Status: this preprint is currently under review for the journal MR.
Dual Bilinear Rotations
Yannik T. Woordesand Burkhard Luy
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.
Received: 12 Jan 2026 – Discussion started: 19 Feb 2026
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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 …”
Institute of Organic Chemistry and Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
Institute of Organic Chemistry and Institute for Biological Interfaces 4 - Magnetic Resonance, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
Dual bilinear rotations are introduced, which lead to well-defined rotations for both heteronuclear spins I and S that depend on the presence or absence of a (large) coupling between them. It is therefore an extension of conventional bilinear rotations, which cause such a spin-system-dependent rotation only for the spin I. A general derivation of the approach is given and a quadruple J-resolved type experiment is introduced for demonstration.
Dual bilinear rotations are introduced, which lead to well-defined rotations for both...
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 …”