Fivefold symmetric homonuclear dipolar recoupling in rotating solids: Application to double quantum spectroscopy

We describe a new fivefold symmetric approach to homonuclear recoupling in rotating solids that is based on rotor-synchronized, spin-lock rf irradiation of the type employed previously in MELODRAMA and C7 (and their derivative sequences) for ${}^{13}\mathrm{C}{–}^{13}\mathrm{C}$ recoupling. The fivefold sequence, like its sevenfold relatives, is γ-encoded, and therefore exhibits a theoretical efficiency of ∼73% for double quantum filtering (2QF). However, since the ratio of rf field strength, ${\omega }_{\mathrm{rf}}\text{/2π,}$ to spinning frequency, ${\omega }_r\text{/2π,}$ is lower, it is possible to operate the sequence at higher spinning rates, and we have investigated the 2QF efficiency as a function of ${}^1\mathrm{H}$ decoupling field strength at high spinning frequencies. We observe dramatic oscillations of the recoupled signal with a period ${\mathrm{\sim \omega }}_r\text{/2π}$ indicating that the ${}^1\mathrm{H}$ reservoir is behaving partially inhomogeneously. This kind of double quantum recoupling is explored in multiple spin systems and we derive analytical forms for polarization transfer and double quantum excitation relevant for uniformly labeled systems. Finally, the wide applicability of the fivefold sequence is demonstrated with INADEQUATE type spectra of uniformly ${}^{13}\mathrm{C}$ labeled sucrose and L-alanine.