Analytical theory of γ-encoded double-quantum recoupling sequences in solid-state nuclear magnetic resonance

Many important double-quantum recoupling techniques in solid-state NMR are classified as being γ-encoded. This means that the phase of the double-quantum effective Hamiltonian, but not its amplitude, depends on the third Euler angle defining the orientation of the molecular spin system in the frame of the magic-angle-spinning rotor. In this paper, we provide closed analytical solutions for the dependence of the powder-average double-quantum-filtered signal on the recoupling times, within the average Hamiltonian approximation for γ-encoded pulse sequences. The validity of the analytical solutions is tested by numerical simulations. The internuclear distance in a 13C2-labelled retinal is estimated by fitting the analytical curves to experimental double-quantum data.