the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 05 Jun 2024
1H enhanced 103Rh NMR spectroscopy and relaxometry of Rh(acac)3 in solution
Abstract. Recently-developed polarisation-transfer techniques are applied to the 103Rh NMR of the Rh(acac)3 coordination complex in solution. Four-bond 1H-103Rh J-couplings of around 0.39 Hz are exploited to enhance the 103Rh NMR signal and to estimate the 103Rh T1 and T2 relaxation times as a function of field and temperature. The 103Rh longitudinal T1 relaxation in Rh(acac)3 is shown to be dominated by the spin-rotation mechanism, with an additional field-dependent contribution from the 103Rh chemical shift anisotropy.
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Status: open (until 08 Jul 2024)
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RC1: 'Comment on mr-2024-10', Anonymous Referee #1, 22 Jun 2024
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I was not familiar with the previous work from this team on 103Rh NMR and the polarisation transfer techniques used here, so I am looking at this "fresh". It seems to be a sound piece of work, if rather specialised, and it is always pleasing to see graphs that are properly drawn and labeled and numbers and units used with care.
One thing that particularly interested me, because it is an area I am currently looking at, was the use of composite 180° pulses. How was the "symmetrized BB1" chosen? I've just done a quick simulation and it appears that the symmetrized version yields a larger phase dispersion during refocusing than the original BB1 pulse! However, in contrast, an antisymmetric 180° pulse yields no phase dispersion whatsoever when used for refocusing (JMR 214, 68-75 (2012)) and that is the type of pulse I would have tried first - for example, the F1 or G1 composite pulse (JMR 93, 199-206 (1991)) or, if dual-compensation was required, perhaps one of the ASBO family of pulses (JMR 225, 81-92 (2012)). On the other hand, it is possible that in this particular application, the precise choice of sequence is not that important, with the matching of the 1H and 103Rh field strengths being the key issue?
Citation: https://doi.org/10.5194/mr-2024-10-RC1 -
CC1: 'Reply on RC1', Mohamed Sabba, 24 Jun 2024
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We thank the reviewer for their positive comments on our paper! In this particular paper - chiefly a relaxometry study in which the dual-channel PulsePol or DualPol sequence happened to be the cross-polarization sequence of choice - we have not investigated the aspect of composite pulses in great depth, and this is a theme for future research.
Nevertheless, sharing the reviewer’s passion for composite pulses, and in the spirit of transparency and open discussion in this journal, I will offer a longer answer below, in candid detail, in a personal capacity.
In this work, composite 180 pulses are used in two places: both the cross-polarization (DualPol) sequences, as well as the simple spin-echo train used to measure the T2. While both of these utilize a basic spin echo building block, the behavior of composite pulses is not necessarily identical.
As the reviewer has correctly pointed out, symmetric composite pulses within spin echo trains designed to refocus transverse magnetization are indeed associated with phase distortions, a problem that was first examined by Levitt and Freeman (https://doi.org/10.1016/0022-2364(81)90082-2) during the development of solution-state decoupling sequences. As shown in their early work, the phase distortion cancels out when an even number of spin echoes is used! Care was indeed taken to ensure all experiments used an even number of spin echoes.
Coterminously with the aforementioned paper, Levitt and Freeman also proposed the usage of supercycles (consisting of a pattern of Pi phase shifts) in spin echo trains, combined with (symmetric) composite 180 pulses, as an additional layer of error compensation (https://doi.org/10.1016/0022-2364(82)90042-7, see also Levitt's PhD thesis https://ora.ox.ac.uk/objects/uuid:8365b030-de70-4b96-a9a0-e0fd32290551/files/m854633531469ac51aff713a29e76ab78). This is important; supercycles (MLEV-64) were used both in the T2 sequence in our paper, and arguably the DualPol sequence.
