Increased sensitivity in Electron Nuclear Double Resonance spectroscopy with chirped radiofrequency pulses

Stropp, Julian; Wili, Nino; Nielsen, Niels Christian; Klose, Daniel

doi:https://doi.org/10.5194/mr-2024-14

Preprints

https://doi.org/10.5194/mr-2024-14

Preprints

10 Sep 2024

| 10 Sep 2024

Status: a revised version of this preprint was accepted for the journal MR and is expected to appear here in due course.

Increased sensitivity in Electron Nuclear Double Resonance spectroscopy with chirped radiofrequency pulses

Julian Stropp, Nino Wili, Niels Christian Nielsen, and Daniel Klose

Abstract. Electron Nuclear Double Resonance (ENDOR) spectroscopy is an EPR technique to detect the nuclear frequency spectra of hyperfine coupled nuclei close to paramagnetic centres, which have interactions that are not resolved in continuous wave EPR spectra and may be fast relaxing on the time scale of NMR. For the common case of non-crystalline solids, such as powders or frozen solutions of transition metal complexes, the anisotropy of the hyperfine and nuclear quadrupole interactions renders ENDOR lines often several MHz broad, thus diminishing intensity. With commonly used ENDOR pulse sequences only a small fraction of the NMR/ENDOR line is excited with a typical RF pulse length of several tens of μs, and this limits the sensitivity in conventional ENDOR experiments. In this work, we show the benefit of chirped RF excitation in frequency domain ENDOR as a simple yet effective way to significantly improve sensitivity. We demonstrate on a frozen solution of Cu(II)-tetraphenylporphyrin that the intensity of broad copper and nitrogen ENDOR lines increases up to 9-fold compared to single frequency RF excitation, thus making the detection of metal ENDOR spectra more feasible. The tunable bandwidth of the chirp RF pulses allows the operator to optimize for sensitivity and choose a tradeoff with resolution, opening up options previously inaccessible in ENDOR spectroscopy. Also, chirp pulses help to reduce RF amplifier overtones, since lower RF powers suffice to achieve intensities matching conventional ENDOR. In 2D TRIPLE experiments the signal increase exceeds 10 times for some lines, thus making chirped 2D TRIPLE experiments feasible even for broad peaks in manageable acquisition times.

Received: 02 Sep 2024 – Discussion started: 10 Sep 2024

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Julian Stropp, Nino Wili, Niels Christian Nielsen, and Daniel Klose

Status: closed

CC1:
'Comment on mr-2024-14', Fabian Hecker, 02 Oct 2024
The paper discusses the use of chirped RF pulses in ENDOR spectroscopy of a frozen solution transition metal complex model system at X-band frequencies. It emphasizes the significant sensitivity enhancements provided by chirped pulses, which are particularly notable for broad ENDOR lines associated with nuclei having spin I > 1/2 and transition metal nuclei. The authors carefully examine the trade-off between increased sensitivity and line broadening when the chirp bandwidth approaches or exceeds the linewidth. Additionally, they demonstrate how this sensitivity improvement enables multidimensional ENDOR experiments, such as TRIPLE, to be conducted within practical time frames—overcoming a major limitation that has hindered the adoption of these techniques since their development. There are a few points that benefit from clarification:
Line 32: The authors state that Davies does not suffer from blind spots. While it may not exhibit periodic blind spots, the technique does suffer from a central blind spot at the nuclear Larmor frequency, which is determined by the excitation pulse width. Although this may not be significant in the case discussed, it often has a considerable impact on the analysis of small hyperfine couplings.
Line 120: CuTPP is discussed as a well-known model system. Consequently, the hyperfine couplings should be provided here to facilitate evaluation of the spectra.
Figure 2:
The use of 500 W to achieve maximum RF power is understandable; however, since all other comparisons are made to 100 W spectra, it might be advisable to omit the 500 W data from the figure to avoid confusion.

It is unclear whether integrated signals or peak intensities are being discussed in panels b) and d).

The color code in panel b) is somewhat confusing, as red represents ¹H and blue represents ¹⁴N, but pale blue is used for ¹H and pale red for ¹⁴N.

Line 186 and Figure 3: The convolution of the experimental single-frequency ENDOR spectrum is a clever method for analyzing the effect of the chirp pulse. This suggests that the same analysis could be achieved with a standard frequency-domain simulation of the spectrum, potentially improving the interpretation of the ENDOR spectra without requiring a dedicated spin dynamics simulation.
Technical:
Line 130: \mu s instead of \muand
Citation: https://doi.org/10.5194/mr-2024-14-CC1
- AC1:
  'Reply on CC1', Daniel Klose, 07 Oct 2024
  We thank Dr. Fabian Hecker for his constructive feedback.
  L32: Thank you. We will revise this section to include the central blind spot behaviour of the Davies ENDOR sequence due to the excitation pulse length.
  
