Substituent effects on the stability of arene-arene complexes: An AM1 study of the conformational equilibria of cis-1,3-diphenylcyclohexanes

Molecular orbital calculations at the AM1 level have been performed on cis-1,3-diarylcyclohexane systems (1, 2) in order to provide a theoretical model and suggest novel experimental models for the investigation of arene-arene π-stacking. Energy minima were located for diaxial conformers (a) in which aryl rings are coplanar and π-stacked and (b) in which aryl rings adopt an edge-to-face or intermediate conformation. The average face-to-face distance varies from 4.1 to 4.4 Å, outside the van der Waals contact distance of 3.4 Å, and the minimum inter-ring distance varies from 3.1 to 3.5 Å. The diaxial-diequatorial conformational equilibria (ΔE_ax-eq) were calculated for a large series of para-substituted and meta-substituted 1,3-diarylcyclohexanes and plotted against Σσ_p, Δσ_p, and E_HOMO - E_LUMO. The best correlation was observed using electrostatic potentials calculated at the electron density surface on the π-face of individual arenes. Similar correlations were observed for conformational equilibria associated with the improved 1,3-dimethyl-1,3-diarylcyclohexane series (3). More limited correlations were drawn for the diaxial-diequatorial conformational equilibria involving (i) edge-to-face diaxial cis-1,3-diarylcyclohexanes and (ii) π-stacked diaxial cis-1,3-diarylcyclohexanes in which one aryl ring is perfluorinated (5, 6). In all cases, the results (a) showed good agreement with literature data on related experimental systems and (b) demonstrated the dominance of arene-arene electrostatic contributions to conformational energy over the negligible orbital mixing and charge-transfer interactions.