1.6 Dipolar DA fluorenes and related spirobifluorenes: bichromophores
1.6.4 Fluorescence anisotropies, excitation and emission spec-
80 Dipolar DA fluorenes and related spirobifluorenes
fluorescence results from the sum of both contributions. For 4 a small negative V = −0.4 eV is required to reproduce the red-shift of absorption and fluores-cence bands when going from 4a to 4.
1.6.4 Fluorescence anisotropies, excitation and emission
Fluorescence excitation and emission anisotropy were calculated for 1* and 4* using the same model developed for absorption and fluorescence spectra.
The calculation of the fluorescence anisotropy in frozen solvent in presence of the two internal conformational coordinates leads to a subtle problem. In fact the fx and fy distributions are frozen in glassy solutions, but u1 and u2 does relax after excitation. The relevant sampling of the grid for the spirobifluorenes is actually six-dimensional
fx, fy, u(g)1 , u(g)2 , u(e)1 , u(e)2
, where u(g)and u(e) refer to the ground and excited state sampled internal coordinates. The computa-tional cost become then fairly high and to save computacomputa-tional time is important to adopt operative criteria to minimiza the sampling. The detailed procedure to calculate anisotropy spectra in the presence of internal coordinates is de-scribed in the appendix B (see sect. B.3.2 in particular). A very large number of phonons is in general required to get stable results for anisotropy, that, being a difference of two spectra is particularly sensitive to small perturbations. The os-cillations present in the calculated anisotropy spectra (lower panels of fig. from 1.47 to 1.58), can be due to some extent to the non-complete convergency of the calculated anisotropies.
Since measurements in decalin are performed at 200K, where solvent is con-sidered a supercooled liquid with reduced molecular mobilites, we set T = 200K in the calculation.
On the opposite, measurements in MeTHF are performed at 77K. Since the liquid to glass transition is expected to occur at 90K, the solvent molecules are actually frozen at this thermodinamic temperature. We then set the temperature for the calculated properties in glassy MeTHF equal to 90K.
The refractive index of the solvent depends on the temperature. Since the fast degree of freedom are treated in the antiadiabatic approximation, this af-fects mainly the z0parameter [19]. We then adjust the z0value for T = 90 K calculations to 1.15 eV (vs. z0=1.28 eV at high temperature) for 1* to 1.27 eV (vs. z0=1.20 eV at high temperature) for 4*. All other model parameters are the ones listed in the tables 1.14 and 1.15.
Fig. 1.47 - 1.52 and 1.53 - 1.57 report the experimental (upper panel) and the calculated (bottom panel), anisotropies for compounds 1* and 4* respec-tively. For all molecules calculated spectra agree very well with experimental spectra. Low temperature excitation and emission bandshapes and even vibra-tional structure are in most cases completely reproduced.
The excitation and emission anisotropy for dipolar molecules, as DA fluo-renes 1a and 4a, is expected to be equal to 0.4, because the CT excitation and emission transition dipole moment are necessarily coinciding. Indeed, all our
82 Dipolar DA fluorenes and related spirobifluorenes
calculated anisotropy with the two state model are exactly equal to 0.4. How-ever, in experimental measurements it is common to obtain anisotropies that are slightly less than 0.4. This occurs for the anisotropy excitation of 4a in de-caline, where a value around 0.3 is obtained also because decalin is not strictly glassy in the experimental condition. However, the value is completely constant inside the bands, confirming the validity of our approach.
We notice that, at variance with results obtained for liquid solutions, calcu-lated excitation and emission spectra in frozen solvents for 1 (V = 0) are not identical to the monomer 1a spectra multiplied by a factor 2. This puzzling result will be explained in the next section, where we also address the phe-nomenon called red edge effect. This name is used in the literature to describe the fact that for some chromophore the anisotropy smoothly increases inside the excitation band moving toward the red edge, where r reaches the limiting 0.4 value [68, 69, 70].
14000 16000 18000 20000 22000
0 0.1 0.2 0.3 0.4
r anisotropy
exc@370 nm (27030cm-1) exc@400nm
(25000cm-1) exc@425nm
(23530cm-1) exc@440nm
(22730cm-1)
14000 16000 18000 20000 22000 ω (cm-1)
0 0.1 0.2 0.3 0.4
r anisotropy
20000 22000 24000 26000 28000
exc@460nm (21739cm-1) exc@470nm
(21276cm-1) exc@500nm
(20000cm-1) exc@530nm
(18868cm-1)
20000 22000 24000 26000 28000 ω (cm-1)
normalized intensity (a.u.)normalized intensity (a.u.)
calculated emission 1a calculated excitation 1a experimental emission 1a
decalin, 200K
experimental excitation 1a
Figure 1.47: Experimental (top) and calculated (bottom) excitation (right) and emission (left) spectra (dashed lines) and anisotropies (cont. thick lines) of 1ain decalin. Parameters for calculated spectra in tab. 1.14.
