This is a very nice report continuing the interesting research line of long-lived states in chains of CH2 groups, initiated recently by this group. The authors explore the relaxivities of LLS in a variety of CH2 groups, and also different LLS groups within the same molecule, with respect to the common DNP agent TEMPOL. The paper is well-reasoned and well-presented and is highly suitable for publication.

I have a few minor comments:

The introduction on page 1 is slightly misworded, in my view. The singlet-triplet population imbalance for spin-1/2 pairs, also known as singlet order, is just one special case of a long-lived state. Singlet order is indeed immune to intramolecular dipole-dipole relaxation. but that is not necessarily the case for more complex LLS, including some of the ones discussed later on in the paper.

on page 2 it is stated that fast proton relaxation is the reason for d-DNP being performed mainly on 13C and 15N nuclei: This is true in part, but an even more important reason, in some contexts, is the interference from strong proton background signals.

Presumably the buffer solution is aqueous. This should be stated, and if possible, the precise composition of the buffer should be given.

In Fig.3 the signals are presumably normalized such that “100%” is the first point in the decay. This should be stated.

The statement that PRE is less effective for ZQCs than other coherences is usually true, but at least in principle, anti-correlation of the fluctuating fields could cause the opposite relationship. 

In common with numerous others, the paper confuses “rates” (which become smaller as a process approaches equilibrium) with “rate constants” which (as the name implies) are time-independent for an exponential decay. So most of the reported “rates” in the paper are actually “rate constants”. 

The discussion on the long-lived states in chains of three CH2 groups is particularly interesting. I much appreciated Figure 6. 

As the authors state, a random-field model may be used to relate the rate constant of singlet order relaxation to the correlation factor for fluctuating random fields at the two nuclear sites. I wonder what the corresponding expressions would be for the “delocalised” long-lived states explored by the authors. Many pairs of correlated fields could be involved. Are such rate constants dominated by the “least correlated pair” of fluctuating random fields?

This is very interesting work, presenting the surprising results that delocalized long lived states can be longer lived than T1 by factors of 3-5 in systems with paramagnetic interactions. The context is DNP, where radicals would typically be present, and hence these findings can be of practical use as well. The insights gained with respect to the sizes of the paramagnetic agents and the simulations of Fig. 6 are particularly useful. 

Here are my minor comments:

(1) The text refers to single, double, and triple SLIC sequences. Perhaps this requires a minor clarification: do you mean single, double, and triple frequency irradiation? One could also read this as several cycles of SLIC pulses. 

(2) It would seem suitable to cite our recent work on paramagnetic relaxation (and other mechanisms) of singlet order by experiment and MD simulations: Kharkov et al,  Phys. Chem. Chem. Phys., 2022, 24, 7531-7538, https://pubs.rsc.org/en/content/articlehtml/2022/cp/d1cp05537b?casa_token=gMiUwO-MKY0AAAAA:N3Uh0TjOIoCxkD6BfVIFo1NoabXKCWK6mVqq5XN_G5F_ntohz0qsuLv0LAxW4veolRTxIBzBN0DLATE

Razanahoera et al. present the results of experimental investigations into long-lived nuclear spin states (LLSs) excited in delocalized pairs of protons, i.e., CH₂ groups, of several molecules and within the chain of the same molecule. The context of their exploration was relaxivity from the common ¹H d-DNP agent TEMPO dissolved in solution at typical post-dissolution radical concentrations. The manuscript is well-written, well-thought out and contains clear figures. The work is interesting and suitable for publication after minor corrections.

Major comments:

1/ The authors frequently refer to relaxation rates and relaxation times. However, this is not what is gleamed from the experimental results. These are relaxation rate constants and relaxation time constants. This is especially true in this case since mono-exponential decay curves are observed. This comment was also pointed out by Reviewer 1 and should be corrected throughout the manuscript.

2/ In the abstract, the authors note that “…the yield of conversion of observable magnetization into LLS and back are on the order of 10% or less…”. This is likely quite an unfair lower bound to use as motivation. Typically, 30-45% of the 2/3 theoretical maximum can be achieved with such a rf-pulse sequence. Furthermore, the contribution to signal is given, whilst the conversion yield vs. observable magnetization is not. A typical value should be quoted in the manuscript.

3/ There are a number of important works from the LLS community that are not cited.

Ratio of T_LLS/T₁:

Angew. Chem. 2015, 127, 3811-3814.

J. Am. Chem. Soc. 2012, 134, 17494-17497.

T₀₀ Filter:

J. Am. Chem. Soc. 2013, 135, 2120-2123.

These should be incorporated into the manuscript.

Minor comments:

1/ The authors mention that LLSs in homonuclear spin-1/2 pairs are immune to intra-pair dipole-dipole interactions. It is more likely to be correct to say intra-pair dipole-dipole relaxation.

2/ Were the samples degassed? Would the results differ significantly is the samples were degassed?

3/ In Table 1, the ratios of the relaxation rate/time constants would also be nice to see.

4/ It would be nice to know the number of scans used for experiments.

5/ “reconversion” is incorrectly spelt in the caption of Table 1.

6/ “relaxation ” is incorrectly spelt in the short summary.