  L120: We will include a table with hyperfine (& quadrupole) couplings of the relevant coupled nuclei observed in the ENDOR experiments to the supporting information.
  
  Figure 2:
  We would prefer to keep the 500 W single frequency ENDOR spectrum in the figure to clearly show that higher sensitivity can be achieved with much lower power by chirp RF pulses.
  
  Peak intensities are compared in these panels. We will clarify this upon revision in the figure legend.
  
  We apologize that the position/color of the pale arrows is swapped in panel 2b) and will update this in the revision.
  
  L186 & Figure 3: Thank you for this comment. As noted, in the figure we show that a convolution-based approach is valid to simulate the chirp ENDOR spectrum. This is most apparent by comparing with a convoluted experimental single frequency spectrum rather than a convoluted frequency domain ENDOR simulation of the spectrum because this provides the most accurate comparison by overlaying experimental data with RF-excitation width broadening together with single-frequency data broadened in post processing. Accordingly, a frequency domain simulation which describes the single frequency spectrum well, will also describe the chirp ENDOR spectrum well after convolution (note, not necessarily the other way around).
  
  To strengthen this point, we will emphasize in the revision that simulation-based spectral analysis can be used for chirp ENDOR data in an analogous manner as for single frequency ENDOR, just with convolution as an additional step as shown in the figure.
  L130: Thank you for noticing the typo.
  
  Citation: https://doi.org/10.5194/mr-2024-14-AC1
RC1:
'Comment on mr-2024-14', Anonymous Referee #1, 04 Oct 2024
The manuscript by Stropp et al reports ENDOR experiments using a chirped inversion pulse and are demonstrated on a model CuII-tetraphenylporphyrin complex in frozen solution. Hyperfine couplings in this molecular complex arise from protons, nitrogen of the ligands as well as the Cu(II) nucleus itself. Due to the intrinsic nature of the paramagnetic metal center, these couplings are anisotropic and spread out over tens of MHz. In the standard Davies and Mims ENDOR sequences, the ENDOR spectrum is probed stepwise (frequency domain) by a rectangular RF pulse. Replacing this pulse by a frequency-swept (or chirped) RF pulse, substantially increases the excitation bandwidth and results in a stronger ENDOR effect.
Chirp RF pulses in ENDOR have been introduced about three decades ago by Jeschke and Schweiger (1995) in the context of time-domain ENDOR experiments. Nevertheless, a demonstration in conjunction with the widespread frequency-domain experiment was somehow missed. This paper is now providing this information and also demonstrates the sensitivity gain but also the tradeoff with resolution for different types of hyperfine couplings. The experimental work is well-performed and complemented by more quantitative spin dynamics simulations. I can recommend publication after clarifying following points:
Page 3, phase cycle: I cannot find information on the phase cycle. Please explain better what kind of phases etc. are used.

Page 7, Setting up the chirp pulse: I’m missing a discussion on how to set up or optimize the chirp inversion pulse. Lines 138-140 state that the performance depends on RF pulse power, pulse length and desired band width. However, the dependency on the inversion profile on these parameters is not discussed. Since this is the central part of the paper, a few more sentences would be desirable.

Page 7, lines 148 – 149: .. 2c and d show that the length of a 1 MHz chirp pulse does not have influence on the line intensity… I’m confused by this statement as Fig. 2d) shows a clear dependence for 1H and 14N.

Page 8, line 172: what is a ‘mean’ hyperfine coupling ? Please give the full tensor used in the simulation. What is the origin of the 1.2 MHz width (hyperfine anisotropy or convolution with a line width parameter) ?

Simulation of the ENDOR spectra, Fig. 3B: The frequency domain spectrum is recorded by stepping the RF frequency. How is the convolution with the chirp pulse excitation profile performed ?

The reported TRIPLE ENDOR spectra are nice but in future it would be important to see a demonstration on a non-metal center. This type of experiment potentially suffers from T1n saturation as the same ENDOR transition is inverted/pumped at each step of the sequence. The nuclei close to a metal center might relax faster than in organic radicals, thus there might be a difference in performance.

In conjunction with point (6), on page 2 line 7, the issues of nuclear saturation effects was reported in the paper by Rizzato et al, PCCP 2014 and not in Epel 2003. The latter discusses stochastic excitation for other reasons. This should be cited correctly.
Citation: https://doi.org/10.5194/mr-2024-14-RC1
- AC2:
  'Reply to RC1', Daniel Klose, 08 Oct 2024
  We thank Anonymous Referee 1 for the appreciation of our work and the detailed comments. Our point-by-point answers to the comments are:
  Page 3 phase cycle: Thank you for noting this and we apologize for the missing description. The 4-step phase cycles used in the experiments are:
  
  Mims: π/2 ( 0, π, 0, π) – π/2 (0, 0, π, π) – p_RF (0, 0, 0, 0) - π/2 (0, 0, 0, 0) – Det. (1, -1, -1, 1)
  
  Davies: π ( 0, 0, 0, 0) – p_RF (0, 0, 0, 0) – π/2 (0, 0, π, π) - π (0, π, 0, π) – Det. (1, -1, -1, 1)
  
  We will include the phase cycles in section 2.2 of the revised manuscript.
  Page 7 Setting up the chirp pulse: Thank you for this important comment.
  
