Negative Thermal Expansion in Cubic Ice: A Collective Quantum Effect of the hydrogen-bond network

A. Marco Saitta; Livia Eleonora Bove; Loan Renaud; Michele Casula; Richard Gaal; Tomasz Poreba

REVIEW 3 major objections 6 minor 25 references

Negative Thermal Expansion in Cubic Ice: A Collective Quantum Effect of the hydrogen-bond network

T0 review · 3 major / 6 minor · reviewed 2026-07-31 · grok-4.5

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

Pith's one-line read Cubic ice contracts on warming near 70 K for the same quantum network reason as hexagonal ice.

desk verdict Clean Ic NTE data plus MB-pol PIMD make the network+NQE case; the embedding step overclaims collectivity for the finite-T slope. read the letter →

arxiv 2607.28244 v1 pith:H7WEJXT4 submitted 2026-07-30 cond-mat.mtrl-sci

Loan Renaud , Tomasz Poreba , Richard Gaal , A. Marco Saitta , Michele Casula , Livia Eleonora Bove This is my paper · ORCID

classification cond-mat.mtrl-sci

keywords negativethermalexpansioncubicicenuclearquantumeffectspath-integralmoleculardynamicshydrogen-bondnetworkGrüneisenparametersprotonanisotropyMB-pol

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

Ice usually expands when heated, but hexagonal ice shrinks below about 70 K. This paper shows that pure cubic ice does the same thing, even though its long-range stacking of water layers is different. The shared open tetrahedral hydrogen-bond network is what matters. Neutron diffraction on stacking-disorder-free cubic ice finds a density maximum near 70 K that matches hexagonal ice. Path-integral molecular dynamics with the MB-pol potential recovers the anomaly only when nuclei are treated as quantum particles; classical nuclei do not. The density maximum lines up with the peak anisotropy of the proton quantum distribution, neutron data show large transverse proton displacements, and the modes with the most negative Grüneisen parameters are low-frequency transverse network vibrations. The contraction is therefore a collective quantum effect of the network under Bose–Einstein statistics, not a local zero-point correction on single O–H bonds or a stacking-specific feature.

What carries the argument

The anisotropic gyration radius of the path-integral proton ring polymer (transverse over longitudinal components), whose temperature maximum coincides with the density maximum and is linked to low-frequency transverse acoustic and optical modes that carry the most negative Grüneisen parameters and are weighted by Bose–Einstein statistics.

What would settle it

A stacking-disorder-free cubic-ice density curve (experiment or PIMD) that lacks a maximum near 70 K, or a classical simulation with the same potential that still produces the density maximum.

Watch

Extended reading notes

Core claim

Negative thermal expansion in ice I is an intrinsic response of the open tetrahedral hydrogen-bond network and is largely independent of stacking sequence. Stacking-disorder-free cubic ice Ic has a density maximum near 70 K that closely matches hexagonal ice Ih. MB-pol simulations reproduce the anomaly quantitatively only when nuclear quantum effects are included; classical dynamics do not. The temperature of the density maximum coincides with maximal anisotropy of the proton quantum path, transverse proton displacements are strongly enhanced, and the contractive free-energy contributions come from low-frequency transverse modes under quantum statistics.

Load-bearing premise

That comparing a single quantum proton in a classical versus quantum environment, while neglecting explicit coupling to the surroundings, is enough to prove the effect must be collective rather than local.

Editorial extensions

If this is right

NTE in ice I is a property of the shared open tetrahedral network, not of hexagonal stacking.
Classical molecular dynamics cannot capture the cryogenic density maximum of ice I even with an accurate potential; nuclear quantum statistics are required.
Low-frequency transverse network modes, not intramolecular stretches or bends, dominate the contractive response under quantum weighting.
Denser ice phases are expected to lose this cryogenic NTE because compression stiffens the relevant network modes and alters proton delocalization.
Stacking-disorder-free ice Ic is a clean reference system for quantum thermodynamic anomalies in other open tetrahedral networks.

Reading between the lines

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

The same transverse-network plus quantum-statistics mechanism should appear in other low-density tetrahedral frameworks (certain clathrates or ices) once stacking disorder and classical nuclear treatments are removed.
Isotope substitution that leaves the anisotropy ratio almost unchanged while shifting absolute delocalization offers a clean experimental dial on whether the density-maximum temperature tracks anisotropy or absolute zero-point amplitude.
If the single-proton embedding is replaced by a fully coupled multi-proton quantum treatment, the classical-versus-quantum environment contrast should still be required to recover the anomalous zero-kelvin density, or the collectivity argument would need revision.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The real news is a stacking-disorder-free Ic density curve from the C2 route that tracks Ih’s ~70 K maximum, plus MB-pol classical MD vs PIMD that isolates nuclear statistics and matches experiment to ~0.2%. That is new, useful, and low-circularity: the diffraction is external, MB-pol was not fit to this peak, and the same PES fails classically.

