The effects of orbital interactions on the geometries of some annelated benzenes

In order to investigate C–C bond-length alternation in benzenes, tris-annelated with benzo ( 1 ), 1,3-cyclobutano ( 2 ), etheno ( 3 ), and ethano ( 4 ) groups, B3LYP/6-31G(d) calculations have been performed. The calculations were carried out not only at the fully optimized geometries of 1 – 4 , but also at partially optimized geometries in which the C–C bond lengths in the benzene rings were all constrained to be R = 1.397 Å (the optimized C–C bond length of D 6h benzene). This mode of analysis allowed the annelation energies for forming 1 – 4 to be separated into contributions from (a) the effects of the orbital interactions, which, to different extents in 1 – 4 , localize the π bonds in the benzene rings, even at R = 1.397 Å and (b) the resulting changes in the C–C bond lengths that lead to the optimized, bond-alternated, geometries. The degree of cooperativity in steps (a) and (b) has been investigated by computing the annelation energies as a function of n , the number of annelating groups. Cooperativity has been found in step (a) for both 1 and 3 , but not for 2 , due to the absence of a low-lying, unfilled orbital in cyclobutane. Cooperativity has been found in step (b) for 1 – 3 , where the energy liberated on allowing the benzene bond lengths to alternate has been found to vary as n 2 , the square of the number of annelating groups. The dependence on n of both contributors to the annelation energies is discussed.