Prompt, um in der wissenschaftlichen Literatur Gegenbeispiele zur Universalität meiner Hypothese eines Interpretationsfehlers der CRESU-Ergebnisse zu finden. Ein Versuch, mir zu widersprechen und die Technik zu retten!

1. Counterexamples

The literal “no exception” claim is contradicted by the published literature. Particularly clear examples are the approximately temperature-independent CN + H₂S measurements at 11.7–45.5 K and the positive temperature dependence reported for N + CN. Their experimental references are, respectively, DOI 10.3847/1538-4357/ae421d and DOI 10.1073/pnas.1200017109.

Here, “flat” means no resolved temperature dependence within the experimental uncertainties, not proof that $dk/dT$ is exactly zero. An upper limit is a different category: it establishes limited reactivity under the measurement conditions, but does not establish a temperature derivative.

Search scope. I checked publisher records, PubMed/PMC, arXiv, author manuscripts, and NIST/KIDA records, using combinations of “CRESU,” “uniform supersonic,” “temperature independent,” “positive temperature dependence,” “upper limit,” “barrier,” and reaction-specific searches. This is a verified set of hits, not an exhaustive census. Access limitations are identified below.

All numerical bimolecular coefficients below are in cm³ molecule⁻¹ s⁻¹.

1A. N + CN → N₂ + C: decreases on cooling

Reference: J. Daranlot, U. Hincelin, A. Bergeat, M. Costes, J.-C. Loison, V. Wakelam and K. M. Hickson, 2012, PNAS, “Elemental nitrogen partitioning in dense interstellar clouds.” DOI: 10.1073/pnas.1200017109. Read: full text.

Facts read: Measurements cover 56–296 K, including Laval-nozzle measurements at 56, 87, 152 and 169 K. The authors report approximately $9\times10^{-11}$ at 296 K and $5\times10^{-11}$ at 56 K, with the fit

Thus the reported fitted dependence is positive in temperature, meaning slower on cooling. These are relative-rate measurements using N + OH as reference. The paper’s 10 K value is an extrapolation, not a measurement.

Barrier status: An associated quantum-capture calculation reproduces the positive temperature dependence: J. Ma, H. Guo and R. Dawes, 2012, PCCP, DOI: 10.1039/C2CP41621B. Not read, abstract only. I would not infer a positive entrance barrier merely from the positive temperature exponent.

Qualification: The exponent is fitted across 56–296 K; it should not be presented as an independently measured local derivative throughout 10–100 K.

1B. O(³P) + OH → O₂ + H: approximately flat

Reference: D. Carty, A. Goddard, S. P. K. Köhler, I. R. Sims and I. W. M. Smith, 2006, Journal of Physical Chemistry A, “Kinetics of the radical–radical reaction … at temperatures down to 39 K.” DOI: 10.1021/jp054429u. Not read, abstract only.

Facts read in the abstract: CRESU measurements over 39–142 K give approximately

with little temperature variation and no observed pressure dependence. This directly qualifies as an experimentally approximately flat case.

Barrier status: I did not verify a numerical barrier height from the original paper. Its abstract does not provide one; I therefore do not assign one here.

1C. N + OH → NO + H: approximately flat

Reference: J. Daranlot et al., 2011, Science, “Revealing atom-radical reactivity at low temperature through the N + OH reaction.” DOI: 10.1126/science.1213789. Not read, abstract only.

Facts: The original abstract describes a barrierless reaction investigated using a Laval-nozzle apparatus. The authors’ subsequent account reports approximately constant experimental coefficients over 56–296 K, around $4.5\times10^{-11}$. That account is A. Bergeat, J. Daranlot, K. M. Hickson and M. Costes, 2012, EAS Publications Series, DOI: 10.1051/eas/1258046. Read: full account, including the experimental figure.

Interpretation: This is another flat measured dependence, including measurements below 100 K—not evidence that its rate must remain constant at still lower, unmeasured temperatures.

1D. CN + H₂S: approximately flat entirely below 50 K

Reference: M. Antiñolo, F. Martínez, D. González, A. Lema-Saavedra, E. Martínez-Núñez, A. Fernández-Ramos, M. Agúndez, J. Cernicharo and E. Jiménez, 2026, Astrophysical Journal, “Revealing that the Gas-phase Reaction of CN with H₂S Can Be a Source of HSCN in Interstellar Molecular Clouds.” DOI: 10.3847/1538-4357/ae421d. Read: author-posted full text.

Facts read: Pulsed-CRESU/PLP-LIF measurements cover 11.7–45.5 K. The authors report negligible temperature dependence, with coefficients around $4\times10^{-10}$. For example:

Their calculations predict a weak inverse temperature dependence, but the experimental results are described as nearly temperature-independent.

