Theory of broadband heteronuclear decoupling in multispin systems

Abstract

The Waugh theory of broadband decoupling in NMR for I-S Spin 1/2 pairs is extended to arbitrary spin systems. It is shown that complete decoupling is achieved over a certain bandwidth if the irradiation scheme generates an average Hamiltonian for the I spins whose eigenvectors and eigenvalues are independent of resonance offset. If the observed S spins are only weakly coupled, it is possible to calculate the resulting spectrum directly from the offset dependence of the average Hamiltonian of the isolated I-spin system under the influence of the periodic decoupling sequence. The treatment applies to indirectly observed multiple-quantum transitions as well as to directly observable single-quantum resonance lines.