Which electron count rules are needed for four-center three-dimensional aromaticity?

A series of charged and neutral four-center n-electron (4c-ne, n = 1-4) molecules based on the adamantane framework, but which include combinations of boron, nitrogen, and phosphorus atoms at bridgehead positions, were studied computationally at the B3LYP/6-31G* level of density functional theory (DFT). The three-dimensional aromaticity, observed earlier for the 1,3,5,7-bisdehydroadamantane dication (1), is found to be general for 4c-2e electron systems. The degree of electron delocalization, evaluated by energetic, geometric, and various magnetic criteria, is quite independent of the molecular symmetry (point groups vary from Td to Cs), the degeneracy of the orbitals, the molecular charges, and the nature of the atoms participating in the delocalized bonding. Although the multiple positive (e.g., in 1 and some of the heteroatom systems) and multiple negative charges are strongly repulsive, the rigid adamantane frameworks help hold the bridgehead atoms within bonding distances with the fewer available electrons. The corresponding 4c-1e doublets are approximately half as aromatic as the 4c-2e singlets based on the same criteria. However, the three-electron systems may either adopt distorted but still four-center delocalized structures, or alternative 3c-2e two-dimensional arrangements in which the fourth bridgehead atom is more distant. There is no need to derive special rules for each point group for 4c-ne systems. Although the three-dimensional stabilization is computed to be quite appreciable, ranging between 10 and 50 kcalmol(-1), this delocalization energy is generally not sufficient to overcome distortion due to strain in higher homologues of 1 and in analogous noncage systems. Among the various 4c-2e homoadamantanedehydro dications studied, only the 1,8-dehydrohomoadamandiyl-3,6-dication forms a three-dimensional aromatic system.