Sensitivity enhancement by multiple-contact cross-polarization under magic-angle spinning

Multiple-contact cross-polarization (MC-CP) is applied to powder samples of ferrocene and l-alanine under magic-angle spinning (MAS) conditions. The method is described analytically through the density matrix formalism. The combination of a two-step memory function approach and the Anderson-Weiss approximation is found to be particularly useful to derive approximate analytical solutions for single-contact Hartmann-Hahn CP (HHCP) and MC-CP dynamics under MAS. We show that the MC-CP sequence requiring no pulse-shape optimization yields higher polarizations at short contact times than optimized adiabatic passage through the HH condition CP (APHH-CP) when the MAS frequency is comparable to the heteronuclear dipolar coupling, i.e., when APHH-CP through a single sideband matching condition is impossible or difficult to perform. It is also shown that the MC-CP sideband HH conditions are generally much broader than for single-contact HHCP and that efficient polarization transfer at the centerband HH condition can be reintroduced by rotor-asynchronous multiple equilibrations-re-equilibrations with the proton spin bath. Boundary conditions for the successful use of the MC-CP experiment when relying on spin-lattice relaxation for repolarization are also examined.