedorov et al. radii with a fitted constant. No new physical entities are introduced; TS_alkali is a parameter-selection variant, not a new entity.

free parameters (3)
  • Damping coefficient s_R for PBE = 0.94
    Empirical functional-specific scaling of the damping onset in Eq. 5, inherited from TS_2009 and used by all benchmarked TS variants.
  • Proportionality constant C in the vdW radius relation = 2.54 a.u.
    Fitted in Fedorov et al. 2018 to noble-gas vdW radii; defines the TS_2018 radii that drive the alkali improvement.
  • Damping steepness d = 20 a0
    Fixed parameter in the Fermi damping function (Eq. 5) that controls how abruptly the dispersion correction is switched on.
assumptions (5)
  • domain assumption Dispersion energy has the pairwise C6/R^6 form with a Fermi damping function (Eqs. 1 and 5).
    This is the foundation of all TS variants benchmarked in the paper.
  • domain assumption Hirshfeld volume ratios scale free-atom polarizabilities and C6 coefficients (Eqs. 2-4).
    Used to define the environmental dependence of the TS correction.
  • domain assumption RPA@PBE with counterpoise correction is an accurate reference for alkali dimer binding curves.
    Used in Figures 2 and 3 to identify TS_2009 overbinding; RPA is an approximation and could carry systematic errors for alkali dimers.
  • domain assumption The Debye model with the Dugdale-MacDonald approximation gives unbiased zero-point volume corrections for all 45 reference solids.
    Appendix B applies this model with experimental B0, B1, and Debye temperatures; a biased correction would shift the benchmark errors by up to about 1.5 percent.
  • domain assumption Many-body screening is negligible in the highly symmetric solids studied, so pairwise and MBD results can be compared directly.
    Stated in the 'Strongly bound solids' section to explain why pairwise methods can match MBD for these materials.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Performance of Tkatchenko-Scheffler Dispersion Method with Updated van der Waals Radii: Importance for Alkali-Containing Systems." pith.science (2026). https://pith.science/paper/6EBPFL6R

@misc{pith2026260801501,
  author       = {Pith},
  title        = {Pith review of: Performance of Tkatchenko-Scheffler Dispersion Method with Updated van der Waals Radii: Importance for Alkali-Containing Systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6EBPFL6R}},
  note         = {Machine review of arXiv:2608.01501}
}
abstract

The Tkatchenko-Scheffler (TS) pairwise method to calculate dispersion interactions is a widely used approach to incorporate missing long-range van der Waals contributions in semilocal and hybrid density functional calculations. Despite numerous refinements of the approach to include many-body terms, the original formulation still remains highly relevant as an efficient and robust method, especially for organic and/or insulating materials. In 2018, Fedorov et al. reported updated van der Waals radii to the seminal work published in 2009. The present work examines the accuracy of the TS method with updated van der Waals radii (abbreviated as TS_2018), coupled with the semilocal Perdew-Burke-Ernzerhof density functional, for structural predictions of semiconducting and insulating materials in comparison to the non-local many-body dispersion method and the original TS method (TS_2009). Special attention is paid to materials containing alkali elements, for which the TS_2009 method exhibits a large overbinding, associated with potentially large errors in predicted atomic structures. We also consider a more narrow reformulation (TS_alkali) where only the the alkali atoms are corrected, so the method remains otherwise compatible with TS_2009. The binding energy curves of five alkali dimers are used to assess the TS_2009 and the TS_2018 methods in comparison to the random phase approximation. Using 45 inorganic solid compounds with available experimental reference data, as well as three widely studied, Cs-containing halide perovskites, CsPb$X_3$ ($X$ = Cl, Br, I), we then examine the performance of the TS_2018 and TS_alkali approaches compared to TS_2009 and the beyond-pairwise, nonlocal many-body dispersion method; the latter found to give good results as well.

Figures

Figures reproduced from arXiv: 2608.01501 by the authors.

Figure 1
Figure 1. While most main group and transition metals elements have similar vdW radii [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 1
Figure 1. Change of the free-atom vdW radii between TS [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. Reference binding energy curves of alkali metal dimers Li [PITH_FULL_IMAGE:figures/full_fig_p012_2.png] view at source ↗
Figures from the paper (6 more)
Figure 3
Figure 3. Figure 3: The error in binding energies calculated using PBE, PBE+MBD [PITH_FULL_IMAGE:figures/full_fig_p013_3.png]
Figure 4
Figure 4. Figure 4: The unit cell volume difference between the relaxed geometries calculated using [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: The unit cell volume difference between the relaxed geometries calculated using [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: Errors in the (a) a lattice constant (expressed in the 40-atom supercell, where it is equal to the c lattice constant in the P nma space group), (b) the b lattice constant, (c) the unit cell volume, (d) the b/a ratio, and (e) the β angle of CsPbCl3 , CsPbBr3 , and CsPb…
Figure 7
Figure 7. Figure 7: Binding energy of alkali dimers calculated at the RPA@PBE level using different [PITH_FULL_IMAGE:figures/full_fig_p024_7.png]
Figure 8
Figure 8. Figure 8: Binding energy of alkali dimers calculated at the PBE level using different basis [PITH_FULL_IMAGE:figures/full_fig_p025_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

143 extracted references · 80 canonical work pages

  1. [1]

    Theory of van der Waals Attraction

    Langbein, D. Theory of van der Waals Attraction. Springer tracts in modern physics 1974, 1--139

    1974

  2. [2]

    Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory

    Klime s , J.; Michaelides, A. Perspective: Advances and challenges in treating van der Waals dispersion forces in density functional theory. The Journal of chemical physics 2012, 137, 120901

    2012

  3. [3]

    P.; Taylor, S.; Baran, J

    Jarvis, S. P.; Taylor, S.; Baran, J. D.; Champness, N. R.; Larsson, J.; Moriarty, P. Measuring the mechanical properties of molecular conformers. Nature communications 2015, 6, 8338

