Herzberg - Teller effects

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... 

Such an alternative derivation is interesting since it allows us to connect the approximations behind the derivation of Eq. 10.83 with the dynamics on the excited state. First, it highlights that in cases where Herzberg-Teller effects are important, Eq. 10.83 is expected to work worse than in FC transitions, where fig/Q) can be considered constant and hence [r, /ije(Q)] 0. Second, expanding the exponentials in Eq. 10.84 in powers of t, we have... 

Santoro, F., Lami, A., Improta, R., Bloino, J., and Barone, V [2008] Effective method for the computation of optical spectra of large molecules at finite temperature including the Duschinsky and Herzberg-Teller effect The Qx band of porphyrin as a case study, ]. Chem. Phys., 128, 224311/1-17. 

Finally, we have simulated the vibronic spectra, including Duschinsky and Herzberg-Teller effects, for the Betaine-26 in 1,4-dioxane and in methanol. In Fig. 17.13 the computed vibronic spectra (convolution of all vibronic transitions by Gaussian functions with FWHM = 0.1 eV by means of the VMS-Draw toolkit [230]) are plotted together with the experimental ones. The predicted position of the maxima (1.48 eV and 2.20 eV in 1,4-dioxane and in methanol, respectively) and the band shapes around them are extremely accurate, in particular at lower energies. The vibronic analysis points out the dominant role of the 0-0 transition and the... 

Note that when the Franck-Condon factors in Eq. (44) are small, it is also possible to obtain resonance Raman intensity from the second term in Eq. (41), when similar considerations apply. However, in this case we must consider contributions from the Herzberg-Teller effect, which is described in the next section. 

The vibronic theory of the RR effect distinguishes two major intensity enhancement mechanisms that play a dominant role in the RR spectra (i) Franck-Condon (FC) principle and (ii) Herzberg-Teller (FIT) vibronic coupling, which have quite different properties. The FC scattering mechanism involves displacement of the potential minima of the ground and excited electronic states along a vibrational normal... 

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