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.