Double-quantum cross-polarization NMR in solids

Double-quantum NMR is a useful way to obtain spectra of quadrupolar nuclei ('D, "N, ...) in solids. This allows measurements of the chemical shifts for these nuclear spins. The theory of Hartmann-Hahn cross polarization between I = 1/2 and such S = 1 spins is discussed. Particular attention is drawn to the cross polarization of the double-quantum transition. The thermodynamics and the dynamics of the process are evoked in detail using a fictitious spin-1/2 formalism. The spin S = 1 Hamiltonian can always be factored into two commuting parts (independent thermodynamic reservoirs), one of which behaves as a fictitious spin 1/2 which is cross polarized with the I = 1/2 spins. Modified Hartmann-Hahn conditions emerge from the theory, and the dependence of cross-polarization times Trs on rf intensity and frequency for spin locking and adiabatic demagnetization in the rotating-frame experiments are calculated. Measurements on the 'H-'D double resonance in dilute solid benzene-d, are reported, verifying the predictions and indicating that cross polarization provides a sensitive means of detecting the 'D double-quantum transition, Values are reported for the thermodynamic parameters and cross-polarization times as a consequence. Three possible versions of double-resonance detection of double-quantum spectra are possible —direct detection of the cross-polarized double-quantum decay, indirect detection of the frequency spectrum following Hartmann and Hahn, and indirect detection of the free-induction decay following Mansfield and Grannell.