Partial alignment, residual dipolar couplings and molecular symmetry in solution NMR

Residual dipolar couplings (RDCs) and residual anisotropic chemical shifts (RACSs) are produced by the partial alignment of solution NMR samples. RDCs and RACSs yield high-resolution structural and dynamic information on the orientation of bonds and chemical groups in molecules. Many molecules form oligomers or have intrinsic symmetries, which may simplify the analysis of their partial alignment datasets. In this report, we explore the theory of partial alignment using an irreducible spherical representation, and we investigate the impact of molecular symmetry on the alignment of molecules. Though previous studies have reported simplified relationships on the partial alignment of molecules bearing different symmetry groups, we show that these simplified relationships may not be universal and only apply to a limited set of systems.