Spherical aromaticity and electron delocalization in $${\text{C}}_8$$ C 8 and $${\text{B}}_4{\text{N}}_4$$ B 4 N 4 cubic systems

The electronic structure of the two isoelectronic species $${\text{C}}_8$$ and $${\text{B}}_4{\text{N}}_4$$ has been studied at several ab initio levels (Hartree–Fock, CASSCF, CASPT2, and coupled cluster). For both systems, the total position spread tensor and the electron entropy have been computed and compared. These quantities are indicators that give insight into the electron mobility (and, in the case of the spread, the behavior of different-spin electrons), and are a measure of the multi-reference character of an electronic wavefunction. Our results indicate that the two systems are deeply different. In fact, the $${\text{C}}_8$$ cluster shows a pronounced multi-reference character. The $${\text{B}}_4{\text{N}}_4$$ system, on the other hand, is very well described by a single reference wave function. Analysis of ground-state electronic structure unveils different electron delocalization behavior in the studied systems.