a All values are computed based on the optimized geometries at SOS-CIS(D0)/aDZ level. bBEes and BEesCPrepresent the excited-state binding energies without and with the basis set superposition error (BSSE) correction, respectively; BEescc includes the correction from the CC calculation c ΔEopt. denotes the excitation energy reduction in the dimer with respect to the monomer excitation energy at the PT2/aDZ level, i.e. , EoptD – EoptM; EoptM values are ca. 4.01 and 3.27 eV for the S1 and T1 states, respectively (Table 1). The values within parentheses are based on BEescc. dRπ-π represents the interplanar distance between carbazole molecules in a given dimer. e Ref.[8]
One should bear in mind, however, that the relative population in the excited states of a given dimer is determined more precisely by its stabilization energy, BEes, rather than the reduction in the optical excitation energy, ΔEopt. Table 3 collects their calculated values and interplanar distances of the excited-state Cz dimers in various conformations. In the S1 state, the dimer in the Stg conformation turned out to be as nearly stable as that in the syn conformation, which is consistent with the PES results and indicates the limited impact of the structural relaxation on their relative stabilities; the BSSE corrected BE value, BEesCP, of the Stg dimer is computed at the SOS-CIS(D0) level to be ca. 0.45, whereas that of the syn dimer is calculated to be ca. 0.44 eV. The BSSE uncorrected BE values (ca. 1.15 eV vs 1.17 eV, respectively), and the values at higher calculation level, i.e. , EOM-CCSD (ca. 0.97 and 0.93 eV, respectively), also draw the same picture that the dimers in both the Stg and syn conformations are practically degenerate in the S1 state. The antidimer in the S1 state is also close in energy with BEesCP being 0.43 eV. In the T1 state, on the other hand, the Stg dimer is more stable than the syn dimer. The BEesCP values are ca. 0.43, 0.39, and 0.26 eV for the Stg , anti , and syn conformations, respectively; the BSSE uncorrected BE values are also in the same trend (ca. 1.05, 0.99, and 0.97 eV, respectively).
Given that the excimer formation of a π-conjugated molecule is in general interpreted as a considerable stability, this remarkable stability of the Stg dimer in the excited state is somewhat puzzling. It is useful to recall here that the intermolecular interactions in the excited states are nearly the same as those in the ground state, when the exciton is localized within a single molecule (excited dimer), as in the Stg and anti dimer conformations (Figures 4 and S2).[36, 41] As expected, the BEesCP values for the Stg dimer in the S1 and T1 states (ca. 0.45 and 0.43 eV, respectively) are quite compatible with that for their ground-state counterpart, BEgsCP, (ca. 0.37 eV). For the anti dimer, the BECP values are computed to be 0.43, 0.39, 0.25 eV, for the S1, T1 and S0 states. On the other hand, the BEgsCP value of the syn dimer (ca. 0.09 eV) is significantly small compared to its BEesCP values (ca. 0.44 and 0.26 eV for the S1 and T1 states, respectively). Therefore, such a remarkable stability of the Stg dimer in the excited state can be ascribed to its significant stability in the ground state, while the excited-state stability of the syn dimer is related to the excimer formation; see Figure 5.