New insights on the bridge carbon-carbon bond in propellanes: a theoretical study based on the analysis of the electron localization function

The nature of the bonding between bridgehead carbon atoms (Ca, Ca') as well as the ring strain in a family of 10 propellanes formed by three-, four-, or five-member rings: 1.1.1] (I), 2.1.1] (II), 3.1.1] (III), 2.2.1] (IV), 3.2.1] (V), 2.2.2] (VI), 3.3.1] (VII), 3.2.2] (VIII), 3.3.2] (IX), and 3.3.3] (X) are studied by means of the electron localization function (ELF) at the DFT level (B3LYP/cc-pVTZ). The ELF analysis of smaller propellanes (I, II, and III) reveals the coexistence of two resonance forms: one with a nonbonding electron pair partially delocalized between Ca and Ca' atoms outside the cage (ionic) and the other with a bridge bond between the same atoms (covalent). The weights of each form are calculated according to the ELF-basin populations, yielding 94, 88, and 53% for the ionic structure of I, II, and III, respectively, while larger propellanes (IV-X) present only the covalent form. The question of the s-character of the bridge bond is addressed by dissecting the bridge-bond ELF basin into the molecular orbital contributions. Finally, sigma-aromaticity associated to surface electron delocalization has been analyzed by means of nucleus-independent chemical shift (NICS) calculations. The results point out that the stability of the fused ring structure of propellanes I, II, and III, can be assigned to the remarkable sigma-aromaticity of the involved three-member rings.