The selected high-resolution spectra and the simulated spectra (as shown in
Fig. 23) did not directly reveal any reason why the appearance of PMI and PDI bulk
spectra was so different. The calculations showed, however, that PMI has a
significant static dipole moment in the S 0 state (around 6 Debye units), which
increases by 1 Debye unit upon excitation into the S 1 state. By symmetry, PDI
has no dipole moment in either state. This pointed to strong linear electron–phonon
coupling in the case of PMI, which was in line with the measured Debye–Waller
factors for PMI (α D ¼ 0.15) and PDI (α D ¼ 0.4).
Efforts to provide a quantitative model for the coupling of vibronic transitions to
the phonons of the host material have been undertaken recently. The theory and first
results will be published elsewhere.
4.2 Electronic Coupling in Donor–Acceptor Dyads
As outlined before, D–A dyads 1 and 2 allowed detailed investigation of EET
mechanisms, in particular since they provide a well-defined geometrical arrangement of the chromophores. Experimental investigations have found much higher
transfer rates than predicted by Fo ¨rster theory [2, 9] (see also Sect. 3). To explain
this finding, a number of hypotheses have been investigated both experimentally
and by theoretical modeling.
One issue is the potential flexibility of such dyads, which might lead to significantly shorter interchromophoric distances than expected from a naı ¨ve linear
structure. This idea was examined in the case of 1 [124]. Quantum chemical
calculations, employing density functional theory, were carried out to check the
influence of strong perturbations like point charges or strong uniform electric fields.
Neither the transition energy nor the transition dipole moment were found to change
significantly, even for very strong fields (10
7 –10
9 V/m). In particular, the orientation of the transition dipole remains along the long chromophore axis in all cases.
The transition properties also remain nearly unchanged when the molecular
structure is distorted. Hence the orientations of the transition dipoles can be
unequivocally used as a probe for chromophore orientation. This information is
accessible in single-molecule experiments as described in [124] and reveals some
flexibility of 1, with an average relative angle of 22
between donor and acceptor.
As shown in [3], this cannot explain the large rates because the decreased
interchromophoric distance is counteracted by a reduced orientation factor due to
the deviation from the optimal collinear arrangement. As a further point, the
validity of the dipole approximation, Eq. (7), was investigated [3]. To this end,
the electronic coupling matrix element in Eq. (6) was calculated from the Coulomb
integral over the one-particle transition densities of the donor γ D (r,r
0 ) and the
acceptor γ A (r,r
0 ):
Optical Properties of Assemblies of Molecules and Nanoparticles
105
Fig. 23) did not directly reveal any reason why the appearance of PMI and PDI bulk
spectra was so different. The calculations showed, however, that PMI has a
significant static dipole moment in the S 0 state (around 6 Debye units), which
increases by 1 Debye unit upon excitation into the S 1 state. By symmetry, PDI
has no dipole moment in either state. This pointed to strong linear electron–phonon
coupling in the case of PMI, which was in line with the measured Debye–Waller
factors for PMI (α D ¼ 0.15) and PDI (α D ¼ 0.4).
Efforts to provide a quantitative model for the coupling of vibronic transitions to
the phonons of the host material have been undertaken recently. The theory and first
results will be published elsewhere.
4.2 Electronic Coupling in Donor–Acceptor Dyads
As outlined before, D–A dyads 1 and 2 allowed detailed investigation of EET
mechanisms, in particular since they provide a well-defined geometrical arrangement of the chromophores. Experimental investigations have found much higher
transfer rates than predicted by Fo ¨rster theory [2, 9] (see also Sect. 3). To explain
this finding, a number of hypotheses have been investigated both experimentally
and by theoretical modeling.
One issue is the potential flexibility of such dyads, which might lead to significantly shorter interchromophoric distances than expected from a naı ¨ve linear
structure. This idea was examined in the case of 1 [124]. Quantum chemical
calculations, employing density functional theory, were carried out to check the
influence of strong perturbations like point charges or strong uniform electric fields.
Neither the transition energy nor the transition dipole moment were found to change
significantly, even for very strong fields (10
7 –10
9 V/m). In particular, the orientation of the transition dipole remains along the long chromophore axis in all cases.
The transition properties also remain nearly unchanged when the molecular
structure is distorted. Hence the orientations of the transition dipoles can be
unequivocally used as a probe for chromophore orientation. This information is
accessible in single-molecule experiments as described in [124] and reveals some
flexibility of 1, with an average relative angle of 22
between donor and acceptor.
As shown in [3], this cannot explain the large rates because the decreased
interchromophoric distance is counteracted by a reduced orientation factor due to
the deviation from the optimal collinear arrangement. As a further point, the
validity of the dipole approximation, Eq. (7), was investigated [3]. To this end,
the electronic coupling matrix element in Eq. (6) was calculated from the Coulomb
integral over the one-particle transition densities of the donor γ D (r,r
0 ) and the
acceptor γ A (r,r
0 ):
Optical Properties of Assemblies of Molecules and Nanoparticles
105