Further perspective on the theory of heteronuclear decoupling

An exact general theory of heteronuclear decoupling is presented for spin-1/2 IS systems. RF irradiation applied to the I spins both modifies and generates additional couplings between states of the system. The recently derived equivalence between the dynamics of any N-level quantum system and a system of classical coupled harmonic oscillators makes explicit the exact physical couplings between states. Decoupling is thus more properly viewed as a complex intercoupling. The sign of antiphase magnetization plays a fundamental role in decoupling. A one-to-one correspondence is demonstrated between ±2SyIz and the sense of the S-spin coupling evolution. Magnetization Sx is refocused to obtain the desired decoupled state when ∫2SyIzdt=0. The exact instantaneous coupling at any time during the decoupling sequence is readily obtained in terms of the system states, showing that the creation of two-spin coherence is crucial for reducing the effective scalar coupling, as required for refocusing to occur. Representative examples from new aperiodic sequences as well as standard cyclic, periodic composite-pulse and adiabatic decoupling sequences illustrate the decoupling mechanism. The more general aperiodic sequences, obtained using optimal control, realize the potential inherent in the theory for significantly improved decoupling.