  The first parameter to choose is the bandwidth of the chirp pulse and therefore the resolution desired in the experiment (e.g. 1 MHz chirp bandwidth gives approximately 1 MHz potential resolution in the ENDOR spectrum as visible in Figs. 3 and S2). As a second step the pulse length should be chosen such that the spectral power density is high enough to achieve full inversion for all couplings with the selected chirp bandwidth. This depends on the available RF amplifier output power, the ENDOR resonator and their frequency responses. In our case, for a 100 W RF amplifier output power and a Bruker X-band MD4 ENDOR resonator an RF pulse length of ca. 100 µs was sufficient for maximum sensitivity and full inversion (see Fig. 2d). Note that further increase of the RF pulse length maintains the ENDOR sensitivity (Fig. 2d).
  
  As we fully agree with the reviewer that the experiments should be as accessible as possible, we will include a new SI section 2 “Setup and Optimization of RF chirp pulses in ENDOR experiments” in the revised version of the manuscript.
  
  Page 7, lines 148 – 149: We apologize for the ambiguous sentence. We wanted to convey that RF pulses longer than 100 µs do not change the ENDOR intensity anymore and are therefore not needed. We will change l148 – 149 accordingly upon revision: “Figure 2c and d show that for a chirp bandwidth of 1 MHz a pulse length of about 100 µs is sufficient to achieve maximum intensity.”
  
  P8, line 172: For the simulation a Gaussian distribution of purely isotropic hyperfine couplings was used. Each coupling in this distribution is described by a delta peak with an infinitesimally small linewidth. The maximum of this distribution (“mean”) was set to 4 MHz. The width of this Gaussian distribution (FWHM) is 1.2 MHz corresponding to a standard deviation of 0.5 MHz as introduced in methods section 2.3. We will clarify this, by adding “isotropic” hyperfine coupling to the explanation in 3.3, and phrase the description as the “mean of the distribution of isotropic hyperfine couplings”.
  
  Fig 3B: For the ENDOR simulations using convolution (Fig. 3b) the chirp pulse excitation profile is calculated from pulse length and amplitude/power with EasySpin, as we will describe in more detail in the methods section 2.3 and in the SI section 1. This pulse excitation profile (as function of frequency offset from chirp center frequency) is convoluted with the experimental single frequency ENDOR spectrum. For full transparency and for those interested in the script of this simulation, we refer to the data and script accompanying this manuscript on zenodo 10.5281/zenodo.11082486.
  
  TRIPLE: We agree that a demonstration on different systems (e.g. including organic radicals) will be useful to get a better understanding of the performance of TRIPLE on diverse paramagnetic systems, however, for the application class of metal sites (as e.g. in catalysis) CuTPP is a relevant model system and hence test case. Thus, for applications in fields as catalysis, material science and bioinorganic chemistry, the chirp TRIPLE experiment on CuTPP in this paper showcases the utility of chirp pulses in 2D experiments. However, we do agree with the reviewer that on other systems such as slow-relaxing organic radicals, the performance of TRIPLE may well be somewhat worse, as also the case for TRIPLE without chirp pulses – however, this is beyond the scope of this paper.
  
  P2 line 7: We thank the reviewer for noting this incorrect citation, we will correct this in the revised manuscript.
  
  Citation: https://doi.org/10.5194/mr-2024-14-AC2
  - AC4: 'Reply on AC2', Daniel Klose, 25 Oct 2024
    
    Please note that the correct zenodo doi is 10.5281/zenodo.13625320.
    
    Citation: https://doi.org/10.5194/mr-2024-14-AC4
RC2:
'Comment on mr-2024-14', Anonymous Referee #2, 19 Oct 2024
In this manuscript by Stropp et al. the application of chirped RF pulses in pulsed ENDOR and TRIPLE experiments on the example of Cu(II)-tetraphenylporphyrin is demonstrated. All experiments are in the frequency-domain, i.e. the spectra a recorded stepwise incrementing the rf frequency. Since the Cu-TPP complex in frozen solution features anisotropic hyperfine couplings with broad line in particular for ¹⁴N and ^63,65Cu, through the introduction of a chirped rf pulse the authors can show a considerable intensity improvement in particular for the broader ¹⁴N and ^63,65Cu lines. The authors also demonstrate the balance of intensity enhancement vs. spectral broadening by approaching the ENDOR line width with the bandwidth of the chirp pulse.
The experimental work is carefully performed and mostly well described. I can recommend publication after sorting out a few points:
There is no EPR spectrum of Cu-TPP given, for completing the description at which B-field position the ENDOR/TRIPLE spectra are recorded there should be one displayed.

