the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 19 Feb 2026
Dual Bilinear Rotations
Abstract. Bilinear rotations imply differing rotations on a spin I depending on the presence or absence of a bilinear coupling Hamiltonian to a heteronucleus S. As such, spin system selective inversions using BIRD elements, excitations using TANGO, or general (effective) rotations using BANGO and/or BIG-BIRD, as well as multiplicity edited rotations are achievable. So far, the well-defined rotations were only imposed on a single spin, e.g. I, while the coupled heteronucleus experienced only an inversion or no rotation at all. Here, we introduce Dual Bilinear Rotations, that simultaneously allow spin system selective manipulations on both spins I and S as compared to the coupled spin system IS. Particularly with the advent of multi-receive experiments and/or supersequences with the necessity to excite and store specific spin systems in a flexible way, this may open new possibilities in pulse sequence design. A general derivation of the approach is given and a quadruple J-resolved type experiment for obtaining fully decoupled spectra optmized for different spin systems is introduced for demonstration.
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Status: open (until 19 Mar 2026)
- RC1: 'Comment on mr-2026-1', Anonymous Referee #1, 06 Mar 2026 reply
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RC2: 'Comment on mr-2026-1', Anonymous Referee #2, 13 Mar 2026
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General comments
The article presented by Woordes and Luy presents a new approach to application of multitude of Bilinear Rotation (BIR) elements that could be used in NO Relaxation Delay (NORD) NMR super-sequences, allowing to simultaneously acquire multiple different experiments with the same recycle delay. The family of four BIR elements (BIRD, TANGO, BANGO and BIG-BIRD) allowing to achieve different rotations on different coherences in the same time is presented. Thanks to the use of uniform rotation pulses, almost any combination of rotation angles may be achieved independently and concurrently for directly or remotely J-coupled spin systems on the chosen spectral widths. These Dual Bilinear rotations have been applied to the quadruple J-resolved experiment, in the same time revealing up to four different spectra, acquired with one relaxation delay. The manuscript is written well, and thanks to introduction to the nomenclature of the BIR elements, it should be understandable for an NMR spectroscopist, who had limited knowledge on the matter beforehand. The presented experiment has been discussed in detail with benefits and possible issues inherent to the method. However, the quality of the suppression of undesired coherences in the quadruple J-resolved experiment is slightly disappointing, and I would like to propose to test the method on a different sample, free from homonuclear 13C couplings (vide infra). On the general side, I find that currently sufficient experimental information has been given to reproduce the experiments independently.
Specific comments
As in NMR spectroscopy, the rate limiting factor influencing the duration of a pulse sequence often is determined by up to a few-second long recycle delay, the presented method may bring significant time savings in the acquisition of multiple experiments following the NORD principles. I find the quadruple J-resolved experiment an elegant illustration of the capabilities of the Dual Bilinear Rotation elements, as it allows to concurrently obtain complementary information on the spin systems featured by the molecules in question.
It would be intriguing to elaborate more on the potential ways of handling: (1) the long range heteronuclear couplings and (2) homonuclear couplings. Presumably, the first should be easier to handle, while the latter would lead to significant magnetization losses as it is inherent to the free from homonuclear couplings pure shift spectra. The numerical or experimental verification of such approach would probably be beyond the scope of this article, but explanation on how one can potentially deal with the two aspects could be mentioned in the main text.
Concerning the application of the Coupling Offset B1-compensated (COB) principle to the Dual Bilinear Rotation Elements, it would be interesting to present the method on a slightly more complex molecule but with less complexity in terms of homonuclear couplings spin system than glucose. For instance, one could try to apply the experiment to some other small molecule, which features a range of heteronuclear J-coupling values (weak long-range and strong short-range), and for which the presence of homonuclear 13C-13C couplings is less problematic. For instance, one could use 13C sample specifically labelled at certain distant positions, to avoid the presence of strong homonuclear 13C couplings. In the same time this sample could feature a range of (short- and long-range) heteronuclear couplings for which one could design the method to either suppress or promote to give the signal, depending on the delays in the COB element(s). This addition to the article would enhance the illustration of applicability of the J-resolved method, as it is postulated in the manuscript.
Technical comments
In the line 107: I presume that “Cq” denotes quaternary carbon. Please make the assignment more explicit, as it might be not obvious for the reader.
In the figure 3, there is a plethora of spin rotations happening. One could benefit from addition of a subfigure with simplified effect of the Dual Bilinear Rotations in each sandwich (e.g. Pi_x on spin I, Pi_x on spin S) similarly to the colored parts of the Figure 2.
In the figures 4 and 5, one could increase the font size of the x-axis labels, to match the one of the titles of the spectra. The way it is right now requires to zoom-in to better see the numbers and the [ppm] marker.
Citation: https://doi.org/10.5194/mr-2026-1-RC2
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The novelty of this work is in the introduction of the Dual Bilinear Rotations which allows simultaneous spin system selective manipulations on both spins I and S as compared to the coupled spin system IS. The material is well presented and argued. Its value is in the introduction of a new concept rather than in the current presented example. I support publication of this manuscript and have only minor comments.
Can authors present the 2D spectra in the SI, rather than just their projections?
The authors have chosen to illustrate the technique on a fully 13C labelled glucose. This introduces complications because of the presence of 13C-13C coupling constants. How would these experiments behave on 13C natural abundance samples? How would these experiments behave on 5-10% enriched 13C natural abundance samples that are typically used to boost the sensitivity yet limiting complication of 13C,13C coupling constants?
Fig. 4c: “The blue sub spectrum is designed to mainly contain directly 13C bound” Can the authors comment on why is the ß-D glucose signal so pronounced?
Page 6, line 119: typo in “ homonuclear and heteronuclear couplings evolvle to the …”