Barrier status: The calculated dominant pathway has submerged transition states, not a positive activation barrier above the separated reactants. HSCN + H is the theoretically assigned dominant product channel; the kinetic measurement follows CN removal.

Inference: This is an especially relevant counterexample because the entire measured interval lies well below 100 K and involves a radical plus a stable molecule.

1E. F + H₂ → HF + H: a low-temperature plateau despite a barrier

Reference: M. Tizniti, S. D. Le Picard, F. Lique, C. Berteloite, A. Canosa, M. H. Alexander and I. R. Sims, 2014, Nature Chemistry, “The rate of the F + H₂ reaction at very low temperatures.” DOI: 10.1038/nchem.1835. Read: author-posted paper and supplementary material.

Facts read: For normal H₂, the CRESU measurements give

These are consistent with a plateau, not a resolved low-temperature acceleration. The reaction has a positive barrier of roughly $E/R\sim800$ K, or 6.6 kJ mol⁻¹. Quantum calculations describe the low-temperature behaviour.

Important qualifications: The paper’s 77 and 295 K measurements used subsonic flow, so the large decrease between 77 and 20 K is not an exclusively CRESU temperature series. Also, these measurements concern normal H₂, with its approximately 3:1 ortho:para mixture, not equilibrium rotational populations at 11 K.

1F. CN + C₂H₂ and CN + C₂H₄: reported turnover below approximately 44 K

Reference: I. R. Sims, J.-L. Queffelec, D. Travers, B. R. Rowe, L. B. Herbert, J. Karthäuser and I. W. M. Smith, 1993, Chemical Physics Letters, “Rate constants for the reactions of CN with hydrocarbons at low and ultra-low temperatures.” DOI: 10.1016/0009-2614(93)87091-G. Not read, abstract only.

Facts read in the abstract: For both acetylene and ethylene, the coefficients increase between ambient temperature and approximately 44 K, but the coefficients at 25 K are lower than at 44 K. These therefore constitute reported low-temperature turnovers rather than monotonic increases on cooling.

Unknown: Without the full numerical tables and uncertainties, I cannot establish the statistical significance of either turnover. I also did not verify a barrier height from this paper. These are qualified counterexamples, not the principal basis for rejecting the universal claim.

1G. NH₂ + H₂CO: too slow to measure at 34 K

Reference: K. M. Douglas, D. Lucas, C. Walsh, N. A. West, M. A. Blitz and D. E. Heard, 2022, Astrophysical Journal Letters, “The gas-phase reaction of NH₂ with formaldehyde (CH₂O) is not a source of formamide (NH₂CHO) in interstellar environments.” DOI: 10.3847/2041-8213/ac8cef. Read: accepted paper and supplementary material.

Facts read: Pulsed uniform-supersonic-flow measurements at 34 K establish only

The accompanying calculations give approximately $6.2\times10^{-14}$ at 35 K, consistent with that experimental upper limit but not experimentally validated by it. The reported zero-point-corrected barriers include 18.35 kJ mol⁻¹ for the addition pathway toward formamide and 23.14 kJ mol⁻¹ for hydrogen abstraction, relative to separated reactants.

Interpretation: This meets your category (c). It does not establish that $k$ decreases on cooling: only one low-temperature upper limit was obtained.

2. Barrier test

First distinguish a positive barrier from a theory–experiment contradiction

For this test, I use a positive barrier to mean

not merely a transition state above a deep intermediate well.

The verified examples below involve formation of a prereactive complex followed by passage through a positive barrier toward products. They should not automatically be described as having a barrier to the initial capture step. This distinction is explicit in the methanol and carbon–water reaction mechanisms. DOIs: 10.1038/nchem.1692; 10.1021/acs.jpclett.6b01637.

2A. OH + CH₃OH: positive product-forming barriers and a low-T increase

Theoretical barrier reference: S. Xu and M.-C. Lin, 2007, Proceedings of the Combustion Institute, “Theoretical study on the kinetics for OH reactions with CH₃OH and C₂H₅OH.” DOI: 10.1016/j.proci.2006.07.132. Not read, abstract only.

Barrier heights verified in the experimental paper’s discussion of that potential: approximately 4.2 kJ mol⁻¹ for formation of CH₂OH + H₂O and 15.0 kJ mol⁻¹ for CH₃O + H₂O, above separated reactants. The experimental paper is R. J. Shannon, M. A. Blitz, A. Goddard and D. E. Heard, 2013, Nature Chemistry, DOI: 10.1038/nchem.1692. Read: full author manuscript. Its new CRESU points were at 63 and 82 K; the reported coefficient at 63 K is 72 times that at 210 K. Methoxy formation was also observed directly.

Independent lower-temperature measurements: M. Antiñolo et al., 2016, Astrophysical Journal, DOI: 10.3847/0004-637X/823/1/25. Read: full text. Two CRESU apparatuses gave, over 22–64 K,

This directly establishes an inverse measured dependence below 100 K.