The chirp ENDOR simulatins are not exhaustive explained enough, the zenodo link given in the previous reply to RC1 refers ot another manuscript.

The loss in resolution in the chirp ENDOR spectrum when the bandwidth of the chirp rf pulse approaches the ENDOR linewidth can be understood similar to "overmodulating" a line in cw-EPR, spectral contributions add then to the line intensity which don't belong to the center rf frequency of the pulse.

Unfortunately the authors stop their chirp ENDOR simulations at more interesting cases: ¹⁴N ENDOR lines with NQI, where the chirp rf pulse can excite adjacent transitions in the same m_s manifold. The authors should explain, why the simulations become then "infeasible".

l178-184: The authors mix here chirp rf pulses (with too large bandwidth) with special TRIPLE experiments, which are not comparable: the chirp ENDOR are broadened beyond the overall spectral width, whereas in the special TRIPLE case (with small bandwidth) the 2 NMR transitions are hit simultaneously inreasing sensitivity and enabling quantitative experiments.

l155: The discussion of overtones from the rf amplifier leading to artificial lines in the ENDOR spectrum should be taken with care. Usually the occurance of higher harmonics of an amplifier is specified at 0 dBm rf input. Working within this limit or beyond is in the hands of the operator.

When it comes to the presentation of the TRIPLE results, it would be more insightful, if the authors not only explain how the spectra were acquired, but also how they can be interpreted. In this regards I can only emphasize the need of tabularised hyperfine couplings and their signs for Cu-TPP. This would make these experiments more attractive for readers, who are aiming for this information on other systems. In this context fig.4a stands rather unexplained, and the reader doesn't really know, how to interpret the 2D TRIPLE experiment (and if its worth to perform it for 2 days rather than a few 1D TRIPLE traces at specific hfc's).

In fig.4b the 1D difference TRIPLE traces and the improvement of intensity are shown, the measurement time would be interesting here, too, to compare with 2D TRIPLE and ENDOR.

For the TRIPLE experiments the bandwidth-dependent intensity/broadening effects are not unfortunately not investigated, which are to be expected in favour of intensity enhancement:

Since anisotropic lines are excited with nu(rf1), the higher the fraction of the excited anisotropic hyperfine line, the higher the intensity effect should be. Have the authors this possible effect taken into consideration, or even investigated?
Citation: https://doi.org/10.5194/mr-2024-14-RC2
- AC3:
  'Reply on RC2', Daniel Klose, 25 Oct 2024
  We thank Anonymous Referee 2 for the nice feedback and the detailed comments. Our answers to the comments are:
  We will add the experimental EPR spectrum to the supporting information and indicate the field position used for ENDOR, along with a table of the known spin Hamiltonian parameters for overview.
  
  We apologize for sharing the wrong zenodo link in the reply to Anonymous Referee 1. The correct zenodo doi is 5281/zenodo.13625320. Also, we will update the experimental section with a more thorough explanation of the ENDOR simulations.
  
  What we meant with the simulations “become infeasible” is that the computational cost to do time domain simulations for spin systems with a high number of spins increases exponentially, thus hampering spectral analysis by least-squares fitting of spin Hamiltonian parameters. This is the reason, why we think the convolution approach is of interest for the typical ENDOR spectroscopist: One can still use frequency domain simulations (as implemented in EasySpin) to analyze the experimental chirp ENDOR spectra as described. Regarding spin dynamics simulations of 14N: Thank you for pointing this out. We will consider this in the revision.
  
  We apologize for writing this not clearly enough. We did not to compare chirp ENDOR with special TRIPLE experiments, but just point out to the reader that in contrast to the chirp ENDOR experiments, in special TRIPLE experiments the excitation of 2 NMR transitions is exploited in a favorable, quantitative fashion. We will clarify this in the revision.
  
  We agree that it is in the hands of the operator to adjust the RF power carefully. Nevertheless, if samples have low signal intensities, sometimes one may choose higher sensitivities with shorter/stronger RF pulses at the compromise of introducing amplifier overtones. As explained in the manuscript, chirp pulses with lower power can be superior to single frequency pulses with high power and we encourage spectroscopists to use chirp pulses without introducing overtones in the spectrum. We will clarify this in the revision of the manuscript.
  
  As already mentioned in point 1 and the reply to the community comment by Fabian Hecker, we will include a table with hyperfine couplings for Cu-TPP in the manuscript. We will annotate the 2D TRIPLE spectrum with hyperfine and nuclear quadrupolar couplings. We agree that for CuTPP it is enough to record 1D TRIPLE traces at a few hfcs to read out the same information as from the 2D TRIPLE. However, this is a demonstration for more complicated systems with multiple paramagnetic centres, where 2D TRIPLE is required for a clear interpretation and we show (although on the comparably simple CuTPP system) that chirp RF pulses are valuable also for such cases.
  
