Analysis of electric field gradient tensors at quadrupolar nuclei in common structural motifs

This article is concerned with the analysis of electric field gradients (EFGs) using first-principles theory along with model calculations. Simple atomic orbital (AO) models for the EFG are developed in the spirit of the Townes-Dailey (TD) analysis and applied to various sets of spⁿ hybrid orbitals and to atomic d orbital shells. These AO models are then combined with modern analysis methods rooted in first principles theory which provide accurate localized molecular orbital contributions to the EFG. It is shown by density functional computations how such analyses of the EFG for a variety of typical structural motifs can provide an intuitive way of understanding the chemical origin of the magnitude and the sign of EFG tensors at atomic nuclei, as well as of their orientation with respect to the molecular coordinate frame. The utility of graphical visualizations of EFG tensors is also emphasized. The systems that are investigated span the range from very small molecules (carbon and sulfur EFGs in CO, CS, OCS) to small- and medium-sized molecules (nitrogen and aluminum EFGs in ammonia, methyl-cyanide and -isocyanide, aluminum AlX₃ model systems and various alumino-organic systems), to the metal atom field gradient in transition metal complexes with Ru and Nb and a variety of ligands.