Importance of Tensor Asymmetry for the Analysis of ²H NMR Spectra from Deuterated Aromatic Rings

We have used ab initio calculations to compute all of the tensor elements of the electric field gradient for each carbon−deuterium bond in the ring of deuterated 3-methyl-indole. Previous analyses have ignored the smaller tensor elements perpendicular to principal component V_zz which is aligned with the C−²H bond (local bond z-axis). At each ring position, the smallest element V_xx is in the molecular plane and V_yy is normal to the plane of the ring. The asymmetry parameter η = (|V_yy| − |V_xx|)/|V_zz| ranges from 0.07 at C4 to 0.11 at C2. We used the perpendicular (off-bond) tensor elements, in concert with an improved understanding of the indole ring geometry, to analyze prototype ²H NMR spectra from well-oriented, hydrated peptide/lipid samples. For each of the four tryptophans of membrane-spanning gramicidin A (gA) channels, the inclusion of the perpendicular elements changes the deduced ring tilt by nearly 10° and increases the ring principal order parameter S_zz for overall “wobble” with respect to the membrane normal (molecular z-axis). With the improved analysis, the magnitude of S_zz for the outermost indole rings of Trp¹³ and Trp¹⁵ is indistinguishable from that observed previously for backbone atoms (0.93 ± 0.03). For the Trp⁹ and Trp¹¹ rings, which are slightly more buried within the membrane, S_zz is slightly lower (0.86 ± 0.03). The results show that the perpendicular elements are important for the detailed analysis of ²H NMR spectra from aromatic ring systems.