Analysis of aromatic delocalization: Individual molecular orbital contributions to nucleus-independent chemical shifts

Individual molecular orbital (MO) contributions to the magnetic shielding of atoms as well as to the nucleus-independent chemical shifts (NICS) of aromatic compounds can be computed by the widely used gauge-including atomic orbital (GIAO) method. Detailed analyses of magnetic shielding MO-NICS contributions provide interpretive insights that complement and extend those given by the localized MO ("dissected NICS", LMO-NICS) method. Applications to (4n + 2) pi-electron systems, ranging from [n] annulenes to D-nh S-3, S-5, and N6H62+ rings as well as to D-2h cyclobutadiene, show the extent to which their diatropic character results from the sigma framework and from the pi orbitals. The diatropicity of both these contributions decreases with the number of nodes of the wave function around the ring. The highest-energy orbitals can become paratropic. This is generally the case with the sigma orbitals, but is found only for "electron-rich" pi systems such as sulfur rings. MO-NICS contributions, which can be interpreted using London-Huckel theory, correlate with inverse ring size.