Determining relative proton–proton proximities from the build-up of two-dimensional correlation peaks in 1H double-quantum MAS NMR: insight from multi-spin density-matrix simulations

The build-up of intensity—as a function of the number, nrcpl, of POST-C7 elements used for the excitation and reconversion of double-quantum (DQ) coherence (DQC)—is analysed for the fifteen distinct DQ correlation peaks that are observed experimentally for the eight separate 1H resonances in a 1H (500 MHz) DQ CRAMPS solid-state (12.5 kHz MAS) NMR spectrum of the dipeptide β-AspAla (S. P. Brown, A. Lesage, B. Elena, and L. Emsley, J. Am. Chem. Soc., 2004, 126, 13230). The simulation in SPINEVOLUTION (M. Veshtort and R. G. Griffin, J. Magn. Reson., 2006, 178, 248) of t1 (1H DQ evolution) FIDs for clusters of eight dipolar-coupled protons gives separate simulated 1H DQ build-up curves for the CH2(a), CH2(b), CH(Asp), CH(Ala), NH and OH1H single-quantum (SQ) 1H resonances. An analysis of both the simulated and experimental 1H DQ build-up leads to the following general observations: (i) considering the build-up of 1H DQ peaks at a particular SQ frequency, maximum intensity is observed for the DQC corresponding to the shortest H–H distance; (ii) for the maximum intensity 1H DQ peak at a particular SQ frequency, the recoupling time for the observed maximum intensity depends on the corresponding H–H distance, e.g., maximum intensity for the CH2(a)–CH2(b) (H–H distance = 1.55 Å) and OH–CH(Asp) (H–H distance = 2.49 Å) DQ peaks is observed at nrcpl = 2 and 3, respectively; (iii) for DQ peaks involving a CH2proton at a non-CH2 SQ frequency, there is much reduced intensity and a maximum intensity at a short recoupling time; (iv) for the other lower intensity 1H DQ peaks at a particular SQ frequency, maximum intensity is observed for the same (or close to the same) recoupling time, but the relative intensity of the DQ peaks is a reliable indicator of the relative H–H distance—the ratio of the maximum intensities for the peaks at the CH(Ala) SQ frequency due to the two DQCs with the NH and OH protons are found to be approximately in the ratio of the squares of the corresponding dipolar coupling constants. While the simulated 1H DQ build-up curves reproduce most of the features of the experimental curves, maximum intensity is often observed at a longer recoupling time in simulations. In this respect, simulations for two to eight spins show a trend towards a faster decay for an increasing number of considered spins. Finally, simulations show that increasing either the Larmor frequency (to 1 GHz) or the MAS frequency (to 125 kHz) does not lead to changes in the marked differences between the 1H DQ build-up curves at the CH(Asp) SQ frequency for DQCs to the CH2(a) and OH protons that correspond to similar H–H distances (2.39 Å and 2.49 Å, respectively).