Vertical transitions Franck-Condon maxima

Evaluation of the Work Term from Charge Transfer Spectral Data. The intermolecular interaction leading to the precursor complex in Scheme IV is reminiscent of the electron donor-acceptor or EDA complexes formed between electron donors and acceptors (21). The latter is characterized by the presence of a new absorption band in the electronic spectrum. According to the Mulliken charge transfer (CT) theory for weak EDA complexes, the absorption maximum hv rp corresponds to the vertical (Franck-Condon) transition from the neutral ground state to the polar excited state (22). 

For all the polyacenes studied the first maximum in the kinetic spectrum always exceeds the work function by 0.8 e.v. This excess can be explained by the vertical Franck-Condon transition from the potential surface of the neutral molecule to that of the positive molecular ion, which possess different equilibrium interatomic distances. 

Figure 2. Franck-Condon windows lVpc(Gi, r, v5) for the Na3(X) - N83(B) and for the Na3(B) Na3+ (X) + e transitions, X = 621 nm. The FC windows are evaluated as rather small areas of the lobes of vibrational wavefunctions that are transferred from one electronic state to the other. The vertical arrows indicate these regions in statu nascendi subsequently, the nascent lobes of the wavepackets move coherently to other domains of the potential-energy surfaces, yielding, e.g., the situation at t = 653 fs, which is illustrated in the figure. The snapshots of three-dimensional (3d) ab initio densities are superimposed on equicontours of the ab initio potential-energy surfaces of Na3(X), Na3(B), and Na3+ (X), adapted from Ref. 5 and projected in the pseudorotational coordinate space Qx r cos

Fig. 18. Franck-Condon progressions, (a) The equilibrium positions of the potential surfaces of the excited state II and the ground state 0 are shifted by AQ. This leads to a progression, if the dipole moment of the transition between the states II and 0 is non-zero. The progression is characterized by vertical transitions that are depicted for a low-temperature emission, (b) The intensity distribution of a progression of vibrational satellites depends on the Huang-Rhys parameter S which is proportional to (AQ) (see Eq. (12)). The examples given in (b) are calculated according to Eq. (13). The peaks of highest intensity are normalized for the different diagrams. It is marked that the maximum Huang-Rhys parameter for Pd(2-thpy)2 and Pt(2-thpy)2 have been determined to = 0.3 and = 0.08, respectively. (Compare also Sect. 4.2.4)...

The shapes of absorption and emission bands are determined in the same way by Franck-Condon factors. The shift of the emission maximum with respect to the absorption maximum, which is referred to as Stokes shift, increases with the increasing difference between the equilibrium geometries of the ground and the excited states. This is schematically shown for a diatomic molecule in Figure 5.8 the maximum intensity of absorption will be observed for the vertical transition v = 0 v = n. whereas emission will occur after vibrational relaxation, with the highest probability for the transition form v = 0 to a different ground-state vibrational level, V = m. 

Because of the several qualitative diflFerences between the concepts of ligand field and thermally equilibrated excited states, it is useful to develop a distinguishing vocabulary. Conventional ligand field excited states will be called Franck-Condon states since the energies are those of band maxima and the transitions between them are essentially those vertical ones with maximum Franck-Condon overlap. The abbreviation thexi state has been proposed (12) for a thermally equilibrated excited state. The gist of the foregoing is that conventional ligand field theory treats hypothetical electronic excited states which are in reality Franck-Condon states, whereas it is thexi states that are important in photophysical and photochemical processes. New theory or new extensions of present theory are clearly needed to treat the latter type of state. 

Due to their direct relation to the spectral overlap integral, see Eq. (9), the emission and absorption spectra of the dye molecules are of interest in the context of EET processes. The simplest way to model excitation spectra employs the calculation of vertical energy separations, i.e., the separation of the Bom-Oppenheimer potential energy surfaces of the initial state and the final state at the equilibrium structure of the initial state. This energy separation is expected to coincide with the absorption maximum, as rationalized by the Franck-Condon principle (see for example [135]). This assumption is not always appropriate, rylene dyes being a prominent example. These dyes feature a strong 0-0 transition and a pronounced vibronic progression that is even visible in solution at room temperature (see for example [137]). A detailed simulation of the vibrational substructure of the absorption and emission bands is necessary to understand the details of the spectram. 

The relevant molecular potential curves and energy levels are shown schematically. The vertical arrows show the optical transitions and their positions indicate the internuclear distances where maximum Franck-Condon overlap is expected near the classical turning points, (b) Variation of the Rabi frequencies during the pulse sequence, (c) Experimental results showing the measured molecule population in a> as a function of time through a double-STlKAP sequence. (Adapted from Danzl, J.G. et al., Science, 321,1062, 2008. With permission.)... 

Problem 5.4. According to the Franck-Condon principle, the maximum absorption of Na adatoms corresponds to a vertical transition from the minimum of the ground electronic state to the excited electronic state (see Fig. 5.8). This... 

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