the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 31 Dec 2025
Pulsed Electron Paramagnetic Resonance on two Cu(II)-Cage Compounds With Six, Respectively Eight Copper Ions
Abstract. The copper(II) cages Pd12Cu6LDMAP24(Cu6) and Pd12Cu8LPro24 (Cu8), contain six, resp. eight, Cu(II) ions in a complex constituted by palladium ions and organic ligands in a self-assembled nano-meter sphere. Within the sphere, the Cu(II) ions are expected to form polyhedral-like structures. The parent compounds Pd12M6LDMAP24 and Pd12M8LPro24 are of interest because of the possibility of introducing a different metal ions for M, such as Cu(II), in a defined arrangement and for catalytic applications, see Bobylev et al. (Chemical Science, 2023, 14, 11840–11849). For structure information, nano-meter distances where measured between the six, respectively eight Cu(II) ions in Cu6 and Cu8. Distances were measured by pulsed double electron electron resonance (DEER) spectroscopy. While DEER is established for measuring distances between pairs of spins, application to multi-spin systems is less common. Since, so far, no reports of DEER with multi-spin interactions between Cu(II) ions were reported, the copper-cages are an ideal model to study them. For Cu6 and Cu8, DEER shows multi-spin interaction, and the method enabled to establish an octahedral arrangement for the Cu-ions in Cu6. For Cu8, two distances were observed that are consistent with two structural models proposed for Cu8, one of which is a cube of Cu-ions.
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Status: closed (peer review stopped)
- RC1: 'Comment on mr-2025-17', Anonymous Referee #1, 19 Jan 2026
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RC2: 'Comment on mr-2025-17', Anonymous Referee #2, 20 Jan 2026
This reviewer cannot support publication of this manuscript.
The quality of the manuscript is quite disappointing. I will point out some of the issues but if authors cannot be bothered to carefully proofread their manuscript, I will not compensate this.
The progress this manuscript makes with respect to reference 5 is minimal and does not justify separate publication. There are no new insights in the present manuscript that go beyond the state-of-the-art.
The authors should clearly define their terms. Determining of spin numbers per cluster through modulation depth analysis and effects of sum and difference frequencies on the experimental distance distribution are two very different phenomena arising from the presence of multiple spins in the nanoobject. This manuscript uses “multi-spin effects” indiscriminately.
Equation 1 is introduced without discussion of the underlying assumptions and approximations made. Especially for a submission to a specialised magnetic resonance journal this manuscript is very thin on background and theory. The main approximation of negligible orientation correlation of spin centres is not well met here and I would not expect eq 1 to be valid in this application. In fact, I would expect very strong effects from orientation selection and very weak effects from multiple spins being excited by the pump pulse. However, the manuscript hinges on the latter and makes no plausible attempt in rationalising or quantifying the former.
As the experiments are set-up the perpendicular component of the Cu g-tensor is selected. This means that Cu ions with the parallel component oriented along the field will not contribute to the echo nor be pumped. In an octahedron (Cu6) the opposite vertices will have inverted orientations and thus identical g-tensor orientations. This might indeed increase the modulation depth. If one Cu is in g_perp the opposite one is as well. The 4 nearest neighbours will be in an orientation 90 degrees rotated and this might match g_perp with g_par (no modulation depth) or g_perp with g_perp (high modulation depth). This might rationalise the observed 1:1 distance ration with 4:1 expected. This effect of increased modulation depth is missing from the discussion of orientation selection.
The SNR is not given but likely too low <10:1 to quantify complex distributions with multiple distance populations and different peak widths (how were peak ratios determined?). This any detailed analysis is likely leading to data overinterpretation.
The modulation depth analysis pivots on the calibration with model system Cu2. This is actually not a good model system. If the excitation of a 16 ns pump pulse in the Cu spectrum is estimated, you would expect anywhere around 3-7%. That this is much higher here hints at orientation selection and the molecular structure (likely again inversion symmetry between the centres) matching g_perp with g_perp. If this is true, the present calibration is not robust. This is further evidenced by the distance distribution not reflecting what is expected. This will be an effect of exchange interaction and strong orientation correlation effects. Either of which would make this a poor model system the combination only makes it worse. I would recommend a calibration sample that shows the expected distance distribution to start with.
That means the main conclusion of low spin numbers found in the clusters is based on a flawed calibration.
