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.