TD-DFT with the CAM-B3LYP functional of
o-1 and
o-2 in the crystalline states was also carried out to better understand the CPL properties. CD and CPL spectra are closely related to the dihedral angles of BINOL in ground states. As shown in Figure
9, the crystalline-phase calculations with the finite-size cluster model based on the single-crystal data predicted that the dihedral angles
((O)C-C-C-C(O)) of BINOL are obviously different (-62.88° for
o-1, -124.41° for
o-2), taking reversible signs in CD, whereas the dihedral angles
((O)C-C-C-C(O)) of BINOL are -60.49° and -124.76° for
o-1 and
o-2 in the excited states, respectively. Dihedral angles of BINOL units for
o-1 and
o-2 are dynamically regulated by the excitation, and the values of the angle change are 2.39° for
o-1 and -0.35° for
o-2. The results demonstrated that
o-1 underwent a large dynamic conformational change upon
excitation in the crystalline states. However, the conformational transitions upon
excitation of
o-2 were substantially suppressed in the crystalline phase. To put it simple,
o-1 adopted a more twisted conformation than that of
o-2, driven by the bulky substituents attached onto the open-type BINOL. There is no denying, though, that the detected larger
value of
o-1 in the crystalline state is ascribed to subtle variations in the excited-state conformations, resulting in an amplification of magnetic transition dipole moment, whereas the conformation of
o-2 was almost not altering, leading to no alteration of the magnetic and electric transition dipole moments. Natural transition orbital (NTO) is employed to analyze a
-
transition of the BINOL moiety and additional TICT contribution from the central BINOL donor to the peripheral
o-carborane acceptor for
o-1 and
o-2, as shown in Figure S10 [
39]. Hence, the nature of the CPL for
o-1 and
o-2 is the result of TICT states in the crystalline phases. Theoretically,
is defined as
. Accordingly, high
values could only be achieved for
-allowed and
-forbidden transitions, while low values are generally expected for
-forbidden and
-allowed transitions. To deduce the origin of these anomalous
values, we performed TD-DFT analysis at the TD-TPSSTPSS/6-31G(d,p) level [
40]. The magnetic and electric transition dipole moments from
state for
o-1 were 0.063 and 0.068, respectively, and for
o-2 were 0.144 and 0.645, respectively. Meanwhile, the two transition dipole moments from
state,
and
, for
o-1 (i.e., with an angle of 75.51°) were 0.800 and 1.002, respectively, and for
o-2 (i.e., with an angle of 176.10°) were 0.153 and 1.887, respectively. These data showed that
o-1 possessed an anomalously magnetic transition dipole moment in the
state. The
value is derived as a combination of
and
in a relationship of
by (
). Thus, unlike conventional organic molecules with negligible magnetic transition dipole moment contributions, it stands to reason that the choice of 3,3
- and 6,6
-substituted
o-carborane in
o-1 and
o-2 exerts a great influence on the molecular packing and electronic transmission, responsible for modulating the magnetic and electric transition dipole moments. The dynamic rotational movements of
o-carborane moieties may lead to a small
value and enhance the corresponding
value, arising an enhancement of the
value [
41]. This is why
o-1 manifests a larger
than that of
o-2 in crystalline states [
42]. Moreover, the choice of 3,3
- and 6,6
-substituted
o-carborane in
o-1 and
o-2 can regulate their arrangement of dipoles in the crystalline and even resolve their electronic spin directions upon photoexcited states, which have a direct correction with their chirality organizations, as shown in Figure
1(d). This gives a direct explanation that
o-1 and
o-2 exhibit inverse signals.