In these clusters, I would expect negligible effects of multiple simultaneous excitations of B-spins in the same cluster, and this is what you find. I would further expect strong orientation selection effects, and you seem to observe them but neither test to confirm them or rule them out and do not analyse them. These are the core findings of this manuscript. Conclusions about reliable distances and tackling of multi-spin effects are overblown.
Minor
The references are not numbered in order of appearance
The reference section needs careful formatting – the care taken here seems to reflect on the general care taken when preparing the manuscript.
Line 31 ref 27 is given, but it should be 29
Line 82 refs 4,5 are not the most appropriate for 4-pulse DEER
Line 93 The “known artefact” should be explained. It could be crossing the refocusing pulse or a crossing echo by detection and pump pulses.
Line 107 is the concentration of Cu2 0.6 mM or the Cu concentration?
There is main text between Table 1 and its header.
SI: “So in this case, the advantage of the DeerNet program, namely that processing of baseline and form factor is user-invention free [7, 8], cannot be fully harnessed” Do you mean intervention?
SI page 3 states a DEERNet option of Tikhonov analysis. As this is not an option in the software this needs clarification.
SI page 4: Due to the overall low signal-to-noise ratio of the data we did not expect unambiguous solutions.” It would be helpful if this assessment of the reliability had made it into the main text.
Figure SI.4 The raw data (A) shows no noise but very strong ESEEM-like modulation on top of some typical DEER form-factor. The background corrected data (B) has much stronger noise that masks the high frequency modulation (if it is still there). This data is clearly not just background subtracted (and cut). The noise seems also to increase upon background correction in Figure 2 (main text). Are these the forma factors after validation with added noise?
Citation: https://doi.org/10.5194/mr-2025-17-RC2 -
RC3: 'Comment on mr-2025-17', Anonymous Referee #3, 21 Jan 2026
In this manuscript, the authors apply DEER spectroscopy to two relatively complex copper clusters, referred to as Cu6 and Cu8, both of which are of interest as catalytic systems. The stated aim is to extract inter‑copper distances using DEER and to build upon multispin effects. The problem is introduced reasonably well; however, the experimental results are not sufficiently convincing to support the conclusions drawn.
A central part of the discussion focuses on the modulation depth. Unfortunately, the signal‑to‑noise ratio (SNR) of the DEER data is low. For example, in Figure 2B, the normalization appears unreliable given the noise level. While these experiments are undoubtedly challenging—particularly in light of the short phase memory times (T_m) reported in the Supporting Information—the current data quality does not allow robust conclusions to be drawn.
Significant effort is devoted in the Supporting Information to addressing some of these issues. However, the Supporting Information contains details, particularly regarding orientation selection and its potential impact on the relative intensities of the detected spin pairs, that should be discussed more explicitly in the main text.
For the Cu8 system, the SNR is particularly low, and it is therefore not possible to draw reliable conclusions from the fits. As a result, the proposed discussion of structural flexibility in Cu8 is not convincingly supported by the experimental evidence presented.
In view of these points, and considering previous related work (https://pubs.rsc.org/en/content/articlelanding/2023/sc/d3sc03745b), it is unclear what new insight the present study provides. I therefore cannot recommend the manuscript for publication in its current form.
Minor comments
Equation (1) would benefit from a clearer introduction, including an explanation of its domain of validity. In addition, it does not appear to be used elsewhere in the manuscript.
The origin or the artifact at 1940 ns could be explained.
Given the large g‑anisotropy of Cu(II), and based on the models employed (which could be reported in the main text), the authors should discuss how orientation selection is expected to influence the observed modulation depth.
Citation: https://doi.org/10.5194/mr-2025-17-RC3 -
AC1: 'Comment on mr-2025-17', Martina Huber, 23 Mar 2026
Dear Editor,
We have collected all responses and additional material in the attached pdf file. It contains the point-by-point response to the reviewers comments as well. As several reviewer comments overlap, this seemed to be the best way of answering all points.
