the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
19 Jan 2021
19 Jan 2021
Simple rules for resolved level crossing spectra in magnetic field effects on reaction yields
- 1Voevodsky Institute of Chemical Kinetics and Combustion, Novosibirsk, 630090, Russia
- 2Novosibirsk State University, Novosibirsk, 630090, Russia
- 1Voevodsky Institute of Chemical Kinetics and Combustion, Novosibirsk, 630090, Russia
- 2Novosibirsk State University, Novosibirsk, 630090, Russia
Abstract. In this work we derive conditions under which a level crossing line in magnetic field effect curve for a recombining radical pair will be equivalent to ESR spectrum, and discuss three simple rules for qualitative prediction of the level crossing spectra.
Dmitri V. Stass et al.
Status: final response (author comments only)
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RC1: 'Comment on mr-2021-6', Anonymous Referee #1, 03 Feb 2021
In the paper very interesting and useful results on the detection of the EPR spectra of radicals by the MARY method are obtained. The idea is very similar to the transfer of a low frequency audio signal by means of radio carrier frequency modulation. The "carrier frequency" is the intersection of levels in a high field, caused by a radical with large hfi coupling constants. A detailed analysis of the position and width of the resonance caused by the level crossing is carried out. The hyperfine structure of the second radical of the radical pair acts as a "sound signal". The authors show that the level crossing in the zero field does not allow detecting the EPR signal of the second partner, which is similar to that the low-frequency audio signal is not transmitted directly, that is, without modulation by the carrier frequency. The authors carried out a detailed theoretical analysis of the detection of the EPR spectrum of the second partner for various configurations of the hfi spectrum of the first partner (with large hfi constants). The rules are formulated concerning this detection method. I consider the article very useful for the field of magnetic resonance (ESR) and recommend it for publication in the journal as it is. There are the following notes:
1. It is written: "Laplace transform of singlet state population
as a function of applied static magnetic field ... "- it is necessary to clarify that the Laplace transform is done in time domain, otherwise it can be understood that the Laplace transform is done in the magnetic field domain.
2. It is written: "For the outersmost blocks with \Sigma = + -I... Real outmost states are with \Sigma = + -(I+1). Of course, these states are tripet ones and they does't take part in spin dynamics since they are eigen states but may be it is worth to mention this (?).-
AC1: 'Reply on RC1', Dmitri Stass, 08 Feb 2021
Thank you for a very interesting view at our work. Your interpretation of the behaviour of the spin system of a radical pair in the vicinity of level crossing points that we analysed as a sort of frequency shift similar to FM is really enlightening and triggers quite some further ideas and analogies. Especially valuable for us is the noted analogy to distinction between the zero-field and non-zero field crossings. It would be also interesting to ponder that what we have here is not only a spectrum shift, but also a pitch shift, or spectrum stretching, due to varying intersection angles of the crossing levels.. In radiotechnics pitch shifting is a time-domain rather then frequency-domain transform, realizable by picking samples faster/slower than they were originally taken, and it is really interesting to ponder what the implications of this might be for a spin system. The link to the field of radiofrequency techniques is indeed quite unexpected and potentially very fruitful as leading outside the box. Thank you very much for your input again. Regarding two your more specific notes, they are certainly valid and benefitial for the readers, and we shall incorporate suitable straightforward amendments for both of them to the revised version of this manuscript.
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AC1: 'Reply on RC1', Dmitri Stass, 08 Feb 2021
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RC2: 'Comment on mr-2021-6', Anonymous Referee #2, 09 Feb 2021
The simplest model for analysing the spin dynamics of radical pairs is the so-called ‘exponential model’ and the simplest description of radical pair spin-state evolution is under the action of a spin Hamiltonian that contains only electron Zeeman and hyperfine coupling terms for each of the individual radical pair partners. This description of radical pairs has long been used to provide useful insights into the behaviours of radical pairs and in particular is often the starting point for simulation of dependence of magnetic field effects on applied magnetic field strength - the so-called MARY curve. In this work the authors take a new analytical approach to deconstructing the predictions of this model. This results in a set of rules that provide very useful insights into both the key features of MARY curves, but that also predict the ability to use MARY as a spectroscopic method yielding spectra effectively equivalent to conventional ESR spectra under particular constraints of the relative hyperfine structure of the pair partners.
I believe that the analytical approach is an extremely useful one, with important predictive power. In particular, I found that the insight it provides over the essential ‘canceling’ of crossings and anti-crossings and the resulting impact on, for example, the so-called ‘low-field effect (LFE)’ highly enlightening. In this particular case (and indeed perhaps more so in the other cases discussed) the rules and analytical framework might lead to important new usage cases for ‘MARY spectroscopy.’ The authors do a good job of relating this approach back to existing ones and highlighting the new insights as well as confirming that it leads to the same existing predictions and understanding.
Therefore, I have no hesitation in recommending that this paper be published as is. However, I do have some observations that the authors may wish to consider (i.e. these are fully optional but may be worth giving some thought to).
1) Accessibility
The paper is clearly written and while it contains a large number of equations, it is quite straightforward and logical to follow. However, I think the lack of any visual representation of the findings is to some extent a missed opportunity. I feel that in the key example domains the authors consider, it might be useful to provide example spectra and highlight the features that the interpretation is pointing at. Personally I find some problems easier to think about mathematically and others visually. By providing an additional visual representation, it may increase the accessibility of the findings to a broader audience.
2) Extensions
As I indicated at the beginning of this comment, the rules are based on a very simple model of RP reactions which does not account for electron exchange or dipolar interactions, incoherent spin relaxation or spin-selective reaction (to name a few). Given the importance of some of these factors, particularly in relation to some of the realistic example systems provided, I wonder if the authors could say even a little about how some of these factors might influence the simple predictions? This may also be useful to experimentalists in thinking about real systems that can exploit some of the predictions provided.
3) Small errors.
I provide no adjustment to grammatical errors in the manuscript, but I did notice a small number of typographical errors that either directly impact the scientific meaning, affect technical terms or may confuse. I list these below:
- Line 195 ‘produce crossings Of Eq. (7)’ —> ‘produce crossings of Eq. (7)’
- Line 343 ‘in addition to for equivalent fluorines’ —> ‘in addition to four equivalent fluorines’
- Line 354 ‘donor-acceptor diads’ —> ‘donor-acceptor dyads’
Dmitri V. Stass et al.
Dmitri V. Stass et al.
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