  We will include the measurement (30 min/TRIPLE trace) in the figure caption. Please be aware that the 2D TRIPLE was measured with a slightly different number of points and non-uniform sampling.
  
  Thank you for the comment. We expect that the bandwidth-dependent effects in TRIPLE will be similar to ENDOR results as long as the chirp does not excite multiple transitions, and we therefore did not investigate this further. We agree that for 2D TRIPLE with maximum sensitivity the chirp pulse bandwidth should be adjusted to the width of the anisotropic line, as we note in the text, the chirp bandwidth could even be adapted specifically to the width of each ENDOR line, resulting in a non-uniform bandwidth excitation scheme.
  
  Citation: https://doi.org/10.5194/mr-2024-14-AC3

Status: closed

CC1:
'Comment on mr-2024-14', Fabian Hecker, 02 Oct 2024
The paper discusses the use of chirped RF pulses in ENDOR spectroscopy of a frozen solution transition metal complex model system at X-band frequencies. It emphasizes the significant sensitivity enhancements provided by chirped pulses, which are particularly notable for broad ENDOR lines associated with nuclei having spin I > 1/2 and transition metal nuclei. The authors carefully examine the trade-off between increased sensitivity and line broadening when the chirp bandwidth approaches or exceeds the linewidth. Additionally, they demonstrate how this sensitivity improvement enables multidimensional ENDOR experiments, such as TRIPLE, to be conducted within practical time frames—overcoming a major limitation that has hindered the adoption of these techniques since their development. There are a few points that benefit from clarification:
Line 32: The authors state that Davies does not suffer from blind spots. While it may not exhibit periodic blind spots, the technique does suffer from a central blind spot at the nuclear Larmor frequency, which is determined by the excitation pulse width. Although this may not be significant in the case discussed, it often has a considerable impact on the analysis of small hyperfine couplings.
Line 120: CuTPP is discussed as a well-known model system. Consequently, the hyperfine couplings should be provided here to facilitate evaluation of the spectra.
Figure 2:
The use of 500 W to achieve maximum RF power is understandable; however, since all other comparisons are made to 100 W spectra, it might be advisable to omit the 500 W data from the figure to avoid confusion.

It is unclear whether integrated signals or peak intensities are being discussed in panels b) and d).

The color code in panel b) is somewhat confusing, as red represents ¹H and blue represents ¹⁴N, but pale blue is used for ¹H and pale red for ¹⁴N.

Line 186 and Figure 3: The convolution of the experimental single-frequency ENDOR spectrum is a clever method for analyzing the effect of the chirp pulse. This suggests that the same analysis could be achieved with a standard frequency-domain simulation of the spectrum, potentially improving the interpretation of the ENDOR spectra without requiring a dedicated spin dynamics simulation.
Technical:
Line 130: \mu s instead of \muand
Citation: https://doi.org/10.5194/mr-2024-14-CC1
- AC1:
  'Reply on CC1', Daniel Klose, 07 Oct 2024
  We thank Dr. Fabian Hecker for his constructive feedback.
  L32: Thank you. We will revise this section to include the central blind spot behaviour of the Davies ENDOR sequence due to the excitation pulse length.
  
  L120: We will include a table with hyperfine (& quadrupole) couplings of the relevant coupled nuclei observed in the ENDOR experiments to the supporting information.
  
  Figure 2:
  We would prefer to keep the 500 W single frequency ENDOR spectrum in the figure to clearly show that higher sensitivity can be achieved with much lower power by chirp RF pulses.
  
  Peak intensities are compared in these panels. We will clarify this upon revision in the figure legend.
  
  We apologize that the position/color of the pale arrows is swapped in panel 2b) and will update this in the revision.
  
  L186 & Figure 3: Thank you for this comment. As noted, in the figure we show that a convolution-based approach is valid to simulate the chirp ENDOR spectrum. This is most apparent by comparing with a convoluted experimental single frequency spectrum rather than a convoluted frequency domain ENDOR simulation of the spectrum because this provides the most accurate comparison by overlaying experimental data with RF-excitation width broadening together with single-frequency data broadened in post processing. Accordingly, a frequency domain simulation which describes the single frequency spectrum well, will also describe the chirp ENDOR spectrum well after convolution (note, not necessarily the other way around).
  
  To strengthen this point, we will emphasize in the revision that simulation-based spectral analysis can be used for chirp ENDOR data in an analogous manner as for single frequency ENDOR, just with convolution as an additional step as shown in the figure.
  L130: Thank you for noticing the typo.
  
