When Theory Meets Experiment: What Does it Take to Accurately Predict $^1$H NMR Dipolar Relaxation Rates in Neat Liquid Water from Theory?

Angel Mary Chiramel Tony; Anne Strate; Dietmar Paschek; Dominik Marx; Harald Forbert; Johanna Busch; Nore Stolte; Ralf Ludwig

REVIEW 3 major objections 6 minor 18 references

When Theory Meets Experiment: What Does it Take to Accurately Predict $^1$H NMR Dipolar Relaxation Rates in Neat Liquid Water from Theory?

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The 1H NMR spin-lattice relaxation rate of neat liquid water can be computed from quantum-accurate molecular dynamics and match the measured value within experimental error.

desk verdict The paper makes a quantitatively successful prediction of the 1H NMR relaxation rate of water using CCSD(T)-level path integral simulations, with one untested dynamical assumption that a referee should pin down. read the letter →

arxiv 2411.12545 v2 pith:WMYG2NYG submitted 2024-11-19 physics.chem-ph cond-mat.soft

Dietmar Paschek , Johanna Busch , Angel Mary Chiramel Tony , Ralf Ludwig , Anne Strate , Nore Stolte , Harald Forbert , Dominik Marx This is my paper · ORCID

classification physics.chem-phcond-mat.soft PACS 76.60.-k31.15.Qg

keywords NMRrelaxationliquidwatermoleculardynamicsnuclearquantumeffectsCCSD(T)Hwang-FreedtheorydipolarTIP4P/2005

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 sets out to answer a 58-year-old question: can theory predict the measured 1H NMR spin-lattice relaxation rate of neat liquid water? It computes the dipolar relaxation rate using trajectories from Coupled Cluster Molecular Dynamics at CCSD(T) accuracy with nuclear quantum effects, combined with a recently introduced framework that separates structural and dynamical contributions and corrects for finite-size effects. The central result is that when structure, intramolecular H-H distance, and a rebalanced rotational-translational dynamics (the product $D_0 \times \tau_{\mathrm{HH}}$) are taken from those trajectories, the computed rate at 28 MHz is 0.2782 s$^{-1}$, inside the experimental value $0.280 \pm 0.003$ s$^{-1}$. The paper also concludes that nuclear quantum effects reduce the intramolecular contribution, and that the inter- and intramolecular parts are nearly equal in magnitude.

What carries the argument

The argument is carried by a decomposition of the dipolar correlation function into a structural prefactor (the $r^{-6}$-weighted average) and a normalized dynamical correlation function. For the intermolecular part, the normalized function is written as the analytical Hwang-Freed diffusive correlation function, describing two hard spheres diffusing past each other, plus a short-time 'difference function' $\Delta G_{\mathrm{inter}}(t)$ computed from MD, which carries the librational and hydrogen-bond-jump corrections; the difference function is scaled to infinite system size with a Yeh-Hummer-type correction. The intramolecular part uses the reorientational correlation function of the H-H vector $C_2^{\mathrm{HH}}(t)$, fitted to a Kohlrausch-Williams-Watts stretched exponential for long times, multiplied by the effective distance $\langle r_{\mathrm{HH}}^{-3}\rangle^{-2}$. The key dynamical control is the product $D_0 \times \tau_{\mathrm{HH}}$; the authors treat this rotation-translation balance as the quantity that nuclear quantum effects shift, and they rescale $\tau_{\mathrm{HH}}$ by the ratio $D_0(\mathrm{CCMD})/D_0(\mathrm{expt})$ to bring the computed rate into agreement.

What would settle it

Recompute $\Delta J_{\mathrm{inter}}$ directly from CCMD trajectories (or from experimental-structure simulations) rather than importing the TIP4P/2005 difference function; if the total $R_1$ at 28 MHz then leaves the window $0.277$–$0.283$ s$^{-1}$, the transferability assumption fails. As a second check, field-cycling measurements above 1 GHz would test the predicted roughly 15% drop in the intermolecular contribution.