    2015

  4. [4]

    Validation Challenge of Density-Functional Theory for Peptides—Example of Ac-Phe-Ala _5 -LysH ^+

    Rossi, M.; Chutia, S.; Scheffler, M.; Blum, V. Validation Challenge of Density-Functional Theory for Peptides—Example of Ac-Phe-Ala _5 -LysH ^+ . The Journal of Physical Chemistry A 2014, 118, 7349–7359

    2014

  5. [5]

    Exploring the conformational preferences of 20-residue peptides in isolation: Ac-Ala _19 -Lys + H ^+ vs

    Schubert, F.; Rossi, M.; Baldauf, C.; Pagel, K.; Warnke, S.; von Helden, G.; Filsinger, F.; Kupser, P.; Meijer, G.; Salwiczek, M.; Koksch, B.; Scheffler, M.; Blum, V. Exploring the conformational preferences of 20-residue peptides in isolation: Ac-Ala _19 -Lys + H ^+ vs. Ac-Lys-Ala _19 + H ^+ and the current reach of DFT . Physical Chemistry Chemical Phys...

    2015

  6. [6]

    M.; van de Streek, J.; Sasikumar, K.; Dietrich, H.; Helfferich, J.; Aerts, L.; Braun, D

    Firaha, D.; Liu, Y. M.; van de Streek, J.; Sasikumar, K.; Dietrich, H.; Helfferich, J.; Aerts, L.; Braun, D. E.; Broo, A.; DiPasquale, A. G.; others Predicting crystal form stability under real-world conditions. Nature 2023, 623, 324--328

    2023

  7. [7]

    Bucko, T.; Hafner, J.; Leb \`e gue, S.; Angy \'a n, J. G. Improved description of the structure of molecular and layered crystals: ab initio DFT calculations with van der Waals corrections. The Journal of Physical Chemistry A 2010, 114, 11814--11824

    2010

  8. [8]

    B.; Snaider, J

    Gao, Y.; Shi, E.; Deng, S.; Shiring, S. B.; Snaider, J. M.; Liang, C.; Yuan, B.; Song, R.; Janke, S. M.; Liebman-Pel \'a ez, A.; others Molecular engineering of organic--inorganic hybrid perovskites quantum wells. Nature chemistry 2019, 11, 1151--1157

    2019

Show all 143 references
  1. [9]

    Y.; Song, R.; Liang, J.; Jin, L.; Wang, K.; Li, S.; Shi, E.; Gao, Y.; Zeller, M.; Teat, S

    Park, J. Y.; Song, R.; Liang, J.; Jin, L.; Wang, K.; Li, S.; Shi, E.; Gao, Y.; Zeller, M.; Teat, S. J.; others Thickness control of organic semiconductor-incorporated perovskites. Nature Chemistry 2023, 1--9

    2023

  2. [10]

    K.; Song, R.; Liu, H.; Khanal, D

    Jana, M. K.; Song, R.; Liu, H.; Khanal, D. R.; Janke, S. M.; Zhao, R.; Liu, C.; Valy Vardeny, Z.; Blum, V.; Mitzi, D. B. Organic-to-inorganic structural chirality transfer in a 2D hybrid perovskite and impact on Rashba-Dresselhaus spin-orbit coupling. Nature communications 202...

    2020

  3. [11]

    F.; Brunecky, R.; You, W.; Berry, J

    Kim, Y.-H.; Song, R.; Hao, J.; Zhai, Y.; Yan, L.; Moot, T.; Palmstrom, A. F.; Brunecky, R.; You, W.; Berry, J. J.; others The Structural Origin of Chiroptical Properties in Perovskite Nanocrystals with Chiral Organic Ligands. Advanced Functional Materials 2022, 2200454

    2022

  4. [12]

    B.; Blum, V

    Song, R.; Liu, C.; Kanai, Y.; Mitzi, D. B.; Blum, V. Structure and electronic tunability of acene alkylamine based layered hybrid organic-inorganic perovskites from first principles. Physical Review Materials 2023, 7, 084601

    2023

  5. [13]

    Density functional theory study of two-dimensional hybrid organic-inorganic perovskites: frontier level alignment and chirality-induced spin splitting

    Song, R.; Zhao, R. Density functional theory study of two-dimensional hybrid organic-inorganic perovskites: frontier level alignment and chirality-induced spin splitting. AAPPS Bulletin 2024, 34

    2024

  6. [14]

    H.; Parsegian, V

    French, R. H.; Parsegian, V. A.; Podgornik, R.; Rajter, R. F.; Jagota, A.; Luo, J.; Asthagiri, D.; Chaudhury, M. K.; Chiang, Y.-m.; Granick, S.; others Long range interactions in nanoscale science. Reviews of Modern Physics 2010, 82, 1887

    2010

  7. [15]

    Electronic structure and van der Waals interactions in the stability and mobility of point defects in semiconductors

    Gao, W.; Tkatchenko, A. Electronic structure and van der Waals interactions in the stability and mobility of point defects in semiconductors. Physical review letters 2013, 111, 045501

    2013

  8. [16]

    F.; Zhang, H.; Yang, H.; Yao, X.; Zhao, H

    Wang, Y.; Gould, T.; Dobson, J. F.; Zhang, H.; Yang, H.; Yao, X.; Zhao, H. Density functional theory analysis of structural and electronic properties of orthorhombic perovskite CH 3 NH 3 PbI 3. Physical Chemistry Chemical Physics 2014, 16, 1424--1429

    2014

  9. [17]

    B.; Al-Douri, Y

    Ferjani, H.; Smida, Y. B.; Al-Douri, Y. First-Principles Calculations to Investigate the Effect of Van der Waals Interactions on the Crystal and Electronic Structures of Tin-Based 0D Hybrid Perovskites. Inorganics 2022, 10, 155