What they do well is the multi-messenger stack. Gyration anisotropy peaking near the density max, neutron ADPs with large transverse proton amplitude, and mode-resolved Grüneisen maps pointing at TA/low-TO branches under Bose weighting all line up. The QHA comparison and the SM mode-resolved α_V breakdown make the statistical (not just anharmonic) point concrete. Mass-rescaling checks and isotope notes in the SM are careful. Citation pattern is normal for the subfield.

Soft spot, in proportion: the single-proton embedding (Fig. 4) shows that a quantum environment is needed to get the 0 K volume right, and that local ZPE alone does not. That is a fair 0 K argument. It is not a direct proof that the finite-T NTE slope itself is collective rather than local. NTE is already largely recovered by network phonons in QHA; the embedding neglects explicit coupling and constrains the static V_OO minimum, not the thermal contraction. The broader claim still stands on Ic≈Ih, PIMD vs classical, ADPs/gyration, and negative-γ TA/TO under quantum statistics—the embedding wording just overreaches. Temperature coincidence of anisotropy and density max is within their resolution, not a precision lock. Concurrent polytype NTE work means novelty is shared, not sole.

This is for people who care about water potentials, NQE in ice, and open tetrahedral networks. Serious referee material; tighten the collectivity language and ship the digital artifacts. I would engage and cite the Ic curve and the MB-pol benchmark.

Referee Report

3 major / 6 minor

Summary. The manuscript reports neutron powder diffraction on stacking-disorder-free cubic ice Ic (from topotactic degassing of C2 hydrogen hydrate) together with classical MD and PIMD simulations using MB-pol. Experimentally, Ic shows a density maximum near 70 K that closely matches hexagonal ice Ih. Classical MD yields no density maximum, while PIMD quantitatively reproduces the anomaly (max relative error ~0.2%). The density maximum coincides, within the 15 K grid, with a maximum in the transverse-over-longitudinal proton ring-polymer anisotropy; neutron ADPs independently show enhanced transverse proton displacement. Phonon calculations identify low-frequency TA/TO branches with the most negative Grüneisen parameters, and mode-resolved QHA analysis attributes the cryogenic contraction to Bose-weighted population of those branches. A single-proton embedding construction (classical vs quantum environment PES) is used to argue that the effect is collective rather than a local O–H zero-point correction. The authors conclude that NTE in ice I is an intrinsic, collective nuclear-quantum response of the open tetrahedral hydrogen-bond network, not specific to hexagonal stacking.

Significance. If the result holds, this is a clean and timely contribution: stacking-disorder-free Ic finally allows a controlled comparison of ice-I polytypes that share local tetrahedral coordination but differ in long-range stacking. Demonstrating that the density maximum is essentially the same in Ic and Ih, and that MB-pol PIMD (but not classical MD with the same PES) recovers it quantitatively, substantially strengthens the case that ice-I NTE is a nuclear-quantum network phenomenon. The combination of neutron lattice parameters, ADPs, gyration-radius anisotropy, mode-resolved Grüneisen parameters, and classical-vs-PIMD contrast is a strong multi-messenger package. The work also supplies a chemically transparent reference for quantum-driven anomalies in other open tetrahedral networks. Credit is due for the quantitative MB-pol agreement, the isolation of nuclear statistics via identical PES, and the mode-resolved QHA breakdown in the SM.

major comments (3)

