Results

the coupling with |Dπ^∗A〉, with frequency and vibrational relaxation energy ωv∗

and ǫ_v∗. This coordinate does not add much to the physical description of the system apart from a better reproduction of the structure of the LE band. The total adiabatic hamiltonian reads:

Hel+2ph =









0 −τ 0

−τ 2z0− ωvp2ǫ_vq −β 0 −β 2 y₀− ω_v∗p2ǫ_v∗q_∗







 +1

2ω_vq²+1 2ω_v∗q²

∗ (1.27)

We expect µ₀≫ µ∗, moreover we neglect the permanent dipole moment as-sociated with |Dπ^∗A〉, therefore the solvation model reduces to the one relevant to the standard two state model. We define an effective solvation coordinate along the CT direction (x component) with a relaxation energy ǫ_or. The result-ing total hamiltonian then is:

H = Hel+2ph− f ˆρ + 1

4ǫ_orf² (1.28)

The equation 1.27 represents a coupled electro-vibrational hamiltonian that will be actually solved in a non adiabatic approach over the basis obtained by the direct product of the three electronic states times n states associated at the har-monic oscillator relevant to q, times n_∗states of the harmonic oscillator relevant for q_∗. The general procedure for the calculation of absorption, fluorescence and anisotropy spectra is described in appendix B.1.1 and B.3.1.

36 Annine: CT vs localized excitations

Table 1.6: The three-state model parameters for NAn used to calculate optical properties in fig. 1.18

molecular parameter NAn

z₀/ eV 1.51

t/ eV 1.07

y₀/ eV 1.46

β / eV 0.04

µ₀/ D 19.6

µ_∗/ D 0.85

ϕ /^◦ 50

ǫ_v/ eV 0.28

ω_v/ eV 0.18

ǫ_v∗/ eV 0.15

ω_v∗/ eV 0.14

Γ/ eV 0.075

solvent parameter NAn ǫ_or/ eV cyclohexane 0.0

toluene 0.40

MeTHF 0.50

dichloromethane 0.55

DMSO 0.65

PrG 0.70

20000 25000 30000

ω (cm^-1)

0 1 2

CH2Cl2, DMSO: ε (104 M-1 cm-1) others: normalized ε_or = 0.0

ε_or = 0.4 ε_or = 0.5 εor = 0.55 εor = 0.65 εor = 0.70

20000 25000 30000

0

normalized emission calculated NAn

Figure 1.18: Calculated absorption and fluorescence, parameters in table 1.6, value for ǫ_orin the legend are listed as in the experimental data of fig. 1.13

PES relevant to the three electronic states. For graphical reason at this stage we neglect the q_∗ coordinate and its coupling to electrons setting ǫ_∗ = 0 and renormalizing y₀to 1.37 eV to relocate the energy of the localized state in the proper position.

Figure 1.19: f,q dependent PES for the three basis state. Left: apolar solvent, right:

polar solvent. Parameters are the same in the table 1.6, but with ǫ_v∗(ω_v∗is then irrelevant), and a renormalized y_{0,e f f} =1.37.

Figure 1.19 shows the PES relevant for the basis (diabatic) states in a slightly polar (ǫ_or=0.01eV) and in strongly polar (ǫ_or=0.70eV) solvent. In the first case the states |D π^∗A〉 and |D⁺π A⁻〉 are very close in energy, while the polar solvent largely stabilizes the zwitterionic state.

Figure 1.20: Calculated f,q dependent PES for the three adiabatic eigenstate. Left:

apolar solvent, right: polar solvent. Parameters as defined in the caption of fig.

1.19.

