Double-quantum NMR is a useful way to obtain spectra of quadrupolar nuclei (²D, ¹⁴N,...) 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-{} 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 {} 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 TIS on rf intensity and frequency for spin locking and adiabatic demagnetization in the rotating-frame experiments are calculated. Measurements on the ¹H-²D double resonance in dilute solid benzene-d₁ are reported, verifying the predictions and indicating that cross polarization provides a sensitive means of detecting the ²D 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.
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Vega et al. (1980) studied this question.