  Citation: https://doi.org/10.5194/mr-2024-14-AC1
RC1:
'Comment on mr-2024-14', Anonymous Referee #1, 04 Oct 2024
The manuscript by Stropp et al reports ENDOR experiments using a chirped inversion pulse and are demonstrated on a model CuII-tetraphenylporphyrin complex in frozen solution. Hyperfine couplings in this molecular complex arise from protons, nitrogen of the ligands as well as the Cu(II) nucleus itself. Due to the intrinsic nature of the paramagnetic metal center, these couplings are anisotropic and spread out over tens of MHz. In the standard Davies and Mims ENDOR sequences, the ENDOR spectrum is probed stepwise (frequency domain) by a rectangular RF pulse. Replacing this pulse by a frequency-swept (or chirped) RF pulse, substantially increases the excitation bandwidth and results in a stronger ENDOR effect.
Chirp RF pulses in ENDOR have been introduced about three decades ago by Jeschke and Schweiger (1995) in the context of time-domain ENDOR experiments. Nevertheless, a demonstration in conjunction with the widespread frequency-domain experiment was somehow missed. This paper is now providing this information and also demonstrates the sensitivity gain but also the tradeoff with resolution for different types of hyperfine couplings. The experimental work is well-performed and complemented by more quantitative spin dynamics simulations. I can recommend publication after clarifying following points:
Page 3, phase cycle: I cannot find information on the phase cycle. Please explain better what kind of phases etc. are used.

Page 7, Setting up the chirp pulse: I’m missing a discussion on how to set up or optimize the chirp inversion pulse. Lines 138-140 state that the performance depends on RF pulse power, pulse length and desired band width. However, the dependency on the inversion profile on these parameters is not discussed. Since this is the central part of the paper, a few more sentences would be desirable.

Page 7, lines 148 – 149: .. 2c and d show that the length of a 1 MHz chirp pulse does not have influence on the line intensity… I’m confused by this statement as Fig. 2d) shows a clear dependence for 1H and 14N.

Page 8, line 172: what is a ‘mean’ hyperfine coupling ? Please give the full tensor used in the simulation. What is the origin of the 1.2 MHz width (hyperfine anisotropy or convolution with a line width parameter) ?

Simulation of the ENDOR spectra, Fig. 3B: The frequency domain spectrum is recorded by stepping the RF frequency. How is the convolution with the chirp pulse excitation profile performed ?

The reported TRIPLE ENDOR spectra are nice but in future it would be important to see a demonstration on a non-metal center. This type of experiment potentially suffers from T1n saturation as the same ENDOR transition is inverted/pumped at each step of the sequence. The nuclei close to a metal center might relax faster than in organic radicals, thus there might be a difference in performance.

In conjunction with point (6), on page 2 line 7, the issues of nuclear saturation effects was reported in the paper by Rizzato et al, PCCP 2014 and not in Epel 2003. The latter discusses stochastic excitation for other reasons. This should be cited correctly.
Citation: https://doi.org/10.5194/mr-2024-14-RC1
- AC2:
  'Reply to RC1', Daniel Klose, 08 Oct 2024
  We thank Anonymous Referee 1 for the appreciation of our work and the detailed comments. Our point-by-point answers to the comments are:
  Page 3 phase cycle: Thank you for noting this and we apologize for the missing description. The 4-step phase cycles used in the experiments are:
  
  Mims: π/2 ( 0, π, 0, π) – π/2 (0, 0, π, π) – p_RF (0, 0, 0, 0) - π/2 (0, 0, 0, 0) – Det. (1, -1, -1, 1)
  
  Davies: π ( 0, 0, 0, 0) – p_RF (0, 0, 0, 0) – π/2 (0, 0, π, π) - π (0, π, 0, π) – Det. (1, -1, -1, 1)
  
  We will include the phase cycles in section 2.2 of the revised manuscript.
  Page 7 Setting up the chirp pulse: Thank you for this important comment.
  
  The first parameter to choose is the bandwidth of the chirp pulse and therefore the resolution desired in the experiment (e.g. 1 MHz chirp bandwidth gives approximately 1 MHz potential resolution in the ENDOR spectrum as visible in Figs. 3 and S2). As a second step the pulse length should be chosen such that the spectral power density is high enough to achieve full inversion for all couplings with the selected chirp bandwidth. This depends on the available RF amplifier output power, the ENDOR resonator and their frequency responses. In our case, for a 100 W RF amplifier output power and a Bruker X-band MD4 ENDOR resonator an RF pulse length of ca. 100 µs was sufficient for maximum sensitivity and full inversion (see Fig. 2d). Note that further increase of the RF pulse length maintains the ENDOR sensitivity (Fig. 2d).
  
  As we fully agree with the reviewer that the experiments should be as accessible as possible, we will include a new SI section 2 “Setup and Optimization of RF chirp pulses in ENDOR experiments” in the revised version of the manuscript.
  