38 Annine: CT vs localized excitations

Figure 1.20 shows the corresponding adiabatic PES. In the slightly polar solvent the lowest energy PES corresponds to a state that strongly resemble

|D π^∗A〉, while the second PES has a CT character. The lowest excitation always corresponds to the LE state both in absorption and in fluorescence. The situa-tion is very different in a strongly polar solvent, where the first excited state PES describes either a LE or a CT state in different regions of the q, f plane. Specifi-cally absorption occurs “on the vertical” from the equilibrium position relevant to the ground state. In this point the lowest excitation has a dominant LE char-acter, while the higher excitation corresponds to a CT state. The absorption spectrum then has a weak marginally solvatochromic absorption band (corre-sponding to feature I), and an higher energy intense absorption (feature II), which CT character is demonstrated by its important solvatochromism. How-ever, after excitation the system relaxes and moves toward the global minimum of the excited state PES where the state aequires a dominant CT character (see fig.1.21): in polar solvents fluorescence occurs from the CT state, even if in absorption the lowest excitation has an LE character. Of course the situation is different in frozen solvent, where the solvent cannot relax after the solute excitation. In frozen solvent, quite irrespective of the solvent polarity we expect that fluorescence always occurs from the LE state. First excited state PES are reported in fig. 1.21 too, using contours to clarify the position of the minima.

Figure 1.21: Calculated f,q dependent PES and relative contourn of the first excited state. Left: apolar solvent, right: polar solvent. Parameters as defined in the caption of fig. 1.19.

We are now in the position to calculate the anisotropy excitation and emis-sion spectra. The temperature has to be set properly for the anisotropy cal-culation. We set T = 90K in MeTHF, corresponding to the glassy transition temperature of the solvent. In propylnenic glycole, we set T = 200K. ([55] and see appendix A.3.1).

20000 25000 30000

0

emission intensity (a. u.)

20000 25000 30000

ω (cm^-1) 0

0,2 0,4

anisotropy r

ε=0.5eV T= 90K em @25000cm^-1 (400nm) ε=0.5eV T= 90K ecc@28000cm^-1 (357nm) ε=0.7eV T= 200K em @25000cm^-1 (400nm) ε=0.7eV T= 200K ecc @28000cm^-1 (357nm)

Figure 1.22: Calculated absorbance and fluorescence of NAn, to be compared with experimental data in fig 1.14 (same symbols are used in both figures).

Calculated anisotropies in fig. 1.22 compare very well with experimental spectra in fig. 1.14, and the different anisotropies observed for the two solvents in the plateau region is nicely reproduced in the calculation. Some problem is encountered in reproducing the position of the excitation spectra in PrG, but the complete agreement with the experimental spectra recorded in frozen solvent is a tricky problem, because one should account for the T-dependence of the solvent refractive index and dielectric constant, leading to T dependent model parameters.

The peculiar excited state properties, in term of energies and polar character, make NAn an interesting example of excited state inversion. that can occur any time there are a CT and localized excited states close in energy. This is the first time that the optical properties of a class of chrysene-like compounds is analyzed and understood in a detailed way. In spite of the highly nontrivial picture we succeded in understanding the physics governing low energy optical spectra of this chromophore.

With the same model and the same parameters listed before (table 1.6) we have calculate TPA spectra, reported with the OPA in figure 1.23. Again the level of agreement with experimental data is good. Indeed the presence of a low energy state is correctly accounted for, as confirmed by the low energy side

40 Annine: CT vs localized excitations

Table 1.7: Experimental data for NanMe⁺ in different solvents. For the dichloromethane and the toluene the absorption maxima refer to the fluorescence excitation spectra and for the toluene the emission maximum is estimated by the maximum due to the monomer contribution (spectra not shown).

solvents λ_abs/nm^a λ_{f luo}/nm^a λ_TPA/nm^a (ε/M⁻¹cm⁻¹)^a (FQY)^b (σ_TPA/GM)^a

toluene 425 ∼ 513

dichloromethane 502 621

DMSO 440 493 920

(24000) (0.38) (285)

of the TPA band.

320 360 400 440 480 520 560 600 0

30 60 90 120

σTPA (GM)

TPA NAn OPA NAn

norm. Absorbance (a.u.)

calculated

Figure 1.23: Calculated TPA spectra (circle) and the normalized calculated OPA.