How large is the actual theoretical disagreement? A later calculation is L. G. Gao, J. Zheng, A. Fernández-Ramos, D. G. Truhlar and X. Xu, 2018, JACS, DOI: 10.1021/jacs.7b12773. Not read, abstract only. Its low-pressure predictions and their discrepancy with experiment are reproduced and analysed by N. Balucani et al., 2024, MNRAS, DOI: 10.1093/mnras/stae232. Read: full text. Both experiment and this quantum treatment show low-temperature acceleration; the major disagreement concerns magnitude and pressure-dependent interpretation.

My calculation from the published fits: At 50 K, the experimental fit gives $2.16\times10^{-11}$. Summing the two product-channel fits tabulated for Gao’s low-pressure theory gives $4.49\times10^{-13}$, a difference of approximately 48-fold. Comparing only methoxy formation gives approximately 77-fold, but that requires treating the measured OH loss as methoxy formation. These are comparisons of fitted expressions, not individual experimental points. DOIs: 10.3847/0004-637X/823/1/25; 10.1093/mnras/stae232.

Inference: This is strong evidence against naïve classical Arrhenius extrapolation. However, a CRESU coefficient versus a zero-pressure calculation is not a matched-pressure test, and a positive barrier plus increasing $k$ is not by itself a contradiction of quantum reaction theory.

2B. C(³P) + H₂O and C(³P) + D₂O: substantial positive barriers

Reference for both theory and experiment: K. M. Hickson, J.-C. Loison, D. Nuñez-Reyes and R. Méreau, 2016, Journal of Physical Chemistry Letters, “Quantum Tunneling Enhancement of the C + H₂O and C + D₂O Reactions at Low Temperature.” DOI: 10.1021/acs.jpclett.6b01637. Read: full paper and supplementary material.

Facts read: The calculated zero-point-corrected barriers are +32.9 kJ mol⁻¹ for H₂O and +35.1 kJ mol⁻¹ for D₂O. For H₂O, measured C-atom removal increases from

to

D₂O likewise shows increasing removal on cooling.

Size of disagreement: The initial master-equation treatment predicted negligible bimolecular product formation. Reproducing the observations required substantial adjustment, including approximately halving the barrier width. Thus the final fit was not an unadjusted ab initio prediction. I did not extract a defensible single multiplicative discrepancy for the original product-rate prediction; “negligible” is not a numerical denominator.

Conclusion of the barrier test: Positive-barrier reactions with low-temperature acceleration are verified. A stricter example involving a demonstrated barrier to initial capture itself, rather than an above-asymptote inner barrier, was not verified in this search.

3. Selection bias

What can be quantified?

Historical fact: Sabbah et al. describe the preceding low-temperature literature as comprising approximately 45 neutral–neutral reactions, all fast at room temperature, with $k(298\,\mathrm K)\gtrsim10^{-11}$. Reference: H. Sabbah, L. Biennier, I. R. Sims, Y. Georgievskii, S. J. Klippenstein and I. W. M. Smith, 2007, Science, “Understanding Reactivity at Very Low Temperatures: The Reactions of Oxygen Atoms with Alkenes.” DOI: 10.1126/science.1142373. Read: opening page/introduction; remaining paper not read, abstract only.

Inference: For that historical sample, a concrete selection proxy is approximately 45/45—essentially 100%—already fast at room temperature. But that is not equivalent to “45/45 have rigorously established barrierless potential-energy surfaces.”

Unknown: I found no verified, current reaction-by-reaction census that provides the requested fraction of all CRESU-studied reactions divided into barrierless/capture-type and barrier-limited classes. I therefore cannot justify a percentage such as “90% barrierless.”

Why the method favours fast reactions

Fact read: Fournier, Le Picard and Sims discuss a typical accessible lower rate scale around $10^{-12}$ for conventional dilute-coreactant measurements, with sensitivity approaching $10^{-14}$ when the reactant can constitute the bath gas, as in H₂ experiments. Reference: “Low-temperature Chemistry in Uniform Supersonic Flows,” RSC book chapter, online 2017, DOI: 10.1039/9781782626800-00001. Read. These are method-dependent scales, not universal detection limits.

Illustrative calculation, not a reported measurement: Under pseudo-first-order conditions,

Taking $[B]=10^{15}\,\mathrm{cm^{-3}}$ and $t=200\,\mu\mathrm{s}$ as an illustrative operating point gives approximately 18% reaction for $k=10^{-12}$, but only 0.2% for $k=10^{-14}$. Distinguishing the latter from other losses is plainly harder.