Watch

Extended reading notes

Core claim

In the paper's own terms, the discovery is that the 1H dipolar relaxation rate of liquid water at 298 K is quantitatively predictable from theory. The full calculation, using CCMD structures and dynamics, an effective intramolecular H-H distance of 154.1 pm, and a rebalancing of $D_0 \times \tau_{\mathrm{HH}}$, gives $R_1(28\,\mathrm{MHz}) = 0.2782$ s$^{-1}$; the experimental value is $0.280 \pm 0.003$ s$^{-1}$. The paper attributes the previous 13% overestimation from the TIP4P/2005 model mainly to the intramolecular H-H distance and the missing quantum effects on reorientation. It reports that the intermolecular and intramolecular contributions are each about 0.14 s$^{-1}$, so the intermolecular part is roughly as large as the intramolecular part, contrary to earlier classical predictions.

Load-bearing premise

The paper assumes the short-time part of the intermolecular relaxation—the librations and hydrogen-bond jumps that deviate from plain diffusion—can be taken from a classical water model and applied unchanged to the quantum-accurate and experimental structures; if that short-time behavior differs under nuclear quantum effects or at CCSD(T) quality, the computed intermolecular rate shifts.

Editorial extensions

If this is right

Theory can serve as a quantitative benchmark for interpreting 1H NMR relaxation in water without relying on analytical models of molecular motion.
The intramolecular H-H distance of rigid water models (151.4 pm) is too short; using an effective distance near 154 pm largely removes the systematic overestimation of $R_1$.
Nuclear quantum effects materially change the relaxation prediction by quenching the reorientational correlation function and reducing $D_0 \times \tau_{\mathrm{HH}}$, so classical simulations alone misattribute the relaxation balance.
The near-equality of inter- and intramolecular contributions revises earlier claims that intramolecular relaxation dominates, and implies both channels must be treated on equal footing in future analyses.
The predicted frequency dependence, with the intermolecular contribution dropping roughly 15% at 1.2 GHz, is a concrete signature testable by field-cycling relaxometry.

Reading between the lines

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

Beyond the paper: if the transferred short-time difference function holds at other temperatures, the same framework should reproduce the measured temperature dependence of $R_1$ from 0 to 110 °C, a testable prediction with existing experimental data.
Beyond the paper: the product $D_0 \times \tau_{\mathrm{HH}}$ could serve as a cheap diagnostic for water models—force fields that reproduce this balance without rescaling are likely to predict relaxation rates correctly, and those that do not will need the same correction.
Beyond the paper: the near-equality of inter- and intramolecular contributions suggests that NMR relaxation studies of other hydrogen-bonded liquids, such as alcohols and amides, may need to treat both channels explicitly rather than assuming intramolecular dominance.
Beyond the paper: because the difference function is borrowed from classical TIP4P/2005 dynamics, an explicit path-integral-based computation of $\Delta J_{\mathrm{inter}}$ would remove the main residual model dependence; if it changed the rate beyond $0.003$ s$^{-1}$, the agreement would weaken.

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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 headline result is real: Table I gives R1 = 0.2782 s⁻¹ at 28 MHz versus the experimental 0.280 ± 0.003 s⁻¹, and the path to it is mostly clean. The genuinely new piece is that the intramolecular and intermolecular contributions come out nearly equal, which contradicts earlier classical-MD pictures that put most weight on the intramolecular part. That difference traces to the larger, more realistic H–H distance from CCMD and to the rebalancing of translation versus rotation through D0 × τHH. The paper also does several things right: the target R1 is never used as input, the τHH rescaling uses the experimental self-diffusion coefficient as an external benchmark, structural inputs are checked against Soper's neutron data and Faux et al.'s consensus distance, and the analysis software is on GitHub. This is a strong contribution for the NMR-relaxation and water-simulation communities.

The soft spots are real but not fatal. The most important is the one the paper states explicitly in Section IV.C: the intermolecular difference function ΔJ_inter is computed from classical TIP4P/2005 simulations and applied unchanged to the CCMD and experimental structural datasets. That function is supposed to capture librational and jump-type short-time dynamics, and the paper's own Figure 3 shows that nuclear quantum effects measurably quench those dynamics. The robustness argument offered—that R1_inter depends only weakly on dHH—only varies the static distance of closest approach; it does not test whether the short-time dynamical correction transfers. Given that the final agreement sits within about 0.7% of experiment, a modest change in the intermolecular spectral density could move the total outside the experimental error. A referee should ask for a CCMD-derived ΔJ_inter or at least a sensitivity estimate.

