the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 10 Sep 2024
Increased sensitivity in Electron Nuclear Double Resonance spectroscopy with chirped radiofrequency pulses
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.
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CC1: 'Comment on mr-2024-14', Fabian Hecker, 02 Oct 2024
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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
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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
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RC1: 'Comment on mr-2024-14', Anonymous Referee #1, 04 Oct 2024
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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
reply
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) – pRF (0, 0, 0, 0) - π/2 (0, 0, 0, 0) – Det. (1, -1, -1, 1)
Davies: π ( 0, 0, 0, 0) – pRF (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 - 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:
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