Han et al.
FIGURE 4. Plausible structures for 14+ and 12+
.
have a reduction potential that is more positive than that of 16+
+ e- f 15+, so both reductions happen at the same potential.
That type of potential inversion generally occurs when there is
a large structural rearrangement upon electron transfer,19 and
the crystal structure of 10 shows that at some point between
16+ and 10 a very large structural rearrangement does occur.
Density functional theory (DFT) calculations, described below,
clarify the structural rearrangements that occur in the reduction
steps 16+ f 14+ f 12+ f 10.
FIGURE 5. View along a C2-axis of the calculated (B3LYP/6-31G*)
structure of 12+ in the “twisted” geometry, with n-butyl groups
substituted by methyl groups, and hydrogens not shown.
10) starting in all four of the structures outlined above, for 16
total minimizations. For all four oxidation states, the expected
geometry (16+ benzene, 14+ 1,3-cyclohexadiene, 12+ cyclohex-
ene, 10 chair cyclohexane) was the lowest energy configuration,
with the other configurations either higher in energy, or
converting to the expected configuration during the minimiza-
tion, or converting to another geometry altogether that was
higher in energy than the global minimum.
DFT Calculations. It has not been possible to isolate 1 in
the intermediate oxidation states 12+ or 14+ (or any other
intermediate oxidation state), so we undertook DFT calculations
on 16+, 14+, 12+, and 10 to better understand the intermediate
geometries in the large structural rearrangement that occurs in
the reduction of 16+ to 10. Simply drawing two valence-bond
structures for 14+ and 12+ (Figure 4) suggests one set of plausible
structures for 14+ and 12+. The hexacation 16+ has a benzene-
like core, and neutral 10 has a chair-cyclohexane-like core, and
possible structures for 14+ and 12+ have the 1,3-cyclohexadiene
and cyclohexene-like cores, respectively, shown in Figure 4.
To convert from the structure of 16+ to the suggested 1,3-
cyclohexadiene structure of 14+, one pair of neighboring
peripheral pyridyl rings must twist such that two CH groups
move past each other, from “above” the central C6 ring to
“below” the central C6 ring and vise versa. Similarly, a
conversion from the 1,3-cyclohexadiene core to the cyclohexene
core requires another set of CH groups to move past each other,
as does a conversion from the cyclohexene-like core to the chair-
cyclohexane-like core. Those sterically difficult conversions
separate the four structures (with benzene, 1,3-cyclohexadiene,
cyclohexene, and chair cyclohexane cores) into local energetic
minima.
In one of the geometry optimizations, when 10 was started
in the 1,3-cyclohexadiene geometry, the final structure had a
C6 core with a “twisted” geometry. When the structures of 14+
and 12+ were optimized starting from that twisted geometry,
they had lower energies than any of the other optimized
structures for their respective oxidation states. The optimized
structure of 12+ in the twisted geometry is shown in Figure 5.
It has overall molecular D2 symmetry, with three mutually
perpendicular C2 axes. The structure is very similar to that of
the dication of hexakis(dimethylamino)benzene, which is dis-
cussed further below. It is likely that the twisted D2 structure is
the true global minimum for 12+, as the calculated energy of
the twisted structure is 10 kcal/mol lower in energy than the
structure with the next lowest energy, the cyclohexene core
structure. The situation is somewhat less clear for 14+, where
the twisted structure has an energy only 2.4 kcal/mol lower than
the nearest in energy, the 1,3-cyclohexadiene-like structure. In
addition, all the calculations were done without a solvent model,
and adding a solvent might change the energy ordering. Neither
12+ nor 14+ has an electric dipole in the twisted structure. In
contrast, the cyclohexene-like structure for 12+ has a large
calculated dipole moment of 10.4 D, pointing in the direction
expected from the valence-bond picture of Figure 4. Similarly,
the 1,3-cylohexadiene structure of 14+ has a calculated dipole
moment of 7.1 D, pointing in the direction expected from
Figure 4. The presence of a polar solvent may lower the energies
of the dipolar structures relative to the twisted structures.
However, it is unlikely that a polar solvent would change the
relative energetics of the two structures of 12+ by more than 10
kcal/mol, so the twisted structure is likely to be the true global
minimum for 12+. The atomic coordinates for the optimized
We calculated energy-minimized structures (Gaussian 03,20
B3LYP/6-31G*, with the n-butyl groups substituted by methyl
groups) for all four oxidation states of concern (16+, 14+, 12+
,
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448 J. Org. Chem., Vol. 73, No. 2, 2008