Two smaller issues: the final rates in Table I have no error bars, which is surprising for a paper whose argument depends on matching an experimental error bar; and the paper leans on the earlier TIP4P/2005 work from the same group for the framework and the θ parameter, which is fine conceptually but leaves the finite-size correction somewhat self-referential until independently reproduced.

Overall, the central claim is plausible and the paper deserves a serious referee. It will be useful to anyone benchmarking water potentials or NMR relaxation models, and it should be published after the transferability assumption and error bars are addressed. I would send it to review, not desk reject.

Referee Report

3 major / 6 minor

Summary. This manuscript computes the 1H NMR dipole-dipole relaxation rate R1 of liquid water at 298 K and 28 MHz using a combination of coupled-cluster molecular dynamics (CCMD) trajectories that include nuclear quantum effects, structural data from neutron scattering and from the experimental consensus H-H distance of Faux et al., and a previously introduced framework that separates intermolecular relaxation into a Hwang-Freed diffusion part and a short-time difference function computed from MD. With CCMD-derived structural parameters (intramolecular H-H distance 154.1 pm, DCA 195.68 pm) and a rescaling of the intramolecular correlation time by the ratio D0(CCMD)/D0(expt), the authors obtain R1 = 0.2782 s-1 at 28 MHz, to be compared with the experimental value of (0.280 ± 0.003) s-1. They also find that the intramolecular and intermolecular contributions are nearly equal in magnitude, in contrast to earlier classical simulations.

Significance. If the result holds, the paper would constitute a quantitative, essentially parameter-free prediction of a fundamental NMR relaxation rate in liquid water, and it would demonstrate that nuclear quantum effects and accurate intermolecular structure are both needed for that prediction. The manuscript's strengths are its use of multiple independent structural inputs (CCMD, Soper's neutron data, Faux et al.'s experimental distance) that agree on the key intramolecular H-H distance, the explicit finite-size correction for the intermolecular part, and the open-source availability of the software (MDorado and FreeDRelax). However, the central claim rests on an untested transferability assumption for the intermolecular short-time difference function, and the reported agreement is sensitive to the small rebalancing of rotational and translational dynamics. These issues need to be resolved before the claim of quantitative prediction can be considered fully supported.

major comments (3)

[Section IV.C, Eqs. (43)-(45)] The intermolecular relaxation rate uses the same TIP4P/2005-derived difference function ΔJ_inter for the TIP4P/2005, CCMD, and experimental structural datasets. This is an explicit assumption: the manuscript states 'using the same TIP4P/2005 derived Δ J n inter(ω) functions for all three datasets.' The difference function encodes short-time librational and jump-reorientation dynamics, and Section IV.B shows that these dynamics are significantly altered by nuclear quantum effects (τ_HH drops by 12.8% and D0×τHH changes from 0.570 to 0.506 Å² in CCMD relative to TIP4P/2005). The robustness argument in Section IV.C, based on R1_inter ∝ 1/dHH, only varies the static distance of closest approach and does not test whether the dynamic correction is transferable. Because the final total R1 agrees with experiment to within about 0.7%, an unquantified change in R1_inter can move the prediction outside the reported agreement. The authors should either compute ΔG_inter and ΔJ_inter directly from CCMD trajectories or provide a quantitative sensitivity estimate that bounds the error introduced by using the classical difference function.
[Section IV.D, Eq. (39)] The rebalancing step τG ≈ τ_HH × D0(CCMD)/D0(expt) is essential to the final agreement: without it the intramolecular rate is 0.1380 s-1 and the total at 28 MHz is about 0.2758 s-1, which is outside the experimental lower bound of 0.277 s-1. Although the rescaling is small (about 1.8%), it is introduced because the CCMD diffusion coefficient overestimates experiment by a comparable amount. The manuscript should justify why this procedure is a principled correction rather than an empirical adjustment, for example by showing that the same ratio correctly describes D2O or by propagating the uncertainty in D0 and demonstrating that the result is stable across the experimental and computed D0 values. As written, the headline agreement depends on this rescaling, so its status as a first-principles prediction needs clarification.
[Section IV.C, 'experimental structure' dataset] The 'experimental' dataset combines the Soper neutron-scattering gHH with the Faux et al. consensus intramolecular H-H distance. While both are reasonable independent sources, they are not measured on the same sample at the same thermodynamic state, and the manuscript does not discuss possible systematic differences between the two. This is a relatively minor concern because the dHH sensitivity is small, but the authors should at least state the assumptions implied by combining these two experimental sources.