With kind regards,
Martina Huber
Status: closed (peer review stopped)
-
RC1: 'Comment on mr-2025-17', Anonymous Referee #1, 19 Jan 2026
This manuscript extends on an earlier publication of the authors (Chem. Sci., 2023, 14, 11840; Ref. 5). The authors remeasured DEER data for two Cu(II) cage compounds and supplemented them by a measurement on a model compound with two copper centres. Then they analysed modal distances in distance distributions and modulation depths in DEER time-domain data and compared these parameters to expectations for different models for the cage compounds. The results are inconclusive. Given the limited quality of the experimental data (length of the traces and signal-to-noise ratio), it remains unclear whether the inconsistencies are caused by a simplistic physical model or by differences between crystal and solution structure of the compounds. As detailed below, it is likely that better quality data could have been obtained and that a better model for the spin system could have been designed. In its present form, the manuscript is not suitable for publication as it does not constitute a significant advance beyond Ref. 5.
Major criticism:
- The measurement parameters appear to be far from optimal. Why did the authors measure at 20 K if T1 was still that short? The asymptotic low-temperature maximum of Tm for such compounds would be expected between 6 and 15 K, probably at the lower end of this range. Because achievable maximum dipolar evolution time and signal amplitude at given evolution time depend roughly exponentially on Tm, a too high measurement temperature can have a large effect on data quality.
- It is standard to perform such DEER measurements in deuterated solvents in order to prolong Tm. In this case, it is clear that the effect on achievable maximum evolution time and signal-to-noise ratio is huge, as one can compare the data for the two-spin model compound to those presented in Ref. 31. It is true that perdeuterated butyronitrile (not butylnitrile, as written in the manuscript) is a bit expensive, but compared to the total expense of the project this is a price worth paying for improved data quality. This applies in particular when data quality without deuterated solvent is insufficient for drawing firm conclusions, as is the case here.
- It is somewhat confusing that the authors do not use the nomenclature of Ref. 31 for the Cu2 model compound. According to Fig. SI2, it is the [Cu-TAHA] – [Cu-TAHA] ruler 3 of that paper (see Fig. 1 of Ref. 31). Because of the distributed exchange coupling, this compound is not a good modulation-depth standard for DEER. Conformations with large coupling do not contribute to modulation due to lack in excitation bandwidth. Instead, ruler 4, 23, or 15 should have been used.
- With excitation bandwidth being an issue, also for the cage compounds Cu6 and Cu8, the choice of pulse lengths is not good. An optimal experiment would minimize the length of the longest pulse among both the observer sequence and the pump pulse. With the hardware available to the authors, a maximum length of 24 ns (instead of 32) should have been possible, probably even 20 ns, depending on actual power of the TWT amplifier.
- The authors state that they cannot assess orientation selection, because they do not know relative orientation of the g tensor principal axes systems (PASs). Why didn’t they try DFT computations? The software is free, a relatively small basis set allows for getting orientation right, and it would have been possible to compute only cutouts of the whole cage compounds, because spin population is localized.
- Even without DFT computations, it is clear that the PASs opposite Cu centres (diagonals) must coincide in ideal geometry, as they are related by an inversion centre. With the given pump and observer frequencies, contribution of the cube diagonals in Cu8 should be at least as large as the one of the other distances. Hence, orientation selection cannot be the reason for the expected peak to be missing.
- Error bars should be given for modulation depth and error propagation computed for the number of spins.
- Only the cage models corresponding to the crystal structures are clear. The authors do not exactly specify the alternative models that they consider.
- In the current manuscript, for Cu6 the two expected distances have the same peak amplitude in the distance distribution (Fig. 2C), which is unexpected. In Ref. 5, where data on the same compounds were measured with the same settings, the shorter distance gave rise to higher amplitude, matching expectation at least semi-quantitatively (Fig. 8B of Ref. 5). Why the different results? Given the aim of the current manuscript, this ought to be discussed.
Minor criticism:
- Not all measurement parameters are specified. For instance, what was the shot repetition time? What phase cycle was used? What exactly were t1 and t2?
- The relaxation data reported in Table SI1 are identical to the ones in Ref. 5. This can hardly be coincidence, the data is very likely from this earlier paper. This needs to be mentioned. It is also somewhat problematic, because other measurements were repeated and the samples are not long-time stable (and were probably reprepared).
- It is not true that the setup used by the authors would not have allowed for testing orientation selection (claimed in the SI on p. 3). Essentially the same setup was used in https://doi.org/10.1002/1521-3757(20021018)114:20<4063::AID-ANGE4063>3.0.CO;2-V, where orientation selection was observed.
