Three-spin effects in broadband decoupling

Current procedures for broadband decoupling in carbon-13 spectroscopy are slightly perturbed by a new phenomenon called the "three-spin effect." It arises when there is a spin-spin coupling between two nonequivalent protons and introduces spurious splittings into the carbon-13 spectrum. These are normally too weak to be resolved, leaving a slight line-broadening effect. The three-spin effect is treated theoretically and shown to be a result of bilinear terms in the propagator equation, not compensated by the action of the decoupling sequence. The general case is too complicated to be treated analytically but numerical methods demonstrate that the magnitude of the effect is proportional to the value of the proton-proton coupling constant and the direct proton-carbon coupling constant but virtually independent of the small long-range proton-carbon coupling. The magnitude of the splitting is inversely proportional to the level at which the decoupler operates and is a complex function of the two proton resonance offsets. The effect vanishes if the two protons have the same chemical shift or if the distant proton lies outside the effective bandwidth of the decoupler. Splitting due to the three-spin effect is demonstrated experimentally for an extreme case where there is a large (trans) proton-proton coupling and an unrealistically low decoupler level (750 Hz). The form of the spectrum is in excellent agreement with computer simulations which take into account the spatial inhomogeneity of the decoupler field.