minor comments (6)

[Abstract] The phrase 'structural and dynamical informations' should be 'structural and dynamical information'; similar grammatical slips appear elsewhere (e.g., 'reorienational' in Section IV.B and 'empricial' in Section IV.B).
[Section IV.A] The name 'Gonz´ ales' in the text should be 'González' to match the cited reference (González and Abascal).
[Section IV.B, Eq. (28)] The phrase 'empricial Kohlrausch-Williams Watts (KWW)' should read 'empirical Kohlrausch-Williams-Watts (KWW)'.
[Section IV.C, Fig. 4] The caption of Fig. 4 would benefit from stating explicitly which system size (8192 molecules) and which DCA value are used for the Hwang-Freed reference curve, since the figure is central to understanding ΔG_inter.
[Section IV.D, Table I] The rows for νH=0 and νH=28 MHz show R1,intra values of 0.1404 s-1 in both cases, which is consistent with extreme narrowing but could be clarified in the text.
[Data Availability] The statement that data are available 'upon reasonable request' is weaker than the open-source software statement; archiving the key correlation functions and fitted parameters would improve reproducibility.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the target relaxation rate R1 is never used as an input; all empirical inputs are external benchmarks, and the transferability assumption flagged by the skeptic is a testable modeling assumption, not a circular reduction.

full rationale

The claimed prediction chain is not circular. The target observable, R1(28 MHz) = 0.280 s^-1, appears only as the experimental comparison value, never inside any equation that produces the computed rate. The structural inputs (Soper rdfs, Faux et al. H-H distance, CCMD intramolecular rHH) and the dynamical inputs (TIP4P/2005 and CCMD correlation functions, D0 values) are all independent of the NMR relaxation rate. The CCMD trajectories from Refs. 21 and 34 are benchmarked against experimental self-diffusion coefficients and are not fitted to R1. The finite-size correction parameter theta ≈ 2.53 is stated to have been calibrated against random-walker simulations in Refs. 30,31, which is an external benchmark rather than a fit to the present target; moreover, the framework is code-reproduced via the open-source MDorado and FreeDRelax packages. Equation (39) rescales tau_G using the experimental self-diffusion coefficient D0, but D0 is a separate experimental observable, not the NMR relaxation rate, and the correction is small because CCMD D0 already agrees with experiment. The explicit statement in Section IV.C that 'the same TIP4P/2005 derived Delta J_inter functions' are used for all three datasets is a transferability assumption about short-time librational and jump dynamics; if wrong, it could shift R1_inter, but it does not make the prediction equivalent to any input by construction. No uniqueness theorem is imported from the authors, no ansatz is smuggled in via citation, and no known result is merely renamed. The identified weaknesses are correctness risks, not circularity.

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

The central prediction uses no free parameter fit to the target R1 value. The listed parameters are empirical calibrations from random walker simulations, fits to simulation correlation functions rather than to the NMR observable, or pragmatic integration cutoffs. The main untested modeling choice is the transfer of the TIP4P/2005-based difference function to CCMD and experimental structures.

free parameters (3)

θ in finite-size Hwang-Freed correction = 2.53
Empirical lower-boundary parameter for the finite-size correction of the Hwang-Freed correlation function, calibrated against random walker simulations in Refs. 30,31. Not fit to NMR data.
KWW parameters (AK, τK, βK) = 0.73995, 2.7622 ps, 0.9057
Fit to the CCMD intramolecular correlation function over 1-100 ps. These parameters shape J_intra but are not fit to the experimental relaxation rate.
t* integration cutoff = 5 ps
Upper limit for the short-time difference function in Eq. 33, chosen where MD and KWW curves become indistinguishable. Pragmatic but reasonable.

