from that of the g factor, exhibiting a nearly linear increase for H1 and H2, but
abrupt leaps for H2P and H4 and a clear saturation for H6. Analogous, but much
smaller, difference can be seen for the g factors of H2 and H2P, and the overall
trends do not extremely differ between the changing patterns of g factor and [α] D
value. It is to note that the optical rotation is a more complex function of molecular
parameters, and the exact reasons for the rather exaggerated profile for observed [α] D
values remain to be elucidated.
7.4 Structure of Hexaarylbenzenes
Prior to discuss on the dynamics of propeller-shaped molecules, we analyze the
relaxed structure of HABs with the aid of theoretical calculations. The geometries of
HABs are optimized by the dispersion-corrected density functional theory at the
DFT-D3(BJ)-TPSS/def2-TZVP level [54–56]. This level of theory, implementing
the dispersion correction to simply augments the pairwise ÀC 6 /R
6 potentials to
describe the van der Waals interactions, has been successfully applied as a costefficient alternative to the more demanding electron correlation methods for a
number of molecular systems, where the weak inter- and intramolecular interactions
play significant roles [10, 13, 14, 16–20, 23, 57–59]. While typical biaryls are known
to have the twist angles of ~40
[13, 60], the average tilt angle is consistently ~59
for all the HABs (H0–H6), due to the greater steric crowding in HABs compared
with simple biaryls. Possessing the point-chiral (R)-auxiliary/ies, all the chiral HABs
(H1–H6) prefer the C rather than CC propeller. Crucially, the core and radial
benzene rings of H0–H6 are essentially superimposable, despite the varying number
of chiral auxiliaries at the periphery (Fig. 7.8). It is to note that the conformation of
chiral methylpropyl group(s) as well as syn/anti orientation of alkoxy moiet(ies) may
differ in chiral HABs, but the effect of such conformational variation is negligible on
the calculated chiroptical properties [8].
X-ray crystallographic study provides a slightly different view on the structure of
HABs. The crystal structure of hexakis( p-hydroxyphenyl)benzene is not C 6 -symmetrical, being expressively affected by the solvent molecules incorporated in the
crystal. The twist angles for the DMF-solvated HAB are 91, 100, 77, 84, 76, and 98
with a fairly complicated hydrogen-bonding network, while those for the
corresponding diethyl ether complex are 100, 68, and 97
(with centrosymmetry)
[61]. In both the cases, the radial aromatic rings are not oriented in one direction (i.e.,
the aR and aS atropisomers coexist), suggesting that the peripheral aryls can rotate,
in good agreement with the shallow potential for the inversion process (vide infra). It
is also to note that each HAB molecule is sterically congested to form a channel
structure without any appreciable interactions with the neighboring molecules. The
crystal structure of fully chiral HAB H6 reveals that the radial aromatic rings are
twisted in one direction and their tilt angles fall in a narrow range (Δ ¼ 9
) with the
individual values of 58, 67, 64, 60, 60, and 65
(Fig. 7.9). The conformations of the
peripheral chiral alkyl groups are rather variable, primarily due to the packing
158
T. Mori
abrupt leaps for H2P and H4 and a clear saturation for H6. Analogous, but much
smaller, difference can be seen for the g factors of H2 and H2P, and the overall
trends do not extremely differ between the changing patterns of g factor and [α] D
value. It is to note that the optical rotation is a more complex function of molecular
parameters, and the exact reasons for the rather exaggerated profile for observed [α] D
values remain to be elucidated.
7.4 Structure of Hexaarylbenzenes
Prior to discuss on the dynamics of propeller-shaped molecules, we analyze the
relaxed structure of HABs with the aid of theoretical calculations. The geometries of
HABs are optimized by the dispersion-corrected density functional theory at the
DFT-D3(BJ)-TPSS/def2-TZVP level [54–56]. This level of theory, implementing
the dispersion correction to simply augments the pairwise ÀC 6 /R
6 potentials to
describe the van der Waals interactions, has been successfully applied as a costefficient alternative to the more demanding electron correlation methods for a
number of molecular systems, where the weak inter- and intramolecular interactions
play significant roles [10, 13, 14, 16–20, 23, 57–59]. While typical biaryls are known
to have the twist angles of ~40
[13, 60], the average tilt angle is consistently ~59
for all the HABs (H0–H6), due to the greater steric crowding in HABs compared
with simple biaryls. Possessing the point-chiral (R)-auxiliary/ies, all the chiral HABs
(H1–H6) prefer the C rather than CC propeller. Crucially, the core and radial
benzene rings of H0–H6 are essentially superimposable, despite the varying number
of chiral auxiliaries at the periphery (Fig. 7.8). It is to note that the conformation of
chiral methylpropyl group(s) as well as syn/anti orientation of alkoxy moiet(ies) may
differ in chiral HABs, but the effect of such conformational variation is negligible on
the calculated chiroptical properties [8].
X-ray crystallographic study provides a slightly different view on the structure of
HABs. The crystal structure of hexakis( p-hydroxyphenyl)benzene is not C 6 -symmetrical, being expressively affected by the solvent molecules incorporated in the
crystal. The twist angles for the DMF-solvated HAB are 91, 100, 77, 84, 76, and 98
with a fairly complicated hydrogen-bonding network, while those for the
corresponding diethyl ether complex are 100, 68, and 97
(with centrosymmetry)
[61]. In both the cases, the radial aromatic rings are not oriented in one direction (i.e.,
the aR and aS atropisomers coexist), suggesting that the peripheral aryls can rotate,
in good agreement with the shallow potential for the inversion process (vide infra). It
is also to note that each HAB molecule is sterically congested to form a channel
structure without any appreciable interactions with the neighboring molecules. The
crystal structure of fully chiral HAB H6 reveals that the radial aromatic rings are
twisted in one direction and their tilt angles fall in a narrow range (Δ ¼ 9
) with the
individual values of 58, 67, 64, 60, 60, and 65
(Fig. 7.9). The conformations of the
peripheral chiral alkyl groups are rather variable, primarily due to the packing
158
T. Mori