Calculations of magnetically induced current densities: theory and applications

A review of computational studies of magnetically induced current density susceptibilities in molecules and their relation to experiments is presented. The history of the investigation of magnetically induced current densities and ring currents in molecules is briefly covered. The theoretical development of relativistic and nonrelativistic computational approaches for computing current densities in closed‐shell and open‐shell molecules is discussed and different state of the art methods to interpret calculated current densities are reviewed. Numerical integration approaches to assess global, semilocal, and local aromatic properties of multiring molecules are presented and demonstrated on free‐base trans‐porphyrin. We show that numerical integration of the current density combined with guiding visualization techniques of the current flow is a powerful tool for studies of the aromatic character of complicated molecular structures such as annelated aromatic and antiaromatic rings. Representative applications are reported illustrating the importance of careful current density studies for organic and inorganic chemistry. The applications include calculations of current densities and current strengths for aromatic, antiaromatic, and nonaromatic molecules of different kind. Current densities in spherical, cylindrical, tetrahedral, toroidal, and Möbius‐twisted molecules are discussed. The aromatic character, current pathways, and current strengths of porphyrins are briefly highlighted. Aromatic properties of inorganic molecules are assessed based on current density calculations. Current strengths as a noninvasive tool to determine strengths of hydrogen bonds are discussed. WIREs Comput Mol Sci 2016, 6:639–678. doi: 10.1002/wcms.1270