With this article Pelupessy continues his interesting and insightful explorations of long-range dipolar field effects in the context of solution-NMR pulse sequences. Following up from his recent work on isotropic-mixing-style pulse sequences, Pelupessy now explores the possibility of compensating for arbitrary magnetic field inhomogeneities by exploiting long-range zero-quantum coherences involving the solvent nuclei, and explores more complex pulse sequences involving double-quantum effects, etc. 

Pelupessy has opened an interesting new(ish) direction for NMR methodology, which will be of interest for many NMR spectroscopists, and I recommend the article for publication in Magnetic Resonance. However, the article could be improved in some ways, as follows:

* the wording is sometimes rather obscure. For example, in the abstract, we read: “the dipolar field can be decomposed into two components, each at the helm of its own transfer”. This sounds rather fine, but I have really no idea what it means. Can this be reworded in a more meaningful way, even if less euphonious?

* Equations (1) and (2) and the neighbouring text underpin this work, but they are discussed very briefly indeed. Take, for example “a PFG oriented at an angle..” - the spatial variation and field direction should be specified more carefully and rigorously.  It is well-known that the distant dipolar field is non-local in nature, so that the field at a certain point depends on the magnetization of points which can be anywhere in the sample and distant from the point of interest. So the equations which are used here, which are stated to be “local”, rely on some very particular circumstances and approximations. This should be made explicit. 

* On page 4 it is stated that only two-spin operators are needed. Why is this?

* The figures are quite poor. The spectra are too small and crowded, the spectra are unassigned, and often have no scale. With very careful reading of the caption and text, I could figure out what is what, but the reader should really not have to go to such trouble. The worst one is probably figure 3. It took me about 6 readings to figure out what all three spectra in pane (e) are. I challenge a reader to do it in less, starting cold. I recommend that the figures are made much larger, and the captions made much clearer, explaining each entry in linear sequence, with all individual spectra clearly labelled, and explained in the caption, with no ambiguity and digression - on the lines of (a, top spectrum): xxx; (a, middle spectrum): yyy, etc. etc. 

* The difficult last section of the paper describing the variations in fig.6 is undoubtedly interesting but I struggled to see the point of it, except to display the impressive agreement between experiment and calculation in a complicated case. Maybe the author can make the motivation more obvious. If not, I think one should consider dropping this section. 

*There are a few minor typos such as “undistinguishable” which should be “indistinguishable” (for no particular reason, but that’s the way it is).

This manuscript presents generally interesting results on dipolar field effects, using somewhat different pulse sequences than have been explored in the past.  Its value comes from the conscious use of the quantum formalism, where dipolar couplings are explicitly invoked along with higher order terms in the equilibrium density matrix, to give insight into pulse sequence evolution.  It is clearly publishable, but it needs some significant polishing.

1.  The classical manifestation of these effects has more commonly been referred to as the distant dipolar field (DDF) as it is the portion of the solution dipolar couplings that is not eliminated by diffusion on an NMR timescale.  That notation, agreed upon by the groups working in this field about two decades ago, is a compromise that does homage to the still-older but more confusing "dipolar demagnetizing field" in the earliest papers.  I would encourage that language instead of "dipolar field" which is baffling to people who are not familiar with these problems.

2.  It is extremely difficult to tell what in this paper is new.  As far as I can tell, the novelty comes from using sequences that are a bit different than what has been explored, including prior work by the author.  For example, coherence transfer had been shown in many other contexts, as has compensation for inhomogeneous broadening.  Much of what is here is simply a rehash of mathematical formalism that is now decades old, and while I don't think that needs to be deleted, a much clearer delineation is needed.  The abstract and the introduction need to be much more focused on separating out what is new.

3.  The figures in general are not of sufficient quality or clarity.

Referee comment

General comments

This is a very interesting manuscript introducing new ideas for 2D NMR methods exploiting intermolecular coherent transfer of magnetization in concert with other building blocks from the liquid state NMR toolbox. The key component of the new pulse sequences is exploitation of intermolecular coherence transfer exploiting dipolar fields under spin lock or (isotropic) mixing conditions.

The most prominent and practically important achievement described is broadband in-phase INTERmolecular transfer achieving high-resolution spectra in inhomogeneous B0 fields, in particular transfer of coherence from the abundant solvent spins to the solute.

The equations appear flawless and the quoted references are highly adequate. Some definitions/assumptions, most prominently though maybe trivially, that the context is spin ½ systems only, need to be stated more clearly. I have a few suggestions concerning the figures, as specified below. As I think the scientific core of the paper is outstanding, I have made a few more detailed suggestion for refinments.

The text and presentation would benefit from improvements with respect to clarity and maybe a more concise title would be in order. The appendix might be moved to the supplementary information.

Overall the structure of the manuscript wrt. to the purpose and motivation of the new experiments introduced should be improved. In the current state it is a relatively lose concatenation of experiments related by their reliance on dipolar field effects. There should also be some justification for the choice of the sample.

The Conclusion Section is a bit terse. The benefits and insights provided by the new experiments should be elaborated there. Is there a  perspective potential future applications or extensions (multiple abundant spins, hyper-polarized systems)?

Recommendation: accept after a major revision.

Specific comments

There are a few sentences with a meaning, which is difficult to understand, due to unusual use of terms. These should be clarified, maybe with a native English speaker (I’m not one myself).

