a All the energy values and distances are in eV and Å,
respectively. b BEgs and
BEgsCP denote the binding energies
without and with the basis set superposition error (BSSE) correction,
respectively; BEgscc represents to the
binding energy with CC calculation correction. cBEgssapt0, Eelst.,Eexch., Eind., and
Edisp. denote the SAPT0 total binding energy,i.e. , the negative sum of all interaction energy components, and
the individual interaction energy components for the electrostatic
interaction, exchange repulsion, induction interaction, and dispersion
interaction, respectively. d Rπ-πrepresents the interplanar distance between carbazole molecules in a
dimer.
To shed more light on the intermolecular interactions between Cz
molecules in the ground state, we also performed an interaction energy
decomposition analysis via SAPT0
calculations.[32-34,
39-40] We first note that the exchange
repulsion is the most significant in the Stg dimer (ca. 2.01 eV),
while it is the least in the anti conformer (ca. 1.17 eV).
However, this significant repulsion in the Stg dimer is fully
compensated by the other attractive components, which are more
substantial than in the other conformations. The induction energy
component, for instance, is larger for the Stg dimer (ca. −0.51
eV) than the anti and syn dimers (ca. −0.42 and −0.26 eV,
respectively). Moreover, the dispersion and electrostatic interactions
are markedly stronger for the Stg dimer (ca. −1.67 and −0.67 eV,
respectively) than the syn dimer (ca. −1.20 and −0.12 eV,
respectively). In particular, dispersion interaction energies
(> ca. −1.20 eV) are much larger in magnitude than the
electrostatic interaction energies (< ca. −0.67 eV),
suggesting the predominant role of the former in keeping individual
molecules bound together in both dimers. We also note that the
electrostatic interaction energy for the Stg dimer is even larger
than that for the anti dimer (ca. –0.67 vs. –0.43 eV). Because
the dipole−dipole interactions, due to their anti-parallel arrangement,
are expected to be more effective for the latter, interactions including
multipoles, e.g. , dipole−quadrupole interactions, etc. ,
also apparently play an important role in the former. As a result of all
these favorable interactions, the Stg dimer is the most stable,
while the syn dimer is the least stable; the total SAPT0
energies, BEgssapt0, for theStg , anti , and syn dimers are ca. 0.84, 0.64, and
0.40 eV, respectively. Likewise, the interplanar distance,
Rπ-π, for the Stg dimer is calculated to be the
shortest (ca. 3.07 Å), and that for the syn dimer is the longest
(ca. 3.54 Å). This shortest Rπ-π also explains why the
exchange repulsion, which is proportional to the wave function overlap,
is the most significant in the Stg dimer.
Now, we turn to the excited-state stabilities of carbazole dimers. In
general, π-conjugated molecules tend to form strong excimers in the
face-to-face conformation, i.e. , syn conformation, making
this dimer significantly stable in the excited
state.[12,
15, 36,
41] Such a stabilizing effect stems
from the strong electronic couplings between frontier molecular
orbitals, e.g. the highest occupied and lowest unoccupied
molecular orbitals (HOMOs and LUMOs, respectively), of individual
molecules, which leads to the wave function delocalization and the
optical energy gap
reduction.[41] Such
strong electronic couplings and a strong excimer formation, however, are
hardly expected in the Stg dimer, due to the symmetry mismatch of
orbitals between individual molecules. The NTO wave functions,
respectively depicted in Figures 3 and 4 for the excited syn andStg dimers, show this difference. The singlet exciton of thesyn dimer is totally delocalized over the dimer, clearly
demonstrating the excimer formation and hence significant stabilization
(Figure 3). In the case of the triplet dimer, we still see a slight
delocalization in the hole wave function, despite the tendency of the
triplet exciton to prefer the contracted wave function to maximize the
exchange energy,K .[15,
25-26,
37] As expected, however, both the
singlet and triplet excitons of the Stg dimer are localized
exclusively within a single Cz molecule (Figure 4). Likewise, theanti dimer also corresponds to a localized exciton, as manifested
by the NTOs in Figure S2 in the Supporting Information. Therefore, thesyn dimer in the excited states corresponds to the excimer,
whereas the Stg and anti dimers are more likely simple
excited dimers.