    2022

  10. [18]

    Ab initio Calculation of van der Waals Bonded Molecular Crystals

    Lu, D.; Li, Y.; Rocca, D.; Galli, G. Ab initio Calculation of van der Waals Bonded Molecular Crystals. Physical Review Letters 2009, 102, 206411

    2009

  11. [19]

    J.; Gould, T.; Lee, E

    Kim, M.; Kim, W. J.; Gould, T.; Lee, E. K.; Leb\` e gue, S.; Kim, H. uMBD : A Materials-Ready Dispersion Correction That Uniformly Treats Metallic, Ionic, and van der Waals Bonding. Journal of the American Chemical Society 2020, 142, 2346–2354

    2020

  12. [20]

    B.; Blum, V

    Liu, C.; Huhn, W.; Du, K.-Z.; Vazquez-Mayagoitia, A.; Dirkes, D.; You, W.; Kanai, Y.; Mitzi, D. B.; Blum, V. Tunable semiconductors: control over carrier states and excitations in layered hybrid organic-inorganic perovskites. Physical Review Letters 2018, 121, 146401

    2018

  13. [21]

    Benchmark thermodynamic analysis of methylammonium lead iodide decomposition from first principles

    Heine, D.; Yu, H.-C.; Blum, V. Benchmark thermodynamic analysis of methylammonium lead iodide decomposition from first principles. Journal of Physics: Energy 2023, 6, 015015

    2023

  14. [22]

    Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data

    Tkatchenko, A.; Scheffler, M. Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data. Physical review letters 2009, 102, 073005

    2009

  15. [23]

    V.; Sadhukhan, M.; St \"o hr, M.; Tkatchenko, A

    Fedorov, D. V.; Sadhukhan, M.; St \"o hr, M.; Tkatchenko, A. Quantum-mechanical relation between atomic dipole polarizability and the van der Waals radius. Physical Review Letters 2018, 121, 183401

    2018

  16. [24]

    J.; Sohail, B.; Rochford, L

    Blowey, P. J.; Sohail, B.; Rochford, L. A.; Lafosse, T.; Duncan, D. A.; Ryan, P. T. P.; Warr, D. A.; Lee, T.-L.; Costantini, G.; Maurer, R. J.; Woodruff, D. P. Alkali Doping Leads to Charge-Transfer Salt Formation in a Two-Dimensional Metal–Organic Framework. ACS Nano 2020, 14...

    2020

  17. [25]

    Accurate description of van der Waals complexes by density functional theory including empirical corrections

    Grimme, S. Accurate description of van der Waals complexes by density functional theory including empirical corrections. Journal of Computational Chemistry 2004, 25, 1463–1473

    2004

  18. [26]

    A.; Car, R.; Scheffler, M

    Tkatchenko, A.; DiStasio Jr, R. A.; Car, R.; Scheffler, M. Accurate and efficient method for many-body van der Waals interactions. Physical review letters 2012, 108, 236402

    2012

  19. [27]

    M.; DiStasio Jr, R

    Ambrosetti, A.; Reilly, A. M.; DiStasio Jr, R. A.; Tkatchenko, A. Long-range correlation energy calculated from coupled atomic response functions. The Journal of chemical physics 2014, 140, 18A508

    2014

  20. [28]

    Density functional model for van der Waals interactions: Unifying many-body atomic approaches with nonlocal functionals

    Hermann, J.; Tkatchenko, A. Density functional model for van der Waals interactions: Unifying many-body atomic approaches with nonlocal functionals. Physical review letters 2020, 124, 146401

    2020

  21. [29]

    D.; Johnson, E

    Becke, A. D.; Johnson, E. R. Exchange-hole dipole moment and the dispersion interaction revisited. The Journal of chemical physics 2007, 127

    2007

  22. [30]

    F.; Johnson, E

    Rumson, A. F.; Johnson, E. R. Low thermal expansion of layered electrides predicted by density-functional theory. The Journal of Chemical Physics 2023, 159

    2023

  23. [31]

    Price, A. J. A.; Otero-de-la Roza, A.; Johnson, E. R. XDM -corrected hybrid DFT with numerical atomic orbitals predicts molecular crystal lattice energies with unprecedented accuracy. Chemical Science 2023, 14, 1252–1262

    2023

  24. [32]

    Can (semi)local density functional theory account for the London dispersion forces? Chemical Physics Letters 1994, 229, 175–180

    Kristy\' a n, S.; Pulay, P. Can (semi)local density functional theory account for the London dispersion forces? Chemical Physics Letters 1994, 229, 175–180

    1994

  25. [33]

    Empirical correction to density functional theory for van der Waals interactions

    Wu, Q.; Yang, W. Empirical correction to density functional theory for van der Waals interactions. The Journal of chemical physics 2002, 116, 515--524

    2002

  26. [34]

    On the Importance of Electron Correlation Effects for the -- Interactions in Cyclophanes

    Grimme, S. On the Importance of Electron Correlation Effects for the -- Interactions in Cyclophanes. Chemistry - A European Journal 2004, 10, 3423–3429

    2004

  27. [35]

    Semiempirical hybrid density functional with perturbative second-order correlation

    Grimme, S. Semiempirical hybrid density functional with perturbative second-order correlation. The Journal of Chemical Physics 2006, 124, 034108

    2006

  28. [36]

    Szabo, A.; Ostlund, N. S. Modern quantum chemistry: introduction to advanced electronic structure theory; Courier Corporation, 2012

    2012

  29. [37]

    A collective description of electron interactions

    Bohm, D.; Pines, D. A collective description of electron interactions. I. Magnetic interactions. Physical Review 1951, 82, 625

    1951

  30. [38]

    Accurate density functionals: Approaches using the adiabatic-connection fluctuation-dissipation theorem

