Multiple-oscillating-field techniques for accurate distance measurements by solid-state NMR.

Dipolar truncation prevents accurate measurement of long-range internuclear distances between nuclei of the same spin species, e.g., within (13)C-(13)C spin pairs in uniformly (13)C-isotope-labeled proteins, using magic-angle spinning solid-state NMR spectroscopy. Accordingly, one of the richest sources of accurate structure information is at present not exploited fully, leaving the bulk part of the experimentally derived structural constraints to less accurate long-range (13)C-(13)C dipolar couplings estimated from methods based on spin diffusion through proton spins in the close environment. In this paper, we extend our previous triple-oscillating field technique [N. Khaneja and N. C. Nielsen, J. Chem. Phys. 128, 015103 (2008)] for dipolar recoupling without dipolar truncation in homonuclear spin systems to a more advanced rf modulation with four independent oscillations and rotations involving nonorthogonal axes. This provides important new degrees of freedom, which are used to improve the scaling factor of the recoupled dipole-dipole couplings by a factor of 2.5 relative to the triple-oscillating field approach. This significant improvement, obtained by refocusing of otherwise defocused parts of the residual dipolar coupling Hamiltonian, may be exploited to measure much weaker (13)C-(13)C dipolar couplings (and thereby longer distances) with much higher accuracy. We present a detailed theoretical description of multiple-field oscillating recoupling experiments, along with numerical simulations and experimental results on U-(13)C, (15)N-L-threonine and U-(13)C,(15)N-ubiquitin.