DQ-DRENAR: A new NMR technique to measure site-resolved magnetic dipole-dipole interactions in multispin-1/2 systems: Theory and validation on crystalline phosphates

Abstract

A new solid state NMR technique is described for measuring homonuclear dipole-dipole interactions in multi-spin-1∕2 systems under magic-angle spinning conditions. Re-coupling is accomplished in the form of an effective double quantum (DQ) Hamiltonian created by a symmetry-based POST-C7 sequence consisting of two excitation blocks, attenuating the signal (intensity S'). For comparison, a reference signal S0 with the dipolar re-coupling absent is generated by shifting the phase of the second block by 90° relative to the first block. As in rotational echo double resonance, the homonuclear dipole-dipole coupling constant can then be extracted from a plot of the normalized difference signal (S0 - S')∕S0 versus dipolar mixing time. The method is given the acronym DQ-DRENAR ("Double-Quantum-based Dipolar Re-coupling effects Nuclear Alignment Reduction"). The method is analyzed mathematically, and on the basis of detailed simulations, with respect to the order and the geometry of the spin system, the dipolar truncation phenomenon, and the influence of the chemical shift anisotropy on experimental curves. Within the range of (S0 - S')∕S0 ≤0.3-0.5 such DRENAR curves can be approximated by simple parabolae, yielding effective squared dipole-dipole coupling constants summed over all the pairwise interactions present. The method has been successfully validated for (31)P-(31)P distance determinations of numerous crystalline model compounds representing a wide range of dipolar coupling strengths.