  Page 7, lines 148 – 149: We apologize for the ambiguous sentence. We wanted to convey that RF pulses longer than 100 µs do not change the ENDOR intensity anymore and are therefore not needed. We will change l148 – 149 accordingly upon revision: “Figure 2c and d show that for a chirp bandwidth of 1 MHz a pulse length of about 100 µs is sufficient to achieve maximum intensity.”
  
  P8, line 172: For the simulation a Gaussian distribution of purely isotropic hyperfine couplings was used. Each coupling in this distribution is described by a delta peak with an infinitesimally small linewidth. The maximum of this distribution (“mean”) was set to 4 MHz. The width of this Gaussian distribution (FWHM) is 1.2 MHz corresponding to a standard deviation of 0.5 MHz as introduced in methods section 2.3. We will clarify this, by adding “isotropic” hyperfine coupling to the explanation in 3.3, and phrase the description as the “mean of the distribution of isotropic hyperfine couplings”.
  
  Fig 3B: For the ENDOR simulations using convolution (Fig. 3b) the chirp pulse excitation profile is calculated from pulse length and amplitude/power with EasySpin, as we will describe in more detail in the methods section 2.3 and in the SI section 1. This pulse excitation profile (as function of frequency offset from chirp center frequency) is convoluted with the experimental single frequency ENDOR spectrum. For full transparency and for those interested in the script of this simulation, we refer to the data and script accompanying this manuscript on zenodo 10.5281/zenodo.11082486.
  
  TRIPLE: We agree that a demonstration on different systems (e.g. including organic radicals) will be useful to get a better understanding of the performance of TRIPLE on diverse paramagnetic systems, however, for the application class of metal sites (as e.g. in catalysis) CuTPP is a relevant model system and hence test case. Thus, for applications in fields as catalysis, material science and bioinorganic chemistry, the chirp TRIPLE experiment on CuTPP in this paper showcases the utility of chirp pulses in 2D experiments. However, we do agree with the reviewer that on other systems such as slow-relaxing organic radicals, the performance of TRIPLE may well be somewhat worse, as also the case for TRIPLE without chirp pulses – however, this is beyond the scope of this paper.
  
  P2 line 7: We thank the reviewer for noting this incorrect citation, we will correct this in the revised manuscript.
  
  Citation: https://doi.org/10.5194/mr-2024-14-AC2
  - AC4: 'Reply on AC2', Daniel Klose, 25 Oct 2024
    
    Please note that the correct zenodo doi is 10.5281/zenodo.13625320.
    
    Citation: https://doi.org/10.5194/mr-2024-14-AC4
RC2:
'Comment on mr-2024-14', Anonymous Referee #2, 19 Oct 2024
In this manuscript by Stropp et al. the application of chirped RF pulses in pulsed ENDOR and TRIPLE experiments on the example of Cu(II)-tetraphenylporphyrin is demonstrated. All experiments are in the frequency-domain, i.e. the spectra a recorded stepwise incrementing the rf frequency. Since the Cu-TPP complex in frozen solution features anisotropic hyperfine couplings with broad line in particular for ¹⁴N and ^63,65Cu, through the introduction of a chirped rf pulse the authors can show a considerable intensity improvement in particular for the broader ¹⁴N and ^63,65Cu lines. The authors also demonstrate the balance of intensity enhancement vs. spectral broadening by approaching the ENDOR line width with the bandwidth of the chirp pulse.
The experimental work is carefully performed and mostly well described. I can recommend publication after sorting out a few points:
There is no EPR spectrum of Cu-TPP given, for completing the description at which B-field position the ENDOR/TRIPLE spectra are recorded there should be one displayed.

The chirp ENDOR simulatins are not exhaustive explained enough, the zenodo link given in the previous reply to RC1 refers ot another manuscript.

The loss in resolution in the chirp ENDOR spectrum when the bandwidth of the chirp rf pulse approaches the ENDOR linewidth can be understood similar to "overmodulating" a line in cw-EPR, spectral contributions add then to the line intensity which don't belong to the center rf frequency of the pulse.

Unfortunately the authors stop their chirp ENDOR simulations at more interesting cases: ¹⁴N ENDOR lines with NQI, where the chirp rf pulse can excite adjacent transitions in the same m_s manifold. The authors should explain, why the simulations become then "infeasible".

l178-184: The authors mix here chirp rf pulses (with too large bandwidth) with special TRIPLE experiments, which are not comparable: the chirp ENDOR are broadened beyond the overall spectral width, whereas in the special TRIPLE case (with small bandwidth) the 2 NMR transitions are hit simultaneously inreasing sensitivity and enabling quantitative experiments.

l155: The discussion of overtones from the rf amplifier leading to artificial lines in the ENDOR spectrum should be taken with care. Usually the occurance of higher harmonics of an amplifier is specified at 0 dBm rf input. Working within this limit or beyond is in the hands of the operator.