    Fuchs, M.; Gonze, X. Accurate density functionals: Approaches using the adiabatic-connection fluctuation-dissipation theorem. Physical Review B 2002, 65, 235109

    2002

  31. [39]

    Theory and practice of modeling van der Waals interactions in electronic-structure calculations

    St\" o hr, M.; Van Voorhis, T.; Tkatchenko, A. Theory and practice of modeling van der Waals interactions in electronic-structure calculations. Chemical Society Reviews 2019, 48, 4118–4154

    2019

  32. [40]

    Resolution-of-identity approach to Hartree–Fock , hybrid density functionals, RPA , MP2 and GW with numeric atom-centered orbital basis functions

    Ren, X.; Rinke, P.; Blum, V.; Wieferink, J.; Tkatchenko, A.; Sanfilippo, A.; Reuter, K.; Scheffler, M. Resolution-of-identity approach to Hartree–Fock , hybrid density functionals, RPA , MP2 and GW with numeric atom-centered orbital basis functions. New Journal of Physics 2012...

    2012

  33. [41]

    Random-phase approximation and its applications in computational chemistry and materials science

    Ren, X.; Rinke, P.; Joas, C.; Scheffler, M. Random-phase approximation and its applications in computational chemistry and materials science. Journal of Materials Science 2012, 47, 7447--7471

    2012

  34. [42]

    C.; Lundqvist, B

    Dion, M.; Rydberg, H.; Schr \"o der, E.; Langreth, D. C.; Lundqvist, B. I. Van der Waals density functional for general geometries. Physical review letters 2004, 92, 246401

    2004

  35. [43]

    A.; Van Voorhis, T

    Vydrov, O. A.; Van Voorhis, T. Nonlocal van der Waals density functional made simple. Physical review letters 2009, 103, 063004

    2009

  36. [44]

    R.; Michaelides, A

    Klime s , J.; Bowler, D. R.; Michaelides, A. Van der Waals density functionals applied to solids. Physical Review B 2011, 83, 195131

    2011

  37. [45]

    D.; Kong, L.; Lundqvist, B

    Lee, K.; Murray, \'E . D.; Kong, L.; Lundqvist, B. I.; Langreth, D. C. Higher-accuracy van der Waals density functional. Physical Review B 2010, 82, 081101

    2010

  38. [46]

    A.; Van Voorhis, T

    Vydrov, O. A.; Van Voorhis, T. Nonlocal van der Waals density functional: The simpler the better. The Journal of Chemical Physics 2010, 133, 244103

    2010

  39. [47]

    Nonlocal van der Waals density functional made simple and efficient

    Sabatini, R.; Gorni, T.; de Gironcoli, S. Nonlocal van der Waals density functional made simple and efficient. Physical Review B 2013, 87, 041108(R)

    2013

  40. [48]

    P.; Sun, J

    Peng, H.; Yang, Z.-H.; Perdew, J. P.; Sun, J. Versatile van der Waals Density Functional Based on a Meta-Generalized Gradient Approximation. Physical Review X 2016, 6, 041005

    2016

  41. [49]

    Next-Generation Nonlocal van der Waals Density Functional

    Chakraborty, D.; Berland, K.; Thonhauser, T. Next-Generation Nonlocal van der Waals Density Functional. Journal of Chemical Theory and Computation 2020, 16, 5893–5911

    2020

  42. [50]

    R.; Lee, K.; Schr\" o der, E.; Thonhauser, T.; Hyldgaard, P.; Lundqvist, B

    Berland, K.; Cooper, V. R.; Lee, K.; Schr\" o der, E.; Thonhauser, T.; Hyldgaard, P.; Lundqvist, B. I. van der Waals forces in density functional theory: a review of the vdW-DF method. Reports on Progress in Physics 2015, 78, 066501

    2015

  43. [51]

    Nonlocal van der Waals functionals for solids: Choosing an appropriate one

    Tran, F.; Kalantari, L.; Traor\' e , B.; Rocquefelte, X.; Blaha, P. Nonlocal van der Waals functionals for solids: Choosing an appropriate one. Physical Review Materials 2019, 3, 063602

    2019

  44. [52]

    Rom\' a n-P\' e rez, G.; Soler, J. M. Efficient Implementation of a van der Waals Density Functional: Application to Double-Wall Carbon Nanotubes. Physical Review Letters 2009, 103

    2009

  45. [53]

    Electronic Exchange and Correlation in van der Waals Systems: Balancing Semilocal and Nonlocal Energy Contributions

    Hermann, J.; Tkatchenko, A. Electronic Exchange and Correlation in van der Waals Systems: Balancing Semilocal and Nonlocal Energy Contributions. Journal of Chemical Theory and Computation 2018, 14, 1361–1369

    2018

  46. [54]

    J.; Lee, E

    Kim, M.; Kim, W. J.; Lee, E. K.; Lebegue, S.; Kim, H. Recent development of atom-pairwise van der waals corrections for density functional theory: From molecules to solids. International Journal of Quantum Chemistry 2016, 116, 598--607

    2016

  47. [55]

    Die gegenseitige einwirkung zweier wasserstoffatome

    Wang, S. Die gegenseitige einwirkung zweier wasserstoffatome. Phys. Z 1927, 28, 663--666

    1927

  48. [56]

    The general theory of molecular forces

    London, F. The general theory of molecular forces. Transactions of the Faraday Society 1937, 33, 8b--26

    1937

  49. [57]

    F.; White, A.; Rubio, A

    Dobson, J. F.; White, A.; Rubio, A. Asymptotics of the Dispersion Interaction: Analytic Benchmarks for van der Waals Energy Functionals. Physical Review Letters 2006, 96, 073201

    2006

  50. [58]

    G.; Kresse, G.; Dobson, J

    Leb\` e gue, S.; Harl, J.; Gould, T.; \' A ngy\' a n, J. G.; Kresse, G.; Dobson, J. F. Cohesive Properties and Asymptotics of the Dispersion Interaction in Graphite by the Random Phase Approximation. Physical Review Letters 2010, 105, 196401

    2010

  51. [59]

    A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu

    Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. The Journal of chemical physics 2010, 132

    2010

  52. [60]

    Extension of the D3 dispersion coefficient model

    Caldeweyher, E.; Bannwarth, C.; Grimme, S. Extension of the D3 dispersion coefficient model. The Journal of Chemical Physics 2017, 147, 034112

    2017

  53. [61]

    Effect of the damping function in dispersion corrected density functional theory

    Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. Journal of computational chemistry 2011, 32, 1456--1465

    2011

  54. [62]

    B.; Head-Gordon, M

    Witte, J.; Mardirossian, N.; Neaton, J. B.; Head-Gordon, M. Assessing DFT-D3 damping functions across widely used density functionals: Can we do better? Journal of chemical theory and computation 2017, 13, 2043--2052

    2017

  55. [63]

    Dobson, J. F. Beyond pairwise additivity in London dispersion interactions. International Journal of Quantum Chemistry 2014, 114, 1157–1161

    2014

  56. [64]

    P.; Rappe, A

    Tao, J.; Zheng, F.; Gebhardt, J.; Perdew, J. P.; Rappe, A. M. Screened van der Waals correction to density functional theory for solids. Physical Review Materials 2017, 1, 020802

    2017

  57. [65]

    Tkatchenko, A.; Ambrosetti, A.; DiStasio, R. A. Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem. The Journal of Chemical Physics 2013, 138, 074106

    2013

  58. [66]

    A.; Van Voorhis, T

    Vydrov, O. A.; Van Voorhis, T. Dispersion interactions from a local polarizability model. Physical Review A 2010, 81, 062708

    2010

  59. [67]

    P.; Burke, K.; Ernzerhof, M

    Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Physical review letters 1996, 77, 3865

    1996

  60. [68]

    K.; Janke, S

    Jana, M. K.; Janke, S. M.; Dirkes, D. J.; Dovletgeldi, S.; Liu, C.; Qin, X.; Gundogdu, K.; You, W.; Blum, V.; Mitzi, D. B. Direct-bandgap 2D silver--bismuth iodide double perovskite: the structure-directing influence of an oligothiophene spacer cation. Journal of the American ...

    2019

  61. [69]

    E.; Levin, A.; Brunecky, R.; Berry, J

    Lu, H.; Xiao, C.; Song, R.; Li, T.; Maughan, A. E.; Levin, A.; Brunecky, R.; Berry, J. J.; Mitzi, D. B.; Blum, V.; others Highly distorted chiral two-dimensional tin iodide perovskites for spin polarized charge transport. Journal of the American Chemical Society 2020, 142, 130...

    2020

  62. [70]

    S.; Politzer, P

    Brinck, T.; Murray, J. S.; Politzer, P. Polarizability and volume. The Journal of chemical physics 1993, 98, 4305--4306

    1993

  63. [71]

    The use of atomic intrinsic polarizabilities in the evaluation of the dispersion energy

    Olasz, A.; Vanommeslaeghe, K.; Krishtal, A.; Veszpr \'e mi, T.; Van Alsenoy, C.; Geerlings, P. The use of atomic intrinsic polarizabilities in the evaluation of the dispersion energy. The Journal of chemical physics 2007, 127, 224105

    2007

  64. [72]

    Linear response time-dependent density functional theory for van der Waals coefficients

    Chu, X.; Dalgarno, A. Linear response time-dependent density functional theory for van der Waals coefficients. The Journal of Chemical Physics 2004, 121, 4083–4088

    2004

  65. [73]

    Toward reliable density functional methods without adjustable parameters: The PBE0 model

    Adamo, C.; Barone, V. Toward reliable density functional methods without adjustable parameters: The PBE0 model. The Journal of Chemical Physics 1999, 110, 6158–6170

    1999

  66. [74]

    Gobre, V. V. Efficient modelling of linear electronic polarization in materials using atomic response functions. Ph.D.\ thesis, Fritz-Haber-institut der Max-Planck-Gesellschaft Berlin-Germany, 2016

    2016

  67. [75]

    V.; Hod, O.; Scheffler, M.; Kronik, L

    Marom, N.; Tkatchenko, A.; Rossi, M.; Gobre, V. V.; Hod, O.; Scheffler, M.; Kronik, L. Dispersion interactions with density-functional theory: benchmarking semiempirical and interatomic pairwise corrected density functionals. Journal of Chemical Theory and Computation 2011, 7,...

    2011

  68. [76]

    Bondi, A. v. van der Waals volumes and radii. The Journal of physical chemistry 1964, 68, 441--451

    1964

  69. [77]

    Relativistic pseudopotential calculations on Xe2, RnXe, and Rn2: The van der Waals properties of radon

    Runeberg, N.; Pyykk \"o , P. Relativistic pseudopotential calculations on Xe2, RnXe, and Rn2: The van der Waals properties of radon. International journal of quantum chemistry 1998, 66, 131--140

    1998

  70. [78]

    V.; Gori, M

    Tkatchenko, A.; Fedorov, D. V.; Gori, M. Fine-Structure Constant Connects Electronic Polarizability and Geometric van-der-Waals Radius of Atoms. The Journal of Physical Chemistry Letters 2021, 12, 9488–9492

    2021

  71. [79]

    The van der Waals potentials between all the rare gas atoms from He to Rn

    Tang, K.; Toennies, J. The van der Waals potentials between all the rare gas atoms from He to Rn. The Journal of chemical physics 2003, 118, 4976--4983

    2003

  72. [80]

    Ab initio molecular simulations with numeric atom-centered orbitals

    Blum, V.; Gehrke, R.; Hanke, F.; Havu, P.; Havu, V.; Ren, X.; Reuter, K.; Scheffler, M. Ab initio molecular simulations with numeric atom-centered orbitals. Computer Physics Communications 2009, 180, 2175--2196