[Fig. 4 and text after Fig. 3] The title/abstract claim that NTE is a 'collective quantum effect' rather than a local O–H ZPE correction rests heavily on the single-proton embedding of Fig. 4 and the following paragraphs. That construction shows that a quantum proton in a classical environment shifts the 0 K V_OO minimum the wrong way (higher density via ZPE(d_OO)), whereas a quantum environment recovers a density nearer PIMD/experiment. Two gaps make this an insecure proof of collectivity for NTE itself. (i) The authors explicitly neglect coupling between the embedded proton and the surroundings, so the contrast is not a controlled isolation of local vs network physics. (ii) More importantly, the embedding constrains the static 0 K minimum of V_OO, whereas NTE is the finite-T slope of density below ~70 K. That slope is already largely recovered by QHA on network phonons (Pamuk comparison; SM mode-resolved γ of TA/TO
[Fig. 3(a) and abstract] The claimed 'direct link' between maximal proton-path anisotropy and the density maximum is stated to hold 'within the temperature resolution.' Both quantities are sampled on a coarse grid (experiment ~15 K; PIMD points similarly sparse), and R_g,z/R_g,x shows a broad maximum rather than a sharp peak. Coincidence on this grid is suggestive but not decisive. Either denser temperature sampling of the anisotropy ratio near 50–90 K, or a quantitative cross-correlation / lag analysis, is needed before the coincidence can carry load-bearing weight in the abstract. Otherwise the language should be softened to 'consistent with' rather than 'coincides… directly linking.'
[Fig. 5; SM Fig. S7 / mode-resolved α_V] The paper argues that classical MD fails because equipartition erases the selective low-T weighting of negative-γ branches, while QHA with Bose statistics succeeds. This is a central mechanistic claim and is supported by the SM mode-resolved α_V breakdown. However, the main text does not show the mode-resolved thermal-expansion decomposition (only the colored dispersion in Fig. 5 and a qualitative narrative). Given that this is what actually ties nuclear statistics to NTE—more directly than Fig. 4—the mode-resolved α_V(T) panel (SM Fig. S7) or an equivalent should appear in the main text, with explicit cumulative contributions from TA, low-TO, and the rest of the spectrum versus T.

minor comments (6)

[Fig. 2 caption] Mass rescaling of D2O experiment onto H2O simulation is validated in the SM (Figs. S1–S2) and is acceptable, but the main-text Fig. 2 caption and related discussion should state explicitly that the experimental Ic curve is mass-rescaled D2O and point to the SM validation, so readers are not left to infer the procedure.
[Fig. 3(a,c)] Neutron ADPs vs ring-polymer gyration radii are correctly flagged as only qualitatively comparable, yet Fig. 3(a) overlays them as crosses on the R_g panel. A separate panel or clearer visual distinction would avoid implying a direct numerical identification.
[Introduction / Discussion] Ref. [20] (del Rosso et al., arXiv:2602.13053) reports NTE in ice-I polytypes and should be discussed briefly in the introduction or discussion so the novelty relative to that concurrent work is explicit.
[Affiliations; SM] Typographical issues: '´Ecole Polytechnique F´ ed´ eerale' (double e); 'F d¯3mspace group' missing space; 'I sd' formatting; 'Gr¨ uneisen' spacing inconsistencies; 'oppure about' left in SM neutron-methods paragraph.
[Fig. 5] Fig. 5 caption notes imaginary modes near Γ as mesh-interpolation artifacts and missing long-wavelength analytic corrections. A brief statement on whether those artifacts affect the extracted γ of the TA/TO branches used in the NTE argument would help.
[SM, PIMD methods] The SM reports P=48 beads at 100 K with P×T constant and PIGLET; a one-sentence convergence check (density vs P at one low-T point) in the SM would strengthen confidence in the NQE isolation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: NTE claim is anchored in external neutron data and an independent potential, not forced by fit or self-definition.

full rationale

The load-bearing chain is experimental density of stacking-disorder-free Ic (neutron powder diffraction, Le Bail lattice parameters) compared to Fortes Ih data; classical MD vs PIMD on the same pre-existing MB-pol PES; gyration-radius anisotropy and neutron ADPs; and mode-resolved Grüneisen parameters from frozen-phonon MB-pol with Bose weighting under QHA. None of these steps defines the target (density maximum / NTE) in terms of itself, fits a parameter to the NTE peak and re-labels it as a prediction, or imports a uniqueness theorem from overlapping authors that forbids alternatives. MB-pol was not tuned here to the Ic anomaly; classical failure vs PIMD success is a genuine nuclear-statistics contrast on a fixed PES. Self-citations (ZPE/embedding methods, anharmonic phonon correlators, prior hydrate work) supply methodology only and are not required to force the central Ic≈Ih or collective-network conclusion. Possible overreach in interpreting the single-proton embedding as proof that finite-T NTE is collective is a correctness/scope issue, not circularity by construction. The derivation is self-contained against external benchmarks.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The claim rests on standard statistical mechanics of path integrals and QHA phonons, on the empirical adequacy of MB-pol for ice densities, on the experimental identification of the recovered phase as stacking-disorder-free Ic, and on interpretive steps that link anisotropy coincidence and embedding contrasts to ‘collective’ causation. No new physical entities are postulated. The main non-standard burdens are the mass-rescaling bridge, the embedding without explicit coupling, and trust in sample purity over 50–200 K.