12000 14000 16000 18000 20000
0 0.1 0.2 0.3 0.4
r anisotropy
exc@365 nm (27397cm-1) exc@395nm
(25316cm-1) exc@425nm
(23530cm-1) exc@460nm
(21739cm-1)
12000 14000 16000 18000 20000 ω (cm-1)
0 0.1 0.2 0.3 0.4
r anisotropy
16000 20000 24000 28000
exc@515nm (19417cm-1) exc@550nm
(18182cm-1) exc@600nm
(16667cm-1) exc@650nm
(15385cm-1)
16000 20000 24000 28000 ω (cm-1)
normalized intensity (a.u.)normalized intensity (a.u.)
calculated emission 1a calculated excitation 1a experimental emission 1a
2-MeTHF
experimental excitation 1a
Figure 1.48: Experimental (top) and calculated (bottom) excitation (right) and emission (left) spectra (dashed lines) and anisotropies (cont. thick lines) in 2-MeTHF of 1a. Model parameters in tab. 1.14.
84 Dipolar DA fluorenes and related spirobifluorenes
22000 24000 26000 28000 30000
0 0.1 0.2 0.3 0.4
r excitation anisotropy
em@500nm (20000cm-1)
22000 24000 26000 28000 30000
ω (cm-1) 0
0.1 0.2 0.3 0.4
r excitation anisotropy normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0
0 1 1 experimental 1
calculated 1 decalin, 200K
normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0
0 1 1
decalin, 200K
Figure 1.49: Experimental (top) and calculated (bottom) excitation anisotropies (cont. thick lines) and excitation spectra (dashed lines) in decalin of 1. Model parameters in tab. 1.14.
16000 18000 20000 22000
0 0.1 0.2 0.3 0.4
r emission anisotropy
exc@370nm (27030cm-1) exc@400nm
(25000cm-1) exc@440nm
(22730cm-1)
16000 18000 20000 22000
ω (cm-1) 0
0.1 0.2 0.3 0.4
r emission anisotropy normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0
0 1 1 experimental 1
calculated 1 decalin, 200K
Figure 1.50: Experimental (top) and calculated (bottom) emission anisotropies (cont. thick lines) and emission spectra (dashed lines) in decalin of 1, at different excitation wavelength. Model parameters in tab. 1.14.
20000 22000 24000 26000 28000 30000
-0.1 0 0.1 0.2 0.3 0.4
r excitation anisotropy
em@550nm (18180cm-1)
20000 22000 24000 26000 28000 30000 ω (cm-1)
-0.1 0 0.1 0.2 0.3 0.4
r excitation anisotropy normalized emission intensity (a.u.)normalized emission intensity (a.u.)
1 1 experimental 1
calculated 1 normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0
0 2-MeTHF
Figure 1.51: Experimental (top) and calculated (bottom) excitation anisotropies (cont. thick lines) and excitation spectra (dashed lines) in 2-MeTHF of 1. In the calculation the T = 90K. Model parameters in tab. 1.14.
14000 16000 18000 20000
0 0.1 0.2 0.3 0.4
r excitation anisotropy
ecc@395nm (25320cm-1) ecc@425nm
(23530cm-1) ecc@460nm
(21740cm-1)
14000 16000 18000 20000
ω (cm-1) 0
0.1 0.2 0.3 0.4
r excitation anisotropy normalized emission intensity (a.u.)normalized emission intensity (a.u.)
1 1 experimental 1
calculated 1 normalized emission intensity (a.u.)normalized emission intensity (a.u.)
1 1 normalized emission intensity (a.u.)normalized emission intensity (a.u.)
1 1 normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0
0 1 1
2-MeTHF
Figure 1.52: Experimental (top) and calculated (bottom) emission anisotropies (cont. thick lines) and emission spectra (dashed lines) in 2-MeTHF of 1. In the calculation T = 90K. Model parameters in tab. 1.14.
