Full Paper
in-plane distortion of the substituents at the 1- and 8-positions
as characterized by the angle C8-C1-C13 is 1038 (and aC1-C8-
C13’=1028), compared with 978 for the respective positions of
4 (Figure 1, top right). In addition, the ethynylene linkages de-
viate from linearity for 8 (aC1-C11-C12+aC11-C12-C13=
3478; aC8-C11’-C12’+aC11’-C12’-C13’=3478). There is signif-
icant out-of-plane bending that is characterized by a torsional
angle t (C16-C1-C8-C16’)=268 (Figure 1, middle right). The
combination of in-plane and out-of-plane distortions results in
a structure in which the phenyl rings are not arranged in
a stacked fashion. In this case, and in contrast to the situation
for 4, the phenyl rings are almost parallel with the naphthalene
scaffold, tilted by ca. 158 and 88 (Figure 1, bottom right), com-
pared with 1158 in 4, and they are significantly offset from one
another with a vertical separation of RV =3.1 and horizontal
displacement of RH =4.7 . Although there is precedence for
dramatic in-plane and out-of-plane bending of arene units,[27]
including 1,8-disubstituted anthracenes,[28] we were surprised
by the dissimilarity of the geometries of 4 and 8 that arise
from differences in the substitution pattern of the phenyle-
thynyl arms. Alkoxy and alkyl side chains are common features
on conjugated polymers and oligomers, including poly(pheny-
lene acetylenes), and discotic liquid crystals. These side chains
are accommodated by, and support the formation of, the
stacked arrangement of the p-systems.
viously been used by our group under the name aug-cc-
pVDZ’). This level of theory not only gives reasonably accurate
energies[33] for noncovalent interactions, but also decomposes
the interaction into the physically meaningful components of
electrostatics, exchange-repulsion (sterics), induction (polariza-
tion), and London dispersion forces to better understand the
physical nature of the interaction. Functional group SAPT can
further break down these interaction energy components into
contributions from each molecular sub-fragment (a group of
atoms chosen by the user).
In the course of analyzing nonbonding contacts in 4 and 8
and their potential influence on the preferred geometries in
these compounds, it is important to bear in mind that crystal-
packing forces may also exhibit a significant influence. Howev-
er, gas-phase optimizations of 4 and 8 at the B3LYP-D/aug-cc-
pVDZ level of theory result in conformations similar to those in
the crystal structures (see Figure S25 and S26 of the Support-
ing Information).[34] Intramolecular interactions are enhanced
slightly (see Figure S29), but our conclusions remain the same
using these optimized geometries. The unusually strained geo-
metries of 4 and 8 led to difficulties in performing the geome-
try optimization using standard quantum program packages.
Enhancements to the optimizer in the Psi4 program[35] allowed
the optimizations to be completed.
In the computations, the naphthalene and ethynyl linkers
were removed from each compound for simplicity of analysis
and to provide the distinct molecular fragments necessary for
SAPT analysis. Severed covalent bonds were capped with hy-
drogen atoms subject to constrained optimizations (keeping
all other nuclei fixed) at the B3LYP-D/aug-cc-pVDZ level of
theory. F-SAPT fragments were chosen to be the propyl groups
(one in each monomer for 4, and two in each monomer for 8)
and the aryl ring plus attached oxygen atoms, as indicated in
Figure 2.
The minor distortions from a cofacial geometry in 4, and the
major deviations away from a p-stacking geometry in 8 might
be ascribed to a combination of steric and Coulombic repul-
sions between electron-rich phenyl rings, with the dialkoxy-
substituted phenyl rings in 8 being more electron-rich and
thus, perhaps, resulting in greater distortions. Such an interpre-
tation would be consistent with the analysis of Cozzi and
Siegel[20] for the rotation barriers in their biarylnaphthalenes,
indicating that p–p interactions are stronger with electron-
withdrawing substituents and weaker for electron-donating
substituents (one of the Hunter–Sanders rules). On the other
hand, recent high-accuracy quantum chemical computations in
the gas phase indicate that all substituents, regardless of elec-
tron-donating or electron-withdrawing character, stabilize p–p
interactions in cofacial phenyl rings.[12] Based on the prior ex-
perimental results reported by Carey et al. for 3,5-substituted
arenes,[13b,c] it is surprising that 8 does not adopt a geometry
that is even more aligned for p-stacking than that of 4; appa-
rently, the proximity of the arenes causes C-ÀH/p interactions
to draw the arenes out of plane and dominate the conforma-
tion of the molecule. Hence, we performed electronic structure
computations to understand this difference.
All SAPT computations were performed within Psi4. Con-
strained optimizations to place capping hydrogen atoms were
performed using the Q-Chem package.[36] Figure S27 and S28
contain the F-SAPT0/jun-cc-pVDZ energy components for the
interaction between the pairs of mono- or di-propyloxyben-
zenes (models of the arms in 4 and 8, respectively). The overall
interaction energies between each pair of model fragments
are provided in the color-coded diagrams in Figure 2. The di-
propyloxybenzenes of the model for 8 interact nearly twice as
strongly as the mono-propyloxybenzenes of 4 (interaction en-
ergies of À6.9 versus À3.6 kcalmolÀ1; more negative values in-
dicate stronger intermolecular attractions). The phenyl rings of
4 are at a vertical separation of RV =3.1 and a horizontal dis-
placement of RH =1.8 . The interaction of the oxyphenyl por-
tion of the molecule alone accounts for 70% (À2.5 kcalmolÀ1
)
Computational analysis
of the model propyloxybenzene–propyloxybenzene interaction
for 4. This interaction is dominated by dispersion, but contains
significant attractive electrostatics (see Figure S27). The interac-
tion of each oxyphenyl unit with each propyl fragment
(À0.5 kcalmolÀ1) and the interaction of the propyl fragments
(À0.1 kcalmolÀ1) both arise primarily from dispersion forces.
The offset-stacked nature of the mono-propyloxybenzene units
of 4 keeps the electronegative oxygen atoms from being
The interactions between the substituted phenyl rings of 4
and 8 were examined by using density-fitted functional group
symmetry-adapted perturbation theory[16,17,29] truncated at
zeroth-order intramonomer correlation[30] (F-SAPT0) combined
with the jun-cc-pVDZ basis set,[31] which is Dunning’s aug-cc-
pVDZ set[32] without diffuse functions on hydrogen and with-
out diffuse d functions on heavy atoms (this basis set has pre-
Chem. Eur. J. 2015, 21, 19168 – 19175
19171
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