- l. 93-95: “Contribution of a known instrumentation artifact at 1940 ns”. This reviewer does not know such an instrumentation artefact. It rather looks like the pump pulse running into (and through) the last observer p pulse. Not knowing t1 and t2, I cannot be sure, though.
- l. 173/174 “For model 2, the same intensity ratios are expected as for model 2, as long as it can be considered an almost ideal geometrical body”. Something is wrong here.
- SI p. 3: “The DEERNet option to do Tikhonov analysis” does not make sense. DEERNet does not use Tikhonov regularization.
- “that a smaller regularization parameter selected in the user-adjusted Tikhonov regularization smoothens out some of the features that we interpret as noise”. This cannot be the case. Noise artefacts in distance distributions are smoothened out by larger, not smaller regularization parameters.
- SI p. 4: In the Section “Modulation depth and the relative intensities of the distance peaks” insufficient excitation bandwidth is dismissed as a reason for too low intensity of the peak at the shortest distance, in Section “Why not all spins in the cages are observed” it is not dismissed but invoked to explain the data. With a 32 ns observer p pulse, I would indeed expect reduced modulation at these short distances.
Citation: https://doi.org/10.5194/mr-2025-17-RC1 -
RC2: 'Comment on mr-2025-17', Anonymous Referee #2, 20 Jan 2026
This reviewer cannot support publication of this manuscript.
The quality of the manuscript is quite disappointing. I will point out some of the issues but if authors cannot be bothered to carefully proofread their manuscript, I will not compensate this.
The progress this manuscript makes with respect to reference 5 is minimal and does not justify separate publication. There are no new insights in the present manuscript that go beyond the state-of-the-art.
The authors should clearly define their terms. Determining of spin numbers per cluster through modulation depth analysis and effects of sum and difference frequencies on the experimental distance distribution are two very different phenomena arising from the presence of multiple spins in the nanoobject. This manuscript uses “multi-spin effects” indiscriminately.
Equation 1 is introduced without discussion of the underlying assumptions and approximations made. Especially for a submission to a specialised magnetic resonance journal this manuscript is very thin on background and theory. The main approximation of negligible orientation correlation of spin centres is not well met here and I would not expect eq 1 to be valid in this application. In fact, I would expect very strong effects from orientation selection and very weak effects from multiple spins being excited by the pump pulse. However, the manuscript hinges on the latter and makes no plausible attempt in rationalising or quantifying the former.
As the experiments are set-up the perpendicular component of the Cu g-tensor is selected. This means that Cu ions with the parallel component oriented along the field will not contribute to the echo nor be pumped. In an octahedron (Cu6) the opposite vertices will have inverted orientations and thus identical g-tensor orientations. This might indeed increase the modulation depth. If one Cu is in g_perp the opposite one is as well. The 4 nearest neighbours will be in an orientation 90 degrees rotated and this might match g_perp with g_par (no modulation depth) or g_perp with g_perp (high modulation depth). This might rationalise the observed 1:1 distance ration with 4:1 expected. This effect of increased modulation depth is missing from the discussion of orientation selection.
The SNR is not given but likely too low <10:1 to quantify complex distributions with multiple distance populations and different peak widths (how were peak ratios determined?). This any detailed analysis is likely leading to data overinterpretation.
The modulation depth analysis pivots on the calibration with model system Cu2. This is actually not a good model system. If the excitation of a 16 ns pump pulse in the Cu spectrum is estimated, you would expect anywhere around 3-7%. That this is much higher here hints at orientation selection and the molecular structure (likely again inversion symmetry between the centres) matching g_perp with g_perp. If this is true, the present calibration is not robust. This is further evidenced by the distance distribution not reflecting what is expected. This will be an effect of exchange interaction and strong orientation correlation effects. Either of which would make this a poor model system the combination only makes it worse. I would recommend a calibration sample that shows the expected distance distribution to start with.
That means the main conclusion of low spin numbers found in the clusters is based on a flawed calibration.
In these clusters, I would expect negligible effects of multiple simultaneous excitations of B-spins in the same cluster, and this is what you find. I would further expect strong orientation selection effects, and you seem to observe them but neither test to confirm them or rule them out and do not analyse them. These are the core findings of this manuscript. Conclusions about reliable distances and tackling of multi-spin effects are overblown.
Minor
The references are not numbered in order of appearance
The reference section needs careful formatting – the care taken here seems to reflect on the general care taken when preparing the manuscript.