free parameters (3)

Mass rescaling factor M_H2O/M_D2O for comparing D2O experiment to H2O simulation = M_H2O/M_D2O (stoichiometric mass ratio)
Used in Fig. 2 to overlay experimental Ic densities on H2O PIMD; validated in SM by collapsing D2O PIMD onto H2O but still a modeling choice that affects the visual quantitative match.
PIMD bead number schedule (P × T constant; P=48 at 100 K) = P=48 at 100 K (PIGLET)
Convergence choice for path-integral discretization; affects quantitative density and gyration radii if under-converged.
Finite-difference phonon displacement and volume strains (±2–3% V) = 0.01 Å displacements; V0−3%, V0+2%
Sets numerical Grüneisen parameters that identify which branches drive NTE in the QHA analysis.

assumptions (6)

standard math Path-integral MD with a sufficient number of beads samples the exact quantum Boltzmann statistics of nuclei on a given Born–Oppenheimer PES.
Underpins the classical MD vs PIMD contrast that isolates nuclear quantum effects.
domain assumption The MB-pol many-body potential is accurate enough for ice Ic/Ih densities and low-frequency network modes that qualitative NTE presence/absence is not a potential artifact.
Same PES used for MD and PIMD; quantitative ~0.2% agreement is offered as validation, but the axiom is still required for mechanism claims.
domain assumption Topotactic degassing of C2 hydrogen hydrate yields stacking-disorder-free Ic that remains free of stacking disorder and Ih over 50–200 K for lattice-parameter extraction.
Stated from Rietveld/Le Bail analysis and prior Komatsu route; above ~200 K disorder develops and cuts the range.
domain assumption Quasi-harmonic free energy with mode Grüneisen parameters captures the leading thermal-expansion mechanism when low-frequency branches remain near-harmonic.
Used to attribute NTE to TA/low-TO branches; supported by PIMD phonon estimators showing little anharmonic renormalization at low frequency.
ad hoc to paper A single-proton Schrödinger problem in a PES from classical vs PIMD-averaged environments diagnoses local vs collective quantum contributions to V_OO without needing explicit system–bath coupling.
Central to the ‘collective’ wording; paper acknowledges neglected coupling yet treats the density shift contrast as decisive.
ad hoc to paper Coincidence (within 15 K grid) of maximum R_g,z/R_g,x with the density maximum implies a direct physical link between proton-path anisotropy and macroscopic NTE.
Correlative within temperature resolution; reinforced by ADP and Grüneisen evidence but not a derived necessity.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Negative Thermal Expansion in Cubic Ice: A Collective Quantum Effect of the hydrogen-bond network." pith.science (2026). https://pith.science/paper/H7WEJXT4

@misc{pith2026260728244,
  author       = {Pith},
  title        = {Pith review of: Negative Thermal Expansion in Cubic Ice: A Collective Quantum Effect of the hydrogen-bond network},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H7WEJXT4}},
  note         = {Machine review of arXiv:2607.28244}
}

abstract

We report neutron powder diffraction measurements and path-integral molecular dynamics simulations of stacking-disorder-free cubic ice I$_c$, produced by topotactic degassing of C2 hydrogen hydrate. Across the cryogenic stability range, ice I$_c$ exhibits a density maximum near 70 K, closely matching that of hexagonal ice I$_h$ despite their different long-range stacking sequences. Negative thermal expansion in ice I is therefore not specific to hexagonal stacking, but arises from the shared open tetrahedral hydrogen-bond network. Simulations with the MB-pol potential quantitatively reproduce the experimental anomaly only when nuclear quantum effects are included. The density maximum coincides, within the temperature resolution, with maximal anisotropy of the proton quantum distribution. Neutron-derived displacement parameters independently reveal a strongly enhanced transverse proton displacement, while phonon calculations identify low-frequency transverse modes with the most negative Gr\"uneisen parameters. Together, these results establish the negative thermal expansion of ice I as a collective quantum effect governed by nuclear statistics and the dynamics of the hydrogen-bond network.

Figures

Figures reproduced from arXiv: 2607.28244 by the authors.

