Theoretical study of a simple rotational-echo double-resonance NMR for homonuclear spin-1/2 pairs

We investigate theoretically intriguing aspects of a simple rotational-echo double-resonance (REDOR) NMR technique for homonuclear spin-1/2 pairs undergoing MAS. The simple technique sets Gaussian soft π pulses at every half MAS rotational period in the pulse sequence. The reduction in rotational echo amplitude (the REDOR echo reduction) is observed at the end of the evolution period te  = (n + 1)Tr, where Tr is a MAS rotational period. The exact average Hamiltonians for the homonuclear REDOR (hm-REDOR) technique are calculated by dividing the evolution period into four periods. We show theoretically and experimentally that the hm-REDOR technique produces the REDOR echo reductions for homonuclear spin-1/2 pairs. In addition, the theoretical results reveal that the REDOR echo reductions are independent of the chemical-shift difference, δ, under a simple condition of κ = δ/ωr  ≥ 6 and te  < 10 ⋅ (1/d'), where ωr is the sample spinning frequency and d' is the dipolar coupling constant expressed in Hz. We call this simple condition the master condition. This means that the REDOR echo reductions for a homonuclear spin-1/2 pair can be calculated under the master condition by considering only d' and ωr , which is the case for a heteronuclear spin pair. Finally, we demonstrate that four-phase cycling yields the multiple-quantum filtered hm-REDOR experiment, where the appearance of the REDOR echo reductions shows that the echo reductions are definitely attributable to the homonuclear dipolar interaction even if there is a slight unwanted effect from the recovered chemical-shift anisotropy in these reductions.