TP excited states

Since the experimental discovery of TPA, multiphoton excitation has become a popular tool in the photochemical sciences to determine the excitation energy of states with parity forbidden transition [3-54], Transitions that are parity forbidden by one-photon (OP) excitation can thus become allowed by two-photon (TP) excitation. TP excitation spectroscopy localizes the energetic position of TP excited states, which cannot be observed by OP excitation. These pioneering works confirmed many quantum chemical studies predicting the existence of TP excited states and therefore experimentally completed the pattern of electronic transitions in organic compounds. In general, TP excitation had been mainly limited to academic interest until the end of the 1980s [2-24, 26-45, 47-52, 55-69]. 

This relation is applicable for excitation with photons of identical frequency (Fig. 3.1a). Thus, the excitation frequency of the virtual state is about one-half that of the TP excited state S . The term e is the complex polarization vector. This term is needed to describe the orientation and polarization affecting TP excitation [23, 238]. 

Three-Level Model A three-level model appropriately describes two-photon absorption of centrosymmetric chromophores in which a higher excited state is directly populated by TP excitation (Figure 3.2a). Thus, the TP excited state is a higher excited state, which is populated under resonant conditions as long as Eq. (27)10 fulfills the necessary conditions. 

This expression is derived from Eq. (18) for the case when the second term dominates control of electronic coupling between two excited states. The first term vanishes for centrosymmetric chromophores in Eq. (18) because A/rol 0. Substitution of Eq. (18) into Eq. (17) results in Eq. (27) for centrosymmetric compounds. This relation shows the proportionality of 8 to the square of Mqi M i and the excitation energy of the TP excited state 02, respectively. The TP excited state is in most cases S2- A further important term in Eq. (27) is the detuning energy 01 02/2 resulting in an increase of 8 if 0i — 02/2... 

The two-photon excitation spectrum of 22h taken as a neat film shows a broad peak with an onset of 1.32 eV and a maximum at 1.63 eV [391]. The larger TP excitation energy (1.32 eV 2hco = 2.65 eV) compared to OP excitation (2.34 eV) implies that the TP transition has a different selection rule than the OP transition. This is similar to behavior obtained in solution [384], A similar excitation pattern as disclosed in Figure 3.2a was obtained for such polymeric materials that is, the TP excited state possesses a higher excitation energy in comparison with the lowest OP excited state. Thus, the results obtained for diphenylpolyenes with more than two ethylene moieties, in which the Sj state is assigned to the TP excited state, are considered as an exception for chromo-phores with no donor substitution pattern [29]. 

Comparison of OP and TP excitation spectra is shown for 38 in Figure 3.34. For this class of oligomers, the TP excited state displays a higher excitation energy in comparison to the lowest OP excited state. The results for 38-40 were essentially the same. Thus, the energetic relations depicted in Figure 3.33 are justified. This has a strong impact on the photochemistry, particularly for 40. Either OP or TP excitation results in the same photochemically active state, Si, and therefore the same photochemical pathways. 

Moment Between Si State and the Lowest TP Excited State (M i), and the Method Used for Determination of TPA. Data for a Series of Chromophores with the General Structures 57-79 in Different Solvents... 

Eq. (27) represents the relationship between 5 and the transition dipole moments Moi and Mn, respectively. In particular, M 2, representing the electronic coupling between the energetically higher TP excited state and the lowest excited singlet state, is important for the effective population of the OP photoactive Sj state. No electronic coupling would result in deactivation of the TP excited state by the release of two photons located in the red/NIR spectral range. Data of some representative D-re-D chromophores are collected in Table 3.7 [83, 132, 425, 447, 468-478]. 

The small hypsochromic shift of TP excitation maximum for 74 compared to 58b reflects the influence of the re-system on TP excitation energy. In contrast, both anthracene bearing chromophores 75b and 75c exhibit significantly smaller 8 compared to 74. This is caused by the smaller electronic coupling between the one-photon (OP) state and the two-photon (TP) excited state (Table 3.7). TPA and OPA spectra for 74 and 75b-c are shown in Figure 3.42. 

TABLE 3.9 Compilation of Extinction Coefficient ( ), TPA Cross Section (5), Maximum for TP Excitation (2 ), Maximum for OPA (2° ), Fluorescence Quantum Yield ( f), Transition Dipole Moment Between States So and the Si (Moi), Transition Dipole Moment for Coupling Between Si State and the Lowest TP Excited State (M12), and the Method Used for Determination of TPA Data for a Series of Chromophores with the General Structures 99-107... 

Comparison of the energies for TPA and OPA shows a higher energy for the TP excited state compared to the lowest allowed OP excited state (Si) for all chromophores (99-107) examined in this section. Hence, the amplitude of TPA can be described by Eq. (27). There are no dipolar contributions, no matter that solvatochromism occurs for the samples 99-104. The influence of the quadrupolar pattern is reflected in M12. Application of models of the symmetry break are not likely to provide clarification of the relation between TPA properties and the distinct quadrupolar substitution of the chromophores 99-107. 

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