The article by Jeschke et al. discusses the dephasing mechanism in the bare and dressed state. It was a great read, and the article fits perfectly MR. While I have enjoyed it, I still have found it at times difficult to read. I have a few comments to mostly improve the readability of manuscript.

The dephasing models discussed are non-trivial, but the authors assume a familiarity with them. Although the spin system and Hamiltonian are thoroughly described, the text introduces the CCE model abruptly, assuming the APPA model is well-known to the reader. I suggest a minor revision to the theory section by briefly reintroducing the CCE model and providing a clearer explanation of Equation 17, without adding excessive detail. Including a figure to visually explain the pCCE approach would also be beneficial, especially since the criteria for determining cluster size are not clearly defined. Similarly, the APPA model could be reintroduced with a brief explanation, helping readers quickly grasp the distinctions between models. It would also be valuable to discuss the assumptions behind these models and how they may fail under certain conditions. Overall, I recommend adding a figure or table to summarize and compare the key aspects of the models for clarity.

L204: negelct -> neglect

Figure 7 is difficult hard to "read". I would either use lines for the theoretical model or various symbol shapes for the different theoretical models

L375: why where the simulations done in vacuum? A solvation model like COSMO may have improved the results and give more accurate tunnel splittings. More importantly, the basis is rather small which may induce errors. PBEh-3c would have been a better approach (yet fast) see 10.1002/anie.202205735 This would justify the scaling mentioned subsequently.

This paper is a significant milestone on the road to understanding spin decoherence in organic matrices with many protons and even methyl groups. Spin decoherence has a significant impact on many forms of magnetic resonance including pulse dipolar spectroscopies such as DEER and RIDME, pulse hyperfine spectroscopy like ENDOR, EPR-based quantum computing, and dynamic nuclear polarization, etc. Spin decoherence limits the ability to control and manipulate spins which directly impacts sensitivity and resolution in techniques that are used in many different fields. Being able to tune and control decoherence will make existing techniques more useful and can enable development of capabilities that do not exist at present.

This paper considers decoherence in a set of three trityl radicals with a range of potential decoherence routes in both proton-containing and deuterated matrices. Perhaps more significantly, it considers both the decoherence of 'bare' spins in the absence of a microwave field and of 'dressed' spins in the presence of a large resonant microwave field.

Decoherence of bare spins is simpler to treat. As the paper notes in more than one place, the different decoherence routes should be independent of each other, basically parallel kinetic pathways. When two pathways are operative in a sample, the decoherence should be the product of the decoherence of the individual paths. This expectation might be confirmed by the bare spin experiments summarized in Fig. 5. FTR has a rapid decoherence, almost entirely due to methyl group tunneling. That route is absent in OX063 and OX071 which have much slower decoherence dominated by matrix protons in the (H) samples. When the matrix proton route is removed by deuteration of the matrix, decoherence again slows to values dominated by the methylene groups in OX071 (D) or the hydroxy-ethyl groups in OX063 (D). Fig. 5 provides an excellent opportunity to demonstrate the multiplicativity of decoherence via the different kinetic pathways for decoherence of bare spins. It can be done by taking simple ratios of decays curves to get the contributions from different routes. Such a demonstration would emphasize the understanding of bare state decoherence and the difference between bare and dressed states.

Some readers may not expect solvent protons to have a larger effect on decoherence than protons on the radical in OX063 and OX071, but  Hyperfine interactions of narrow-line trityl radical with solvent molecules, J. Magn. Reson., 233 (2013) 29-36. https://doi.org/10.1016/j.jmr.2013.04.017 showed that the matrix protons in Finland trityl had hyperfine couplings and spin-flip satellite line intensities comparable to those of the radical protons, consistent with a significant role for matrix protons in decoherence. The detailed dynamics of the nuclear spins determines the relative impact of matrix or radical protons on decoherence for bare spins.

In the case of dressed states, the total decoherence is not the result of kinetic paths operating in parallel, but of a more complicated mechanism involving all possible routes without simple relationships between the decoherence of different samples. The unfortunate result is that you can't see if you predict or calculate decoherence from a single route without also correctly calculating decoherence from all routes. This seems to be illustrated in Fig. 6 where the seems to be little relation between decoherences of all of the samples and appears to reappear frequently in the rest of the paper. The rest of the paper is focused on identifying practical methods for numerically calculating decoherence. Some computational approaches clearly diverge and do not appear promising. However, no method clearly succeeds in predicting the kinetics and timescale of decoherence in a consistent manner. There are several mentions about 'cancellation of errors' and uncertain convergence. But this is not surprising at this stage of a complicated project and is related to one character of dressed spin decoherence: you can't correctly calculate the contribution to decoherence of one route until you can correctly calculate every route. 

This paper is missing a potentially important type of information relevant to the dressed spins. That is the details of the sample composition. These are not so important for the bare spins because each bare spin at this concentration undergoes decoherence independent of other spins. But in the dressed spin experiments, the dressed spins have essentially the same frequency and cross relaxation can occur more rapidly between the degenerate spins. Consequently, a small population of rapidly decohering spins can cause the entire population of spins to decohere at a faster rate. So, in future experiments, several aspects of the samples need to be carefully considered. Fortunately, most can be checked to see if they are significant and then ignored if they have no impact. Some of these aspects of the sample include:

⦁    Isotopic composition of the solvent. Exchange with humidity in the atmosphere by the hygroscopic glycerol/water can result in impactful amounts of protons in the deuterated solvent samples. Contaminating protons can be measured in the solvent by NMR. Whether it affects decoherence can be checked by intentionally spiking a deuterated sample to double or triple its concentration of protons.

⦁    Similarly, the isotopic purity of deuteration of the OX063 and OX071 was not noted. It is readily measured by high resolution mass spectrometry. Its relevance can be probed by adding a small amount of OX063 to a OX071 sample. Another test could be to exploit the convergent synthesis of the trityls to make a chimeric trityl with one OX063-like ring and two OX071-like rings.

⦁    Roughly 10% of the radicals have a C-13 in natural abundance having a hyperfine coupling comparable to twice the C-13 nuclear Zeeman frequency. This provides an opportunity for strong mixing of the electron and C-13 spin states (reminiscent of the 'matched pulse' for ESEEM). The matched pulse may offer a new route for decoherence of dressed spins and could operate in samples with contaminating protons whose nuclear Zeeman frequency is roughly half of the B1 field used to dress the spins.

⦁    In the absence of any protons, there must be some decoherence route. It may involve deuterons and their tunneling, or instantaneous diffusion, or the influence of random 'pairs' of radicals in the sample (or pairs formed with trace amounts of divalent metal ions), or dissolved molecular oxygen, or the very low-frequency phonon and vibrational modes contributing to the anomalous low-temperature properties of glassy matrices, or some other unexpected route.  Its magnitude could be checked by a perdeuterated version of OX061 in deuterated solvent.

However, these are considerations for future work building on the base reported here. I see little need to go back at this point and characterize samples that will likely not be used in future work. I do recommend that the multiplicative nature of bare spin decoherence and its lack for dressed spins, be exposed better by additions to Figs. 5 and 6 with an explanation in the text. A short table or graphic showing the relations and differences between the calculational methods would be extremely useful for readers who are not numerically inclined or that have not been following computational spin dynamics very carefully.

Minor Points:

⦁    Wouldn't the omega-dd in eq. 8 be time dependent from tunnelling if the protons were on different methyl groups?

⦁    The 2nd line in eq. 14 seems to have a + or - sign missing.

⦁    It would help to refer reader at line 220 back to where it was mentioned in the paper.