Multidimensional solid-state nuclear magnetic resonance for determining the dihedral angle from the correlation of C13–H1 and C13–C13 dipolar interactions under magic-angle spinning conditions

Abstract

Multidimensional solid-state nuclear magnetic resonance (NMR) under magic-angle spinning (MAS) conditions has been developed to determine the dihedral angle for a Hα1–Cα13–Cβ13–Hβ1 moiety in powdered states. The pulse sequence for this experiment includes C113H dipolar evolution periods for Cα and Cβ, which are correlated through a coherent Cα1313Cβ dipolar mixing period. Theoretical analysis based on the symmetry of the spin system indicates that the dipolar correlation spectrum only due to the CαHα and CβHβ dipolar couplings is strongly dependent on the dihedral angle χ about the CαCβ bond axis, but two χ angles give the same spectrum in the χ range from 0° to about 140°, where χ=0° corresponds to the cis conformation. Inclusion of the CαCβ dipolar coupling together with the weak CαHβ and CβHα dipolar couplings, however, breaks the symmetry of the system with respect to χ in the range from 0° to 180°. These properties are confirmed by the spectra calculated for the pulse sequence as a function of χ and the root-mean-square deviation between them. The bond lengths, bond angles, and dihedral angle also alter the dipolar correlation spectrum differently. This enables us the experimental determination of all the structural parameters, which improves the accuracy of the dihedral angle determination. The high resolution due to C13 isotropic chemical shifts under MAS conditions in this multidimensional NMR permits its application to molecules having a number of C13-labeled sites. Experimental results are presented for powdered L-valine uniformly labeled with C13 and N15 nuclei. Effects of the structural parameters and noise on the dihedral angle determination are evaluated numerically. The accuracies of the determined structural parameters are discussed.