The reviewer also points out the usage of antisymmetric (which has become a synonym with phase-distortionless) composite pulses, that is, composite pulses whose phase shifts are antisymmetric in time. Composite pulses of the phase-distortionless variety were first examined by the Pines group (https://doi.org/10.1016/0022-2364(85)90270-7) with the theory explicitly laid out in the paper by Tycko, Pines, and Guckenheimer on iterative schemes (see Appendix B of https://doi.org/10.1063/1.449228). Wimperis significantly expanded previous work of the Pines group in the 1990s in a series of papers, the most relevant of which described a class of composite pulses which includes BB1 (https://doi.org/10.1006/jmra.1994.1159), as well as the closely related F1 composite pulse (https://doi.org/10.1016/0022-2364(91)90043-S). As shown in the work by Sami Husain, Minaru Kawamura, and Jonathan Jones (https://doi.org/10.1016/j.jmr.2013.02.007), the BB1 and F1 composite pulses are closely related, and there are subtle advantages to the usage of the symmetrized BB1 sequence (used in our paper) which include better off-resonance performance. More recent work by Wimperis that the reviewer points out includes the description of the ASBO-11 composite pulses (https://doi.org/10.1016/j.jmr.2012.10.003; see also the PhD thesis of Smita Odedra https://theses.gla.ac.uk/5772/).
As for “why this composite pulse” – at the risk of sounding anecdotal – I investigated a variety of composite pulses (including BB1, F1, ASBO-11, and many more) during my PhD, working at the time with spin echo-based sequences that were severely sensitive to pulse strength/rf homogeneity errors. In a nutshell, the symmetrized BB1 sequence struck a perfect balance between efficiency improvements, elegance, and simplicity. Note that the last two qualities are entirely subjective. We were also attracted by the fact that the BB1 composite pulse could be used to replace 90 degree pulses as well as 54.74 degree pulses (used in e.g. the T00 filters of singlet NMR) - we could use a single family of composite pulses in any of our pulse sequences.
Directly after my PhD work on sequence development, we discovered that the PulsePol sequence - invented by Benedikt Tratzmiller of the Ulm group (https://oparu.uni-ulm.de/items/d5648138-630c-44a8-95e7-6b9fddde4a4a) for the purpose of optical DNP in NV centres – was a rather effective sequence for the apparently unrelated purpose of nuclear singlet excitation. It is worth noting that the Ulm group also investigated the effect of composite pulses in the PulsePol sequence (https://www.science.org/doi/10.1126/sciadv.aat8978). At this point, I decided to compare the performance of a few composite pulses incorporated within PulsePol by theory and experiment, including BB1, ASBO-11, and F1 (unpublished) whose robustness comparisons may be found in our paper (https://pubs.aip.org/aip/jcp/article/157/13/134302/2841905). To my surprise, the use of the (antisymmetric) F1 pulse did not appear to have any great difference in performance to the (symmetrized) BB1 pulse in our particular implementations at the time. As for the reasons - I am not prepared to speculate further.
It is worth noting that the PulsePol sequence has what can be argued to be a "built-in" supercycle [0,π,0,π] applied to the 180 pulses we have called "riffling" (https://pubs.aip.org/aip/jcp/article/157/13/134302/2841905). Other (unpublished) possibilities include [0,π,0,π,π,0,π,0]. These phase modifications were shown to be compulsory for the final robustness of the sequence, regardless of whether symmetric or antisymmetric composite pulses were used.
This success with the PulsePol sequence for robust singlet excitation inspired us to adapt it as a heteronuclear cross-polarization sequence (“DualPol”), and I chose to use the symmetrized BB1 pulse in light of the above history.
As for the reviewer’s last point – it is worth noting that the matching of the 1H/103Rh (I/S) field strengths is completely unnecessary in a windowed cross-polarization sequence such as DualPol! Unlike the traditional Hartmann-Hahn experiment (in which there is an extraordinarily stringent condition on the matching of the strengths of the synchronous rf fields), the I-S mixing in the DualPol sequence occurs entirely during the pulse-interrupted free evolution. That is to say, the sequence would still work if the nutation frequency on the I spins was 20,000 kHz and the nutation frequency on the S-spin channel was 4 kHz, under the tacit assumption that both nutation frequencies greatly exceed the IS J-coupling. We intentionally chose to match the 1H/103Rh field strengths largely for reasons of readability. The consequences of a matched vs. unmatched rf field on the final performance of the sequence are unknown, and will be a theme for future research.
Citation: https://doi.org/10.5194/mr-2024-10-CC1
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CC1: 'Reply on RC1', Mohamed Sabba, 24 Jun 2024
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