Quantitative ¹³C-{¹H} NOE spectroscopy at natural abundance. The role of indirect effects

Indirect, three-spin effects in the ¹³C isotopomers arising from abundant or dilute spins are analyzed theoretically and by experiments including mono- and biselective heteronuclear NOE measurements, homonuclear NOE factors, and selective relaxation rates. An extension of the Kuhlmann-Grant-Harris heteronuclear NOE theory to dilute spins allows the determination of direct relaxation rates in AMX spin systems. This method was used successfully for carbon-proton distance measurement in the range of 0.1-0.4 nm in small, rigid, isotropically reorienting organic molecules even in the presence of negative, indirect NOE. The first example of such effects at quaternary carbons in their natural abundance is presented.