CHAPTER 3:13C–13C Distance Measurements by Polarization Transfer Matrix Analysis of 13C Spin Diffusion in a Uniformly 13C-Labeled Molecular Complex under Magic Angle Spinning

Spin diffusion of 13C polarization in NMR provides 13C−13C distances under magic angle spinning over a broad spectral width. However, there are difficulties in obtaining the distances accurately in uniformly 13C-labeled molecular complexes in solids. Effects of the weak long-range couplings are suppressed by strong short-range couplings. In addition, direct polarization transfer should be distinguished from relayed transfer. To address these issues, polarization-transfer rate matrix analysis has been applied to the 13C-driven spin diffusion in a uniformly 13C-labeled bacteriochlorophyll c assembly. The transfer rates due to direct dipolar couplings were derived by matrix analysis. Distances were obtained from the rates by perturbation theory for spin diffusion using zero-quantum lineshapes. This procedure gave distances up to 6 A with an accuracy of 25−50%. Correction of the distances from the zero-quantum lineshapes improved the accuracy by about 5−15%. These results show that rate matrix analysis is beneficial for distance analysis of molecular complexes for solid-state NMR. Also, the coefficient and anisotropy of 13C spin diffusion in solids are discussed quantitatively.