assumptions (5)

standard math The dipole-dipole relaxation formulas (Eqs. 1-3) from Abragam and Westlund/Lynden-Bell are the correct description for spin-1/2 1H nuclei.
Used throughout Section II as the starting point; standard NMR relaxation theory.
domain assumption The Hwang-Freed model accurately captures the long-time translational diffusion contribution to intermolecular relaxation.
Eq. 17 and the t^-3/2 long-time scaling are assumed to describe the diffusion asymptote; validated by prior random-walker tests.
domain assumption Intramolecular H-H distance fluctuations decorrelate quickly from reorientation, justifying Eq. 36.
Eq. 36 replaces ⟨r^-3(0)r^-3(t)⟩ by ⟨r^-3⟩^2 C2(t), supported by fast bending vibrations but not rigorously proven.
ad hoc to paper The short-time difference function ΔG_inter from classical TIP4P/2005 simulations is transferable to CCMD and experimental water structures.
Section IV.C applies the same TIP4P/2005-derived ΔJ_inter to all datasets; no CCMD-based check is provided.
domain assumption The KWW stretched exponential is an adequate representation of the intramolecular correlation function.
Used in Eqs. 28-33 to extrapolate the correlation function and compute spectral densities; standard practice in NMR relaxation modeling.

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Pith. "Pith review of When Theory Meets Experiment: What Does it Take to Accurately Predict $^1$H NMR Dipolar Relaxation Rates in Neat Liquid Water from Theory?." pith.science (2026). https://pith.science/paper/WMYG2NYG

@misc{pith2026241112545,
  author       = {Pith},
  title        = {Pith review of: When Theory Meets Experiment: What Does it Take to Accurately Predict $^1$H NMR Dipolar Relaxation Rates in Neat Liquid Water from Theory?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WMYG2NYG}},
  note         = {Machine review of arXiv:2411.12545}
}

abstract

In this contribution, we compute the $^1$H nuclear magnetic resonance (NMR) relaxation rate of liquid water at ambient conditions. We are using structural and dynamical information from Coupled Cluster Molecular Dynamics (CCMD) trajectories generated at CCSD(T) electronic structure accuracy while considering also nuclear quantum effects in addition to consulting information from X-ray and neutron scattering experiments. Our analysis is based on a recently presented computational framework for determining the frequency-dependent NMR dipole-dipole relaxation rate of spin $1/2$ nuclei from Molecular Dynamics (MD) simulations, which allows for an effective disentanglement of its structural and dynamical contributions, and is including a correction for finite-size effects inherent to MD simulations with periodic boundary conditions. A close to perfect agreement with experimental relaxation data is achieved if structural and dynamical informations from CCMD trajectories are considered including a re-balancing of the rotational and translational dynamics, according to the product of the self-diffusion coefficient and the reorientational correlation time of the H-H vector $D_0\times\tau_\mathrm{HH}$. The simulations show that this balance is significantly altered when nuclear quantum effects are taken into account. Our analysis suggests that the intermolecular and intramolecular contribution to the $^1$H NMR relaxation rate of liquid water are almost similar in magnitude, unlike to what was predicted earlier from classical MD simulations.

Figures

Figures reproduced from arXiv: 2411.12545 by the authors.

**Figure 3.** FIG. 3. Reorientational correlation function of the H-H [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** FIG. 4. Normalized intermolecular dipole-dipole correlation [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

Figures from the paper (4 more)

**Figure 5.** Figure 5: FIG. 5. Scaling of the computed intermolecular ∆ [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: FIG. 6. Intermolecular H-H radial distribution function [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

**Figure 7.** Figure 7: FIG. 7. Frequency-dependent [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: FIG. 8. Refined frequency dependent [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

18 extracted references · 18 canonical work pages

[1]

When Theory Meets Experiment: What Does it Take to Accurately Predict $^1$H NMR Dipolar Relaxation Rates in Neat Liquid Water from Theory?