    2009

  73. [81]

    Abbott, J. W. et al. Roadmap on Advancements of the FHI -aims Software Package. Electronic Structure 2026,

    2026

  74. [82]

    A.; Caldas, M

    Lima, N. A.; Caldas, M. J. Long range van der Waals density functional: Dimers involving alkali-metal, alkaline-earth-metal, and noble-gas atoms. Physical Review B—Condensed Matter and Materials Physics 2005, 72, 033109

    2005

  75. [83]

    Long-range dispersion interactions

    Mitroy, J.; Zhang, J.-Y. Long-range dispersion interactions. II. Alkali-metal and rare-gas atoms. Physical Review A—Atomic, Molecular, and Optical Physics 2007, 76, 032706

    2007

  76. [84]

    P.; Ruzsinszky, A

    Tao, J.; Perdew, J. P.; Ruzsinszky, A. Long-range van der Waals attraction and alkali-metal lattice constants. Physical Review B—Condensed Matter and Materials Physics 2010, 81, 233102

    2010

  77. [85]

    Van der Waals density functional from multipole dispersion interactions

    Alves de Lima, N. Van der Waals density functional from multipole dispersion interactions. The Journal of chemical physics 2010, 132

    2010

  78. [86]

    Molecular tests of the random phase approximation to the exchange-correlation energy functional

    Furche, F. Molecular tests of the random phase approximation to the exchange-correlation energy functional. Physical Review B 2001, 64, 195120

    2001

  79. [87]

    Galano, A.; Alvarez-Idaboy, J. R. A new approach to counterpoise correction to BSSE. Journal of computational chemistry 2006, 27, 1203--1210

    2006

  80. [88]

    J.; Zhu, K

    Li, Z.; Yang, M.; Park, J.-S.; Wei, S.-H.; Berry, J. J.; Zhu, K. Stabilizing perovskite structures by tuning tolerance factor: formation of formamidinium and cesium lead iodide solid-state alloys. Chemistry of Materials 2016, 28, 284--292

    2016

  81. [89]

    R.; McClure, E

    Linaburg, M. R.; McClure, E. T.; Majher, J. D.; Woodward, P. M. Cs _ 1-x Rb _x PbCl _3 and Cs _ 1-x Rb _x PbBr _3 solid solutions: understanding octahedral tilting in lead halide perovskites. Chemistry of Materials 2017, 29, 3507--3514

    2017

  82. [90]

    C.; Malliakas, C

    Stoumpos, C. C.; Malliakas, C. D.; Peters, J. A.; Liu, Z.; Sebastian, M.; Im, J.; Chasapis, T. C.; Wibowo, A. C.; Chung, D. Y.; Freeman, A. J.; Wessels, B. W.; Kanatzidis, M. G. Crystal Growth of the Perovskite Semiconductor CsPbBr _3 : A New Material for High-Energy Radiation...

    2013

  83. [91]

    B.; Guo, S.; Abeykoon, A

    Straus, D. B.; Guo, S.; Abeykoon, A. M.; Cava, R. J. Understanding the Instability of the Halide Perovskite CsPbI3 through Temperature-Dependent Structural Analysis. Advanced Materials 2020, 32, 2001069

    2020

  84. [92]

    A.; J\" o bsis, H

    Muscarella, L. A.; J\" o bsis, H. J.; Baumgartner, B.; Prins, P. T.; Maaskant, D. N.; Petukhov, A. V.; Chernyshov, D.; McMonagle, C. J.; Hutter, E. M. Which Ion Dominates the Temperature and Pressure Response of Halide Perovskites and Elpasolites? The Journal of Physical Chemi...

    2023

  85. [93]

    C.; Wang, Z.; Wong, P

    Cao, Q.; Song, R.; Chan, C. C.; Wang, Z.; Wong, P. Y.; Wong, K. S.; Blum, V.; Lu, H. Chiral Perovskite Nanoplatelets with Tunable Circularly Polarized Luminescence in the Strong Confinement Regime. Advanced Optical Materials 2023, 11, 2203125

    2023

  86. [94]

    Benchmark data is available publicly at https://github.com/aschankler/ts18\_benchmark\_data

  87. [95]

    High order integration schemes on the unit sphere

    Delley, B. High order integration schemes on the unit sphere. Journal of Computational Chemistry 1996, 17, 1152–1155

    1996

  88. [96]

    The basis set superposition error in correlated electronic structure calculations

    Gutowski, M.; Van Lenthe, J.; Verbeek, J.; Van Duijneveldt, F.; Cha asinski, G. The basis set superposition error in correlated electronic structure calculations. Chemical Physics Letters 1986, 124, 370--375

    1986

  89. [97]

    Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

    Lejaeghere, K.; Van Speybroeck, V.; Van Oost, G.; Cottenier, S. Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals. Critical Reviews in Solid State and Materials Sciences 2013, 39, 1–24

    2013

  90. [98]

    Strain and Stress: Derivation, Implementation, and Application to Organic Crystals

    Knuth, F. Strain and Stress: Derivation, Implementation, and Application to Organic Crystals. Ph.D.\ thesis, Freie Universität, Berlin, 2015

    2015

  91. [99]

    B.; Perdew, J

    Alchagirov, A. B.; Perdew, J. P.; Boettger, J. C.; Albers, R. C.; Fiolhais, C. Energy and pressure versus volume: Equations of state motivated by the stabilized jellium model. Physical Review B 2001, 63, 224115

    2001

  92. [100]

    I.; Philipsen, P

    Hao, P.; Fang, Y.; Sun, J.; Csonka, G. I.; Philipsen, P. H. T.; Perdew, J. P. Lattice constants from semilocal density functionals with zero-point phonon correction. Physical Review B 2012, 85, 014111

    2012

  93. [101]

