Determination of internuclear distances from solid-state nuclear magnetic resonance: Dipolar transforms and regularization methods

Many NMR experiments have been designed to measure homonuclear or heteronuclear distances, and often generate time-domain dipolar signals that need to be analysed to extract the relevant dipolar coupling constants. These constants yield internuclear distances directly, and therefore an accurate and easily understandable extraction of these couplings from potentially noisy data is a major concern. Several dipolar signals will be considered in this work, including those obtained from the REDOR, MELODRAMA, and SEDOR experiments, and a new series form for the C7 and DCP signals. A review and discussion of an existing transform-based method for dipolar signal analysis is presented here, along with two new generalized methods for the extraction of coupling constants. One of the new methods is a fast procedure based on asymptotic signal forms, while the other is a regularization method specifically formulated to account for experimental noise, and shows significant performance gains over other methods when applied to noisy time-domain REDOR signals. In addition to its noise-handling ability, the second method also has wide application to many other types of dipolar signals currently available in NMR experiments, and is the only method of those discussed that can effectively yield a C7/DCP 'transform'. The explanation of the methods given here includes fundamental analogies to the 'dePaking' process that has been used to remove broadening effects from static solid-state NMR spectra of 2H nuclei.