Line 31 ref 27 is given, but it should be 29
Line 82 refs 4,5 are not the most appropriate for 4-pulse DEER
Line 93 The “known artefact” should be explained. It could be crossing the refocusing pulse or a crossing echo by detection and pump pulses.
Line 107 is the concentration of Cu2 0.6 mM or the Cu concentration?
There is main text between Table 1 and its header.
SI: “So in this case, the advantage of the DeerNet program, namely that processing of baseline and form factor is user-invention free [7, 8], cannot be fully harnessed” Do you mean intervention?
SI page 3 states a DEERNet option of Tikhonov analysis. As this is not an option in the software this needs clarification.
SI page 4: Due to the overall low signal-to-noise ratio of the data we did not expect unambiguous solutions.” It would be helpful if this assessment of the reliability had made it into the main text.
Figure SI.4 The raw data (A) shows no noise but very strong ESEEM-like modulation on top of some typical DEER form-factor. The background corrected data (B) has much stronger noise that masks the high frequency modulation (if it is still there). This data is clearly not just background subtracted (and cut). The noise seems also to increase upon background correction in Figure 2 (main text). Are these the forma factors after validation with added noise?
Citation: https://doi.org/10.5194/mr-2025-17-RC2 -
RC3: 'Comment on mr-2025-17', Anonymous Referee #3, 21 Jan 2026
In this manuscript, the authors apply DEER spectroscopy to two relatively complex copper clusters, referred to as Cu6 and Cu8, both of which are of interest as catalytic systems. The stated aim is to extract inter‑copper distances using DEER and to build upon multispin effects. The problem is introduced reasonably well; however, the experimental results are not sufficiently convincing to support the conclusions drawn.
A central part of the discussion focuses on the modulation depth. Unfortunately, the signal‑to‑noise ratio (SNR) of the DEER data is low. For example, in Figure 2B, the normalization appears unreliable given the noise level. While these experiments are undoubtedly challenging—particularly in light of the short phase memory times (T_m) reported in the Supporting Information—the current data quality does not allow robust conclusions to be drawn.
Significant effort is devoted in the Supporting Information to addressing some of these issues. However, the Supporting Information contains details, particularly regarding orientation selection and its potential impact on the relative intensities of the detected spin pairs, that should be discussed more explicitly in the main text.
For the Cu8 system, the SNR is particularly low, and it is therefore not possible to draw reliable conclusions from the fits. As a result, the proposed discussion of structural flexibility in Cu8 is not convincingly supported by the experimental evidence presented.
In view of these points, and considering previous related work (https://pubs.rsc.org/en/content/articlelanding/2023/sc/d3sc03745b), it is unclear what new insight the present study provides. I therefore cannot recommend the manuscript for publication in its current form.
Minor comments
Equation (1) would benefit from a clearer introduction, including an explanation of its domain of validity. In addition, it does not appear to be used elsewhere in the manuscript.
The origin or the artifact at 1940 ns could be explained.
Given the large g‑anisotropy of Cu(II), and based on the models employed (which could be reported in the main text), the authors should discuss how orientation selection is expected to influence the observed modulation depth.
Citation: https://doi.org/10.5194/mr-2025-17-RC3 -
AC1: 'Comment on mr-2025-17', Martina Huber, 23 Mar 2026
Dear Editor,
We have collected all responses and additional material in the attached pdf file. It contains the point-by-point response to the reviewers comments as well. As several reviewer comments overlap, this seemed to be the best way of answering all points.
With kind regards,
Martina Huber
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- 1
This manuscript extends on an earlier publication of the authors (Chem. Sci., 2023, 14, 11840; Ref. 5). The authors remeasured DEER data for two Cu(II) cage compounds and supplemented them by a measurement on a model compound with two copper centres. Then they analysed modal distances in distance distributions and modulation depths in DEER time-domain data and compared these parameters to expectations for different models for the cage compounds. The results are inconclusive. Given the limited quality of the experimental data (length of the traces and signal-to-noise ratio), it remains unclear whether the inconsistencies are caused by a simplistic physical model or by differences between crystal and solution structure of the compounds. As detailed below, it is likely that better quality data could have been obtained and that a better model for the spin system could have been designed. In its present form, the manuscript is not suitable for publication as it does not constitute a significant advance beyond Ref. 5.
Major criticism:
Minor criticism: