Particle on a Boron Disk: Ring Currents and Disk Aromaticity in B-20(2-)

The B-20(2-) cluster is predicted to exhibit a planar sheet-like structure with a circular circumference. Orbital plots and energy correlations demonstrate the close correspondence between the electronic structure of B-20(2-) and the Bessel functions describing the waves of a quantum mechanical particle confined to a disk. The pi-band of B-20(2-), and its B-19(-) congener, contains 12 pi-electrons, forming a (1 sigma)(2)(1 pi)(4)(1 delta)(4)(2 sigma)(2) configuration, which corresponds to a "disk aromaticity" electron count. The analogy not only applies to the a-band, but also extends to the 50 valence sigma-electrons. The occupied sigma-orbitals are assigned on the basis of radial and angular nodes of the scalar disk waves. The magnetic response of the cluster was examined by Nucleus Independent Chemical Shift (NICS) values and current density calculations based on the ipsocentric model. B-20(2-) is found to exhibit a remarkable inner paratropic current in the a-channel and an outer diatropic current in the pi-channel. The orbital excitations responsible for the antiaromaticity in sigma and the disk-aromaticity in pi are identified.