When Theory Meets Experiment: What Does it Take to Accurately Predict 1H NMR Dipolar Relaxation Rates in Neat Liquid Water from Theory? Dietmar Paschek ,1, a) Johanna Busch ,1 Angel Mary Chiramel Tony,1 Ralf Ludwig ,1 Anne Strate ,1 Nore Stolte ,2 Harald Forbert ,3 and Dominik Marx2 1)Institut f¨ ur Chemie, Abteilung Physikalische und Theoretische Chemie,...

work page Pith review arXiv 2024
[2]

distance of closest approach

µ0 4π 2 · 2 ∞Z 0 G(t) dt , (5) where the integral over the dipole-dipole correlation func- tion ∞Z 0 G(t) dt = *X j r−6 ij (0) + τG (6) is the product of the r−6 ij averaged constant and a correla- tion time τG, which is the time-integral of the normalized correlation function τG = ∞Z 0 Gn(t) dt , (7) characterizing the dynamical processes within the liqu...

work page 2005
[3]

The corresponding reorientational correlation times are: τ HH 2 = (2.16±0.02) ps (CCMD H2O), τ HH 2 = (2.48± 0.01) ps (TIP4P/2005), and τ DD 2 = (2.80 ± 0.04) ps (CCMD D2O)

Reorientational correlation function of the H-H- vector C HH 2 (t). The corresponding reorientational correlation times are: τ HH 2 = (2.16±0.02) ps (CCMD H2O), τ HH 2 = (2.48± 0.01) ps (TIP4P/2005), and τ DD 2 = (2.80 ± 0.04) ps (CCMD D2O). tions, such that Gn,MD intra (t) ≈ ⟨r−3 HH(0)r−3 HH(t)⟩ ⟨r−6 HH⟩ · C HH 2 (t) . (35) A consequence of the fast de-c...

work page 2005
[4]

Intermolec- ular dynamics from classical MD simulations of TIP4P/2005 water

Normalized intermolecular dipole-dipole correlation function Gn inter(t) computed for water at 298 K. Intermolec- ular dynamics from classical MD simulations of TIP4P/2005 water. Solid red line: Gn,MD inter (t). Solid orange line: Gn,HF inter (t) computed using data shown in TABLE I of Ref. 30,31. Solid turquoise line: difference function ∆ Gn inter(t) = ...

work page 2005
[5]

30,31 as a function of the inverse box length L−1, analogous to the scaling of the translational diffusion coefficient suggested by Yeh and Hummer

Scaling of the computed intermolecular ∆ τG for TIP4P/2005 water at 298 K given in TABLE I of Ref. 30,31 as a function of the inverse box length L−1, analogous to the scaling of the translational diffusion coefficient suggested by Yeh and Hummer. 25 The extrapolated value for L → ∞is indicated in red. 151.4 pm leading to an intramolecular relaxation rate ...

work page 2005
[6]

The average intramolecular H-H distance is obtained to be ⟨r−3 HH⟩−1/3 = 154.1 pm

Intramolecular and total H-H radial distribution function gHH(r) for T = 298 K as obtained from CCMD sim- ulations of H 2O. The average intramolecular H-H distance is obtained to be ⟨r−3 HH⟩−1/3 = 154.1 pm. 10 -2 10 -1 10 0 10 1 t / ps 0 0.2 0.4 0.6 0.8 C2 HH/DD (t) CCMD (D2O) TIP4P/2005 CCMD (H2O) FIG

work page 2005
[7]

Frequency-dependent 1H NMR relaxation rate R1(ω) of water at 298 K at a density of 0 .997 g cm−3 a) based on TIP4P/2005 model data as in Ref. 30,31 using D′ = 2 D0 with D0 = 2.30 × 10−9 m2 s−1 and b) employing refined structural parameters for dHH and ⟨r−3 HH⟩−1/3 either based on CCMD simulations or the experimental data of Soper 35 and Faux et al

work page 2005
[8]

with ∆J n inter(ω) ≈ ttrZ 0 ∆Gn inter(t) cos(ωt) dt

Refined frequency dependent 1H NMR relaxation rate R1(ω) of water at 298 K at a density of 0 .997 g cm−3 computed using the intramolecular spectral densities J n intra(ω) obtained from CCMD scaled to match the experimental balance ofD0 ×τHH a) employing the refined structural parameters from CCMD and b) employing the refined structural parameters based on...

work page 1967

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[10]

break- down

· R2 h , (38) where D0 is the translational self-diffusion coefficient, τl is the reorientational correlation time determined from a correlation function of a l-th order Legendre-polynomial, while Rh represents the hydrodynamic radius. The observation that the corresponding ex...

