Robust Bilinear Rotations II

Abstract. Bilinear rotations are essential building blocks in modern NMR spectroscopy. They allow the rotation of an isolated spin without couplings, i.e. bilinear intereactions, in one way, while rotating spins with a matched coupling in another way. Different classes of rotations form the different bilinear rotations with acronyms BIRD, TANGO, BANGO, and BIG-BIRD. All original elements have in common that hard pulses limit bandwidths and that defined rotations for coupled spins are only possible for a narrow range of coupling constants. We recently introduced the COB-BIRD with a general optimization procedure to obtain robust bilinear rotations well-compensated with respect to couplings, offsets, and B₁-inhomogeneities (Y. T. Woordes et al., Sci. Adv. 11 (2025), eadx7094). Here we show a fundamental principle on how the COB-BIRD can be used to construct all types of bilinear rotations with the same improved robustness covering a coupling range of 120–250 Hz. In addition, a construction principle for universal rotation pulses is adapted to produce bilinear rotations from INEPT-type transfer elements, allowing the construction of bilinear rotations also for higher coupling ranges from e.g. COB3-INEPT with coupling compensation in the range of 120–750 Hz. After introducing the two fundamental design principles, example sequences of the four classes of bilinear rotations and different degrees of robustness are derived and characterized in theory and experiment. In addition, a highly useful HMBC/ASAP-HSQC-IPE-COSY supersequence is introduced with a (COB-)BANGO element for Ernst-angle type excitation. Finally, BIRD-decoupled J-resolved INEPT experiments with extreme compensation for partially aligned samples with with total couplings ranging from 47 Hz up to 434 Hz are demonstrated.