In this article, the authors analyse the ih-RIDME experiment and the conditions under which it can be utilised to determine proton concentrations or density.

The work introduces the core concepts of ih-RIDME, outlines various scenarios where it is applicable, and evaluates the reliability of the fitting procedure. Additionally, the authors discuss the selection of appropriate pulse sequences.

The study is well-executed and sufficiently novel to merit publication in MR. That said, I do have some recommendations. Firstly, the article is rather lengthy and complex, which makes the key findings difficult to discern and may confuse readers who are not experts in the field.

The derivation of the equations is particularly challenging to follow. Considering the simplicity of the final model after all the simplifications, it might be better to include these derivations as an annex. Furthermore, the multiple geometries explored in the study are ultimately not employed in the analysis and therefore appear somewhat irrelevant to the article's main focus. Simplifying these aspects would enhance readability without undermining the significance of the derivations.

L40-42: do you have a reference?

L44: “way stronger” could be replaced by significantly stronger?

The relation between equation 9 and 10 is not obvious, as you only extract a difference in sigma in eq. 10

If the derivation is kept, could you expand and give an example of the derivation of 10?

It is also unclear how eq 13 is obtained.

What does the sentence “R instead of V to emphasize that a simplified model” (L 174) brings to the reader? V is nowhere mentioned previously.

Derivation of R and Gamma is nowhere straightforward, which is why I would either expand or keep the derivation in the annex.

Is a “numerical experiment” commonly referred as a simulation? (L239)

In figure 9(b), the 1.55 nm is difficult to visualise

As a matter of preference, it is worth noting that spin diffusion is not completely blocked (L34); if it were, DNP would not be possible. Several recent DNP studies have demonstrated that spin diffusion remains active, albeit likely slower. For instance, see Pang et al. (10.26434/chemrxiv-2024-zr8zv) or Stern et al. (10.1126/sciadv.abf5735). I would strongly recommend including these findings in your revised manuscript, along with the consideration that spin diffusion may depend on factors such as temperature and electron relaxation times.

ih-RIDME: a pulse EPR experiment to probe the heterogeneous nuclear environment

Sergei Kuzin, Victoriya N. Syryamina, Mian Qi, Moritz Fischer, Miriam Hülsmann, Adelheid Godt, Gunnar Jeschke, and Maxim Yulikov

This manuscript discusses and evaluates the use of the RIDME pulse EPR method for investigating anisotropic proton distributions around electron spins. ih-RIDME is a relatively new and interesting concept that opens new application fields A comprehensive discussion will clearly help dissemination and uptake by the community. There are a few points that might make the manuscript more accessible and open it to a wider readership.

Major points

1. This work clearly builds on and extends prior work by Kuzin and Yulikov. However, the way the current manuscript is written and the general lack of referencing of prior concepts makes it difficult to follow what exactly is new in this manuscript and what is reproduced from earlier work to provide the relevant context to the reader. It would help if a revised version clearly delineated concepts taken from earlier work and what has been newly derived here. The current manuscript meanders between a tutorial and original research results.
2. The purpose of the derivation of eqs 10-12 seems to not be expressed very clearly. The variance of the hyperfine spectrum will depend on the blocking radius more steeply in lower dimensional distributions. However, lower dimensional proton distributions bring fewer protons close to the electron spin effectively reducing the local concentration. How do these tow factors influence the sensitivity of ih-RIDME. Can this sensitivity be defined in a way that is unambiguous with respect to SNR?
3. The theoretical background section does not exhaust the description of all approximations made and all definitions of terms used (e.g., magic angle). The discussion, that looks more like a results and discussion section, starts with an approximation that is not explicitly stated. The accessibility of the manuscript for a wider readership would be helped if all terms are defined clearly, different use of variables clearly stated, and approximations are clearly defined or referenced.
4. The ih-RIDME data that is shown in SI2 is concerning. All traces have a sharp modulation feature around zero time that does not eliminate upon reference division. It grows with mixing time and thus appears to be a PDS signal. Indeed, looking at the synthesis of 1 the final step is a Sonogashira-Hagihara reaction. If significant Glaser reaction product from H-EP_R4-NO is formed, it is not clear how this can be separated or identified. While the collaborative nature of this work is appreciated, it would have been more appropriate to have the synthesis refereed in a journal with some synthetic chemistry scope. Figure S4.3 shows a modulation that would fit the biradical from a homocoupling of H-EP_R4-NO. There is no proof of purity provided for 1 and it seems no alternative experiment such as an NO-NO DEER has been performed to identify the source of this unexpected signal that does not eliminate with division. How would the proton distribution in this biradical look? Different but anisotropic. In this case, what is the analytical value of the experiments presented here if such a prominent impurity (modulation depth 10-15%) has no effect on the data analysis?
5. To reassure readers about point 4, chromatograms from the purification of 1 and mass spectra could have been shown. The Glaser reaction of H-EP_R4-NO could have been performed as a reference for identifing the unassigned modulation of the ih-RIDME and show the retention of this biradical in the chromatogram of 1. In Scheme S-1 two different chemical entities are assigned 1. The first 1 in the last row should be corrected to 14.
6. For consistency ether SNR or RNS should be used That monomodal distributions are only recovered for SNR 50 and above is a point that must be emphasised when discussing Fig 6. It means that ih-RIDME requires a set of ~5+ traces with an SNR greater 50 making this an experiment that requires substantial instrument time.
7. The manuscript revolves around anisotropic proton distributions and in the end a distribution is compared to a model. It is unclear how sensitive this is as there are justifiable doubts that the ih-RIDME signal only arises from what is to be believed 1. Nevertheless, there seems to be no experimental extraction of any anisotropy. Distributions in sigma were extracted earlier and it is unclear what the advance made here really is. This should have been stated explicitly.

Minor points

L18 “’long-range structure’ determination” – EPR has too low resolution to determine structures in the classic NMR, crystallography or microscopy sense.

L21 When citing 3 references for 19 F ENDOR I wonder why the seminal paper that invigorated this field has not been included (https://doi.org/10.1002/anie.201908584).

L28 “exchange interaction” in NMR terminology this would be J-coupling, spin-spin coupling or indirect dipole–dipole coupling.

L33 “Blocked by the gradient of the electron’s magnetic field” The respective protons are hyperfine shifted away from the matrix peak. This does not require a gradient. 

L27-56 review some concepts behind proton spin diffusion/electron spectral diffusion but only cite two references by Kuzin et al. There has been significant work around these concepts prior to these references and this should be appropriately referenced.

When discussing the CP2 sequence (L76) this needs more detail about the sample and solvent protonation as well as pulse sequence timings. As written, this seems to suggest all possible CP2 and RIDME comparisons will look like the curves in Fig. 1c.

When trace division is introduced, there should be appropriate referencing. https://doi.org/10.1021/acs.jpcb.5b02118 has shown this convincingly but earlier work by Astashkin and Savitsky proposed this as well.

Fig S4.3 sample 2 lower has 6 curves with only 5 legend entries. The change in colour between figures is an unfortunate choice that makes this  unnecessarily difficult to follow. Sample 3 seems to have a clipped echo at t = 0, this should have been checked.

There should be one acronym used in the manuscript and if this is to be HYSDEMON the question arises if there is any (resolved) modulation expected?