2005
[11]

a) A comparison of the radial distribution functions obtained for the TIP4P/2005 model 30,31 and from neutron scattering data according to Soper

Intermolecular H-H radial distribution function gHH(r) for T = 298 K in addition to the corresponding step-like gHH(r) according to the Hwang and Freed theory with DCAs of dHH as indicated. a) A comparison of the radial distribution functions obtained for the TIP4P/2005 model ...

2005
[14]

6a, leading to dHH = 188.30 pm, and the CCMD dataset for H2O shown in FIG

We have also com- puted corresponding DCAs from the experimental pair distribution data according to Soper35 shown in FIG. 6a, leading to dHH = 188.30 pm, and the CCMD dataset for H2O shown in FIG. 6b, leading to dHH = 195 .68 pm. When using the same TIP4P/2005 derived ∆ J n i...

2005
[15]

This is, however, not the case for the CCMD simulations, where no constraints with respect to bond distances and bond angles exist

For the case of the rigid TIP4P/2005 model, Gn,MD intra (t) is perfectly identical with C HH 2 (t), since the distance of the H-H vector is being kept fixed during the simulation. This is, however, not the case for the CCMD simulations, where no constraints with respect to bon...

2005
[17]

As shown in Ref. 30,31, Equation 26 very well captures the initial effect due to the limited sampling volumes over a broad range of R/d values that would correspond to liquid wa- ter simulations ranging from 2000 to about 16000 water molecules in a cubic unit cell. Since for l...

2000
[21]

MDorado” which is available via GitHub (github.com/Paschek-Lab/MDorado). Our open source software “FreeDRelax

Self-diffusion coefficients were computed from individual simulations via a maximum entropy formalism58 based on molecular centroid positions at 2 fs intervals, and system- size independent self-diffusion coefficients D0 were ob- tained by extrapolating results from cubic simu...

2005
[23]

Here ∆τG can be computed comfortably via numerical inte- gration of ∆τG ≈ ttrZ 0 ∆Gn inter(t) dt (42) due to the short-time nature of ∆ Gn inter(t). To compute the intermolecular spectral density from MD simulation, we use J n,MD inter (ω) = J n,HF inter (ω) + ∆J n inter(ω) (4...

2005
[30]

Proton spin-lattice relaxation in pure water be- tween 0◦C and 110 ◦C,

By using the information about dHH and rHH from CCMD simula- tions and experimental data we arrive at the frequency- dependent relaxation rates shown in FIG. 7b. Note that refining just the structural parameters already signifi- cantly improves the agreement with the experimen...

1966
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Translational and rota- tional diffusion of glycerol by means of field cycling 1H NMR relaxometry,

Chap. Nuclear spin relaxation in liquids and gases, pp. 230–275. 5D. Kruk, R. Meier, and A. R¨ ossler, “Translational and rota- tional diffusion of glycerol by means of field cycling 1H NMR relaxometry,” J. Phys. Chem. B 115, 951–957 (2011). 6D. Kruk, A. Hermann, and E. A. R¨ ...

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NMR 1H-1H dipole relaxation in fluids: Relaxation of individual 1H-1H pairs versus relaxation of molecular modes,

Chap. 7, pp. 181–206. 66D. N. Asthagiri, W. G. Chapman, G. J. Hirasaki, and P. M. Singer, “NMR 1H-1H dipole relaxation in fluids: Relaxation of individual 1H-1H pairs versus relaxation of molecular modes,” J. Phys. Chem. B 124, 10802–10810 (2020). 67A. V. Parambathu, P. J. Pin...

2020

Pith tools

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

[1] [1]

When Theory Meets Experiment: What Does it Take to Accurately Predict $^1$H NMR Dipolar Relaxation Rates in Neat Liquid Water from Theory?

