NMR double-quantum spin decoupling in solids

The problem of spin-decoupling spin $I=1$ nuclear with large quadrupolar splittings ωQ (e.g. deuterium) from dilute S spins via double-quantum transitions is dealt with. The normal two-spin-{} single-quantum decoupling problem (I=1/2, S=1/2) is first dealt with as a reminder of the coherent averaging approach and to understand the dependence of the S-resonance linewidth on the I rf field intensity (ω₁) and resonance offset (Δω). The double-quantum problem ($I=1$, S=1/2) is then treated analogously by introducing fictitious spin-{} operators for the I double-quantum transition. The decoupling condition is found to be very sensitive to the spin-I resonance condition and to go as ~1ω₁⁴ with the spin-I rf field intensity at resonance in the double-quantum regime (ω₁ωQ). Experimental examples on heavy ice, dimethylsulfoxide-d₆ and benzene-d₆ are presented verifying the quantitative theoretical predictions. Extensions to higher-order multiple-quantum effects for spin $I>1$ and for several coupled spin-{} nuclei are discussed.