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
Σσp,
Δσp, 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.