# Robust bilinear rotations II

## TL;DR

This paper introduces new methods for robust bilinear rotations in NMR spectroscopy, improving performance across a wide range of spin couplings.

## Contribution

The paper presents a general design principle for robust bilinear rotations using COB-BIRD and INEPT-type transfer elements.

## Key findings

- COB-BIRD can construct bilinear rotations with robustness across 120–250 Hz coupling ranges.
- A new method using INEPT-type elements extends robustness to 120–750 Hz coupling compensation.
- Experimental validation of sequences like HMBC/ASAP-HSQC-IPE-COSY and J-resolved INEPT is demonstrated.

## Abstract

Bilinear rotations are essential building blocks in modern NMR spectroscopy. They allow the rotation of an isolated spin without couplings (i.e., bilinear interactions) in one way, while rotating spins with a matched coupling in another way. Different classes of rotations form the different bilinear rotations, with the acronyms BIRD, TANGO, BANGO, and BIG-BIRD. All original elements have in common hard pulses limiting bandwidths and defined rotations for coupled spins that are possible only for a narrow range of coupling constants. We recently introduced the COB-BIRD with a general optimization procedure to obtain robust bilinear rotations that are well compensated for couplings, offsets, and B1 inhomogeneities . 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, for example, 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 total couplings ranging from 47 Hz up to 434 Hz, are demonstrated.