When it comes to the presentation of the TRIPLE results, it would be more insightful, if the authors not only explain how the spectra were acquired, but also how they can be interpreted. In this regards I can only emphasize the need of tabularised hyperfine couplings and their signs for Cu-TPP. This would make these experiments more attractive for readers, who are aiming for this information on other systems. In this context fig.4a stands rather unexplained, and the reader doesn't really know, how to interpret the 2D TRIPLE experiment (and if its worth to perform it for 2 days rather than a few 1D TRIPLE traces at specific hfc's).

In fig.4b the 1D difference TRIPLE traces and the improvement of intensity are shown, the measurement time would be interesting here, too, to compare with 2D TRIPLE and ENDOR.

For the TRIPLE experiments the bandwidth-dependent intensity/broadening effects are not unfortunately not investigated, which are to be expected in favour of intensity enhancement:

Since anisotropic lines are excited with nu(rf1), the higher the fraction of the excited anisotropic hyperfine line, the higher the intensity effect should be. Have the authors this possible effect taken into consideration, or even investigated?
Citation: https://doi.org/10.5194/mr-2024-14-RC2
- AC3:
  'Reply on RC2', Daniel Klose, 25 Oct 2024
  We thank Anonymous Referee 2 for the nice feedback and the detailed comments. Our answers to the comments are:
  We will add the experimental EPR spectrum to the supporting information and indicate the field position used for ENDOR, along with a table of the known spin Hamiltonian parameters for overview.
  
  We apologize for sharing the wrong zenodo link in the reply to Anonymous Referee 1. The correct zenodo doi is 5281/zenodo.13625320. Also, we will update the experimental section with a more thorough explanation of the ENDOR simulations.
  
  What we meant with the simulations “become infeasible” is that the computational cost to do time domain simulations for spin systems with a high number of spins increases exponentially, thus hampering spectral analysis by least-squares fitting of spin Hamiltonian parameters. This is the reason, why we think the convolution approach is of interest for the typical ENDOR spectroscopist: One can still use frequency domain simulations (as implemented in EasySpin) to analyze the experimental chirp ENDOR spectra as described. Regarding spin dynamics simulations of 14N: Thank you for pointing this out. We will consider this in the revision.
  
  We apologize for writing this not clearly enough. We did not to compare chirp ENDOR with special TRIPLE experiments, but just point out to the reader that in contrast to the chirp ENDOR experiments, in special TRIPLE experiments the excitation of 2 NMR transitions is exploited in a favorable, quantitative fashion. We will clarify this in the revision.
  
  We agree that it is in the hands of the operator to adjust the RF power carefully. Nevertheless, if samples have low signal intensities, sometimes one may choose higher sensitivities with shorter/stronger RF pulses at the compromise of introducing amplifier overtones. As explained in the manuscript, chirp pulses with lower power can be superior to single frequency pulses with high power and we encourage spectroscopists to use chirp pulses without introducing overtones in the spectrum. We will clarify this in the revision of the manuscript.
  
  As already mentioned in point 1 and the reply to the community comment by Fabian Hecker, we will include a table with hyperfine couplings for Cu-TPP in the manuscript. We will annotate the 2D TRIPLE spectrum with hyperfine and nuclear quadrupolar couplings. We agree that for CuTPP it is enough to record 1D TRIPLE traces at a few hfcs to read out the same information as from the 2D TRIPLE. However, this is a demonstration for more complicated systems with multiple paramagnetic centres, where 2D TRIPLE is required for a clear interpretation and we show (although on the comparably simple CuTPP system) that chirp RF pulses are valuable also for such cases.
  
  We will include the measurement (30 min/TRIPLE trace) in the figure caption. Please be aware that the 2D TRIPLE was measured with a slightly different number of points and non-uniform sampling.
  
  Thank you for the comment. We expect that the bandwidth-dependent effects in TRIPLE will be similar to ENDOR results as long as the chirp does not excite multiple transitions, and we therefore did not investigate this further. We agree that for 2D TRIPLE with maximum sensitivity the chirp pulse bandwidth should be adjusted to the width of the anisotropic line, as we note in the text, the chirp bandwidth could even be adapted specifically to the width of each ENDOR line, resulting in a non-uniform bandwidth excitation scheme.
  
  Citation: https://doi.org/10.5194/mr-2024-14-AC3

Julian Stropp, Nino Wili, Niels Christian Nielsen, and Daniel Klose

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https://doi.org/10.5194/mr-2024-14-supplement

Julian Stropp, Nino Wili, Niels Christian Nielsen, and Daniel Klose

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Short summary

Sensitivity is often the limiting factor in ENDOR. Here, we demonstrate how using chirp radiofrequency pulses can improve ENDOR sensitivity up to 3-9-fold, with the strongest increase for broader lines often encountered in disordered solids for nuclei such as nitrogen and metals. The resulting drastic speed-up in acquisition times renders also 2D ENDOR more feasible, as we demonstrate in 2D TRIPLE showing correlations of Cu hyperfine couplings.


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