Dispersion-corrected
density functional theory (DFT) calculations
analyze potential energy surfaces (PESs) for the insertion of a certain
polarized π-conjugated molecule, p-(dimethylamino)-p′-nitrostilbene (DANS), inside an (m,m) carbon nanotube (n×DANS@(m,m)), where n is the
number of inner guests. The current study considered two types of
DANS alignments as the dimer structures: linear and stacked alignments,
where their dipole moments are oriented in parallel. DFT calculations
revealed that a single DANS insertion into a tube with a diameter
of approximately 1.0 nm spontaneously proceeds through attractive
host–guest interactions. From an end to the middle of a tube,
various metastable states and a global minimum structure appear. In
2×DANS@(m,m), which is assumed
to be generated by the insertion of another molecule into the tube
that already contains one guest, significant roles of intermolecular
interactions are found to distinguish their PESs from the 1×DANS@(m,m) case. In addition, the strength of
the intermolecular interactions varies depending on the inner DANS
dimer alignment and host tube diameters, and thus, striking contrasts
were found in PESs for 2×DANS@(m,m). In the formation of linearly aligned DANS molecules inside a tube,
the PES is almost identical to that in 1×DANS@(m,m) due to very weak intermolecular interactions.
By contrast, intermolecular interactions between the parallel stacked
DANS molecules are sufficiently stronger to distinguish their PESs
from those in 1×DANS@(m,m);
attractive (repulsive) intermolecular interactions within the (8,8)
((7,7)) tube stabilize (destabilize) PESs that are involved in their
metastable states and global minimum structure. More importantly,
in the stacked alignments, we found the activation energy for the
transformation from a metastable state to a global minimum, for which
the value decreases in the following order: 20 kcal/mol for 2×DANS@(7,7)
> 13 kcal/mol for 2×DANS@(8,8). According to the DFT findings,
one can kinetically control the alignments of the DANS molecules inside
a thicker tube (i.e., (8,8) tube). In fact, through temperature optimization
in heat treatments where the above-mentioned activation energy cannot
be overcome, a one-dimensional array of DANS molecules can be formed
inside a thicker tube despite its thermodynamic instability. Since
linear DANS alignments are responsible for maximizing static hyperpolarizability,
the kinetic control technique can expand the diameter ranges of tubes
as hosts for DANS guest aggregates exhibiting a significant second-order
nonlinear optical response.