When Theory Meets Experiment: What Does it Take to Accurately Predict 1H NMR Dipolar Relaxation Rates in Neat Liquid Water from Theory? Dietmar Paschek ,1, a) Johanna Busch ,1 Angel Mary Chiramel Tony,1 Ralf Ludwig ,1 Anne Strate ,1 Nore Stolte ,2 Harald Forbert ,3 and Dominik Marx2 1)Institut f¨ ur Chemie, Abteilung Physikalische und Theoretische Chemie,...

work page Pith review arXiv 2024

[2] [2]

distance of closest approach

µ0 4π 2 · 2 ∞Z 0 G(t) dt , (5) where the integral over the dipole-dipole correlation func- tion ∞Z 0 G(t) dt = *X j r−6 ij (0) + τG (6) is the product of the r−6 ij averaged constant and a correla- tion time τG, which is the time-integral of the normalized correlation function τG = ∞Z 0 Gn(t) dt , (7) characterizing the dynamical processes within the liqu...

work page 2005

[3] [3]

The corresponding reorientational correlation times are: τ HH 2 = (2.16±0.02) ps (CCMD H2O), τ HH 2 = (2.48± 0.01) ps (TIP4P/2005), and τ DD 2 = (2.80 ± 0.04) ps (CCMD D2O)

Reorientational correlation function of the H-H- vector C HH 2 (t). The corresponding reorientational correlation times are: τ HH 2 = (2.16±0.02) ps (CCMD H2O), τ HH 2 = (2.48± 0.01) ps (TIP4P/2005), and τ DD 2 = (2.80 ± 0.04) ps (CCMD D2O). tions, such that Gn,MD intra (t) ≈ ⟨r−3 HH(0)r−3 HH(t)⟩ ⟨r−6 HH⟩ · C HH 2 (t) . (35) A consequence of the fast de-c...

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[4] [4]

Intermolec- ular dynamics from classical MD simulations of TIP4P/2005 water

Normalized intermolecular dipole-dipole correlation function Gn inter(t) computed for water at 298 K. Intermolec- ular dynamics from classical MD simulations of TIP4P/2005 water. Solid red line: Gn,MD inter (t). Solid orange line: Gn,HF inter (t) computed using data shown in TABLE I of Ref. 30,31. Solid turquoise line: difference function ∆ Gn inter(t) = ...

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[5] [5]

30,31 as a function of the inverse box length L−1, analogous to the scaling of the translational diffusion coefficient suggested by Yeh and Hummer

Scaling of the computed intermolecular ∆ τG for TIP4P/2005 water at 298 K given in TABLE I of Ref. 30,31 as a function of the inverse box length L−1, analogous to the scaling of the translational diffusion coefficient suggested by Yeh and Hummer. 25 The extrapolated value for L → ∞is indicated in red. 151.4 pm leading to an intramolecular relaxation rate ...

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[6] [6]

The average intramolecular H-H distance is obtained to be ⟨r−3 HH⟩−1/3 = 154.1 pm

Intramolecular and total H-H radial distribution function gHH(r) for T = 298 K as obtained from CCMD sim- ulations of H 2O. The average intramolecular H-H distance is obtained to be ⟨r−3 HH⟩−1/3 = 154.1 pm. 10 -2 10 -1 10 0 10 1 t / ps 0 0.2 0.4 0.6 0.8 C2 HH/DD (t) CCMD (D2O) TIP4P/2005 CCMD (H2O) FIG

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[7] [7]

Frequency-dependent 1H NMR relaxation rate R1(ω) of water at 298 K at a density of 0 .997 g cm−3 a) based on TIP4P/2005 model data as in Ref. 30,31 using D′ = 2 D0 with D0 = 2.30 × 10−9 m2 s−1 and b) employing refined structural parameters for dHH and ⟨r−3 HH⟩−1/3 either based on CCMD simulations or the experimental data of Soper 35 and Faux et al

work page 2005

[8] [8]

with ∆J n inter(ω) ≈ ttrZ 0 ∆Gn inter(t) cos(ωt) dt

Refined frequency dependent 1H NMR relaxation rate R1(ω) of water at 298 K at a density of 0 .997 g cm−3 computed using the intramolecular spectral densities J n intra(ω) obtained from CCMD scaled to match the experimental balance ofD0 ×τHH a) employing the refined structural parameters from CCMD and b) employing the refined structural parameters based on...

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