The inter-ring σ/(π/π) covalent interactions of cyclodimes of benzenes

To study the inter-ring σ/(π/π) covalent interactions between non-radical π-systems, five structures of cyclodimers of benzene (C6H6)2 with all the real frequencies, i.e. o–p′-dibenzene (A), the pentacyclic dimer (B), p–p′-dibenzene (C), syn–o,o′-dibenzene (D), and hexaprismane (E), are obtained at the MP2/6-311G(d,p) level. Five inter-ring bonding mode types forming the inter-ring multicenter multielectron σ/(π/π) covalent bonds are represented: A, ring-edge type between a butterfly-shaped ring and a planar ring (4-center 4-electron bond); B, edge–edge and ring–ring types between two identical butterfly-shaped rings (8-center 8-electron bond); C, ring–ring type between two identical butterfly-shaped rings (4-center 4-electron bond); D, edge–edge type between two identical planar rings (4-center 4-electron bond); and E, face–face type between two identical planar rings (12-center 12-electron bond). The order of the large inter-ring interaction energies at the MP2/6-311+G(3d, 2p)+BF level is −99.15 (A with two inter-ring C–C bonds) > −98.57 (B with four C–C bonds) > −85.76 (C with two C–C bonds) > −61.35 (D with two C–C bonds) > −60.40 kcal mol−1 (E with six C–C bonds). However, this does not show an obvious relationship between the interaction energy and the number of the inter-ring C–C bonds. The reason is that the number of decisive influencing factors of the inter-ring interaction energy is not one but five: the number of the favorable inter-ring C–C single bonds, the number of the unfavorable four-membered rings themselves, the participating number of the four-membered rings in unfavorable interaction among those rings, the number of the favorable non-planar melted six-membered ring, and the weak inter-ring π/π interaction (between two π bonds in different rings).