Reexamination of NICSπ,zz: Height Dependence, Off-Center Values, and Integration

Applying fine grids of nucleus independent chemical shift (NICS) probes (BQs) at different distances from the molecular plane of aromatic and antiaromatic molecules suggests that, at short distances, NICS pi,zz is maximal (absolute values) off the geometrical center of the systems. In nonsymmetric systems, the center of the induced ring current may be a little off the geometrical center, but the difference is negligible at distances >= 2 angstrom. At these distances, the change of NICS pi,zz with the distance from the ring follows a power relation. It is shown that the order of diatropicity and paratropicity within a group of molecules depends on the distance from the system (namely, the order of NICS(r)(pi,zz) depends on r). It is thus suggested to use integral NICS pi,zz, as a quantitative measure of aromaticity.