Franck-Condon maxima

For optical ET, the vertical gaps for Franck-Condon maxima hv)max) in absorption (abs) and emission (em) are given by [29,42 14]... 

Fig. 7. The potential energy surfaces of the CuF complex in KZnFj as a function of Q, as determined by spectroscopic measurements [9]. The vertical arrows indicate Franck-Condon maxima in the absorption and fluorescence spectra, the horizontal dotted lines indicate observed zero phonon origins...

The relevant energies associated with each state are, to varying extents affected by the molecular environment, as discussed later. Table 1 contains approximate Franck-Condon maxima for the transitions from the " Aig state. 

TABLE 1. Approximate Franck-Condon maxima for transitions from A-jg ground state to the lower lying ir-electronic states... 

The selective data on Franck-Condon maxima for transitions from A o, recorded in Table 2, were obtained from electron impact (38) and T transient absorption studies (39). They... 

Franck-Condon maxima, corresponding to vertical transitions. fWith the exception of 13 (vapor) and 263b (vapor), the spectra were measured in cyclohexane solutions. 

Table 2. Energies (in cm" )oflow-lying electronic states of simple polyenes. Vertical transition energies (Franck-Condon maxima) are given in parentheses. Other energies refer to the electronic origins (0-0 bands) of S ->T, and Sq transitions. The O, perturbation spectra were obtained in chloroform all other energies refer to the gas phase.

The maxima in the transitions T, S and — S are in each case roughly 2000 cm above the known transition origins, and a similar relationship is also observed between the Franck-Condon maxima and known origins in the S S transitions. Thus the origin of the Tg transition would be in the range 41,600 to 43,200 cm . ... 

Since the Franck-Condon maximum for both the A 1 X E state... 

For the first three clusters, the structures of these emission spectra are clearly similar to the one observed for bare 1-naphthol <- S0 state, with a Franck-Condon maximum situated on the 0-0 band. The small increase of complexity of the spectra is certainly due to intermolecular vibrations. 

Explain why, in the semiclassical wavepacket picture, the width of an absorption band increases with the slope of the excited-state potential surface in the region of the Franck-Condon maximum, whereas the width of an emission band increases with the corresponding slope of the ground-state potential surface. 

Resonance Raman Spectroscopy. If the excitation wavelength is chosen to correspond to an absorption maximum of the species being studied, a 10 —10 enhancement of the Raman scatter of the chromophore is observed. This effect is called resonance enhancement or resonance Raman (RR) spectroscopy. There are several mechanisms to explain this phenomenon, the most common of which is Franck-Condon enhancement. In this case, a band intensity is enhanced if some component of the vibrational motion is along one of the directions in which the molecule expands in the electronic excited state. The intensity is roughly proportional to the distortion of the molecule along this axis. RR spectroscopy has been an important biochemical tool, and it may have industrial uses in some areas of pigment chemistry. Two biological appHcations include the deterrnination of helix transitions of deoxyribonucleic acid (DNA) (18), and the elucidation of several peptide stmctures (19). A review of topics in this area has been pubHshed (20). 

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

It is also interesting to estimate the maximum value of the frequency factor in the case of purely quantum nuclear motion. This can be done with the help of the formula W 2nV2Sp, where V2 exp(—2yR) is the exchange matrix element, S is the Franck-Condon factor, p 1 jco is the density of the vibrational levels, and co 1000 cm-1 is the characteristic vibrational frequency of the nuclei. In the atomic unit system, the multiplier 2np has the order 103 and the atomic unit of frequency is 4.13 x 1016s-1 consequently, in the usual unit system, the frequency factor is of the order 4 x 1019Ss-1. The frequency factor reaches its maximum value when S 1. Thus, in the case of purely quantum nuclear motion, the maximum value of the frequency factor is also 1019-102°s-1. 

The Franck-Condon factors of polarizable chromophores in Eq. [153] can be used to generate the complete vibrational/solvent optical envelopes according to Eqs. [132] and [134]. The solvent-induced line shapes as given by Eq. [153] are close to Gaussian functions in the vicinity of the band maximum and switch to a Lorentzian form on their wings. A finite parameter ai leads to asymmetric bands with differing absorption and emission widths. The functions in Eq. [153] can thus be used either for a band shape analysis of polarizable optical chromophores or as probe functions for a general band shape analysis of asymmetric optical lines. 

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