Understanding chemical shielding tensors using group theory, MO analysis, and modern density‐functional theory

In this article, the relationships between molecular symmetry, molecular electronic structure, and chemical shielding (CS) tensors are discussed. First, a brief background on the CS interaction and CS tensors is given. Then, the visualization of the three‐dimensional nature of CS is described. A simple method for examining the relationship between molecular orbitals (MOs) and CS tensors, using point groups and direct products of irreducible representations of MOs and rotational operators, is outlined. A number of specific examples are discussed, involving CS tensors of different nuclei in molecules of different symmetries, including ethene ( D 2 h ), hydrogen fluoride ( C ∞ v ), trifluorophosphine ( C 3 v ), and water ( C 2 v ). Finally, we review the application of this method to CS tensors in several interesting cases previously discussed in the literature, including acetylene ( D ∞ h ), the PtX 4 2− series of compounds ( D 4 h ) and the decamethylaluminocenium cation ( D 5 d ).