In the abstract, the sentence “In these schemes, the dipolar field can be decomposed into two components, each at the helm of its own transfer.“ is obscure in its meaning.

p.2.l.34: “PFG” is maybe not suitable in this context, “field gradient” might be appropriate here, but are there any assumptions about the field gradient (it appears a linear field gradient is assumed n Eq. 1 and throughout the paper)

p.2.l.36: “and S” the S spins are not involved at that point

p.2. Eq. (2) As the usage of symbols deviates from the cited literature, it might be in order to discuss the relation to previous work more thoroughly. The choice of the symbol ω for both the offset and the rf field strength, while justifiable, is not increasing readability.

p.2. l.47:  the bold symbol m^S is not formally introduced, apparently a vector of magnetization (but is it normalized as well?).

p.3. li.54: eq. A6 should be moved to the main text for reading convenience as it is referred to frequently.

p.3.li55: how (using which program? Probably the one in the supplement, but it isn’t mentioned in the main text) were the simulations made, information for reproducing those simulations should be included

p.3.: Results using WALTZ-16 are mentioned but no data are shown.

p.4.li72:”more laborious simulations“ – simulations should be described more specifically.

p.4: In Section 3 Experiments, a clear structure is missing. I suggest to move the more theoretical discussion up to li. 96 into the Theory Section, and start Section 3 with an overview of tall he experiments used in the paper.

p.4: A more fundamental issue occurs with eq. (4), considering that eq. (3) clearly allows for terms with more than two spin operators. What justifies the restriction to two-spin operators?

p.4.li94: “timescale in which RD occurs can be more than an order 95 of magnitude shorter“ please provide a reference/justification

p.5.Fig.2: The coherence pathway shows the selection of only one coherence during the evolution time. TPPI is designed to allow for +1 and -1 coherence orders during t1, which contradicts the gradient selection scheme shown. This point requires clarification. Does the mixing sequence really only convert -1 to +1 coherence orders? One would assume there must be parallel pathways.

The choice of using indices 1,2,3 for the orthogonal gradients instead of x,y,z is unusual.

p.5.li.100: Does watergate really ensure in-phase spectra?

p.6: Is the  concept of a sliding window in the t2 dimension new?

p.6: The benefits of the spectra obtained by this new pulse sequence are shown but not discussed. It should be clearly pointed out what novel advantages are  achieved, also for a non-expert reader, and which limitations exist. Why were particular sections chosen in Fig. 3?

p.7: Section 3.2

Some introductory sentences justifying the design of the new pulse sequences might be in order. In this reviewer’s opinion, this is the most interesting aspect of this paper. Maybe state first, what the pulse sequences have been designed for.

The first § of this section contains a logical jump. “The commutator of the lowest order term“ what does this refer to?

Maybe the sentence just needs to be rearranged to have eq. 4 upfront?

Definitions seem to be missing for r, p, q

p.8: Fig. 4. The presentation of the pulse sequences (actually all pulse sequences in the paper) should be improved by including delay labels and following more usual visual clues for 90° and 180° pulses (narrow and wide rectangles). The exceptional 0–2 coherence transfer should be commented on, emphasizing its occurrence being due to the DF effects.

p.9: Fig.5 contains a plethora of information on angular and mixing time dependence, which should be discussed in more detail.

p.9. Why was a methyl signal chosen for the investigations? Couldn’t the known “anomalies” of CH3 groups have an impact?

p.9ff. Section 3.3

Similar to the comments on the previous section, first the purpose or motivation for the new experiments should be outlined. The experiments are highly complex and the explanation, while detailed in describing, what the elements of the pulse sequence are doing, the goal seem elusive.

There is a lot of potentially useful insight in this subchapter, but the overall presentation is a bit confusing. Some more systematic structuring would be useful.

The text would also benefit from language editing in particular in this section.

p.10 Fig. 6: It maybe worthwhile to draw the coherence transfer diagram with separate sub-pathways for the rare and the abundant spin, similar to the way in which pathways in heteronuclear pulse sequences are often illustrated.

p.10 eq.8: Where does this eq. come from?

p.11: The decomposition outlined is highly enlightening, it might be more instructive to include some transfer diagrams connecting operator terms by arrows indicating the transfers enabled by the DF, with the DF represented as a (pseudo) propagator.

p.10-13: I believe a clearer designation of the pulse sequence variants can simplify discussion. Thus overly wordy expressions like “except that the PFG Ga which was placed just before acquisition has been moved in front of the DIPSI-2 pulse-train“ can be avoided. Maybe additional panels in Fig. 6 may be a solution.

Technical corrections

I have put some annotations into the pdf-file I am sending separately, which include a few suggestions for fixing language issues.

Figure 1: axis labelling and annotations font sizes should be improved. What is the frequency offset between A and S in (d)?

The pulse sequence diagrams would benefit a lot from improvements wrt. to label positions and sizes and a more conventional representation of 90, 180° pulses by narrow and wide rectangles and for the indication of selective pulses.

Figure 2: The coherence pathway has been commented on above. The spectrum is too small and needs to be annotated to be meaningful (peak assignments). The sample composition could be stated in the caption rather than the main text. The positions of the 13C satellites should be marked. The watergate delays are not given.

The quality (size, graphics resolution) and the labelling of the spectra needs to be improved.

Equation 5 formally is not an “equation”.