90
W. Ota and T. Sato
dimer is 5.429 × 10
−4 a.u. The ratio of the VCCs of dimer to monomer is 0.614,
which is approximately equal to 1/
√
2 ≈ 0.707. This is because the electron density
difference of the dimer is delocalized over molecules [32] as shown in Fig. 5.6.
Since the spatial integration of the electron density difference is zero by definition,
the value of the electron density difference of X 1 (or X 2 ) consisting the dimer is half
of that of the monomer. In addition, the value of the potential derivative of X 1 is
1/
√
2 times that of the monomer because of the normalized condition of vibrational
modes. As a result, the diagonal VCD of X 1 expressed as the product of the electron
density difference and potential derivative is 1/(2
√
2) times that of the monomer.
Therefore, the spatial integration of the diagonal VCD of the dimer gives the diagonal
VCCs that is 1/
√
2 times smaller than those of the monomer. The deviation from
1/
√
2 occurs because the molecules in the dimer do not have the same structures
as the monomer. The rate constant of the internal conversion strongly depends on
the diagonal VCCs, and the slight decrease of the diagonal VCCs reduces the rate
constant in several orders [9]. Thus, the internal conversion from S 2 to S 0 in the
dimer is more suppressed than that from S 1 to S 0 in the monomer originating from
the decrease of the diagonal VCCs, which contributes to the appearance of the AIEE
behavior.
Consequently, the pseudo-degenerate delocalized electronic states for the dimer
suppress the internal conversions from S 2 to S 1 and S 2 to S 0 . It should be noted that
this does not occur when the electronic states are localized on a single molecule.
In the present case, the electronic states are delocalized because the dimer in the
CNPPE solid has C i symmetry. The electronic states could be delocalized even when
a crystal structure has no site symmetry, though the site symmetry in solid phase is
preferable to realize such an excited electronic states. To confirm the delocalization
of adiabatic wave functions, the geometry optimizations of the excited states should
be performed. We have found that the adiabatic wave functions of the dimer are
delocalized so that the vibronic couplings are reduced [33]. This suggests that the
origin of the AIEE observed in the CNPPE solid is the excimer formation in which
the vibronic couplings are reduced to suppress the internal conversions because of
the pseudo-degenerate electronic states.
5.5 Conclusion
We discussed the role of pseudo-degenerate delocalized electronic states on
suppressing the internal conversions between excited states using the VCD theory.
The pseudo-degeneracy gives rise to the cancelations of the electron density differences and overlap densities resulting in the decrease of the diagonal and off-diagonal
VCCs, respectively. This enables the fluorescence using the RISC from high triplet
excited states and the AIEE in cofacial configurations. The control of vibronic
couplings utilizing the pseudo-degeneracy can provide a new design principle for
OLED dopants and AIEE dyes.
W. Ota and T. Sato
dimer is 5.429 × 10
−4 a.u. The ratio of the VCCs of dimer to monomer is 0.614,
which is approximately equal to 1/
√
2 ≈ 0.707. This is because the electron density
difference of the dimer is delocalized over molecules [32] as shown in Fig. 5.6.
Since the spatial integration of the electron density difference is zero by definition,
the value of the electron density difference of X 1 (or X 2 ) consisting the dimer is half
of that of the monomer. In addition, the value of the potential derivative of X 1 is
1/
√
2 times that of the monomer because of the normalized condition of vibrational
modes. As a result, the diagonal VCD of X 1 expressed as the product of the electron
density difference and potential derivative is 1/(2
√
2) times that of the monomer.
Therefore, the spatial integration of the diagonal VCD of the dimer gives the diagonal
VCCs that is 1/
√
2 times smaller than those of the monomer. The deviation from
1/
√
2 occurs because the molecules in the dimer do not have the same structures
as the monomer. The rate constant of the internal conversion strongly depends on
the diagonal VCCs, and the slight decrease of the diagonal VCCs reduces the rate
constant in several orders [9]. Thus, the internal conversion from S 2 to S 0 in the
dimer is more suppressed than that from S 1 to S 0 in the monomer originating from
the decrease of the diagonal VCCs, which contributes to the appearance of the AIEE
behavior.
Consequently, the pseudo-degenerate delocalized electronic states for the dimer
suppress the internal conversions from S 2 to S 1 and S 2 to S 0 . It should be noted that
this does not occur when the electronic states are localized on a single molecule.
In the present case, the electronic states are delocalized because the dimer in the
CNPPE solid has C i symmetry. The electronic states could be delocalized even when
a crystal structure has no site symmetry, though the site symmetry in solid phase is
preferable to realize such an excited electronic states. To confirm the delocalization
of adiabatic wave functions, the geometry optimizations of the excited states should
be performed. We have found that the adiabatic wave functions of the dimer are
delocalized so that the vibronic couplings are reduced [33]. This suggests that the
origin of the AIEE observed in the CNPPE solid is the excimer formation in which
the vibronic couplings are reduced to suppress the internal conversions because of
the pseudo-degenerate electronic states.
5.5 Conclusion
We discussed the role of pseudo-degenerate delocalized electronic states on
suppressing the internal conversions between excited states using the VCD theory.
The pseudo-degeneracy gives rise to the cancelations of the electron density differences and overlap densities resulting in the decrease of the diagonal and off-diagonal
VCCs, respectively. This enables the fluorescence using the RISC from high triplet
excited states and the AIEE in cofacial configurations. The control of vibronic
couplings utilizing the pseudo-degeneracy can provide a new design principle for
OLED dopants and AIEE dyes.