    S.; MacDonald, D

    Dugdale, J. S.; MacDonald, D. K. C. The Thermal Expansion of Solids. Physical Review 1953, 89, 832–834

    1953

  94. [102]

    B.; Sirdeshmukh, L.; Subhadra, K

    Sirdeshmukh, D. B.; Sirdeshmukh, L.; Subhadra, K. G. Alkali Halides: A Handbook of Physical Properties; Springer Series in Materials Science 49; Springer: Berlin Heidelberg, 2001

    2001

  95. [103]

    R\" o ssler, U., Ed. Semiconductors: New Data and Updates for IIa-VI Compounds with Mg and Sr (Structural Properties, Thermal and Thermodynamic Properties, and Lattice Properties) ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer Berlin Heidelberg, 2017; Vol. 44H

    2017

  96. [104]

    II-VI and I-VII Compounds; Semimagnetic Compounds ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer-Verlag, 1999; Vol

    Madelung, O., Rössler, U., Schulz, M., Eds. II-VI and I-VII Compounds; Semimagnetic Compounds ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer-Verlag, 1999; Vol. 41B

    1999

  97. [105]

    Verma, J. K. D.; Aggarwal, M. D. An averaging method for the shear modulus and Debye temperatures of cubic solids. Journal of Applied Physics 1975, 46, 2841–2844

    1975

  98. [106]

    M.; Campbell, A

    Peiris, S. M.; Campbell, A. J.; Heinz, D. L. Compression of MgS to 54 GPa . Journal of Physics and Chemistry of Solids 1994, 55, 413–419

    1994

  99. [107]

    O.; Tompson, C

    Baldwin, T. O.; Tompson, C. W. X -Ray Characteristic Temperatures of Some II—VI Ionic Compounds. The Journal of Chemical Physics 1964, 41, 1420–1426

    1964

  100. [108]

    Properties of diamond under hydrostatic pressures up to 140 GPa

    Occelli, F.; Loubeyre, P.; LeToullec, R. Properties of diamond under hydrostatic pressures up to 140 GPa . Nature Materials 2003, 2, 151–154

    2003

  101. [109]

    E.; Morrison, J

    Desnoyehs, J. E.; Morrison, J. A. The heat capacity of diamond between 12.8° and 277°K. Philosophical Magazine 1958, 3, 42–48

    1958

  102. [110]

    Group IV Elements, IV-IV and III-V Compounds

    Madelung, O., Rössler, U., Schulz, M., Eds. Group IV Elements, IV-IV and III-V Compounds. Part a - Lattice Properties ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer-Verlag, 2001; Vol. 41A1

    2001

  103. [111]

    Nonmetallic crystals with high thermal conductivity

    Slack, G. Nonmetallic crystals with high thermal conductivity. Journal of Physics and Chemistry of Solids 1973, 34, 321–335

    1973

  104. [112]

    The Dependence of the Debye Temperature on the Elastic Constants

    Siethoff, H.; Ahlborn, K. The Dependence of the Debye Temperature on the Elastic Constants. physica status solidi (b) 1995, 190, 179–191

    1995

  105. [113]

    Non-Tetrahedrally Bonded Elements and Binary Compounds I ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer-Verlag, 1998; Vol

    Madelung, O., Rössler, U., Schulz, M., Eds. Non-Tetrahedrally Bonded Elements and Binary Compounds I ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer-Verlag, 1998; Vol. 41C

    1998

  106. [114]

    BHAGAVANTAM, S.; RAO, T. S. Elastic Constants of Galena. Nature 1951, 168, 42–42

    1951

  107. [115]

    I.; Ponyatovskii, E

    Peresada, G. I.; Ponyatovskii, E. G.; Sokolovskaya, Z. D. Pressure dependence of the elastic constants of PbS . Physica Status Solidi (a) 1976, 35, K177–K180

    1976

  108. [116]

    S.; Gibbs, A

    Knight, K. S.; Gibbs, A. S.; Bull, C. L.; Powell, A. V.; Funnell, N. P.; Ridley, C. J. Low-intermediate-temperature, high-pressure thermoelastic and crystallographic properties of thermoelectric clausthalite ( PbSe-I ). Materials Advances 2022, 3, 2077–2088

    2022

  109. [117]

    Structure determination of the intermediate phase of PbSe using experiments and calculations

    Li, Y.; Li, G.; Lin, C.; Li, X.; Liu, J. Structure determination of the intermediate phase of PbSe using experiments and calculations. Journal of Applied Physics 2014, 116

    2014

  110. [118]

    Revisit of Pressure-Induced Phase Transition in PbSe : Crystal Structure, and Thermoelastic and Electrical Properties

    Wang, S.; Zang, C.; Wang, Y.; Wang, L.; Zhang, J.; Childs, C.; Ge, H.; Xu, H.; Chen, H.; He, D.; Zhao, Y. Revisit of Pressure-Induced Phase Transition in PbSe : Crystal Structure, and Thermoelastic and Electrical Properties. Inorganic Chemistry 2015, 54, 4981–4989

    2015

  111. [119]

    Elastic constants of PbSe

    Lippmann, G.; K\" a stner, P.; Wanninger, W. Elastic constants of PbSe . Physica Status Solidi (a) 1971, 6, K159–K161

    1971

  112. [120]

    E.; Belson, H

    Houston, B.; Strakna, R. E.; Belson, H. S. Elastic Constants, Thermal Expansion, and Debye Temperature of Lead Telluride. Journal of Applied Physics 1968, 39, 3913–3916

    1968

  113. [121]

    J.; Saunders, G

    Miller, A. J.; Saunders, G. A.; Yogurtcu, Y. K. Pressure dependences of the elastic constants of PbTe , SnTe and Ge _ 0.08 Sn _0.92 Te . Journal of Physics C: Solid State Physics 1981, 14, 1569–1584