**Figure 2.** FIG. 2. Density of cubic (red) and hexagonal (blue) ice as a [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** FIG. 3. (a, top): Temperature-dependent gyration radius [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (2 more)

**Figure 4.** Figure 4: (e), we report in dashed lines the minimum energy of the PES at each dOO for the two embeddings, defining VOO in the two cases. To examine whether local quantum effects introduce anharmonicity into VOO, we calculated the proton ZPE by solving the effective three-dime…

**Figure 5.** Figure 5: FIG. 5. Phonon dispersion of the low-lying modes in the [PITH_FULL_IMAGE:figures/full_fig_p005_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

25 extracted references

[1]

Komatsu, S

K. Komatsu, S. Machida, F. Noritake, T. Hattori, A. Sano-Furukawa, R. Yamane, K. Yamashita, and H. Kagi, Ice ic without stacking disorder by evacuating hydrogen from hydrogen hydrate, Nature Communications11, 464 (2020)

2020
[2]

A. A. Coelho,TOPASandTOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++, Journal of Applied Crystallography51, 210 (2018)

2018
[3]

Le Bail, Whole powder pattern decomposition methods and applications: A retrospection, Powder Diffraction20, 316–326 (2005)

A. Le Bail, Whole powder pattern decomposition methods and applications: A retrospection, Powder Diffraction20, 316–326 (2005)

2005
[4]

Poreba, Crystallographic information and topas refinement files for ice i c at 50 k (2026)

T. Poreba, Crystallographic information and topas refinement files for ice i c at 50 k (2026)

2026
[5]

Litman, V

Y. Litman, V. Kapil, Y. M. Y. Feldman, D. Tisi, T. Beguˇ si´ c, K. Fidanyan, G. Fraux, J. Higer, M. Kellner, T. E. Li, E. S. P´ os, E. Stocco, G. Trenins, B. Hirshberg, M. Rossi, and M. Ceriotti, i-pi 3.0: a flexible and efficient framework for advanced atomistic simulations, J. Chem. Phys.161, 062505 (2024)

2024
[6]

Babin, G

V. Babin, G. R. Medders, and F. Paesani, Development of a ”first principles” water potential with flexible monomers. ii: Trimer potential energy surface, third virial coefficient, and small clusters, Journal of Chemical Theory and Computation 10, 1599 (2014)

2014
[7]

Babin, C

V. Babin, C. Leforestier, and F. Paesani, Development of a ”first principles” water potential with flexible monomers: Dimer potential energy surface, vrt spectrum, and second virial coefficient, Journal of Chemical Theory and Computation9, 5395 (2013)

2013
[8]

G. R. Medders, V. Babin, and F. Paesani, Development of a ”first-principles” water potential with flexible monomers. iii. liquid phase properties, Journal of Chemical Theory and Computation10, 2906 (2014)

2014

Show all 25 references

[9]

Riera, C

M. Riera, C. Knight, E. F. Bull-Vulpe, X. Zhu, H. Agnew, D. G. Smith, A. C. Simmonett, and F. Paesani, Mbx: A many-body energy and force calculator for data-driven many-body simulations, Journal of Chemical Physics159, 54802 (2023)

2023
[10]

F. Paesani, Getting the right answers for the right reasons: Toward predictive molecular simulations of water with many- body potential energy functions, Accounts of Chemical Research49, 1844 (2016)

2016
[11]

S. K. Reddy, S. C. Straight, P. Bajaj, C. Huy Pham, M. Riera, D. R. Moberg, M. A. Morales, C. Knight, A. W. G¨ otz, and F. Paesani, On the accuracy of the mb-pol many-body potential for water: Interaction energies, vibrational frequencies, and classical thermodynamic and dynam...

2016
[12]

Matsumoto, T

M. Matsumoto, T. Yagasaki, and H. Tanaka, Genice: Hydrogen-disordered ice generator, Journal of Computational Chem- istry39, 61 (2017)

2017
[13]

Matsumoto, T

M. Matsumoto, T. Yagasaki, and H. Tanaka, Genice-core: Efficient algorithm for generation of hydrogen-disordered ice structures, Journal of Chemical Physics160, 094101 (2024)

2024
[14]

F. Uhl, D. Marx, and M. Ceriotti, Accelerated path integral methods for atomistic simulations at ultra-low temperatures, The Journal of Chemical Physics145, 054101 (2016)

2016
[15]

Ceriotti, G

M. Ceriotti, G. Bussi, and M. Parrinello, Langevin equation with colored noise for constant-temperature molecular dynamics simulations, Physical Review Letters102, 020601 (2009)

2009
[16]