86 Dipolar DA fluorenes and related spirobifluorenes
14000 16000 18000 20000
0 0.1 0.2 0.3 0.4
r anisotropy
exc@390 nm (25641cm-1) exc@415nm
(24096cm-1) exc@435nm
(22989cm-1) exc@465nm
(21505cm-1)
14000 16000 18000 20000 ω (cm-1)
0 0.1 0.2 0.3 0.4
r anisotropy
18000 20000 22000 24000 26000
exc@480nm (20833cm-1) exc@528nm
(18939cm-1) exc@570nm
(17544cm-1)
18000 20000 22000 24000 26000 ω (cm-1)
normalized intensity (a.u.)normalized intensity (a.u.)
calculated emission 4a calculated excitation 4a experimental emission 4a
decalin, 200K
experimental excitation 4a
Figure 1.53: Experimental (top) and calculated (bottom) excitation (right) and emission (left) spectra (dashed lines) and anisotropies (cont. thick lines) in decalin of 4a. Model parameters in tab. 1.15.
14000 16000 18000
0 0.1 0.2 0.3 0.4
r anisotropy
exc@390 nm (25641cm-1) exc@410nm
(24390cm-1) exc@445nm
(22472cm-1) exc@490nm
(20408cm-1)
14000 16000 18000 ω (cm-1) 0
0.1 0.2 0.3 0.4
r anisotropy
20000 22000 24000 26000 28000
exc@550nm (18182cm-1) exc@600nm
(16667cm-1) exc@650nm
(15385cm-1) exc@650nm
(14286cm-1)
20000 22000 24000 26000 28000 ω (cm-1)
normalized intensity (a.u.)normalized intensity (a.u.)
calculated emission 4a calculated excitation 4a experimental emission 4a
2-MeTHF
experimental excitation 4a
Figure 1.54: Experimental (top) and calculated (bottom) excitation (right) and emission (left) spectra (dashed lines) and anisotropies (cont. thick lines) in 2-MeTHF of 4a. Model parameters in tab. 1.15.
88 Dipolar DA fluorenes and related spirobifluorenes
20000 22000 24000 26000 28000
0 0.1 0.2 0.3 0.4
r excitation anisotropy
em@540nm (18520cm-1)
20000 22000 24000 26000 28000
ω (cm-1) 0
0.1 0.2 0.3 0.4
r excitation anisotropy normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0
0 1 1 experimental 4
calculated 4 decalin, 200K
normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0
0 1 1 experimental 4
calculated 4 decalin, 200K
Figure 1.55: Experimental (top) and calculated (bottom) excitation anisotropies (cont. thick lines) and excitation spectra (dashed lines) in decalin of 4. Model parameters in tab. 1.15.
16000 18000 20000
0 0.1 0.2 0.3 0.4
r emission anisotropy
exc@400nm (25000cm-1) exc@445nm
(20410cm-1) exc@490nm
(20410cm-1)
16000 18000 20000
ω (cm-1) 0
0.1 0.2 0.3 0.4
r emission anisotropy normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0
0 1 1 experimental 4
calculated 4 decalin, 200K
Figure 1.56: Experimental (top) and calculated (bottom) emission anisotropies (cont. thick lines) and emission spectra (dashed lines) in decalin of 4, at different excitation wavelength. Model parameters in tab. 1.15.
18000 20000 22000 24000 26000 28000
0 0.1 0.2 0.3 0.4
r excitation anisotropy
em@540nm (18520cm-1)
18000 20000 22000 24000 26000 28000 ω (cm-1)
0 0.1 0.2 0.3 0.4
r excitation anisotropy normalized emission intensity (a.u.)normalized emission intensity (a.u.)
1 1 experimental 4
calculated 4 normalized emission intensity (a.u.)normalized emission intensity (a.u.)
1 1 experimental 4
calculated 4 normalized emission intensity (a.u.)normalized emission intensity (a.u.)
1 1 experimental 4
calculated 4 normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0
0 1 1 experimental 4
calculated 4 2-MeTHF
Figure 1.57: Experimental (top) and calculated (bottom) excitation anisotropies (cont. thick lines) and excitation spectra (dashed lines) in MeTHF of 4. In the calculation T = 90K. Model parameters in tab. 1.15.
14000 16000 18000 20000
0 0.1 0.2 0.3 0.4
r emission anisotropy
ecc@458nm (21830cm-1) exc@505nm
(19800cm-1) exc@445nm
(23810cm-1)
14000 16000 18000 20000
ω (cm-1) 0
0.1 0.2 0.3 0.4
r emission anisotropy normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0 1 1 normalized emission intensity (a.u.)normalized emission intensity (a.u.)
0 1 experimental 4
calculated 4 2-MeTHF
Figure 1.58: Experimental (top) and calculated (bottom) emission anisotropies (cont. thick lines) and emission spectra (dashed lines) in MeTHF of 4. In the calculation T = 90K. Model parameters in tab. 1.15.
90 Dipolar DA fluorenes and related spirobifluorenes