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

Many important double-quantuin recoupling techniques in solid-state NMR are classified as being gamma-cncoded. 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 gamma-encoded pulse sequences. The validity of the analytical Solutions is tested by numerical simulations. The internuclear distance in a C-13(2)-labelled retinal is estimated by fitting the analytical Curves to experimental double-quantum data. (C) 2007 Elsevier Inc. All rights reserved.