Ceriotti, G

M. Ceriotti, G. Bussi, and M. Parrinello, Colored-noise thermostats ` ala carte, Journal of Chemical Theory and Computation 6, 1170 (2010)

2010
[17]

Togo, First-principles phonon calculations with phonopy and phono3py, J

A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn.92, 012001 (2023)

2023
[18]

A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Implementation strategies in phonopy and phono3py, J. Phys. Condens. Matter35, 353001 (2023)

2023
[19]

Morresi, L

T. Morresi, L. Paulatto, R. Vuilleumier, and M. Casula, Probing anharmonic phonons by quantum correlators: A path integral approach, Journal of Chemical Physics154, 224108 (2021)

2021
[20]

Morresi, R

T. Morresi, R. Vuilleumier, and M. Casula, Hydrogen phase-iv characterization by full account of quantum anharmonicity, PHYSICAL REVIEW B106, 54109 (2022)

2022
[21]

Monacelli, R

L. Monacelli, R. Bianco, M. Cherubini, M. Calandra, I. Errea, and F. Mauri, The stochastic self-consistent harmonic approximation: calculating vibrational properties of materials with full quantum and anharmonic effects, Journal of Physics: Condensed Matter33, 363001 (2021)

2021
[22]

Giannozzi, O

P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio, A. Fer- retti, A. Floris, G. Fratesi, G. Fugallo, R. Geba...

2017
[23]

Giannozzi, S

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, 9 M. Lazzeri, L. Martin-Samos, N. Marzari, F. ...

2009
[24]

Renaud, T

L. Renaud, T. Poreba, S. D. Cataldo, A. Nicholls, L. Andriambariarijaona, M. Rescigno, R. Gaal, M. Casula, A. M. Saitta, and L. E. Bove, Dual quantum locking: Dynamic coupling of h2 and h2o sublattices in hydrogen-filled ice, Proceedings of the National Academy of Sciences of ...

2026
[25]

Monacelli, Analyzing the anharmonic phonon spectrum: Self-consistent approximation and temperature-dependent effective potential methods, Phys

L. Monacelli, Analyzing the anharmonic phonon spectrum: Self-consistent approximation and temperature-dependent effective potential methods, Phys. Rev. B112, 014109 (2025)

2025

Pith tools

Reviewed July 31, 2026 · model on record in the stance chip above.

[1] [1]

Komatsu, S

K. Komatsu, S. Machida, F. Noritake, T. Hattori, A. Sano-Furukawa, R. Yamane, K. Yamashita, and H. Kagi, Ice ic without stacking disorder by evacuating hydrogen from hydrogen hydrate, Nature Communications11, 464 (2020)

2020

[2] [2]

A. A. Coelho,TOPASandTOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++, Journal of Applied Crystallography51, 210 (2018)

2018

[3] [3]

Le Bail, Whole powder pattern decomposition methods and applications: A retrospection, Powder Diffraction20, 316–326 (2005)

A. Le Bail, Whole powder pattern decomposition methods and applications: A retrospection, Powder Diffraction20, 316–326 (2005)

2005

[4] [4]

Poreba, Crystallographic information and topas refinement files for ice i c at 50 k (2026)

T. Poreba, Crystallographic information and topas refinement files for ice i c at 50 k (2026)

2026

[5] [5]

Litman, V

Y. Litman, V. Kapil, Y. M. Y. Feldman, D. Tisi, T. Beguˇ si´ c, K. Fidanyan, G. Fraux, J. Higer, M. Kellner, T. E. Li, E. S. P´ os, E. Stocco, G. Trenins, B. Hirshberg, M. Rossi, and M. Ceriotti, i-pi 3.0: a flexible and efficient framework for advanced atomistic simulations, J. Chem. Phys.161, 062505 (2024)

2024

[6] [6]

Babin, G

V. Babin, G. R. Medders, and F. Paesani, Development of a ”first principles” water potential with flexible monomers. ii: Trimer potential energy surface, third virial coefficient, and small clusters, Journal of Chemical Theory and Computation 10, 1599 (2014)

2014

[7] [7]

Babin, C

V. Babin, C. Leforestier, and F. Paesani, Development of a ”first principles” water potential with flexible monomers: Dimer potential energy surface, vrt spectrum, and second virial coefficient, Journal of Chemical Theory and Computation9, 5395 (2013)

2013

[8] [8]

G. R. Medders, V. Babin, and F. Paesani, Development of a ”first-principles” water potential with flexible monomers. iii. liquid phase properties, Journal of Chemical Theory and Computation10, 2906 (2014)

2014