A concrete additional restriction: In the NH₂ + formaldehyde study, increasing formaldehyde concentration was limited by clustering, and the published result remained an upper limit. Thus simply increasing $[B]$ is not an unrestricted solution. DOI: 10.3847/2041-8213/ac8cef.

Is “no exception” mostly a selection effect?

My assessment: Strong selection toward readily measurable reactions is documented, and it plausibly contributes substantially to the prominence of fast, complex-forming chemistry. But three separate propositions must not be collapsed:

First, the historical sample was strongly selected toward fast reactions; that is documented by Sabbah et al. Second, “only fast reactions are studied” is too strong: the F + H₂ measurements and NH₂ + formaldehyde upper limit demonstrate otherwise. Third, selection cannot rescue “no exception,” because published flat and positive-temperature-dependence results exist. DOIs: 10.1126/science.1142373; 10.1038/nchem.1835; 10.3847/2041-8213/ac8cef.

For a quantitative modern fraction, the denominator would need to distinguish unique reactant pairs, isotopologues, measured temperature intervals, failed measurements, and pressure-dependent association versus product formation. A compilation of recommended $k(T)$ expressions alone would not answer that question. For example, the N + CN paper explicitly distinguishes its measured 56–296 K interval from its extrapolated 10 K recommendation. DOI: 10.1073/pnas.1200017109.

5. Steelman the opposite: three strong physical arguments

You supplied one explicit claim, not four separately formulated claims. I therefore cannot accurately map these arguments onto “your four claims.” Instead, I identify the inference each argument challenges, without attributing that inference to you.

Argument 1: Tunnelling permits reaction below a positive barrier

Specialist’s argument: A positive potential-energy barrier does not require a vanishing rate when $k_{\mathrm B}T$ falls below its height. The carbon–water study provides more than reactant disappearance: H/D products were detected, while the modelling also identified a contribution from complex stabilization. DOI: 10.1021/acs.jpclett.6b01637.

What this undermines: The inference “theory predicts a positive barrier, therefore substantial low-temperature chemistry is necessarily unphysical.”

What it does not establish: Tunnelling does not require every rate coefficient to increase on cooling. F + H₂ supplies an experimentally relevant low-temperature plateau. DOI: 10.1038/nchem.1835.

Argument 2: Prereactive-complex kinetics can reverse the apparent temperature dependence

Specialist’s argument: The measured reaction rate need not be controlled by one isolated barrier-crossing event. In a minimal kinetic model,

the effective product coefficient is approximately

This equation is a schematic steady-state derivation: a lower redissociation rate can increase the probability of reaction per captured encounter without removing the positive inner barrier. Complex-assisted tunnelling is the mechanism advanced for OH + methanol. DOI: 10.1038/nchem.1692.

An important experimental distinction: CN + CH₃CN exhibits strongly increasing low-temperature removal and pressure dependence interpreted through competition between reaction and complex formation. Reference: C. Sleiman, S. González, S. J. Klippenstein, D. Talbi, G. El Dib and A. Canosa, 2016, PCCP, DOI: 10.1039/C6CP01982J. Not read, abstract only. The study spans 23–354 K; the abstract reports a 130-fold increase between 168 and 123 K. I did not verify a positive barrier height, so I do not count it as a strict barrier-test hit.

What this undermines: The inference “negative apparent activation energy contradicts an above-asymptote product-forming barrier.”

What it also warns against: A coefficient obtained from reactant removal can include stabilized association. It need not equal the zero-pressure coefficient for a particular product channel.

Argument 3: Capture dynamics can produce a physical inverse dependence—but do not require one

Specialist’s argument: Entrance-channel capture is a dynamical process, not necessarily a temperature-independent collision frequency. Quantitative capture/statistical theories can reproduce low-temperature behaviour, as illustrated by the oxygen–alkene study and the N + CN quantum-capture calculation. DOIs: 10.1126/science.1142373; 10.1039/C2CP41621B. Access statuses are given above.

Illustrative derivation: For ideal classical capture on an isotropic attractive potential $V(R)=-C_n/R^n$,

Thus the model yields $T^{-1/6}$ for $n=3$, but $T^{+1/6}$ for $n=6$. This is a model calculation, not a fit to the reactions listed here.

What this undermines: The inference “an inverse temperature dependence must be an experimental artifact.”

What it does not establish: “Barrierless” does not imply “increases on cooling.” Indeed, capture theory’s ability to accommodate different signs makes it an argument against universality, not for it.

Overall inference: The literature supports physical low-temperature acceleration in particular systems, including systems with positive product-forming barriers. It does not support a universal sign for $dk/dT$, nor does the present search support a numerical allocation of the observed prevalence between reaction-selection bias and underlying dynamics.

Final evidence table

“Flat” below means experimentally unresolved or negligible temperature dependence. The table includes both counterexamples and the increasing-rate systems examined in the barrier/mechanism tests.