Accurate measurement of ^{13}C - ^{15}N distances with solid-state NMR

Nuclear magnetic resonance (NMR) can measure the distance between two atoms because the interaction between their nuclear magnets gets stronger as they get closer. In solid powders, this interaction creates a characteristic powder pattern spectrum. This paper describes a pulse sequence that keeps the sample still instead of spinning it, refreshes the carbon signal by an adiabatic transfer from hydrogen, and records a two-dimensional echo that removes the blurring from chemical shifts. The key measured quantity is the frequency separation between two edges of the powder pattern, which is directly related to the carbon-nitrogen distance through a simple cube-root formula. The authors tested the method on two labeled forms of the amino acid glycine and report distances of 1.496 Å and 2.50 Å with small error bars. To get those numbers, they had to correct for line broadening, for the electron-mediated J-coupling, and for a small delay caused by the finite length of the radio-frequency pulses. The correction for the delay uses an empirical formula obtained from numerical simulations. The authors also discuss how atomic vibrations affect the meaning of the NMR distance, noting that NMR measures a vibrationally averaged value rather than the exact crystallographic distance. The experiments lasted many hours and used samples diluted to 1% or 2% to ensure the pairs are isolated. The paper also shows nitrogen-detected spectra, which have less broadening but more noise. The main limitation the authors identify is imperfect proton decoupling, which broadens the lines and limits accuracy. With better hardware, they argue, the method could be accurate enough to refine structures from X-ray or neutron diffraction, once vibrational corrections are understood.