Bilinear rotations like BIRD, TANGO, BANGO, and BIG-BIRD are essential building blocks in modern nuclear magnetic resonance (NMR) spectroscopy that 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. Two ways for constructing particularly robust bilinear rotations (compensated for couplings, offsets, and B₁ inhomogeneities, or COB/COB3) are provided and demonstrated in both theory and experiment.

This research reveals the hidden rules that connect the perfect mirror-image shape of a high-resolution nuclear magnetic resonance spectrum to the properties of a molecule's nuclear spin system. We found that this symmetry occurs only when specific, balanced conditions are met within the spin system. Testing these rules on various theoretical models confirmed their universal nature, providing a new framework for interpreting molecular symmetry from spectral patterns.

The developed probe head, which is a combination of the bimodal resonator operating in transmission mode and the low-noise amplifier, led to at least a 2-fold improvement in the sensitivity of the electron paramagnetic resonance spectrometer independent of sample temperature. The probe head is compatible with commercial Bruker spectrometers without their modification.