Effective dipolar couplings determined by dipolar dephasing of double-quantum coherences

It is shown how homonuclear distances and homonuclear dipolar lattice sums between spin-1/2 nuclei can be measured by a pulsed solid-state NMR experiment under magic-angle spinning conditions. The presented technique is based on double-quantum coherence filtering. Instead of measuring a build-up of double-quantum coherence the pulse sequence is designed to dephase double-quantum coherence. This is achieved by exciting double-quantum coherence either with the help of the through-space dipolar coupling or the through-bond dipolar coupling while the dephasing relies on the through-space dipolar coupling as selected by a γ-encoded pulse sequence from the C/R symmetry class. Since dephasing curves can be normalized on zero dephasing, it is possible to analyze the initial dephasing regime and hence determine dipolar lattice sums (effective dipolar couplings) in multiple-spin systems. A formula for the effective dipolar coupling is derived theoretically and validated by numerical calculations and experiments on crystalline model compounds for 13C and 31P spin systems. The double-quantum dephasing experiment can be combined with constant-time data sampling to compensate for relaxation effects, consequently only two experimental data points are necessary for a single distance measurement. The phase cycling overhead for the constant-time experiment is minimal because a short cogwheel phase cycle exists. A 2D implementation is demonstrated on [13C3]alanine.