Duschinsky effects

The fitting parameters in the transfomi method are properties related to the two potential energy surfaces that define die electronic resonance. These curves are obtained when the two hypersurfaces are cut along theyth nomial mode coordinate. In order of increasing theoretical sophistication these properties are (i) the relative position of their minima (often called the displacement parameters), (ii) the force constant of the vibration (its frequency), (iii) nuclear coordinate dependence of the electronic transition moment and (iv) the issue of mode mixing upon excitation—known as the Duschinsky effect—requiring a multidimensional approach. 

In summary, for displaced oscillators, absorption and emission spectra show a mirror image relation and for the strong coupling case, a(oo) will exhibit a Gaussian band shape, absorption maximum independent of temperature, and bandwidth increasing with temperature. It should be noted that the distortion effect and Duschinsky effect have not been considered in this chapter, but these effects can be treated similarly. 

The extension of the formulas to degenerate accepting modes which occur when a Jahn-Teller effect in the excited state is present is relatively easy. In this case the products of distribution functions can be rewritten by convolution into fundamental distributions which does not change the overall expression of Eq. (29) [38, 66]. Also, it is possible to consider an intermixing of modes in the excited state by virtue of the bi-linear term in Eq. (1) (Duschinsky effect [67]). Since it is difficult to decide from most of the spectra if this effect is really observed in the case of the present complex compounds, we will not consider it here and refer to the literature [68,69]. This is justified as long as we can explain the experimental spectra satisfactorily applying the parallel mode approximation leading to the line shape function of Eq. (29) as it has been described in the method above. 

However, it should be noted that the effect of distortion and mode mixing (i.e., Duschinsky effect) of potential surfaces has been studied [30,37]. 

Several papers with theoretical bases have appeared in the past year. Olbrich and Kupka have treated the influence of normal mode rotation (Duschinsky effect) on the molecular electronic spectra and on the shape of the observed bands. A model has been proposed for interpreting of effects of solvent and pressure on charge-transfer absorption bands, and Andrews and Harlow have extended their earlier work to co-operative two-photon absorption. 

The Time Scales and Mechanism of Quasi-coherent Excitation Hopping Within B850/B875 Rings. This appears to be an area where simple theory cannot apply. It will be a challenge for experimentalists and theorists to address this issue collaboratively. For example, it is not clear whether linear coupling to a harmonic bath is adequate to describe such systems. For example, it may be necessary to include multiphonon and Duschinsky effects on the dynamics in order to describe the influence of temperature on such systems. 

The analysis of Franck-Craidon factors described in Boxes 4.13 and 4.14 assumes that the chromophore s vibrational modes are essentially the same in the excited and ground electronic states, differing only in the location of the energy minimum on the vibrational coordinate and a possible shift in the vibrational frequency. Breakdowns of this assumption are referred to as Duschinsky effects. They can be treated in some cases by representing the vibrational modes for one state as a linear combination of those for the other [58-60]. 

We have assumed that the normal modes of the chromophore do not change significantly when the molecule is excited. For a more general treatment that covers breakdowns of this assumption (Duschinsky effects), the vibrational modes of the excited molecule can be written as linear combinations of the modes in the ground state [28-30]. 

To compute these moments, and in lack of detailed information, the Duschinsky effect is usually neglected between the solvent mqdes and, in Eq. 8.108, the medium Hamiltonian for the final state, namely can be recast as... 

The way in which the diagonal excited-state potentials are written in Eq. 8.138 emphasizes the fact that their difference with respect to the ground potential is expanded in power of the dimensionless normal coordinates. According to the discussion in Section 8.3.2.1, linear terms in Eq. 8.138 introduce equilibrium displacements and bihnear terms, the so-called Duschinsky effect (see below). In symmetric systems, the value of the parameters in Eq. 8.138 are restricted by the requirement that each term of the total Hamiltonian must belong to the total symmetric irreducible representation (irreps) Fa- Therefore, in analogy with the discussion on the Herzberg-Teller effect in Section 8.3.1.1, it can be easily proven that displacements k 0) are only allowed for totally symmetric modes, and the interstate coupling constants (2 V 0) only when... 

In Table 4.6, the long progression of the 26 mode has been observed and the corresponding tunneling splitting decreases monotonically with its excitation. To know the symmetry of the potential energy surface, we need information on the normal mode. It has been repeatedly pointed out [75,76] that the strong Duschinsky effect between the V25 mode and the V26 mode is found in the X - A electronic... 

Small, G.J. (1971) Herzberg-Teller vihronic coupling and the Duschinsky effect. J. Chem. Phys., 54, 3300. 

Berezin, V.l. and Sverdlov, M.L. (1985) Normal vibrations, geometry and the Duschinsky effect in the Bj excited electronic state of molecules of s-tetrazine-do and - 2. Opt. Spectrosc. (USSR), 58, 764. 

Bacon, A.R. and Hollas, J.M. (1985) Duschinsky effect caused by Herzberg-Teller vibronic coupling of two b2 vibrations in the Si-So systems of benzonitrile and phenylacetylene. Chem. Phys. Lett., 120, 477. 

Chang, J.L. (2008) A new method to calculate Franck-Condon factors of multidimensional harmonic oscillators including the Duschinsky effect./. Chem. Phys., 128, 174111. 

Ledwig, Th., Kupka, H., and Perkampus. H.-H. (1989) Lineshapes in phosphorescence spectra of diazaphenanthrenes and protonated analogues. Evidence of the Duschinsky effect. /. Lumin., 43, 25. 

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