    1981

  114. [122]

    H.; Quarrington, J

    Parkinson, D. H.; Quarrington, J. E. The Molar Heats of Lead Sulphide, Selenide and Telluride in the Temperature Range 20 K to 260 K . Proceedings of the Physical Society. Section A 1954, 67, 569–579

    1954

  115. [123]

    C.; Loong, C.-K

    Nipko, J. C.; Loong, C.-K. Phonon excitations and related thermal properties of aluminum nitride. Physical Review B 1998, 57, 10550–10554

    1998

  116. [124]

    Group IV Elements, IV-IV and III-V Compounds

    Madelung, O., Rössler, U., Schulz, M., Eds. Group IV Elements, IV-IV and III-V Compounds. Part b - Electronic, Transport, Optical and Other Properties ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer-Verlag, 2002; Vol. 41A1

    2002

  117. [125]

    Elastic constants of gallium nitride

    Polian, A.; Grimsditch, M.; Grzegory, I. Elastic constants of gallium nitride. Journal of Applied Physics 1996, 79, 3343–3344

    1996

  118. [126]

    C.; Loong, C.-K.; Balkas, C

    Nipko, J. C.; Loong, C.-K.; Balkas, C. M.; Davis, R. F. Phonon density of states of bulk gallium nitride. Applied Physics Letters 1998, 73, 34–36

    1998

  119. [127]

    A.; Paszkiewicz, T.; Wolski, S.; Jeżowski, A.; Plackowski, T

    Danilchenko, B. A.; Paszkiewicz, T.; Wolski, S.; Jeżowski, A.; Plackowski, T. Heat capacity and phonon mean free path of wurtzite GaN . Applied Physics Letters 2006, 89

    2006

  120. [128]

    P\" a ssler, R. Limiting Debye temperature behavior following from cryogenic heat capacity data for group- IV , III-V , and II-VI materials: Limiting Debye temperature behavior detected from cryogenic heat capacity data. physica status solidi (b) 2009, 247, 77–92

    2009

  121. [129]

    Steigmeier, E. F. THE DEBYE TEMPERATURES OF III-V COMPOUNDS. Applied Physics Letters 1963, 3, 6–8

    1963

  122. [130]

    F.; Sladek, R

    Boyle, W. F.; Sladek, R. J. Elastic constants and lattice anharmonicity of GaSb and GaP from ultrasonic-velocity measurements between 4.2 and 300 K . Physical Review B 1975, 11, 2933–2940

    1975

  123. [131]

    Holste, J. C. Specific Heats of GaSb , GaAs , InSb , InAs , Bi , Cd , Sn , and Zn below 30 K. Physical Review B 1972, 6, 2495

    1972

  124. [132]

    Yao, L. et al. Structural stability and Raman scattering of InN nanowires under high pressure. Journal of Materials Research 2010, 25, 2330–2335

    2010

  125. [133]

    Y.; Emtsev, V

    Davydov, V. Y.; Emtsev, V. V.; Goncharuk, I. N.; Smirnov, A. N.; Petrikov, V. D.; Mamutin, V. V.; Vekshin, V. A.; Ivanov, S. V.; Smirnov, M. B.; Inushima, T. Experimental and theoretical studies of phonons in hexagonal InN . Applied Physics Letters 1999, 75, 3297–3299

    1999

  126. [134]

    Rössler, U., Ed. New Data and Updates for several Semiconductors with Chalcopyrite Structure, for several II-VI Compounds and diluted magnetic IV-VI Compounds ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer Berlin Heidelberg, 2013; Vol. 44F

    2013

  127. [135]

    High-density phases of ZnO : Structural and compressive parameters

    Desgreniers, S. High-density phases of ZnO : Structural and compressive parameters. Physical Review B 1998, 58, 14102–14105

    1998

  128. [136]

    G.; White, G

    Collins, J. G.; White, G. K.; Birch, J. A.; Smith, T. F. Thermal expansion of ZnTe and HgTe and heat capacity of HgTe at low temperatures. Journal of Physics C: Solid State Physics 1980, 13, 1649–1656

    1980

  129. [137]

    Birch, J. A. Heat capacities of ZnS, ZnSe and CdTe below 25K. Journal of Physics C: Solid State Physics 1975, 8, 2043–2047

    1975

  130. [138]

    Pressure dependence of single crystal elastic constants and anharmonic properties of wurtzite

    Chang, E.; Barsch, G. Pressure dependence of single crystal elastic constants and anharmonic properties of wurtzite. Journal of Physics and Chemistry of Solids 1973, 34, 1543–1563

    1973

  131. [139]

    F.; Dunegan, H

    Cline, C. F.; Dunegan, H. L.; Henderson, G. W. Elastic Constants of Hexagonal BeO , ZnS , and CdSe . Journal of Applied Physics 1967, 38, 1944–1948

    1967

  132. [140]

    Lee, B. H. Elastic Constants of ZnTe and ZnSe between 77°–300°K. Journal of Applied Physics 1970, 41, 2984–2987

    1970

  133. [141]

    New Data and Updates for II-VI Compounds ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer Berlin Heidelberg, 2009; Vol

    Rössler, U., Ed. New Data and Updates for II-VI Compounds ; Landolt-B\" o rnstein - Group III Condensed Matter; Springer Berlin Heidelberg, 2009; Vol. 44B

    2009

  134. [142]

    A.; WHITSETT, C

    LEHOCZKY, A.; NELSON, D. A.; WHITSETT, C. R. Elastic Constants of Mercury Selenide. Physical Review 1969, 188, 1069–1073

    1969

  135. [143]

    D.; Pearson, W

    Villars, P.; Calvert, L. D.; Pearson, W. B. Pearson's Handbook of Crystallographic Data for Intermetallic Phases. Volumes 1, 2, 3. American Society for Metals, 1985, 1985, 3258 mcitethebibliography

    1985

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.