Herzberg-Teller contribution

Figure 3.8 Vibronic two-photon absorption spectra of Sila-1f and 2 2a-2f of 4-dimethylamino-4 -Me-trans-stilbene calculated with B3LYP at the HF geomet7. Franck-Condon contribution, Herzberg-Teller contribution, and total spectra are shown for lifetime broadening of 0.10 eV (left panels) and 0.01 eV (right panels), respectively. The dashed line corresponds to the vertical transition [18]. (Reproduced with permission.)...

Lombardi, J.R., Birke, R.L., Lu, T., Xu, J. Charge-transfer theory of surface enhanced Raman spectroscopy Herzberg-Teller contributions. J. Chem. Phys. 84, 4174-4180 (1986)... 

Finally, both anharmonic and vibronic effects (with the inclusion of Duschinsky mixing and Herzberg-Teller contributions) have been considered for the simulation of resonance Raman spectra, along with the environment description by a mbced discrete/continuum solvent model. The resulting RR spectrum up to the... 

In the present simulation we apply a simple model consisting of two vibrational modes in the relevant system. The first one will contribute to the Stokes shift as well as to the Herzberg-Teller correction, while the second one only to the Stokes shift. Next, we will assume a mutual coupling of the modes in the bilinear form Q Qi for the excited state. This type of coupling is usually omitted in literature. The Hamiltonian 77s is written as... 

In centrosymmetric molecules, HRS gains intensity via Herzberg-Teller term (the first vibronic B-term), indicating that IR-active modes and silent modes are enhanced. In the case of non-centrosymmetric molecules, however, Franck-Condon mechanism (A-term) dominantly contributes to the enhancement. Moreover, the mutual exclusive rules between HRS and RS are broken, and hence, some of RS-active modes selectively appear in the spectra. In the case of plasmonic enhancement, the spectral appearance is more sensitive to molecular orientations at the metal surface because of the surface selection rules [25]. 

Vibrational Contributions Contribution of vibrational modes has been described for TPA [5-9, 11-17, 19, 22, 23, 31, 37, 61, 235, 309, 343-345] and for other nonlinear optical processes [346]. One classical example is the 1A j -1 B2u TP transition of benzene, the so-called green band. This electronic transition is allowed due to a vibronic coupling mechanism [346]. Semiempirical [60, 61] as well as ab initio response theory calculations using the Herzberg-Teller expansion [344] demonstrate the role of vibronic coupling. Such contributions can either enhance an allowed transition or intensify a symmetry-forbidden transition. 

Fig. 5. The Herzberg-Teller scattering mechanism. A and B illustrate the first-order contributions to fundamental scattering for non-totally symmetric modes where the excited-state potential curves are unshifted relative to those of the ground state. C and D show the dominant second-order contributions to overtone scattering.

Corio, R, J.C. Rubim, and R. Aroca (1998). Contribution of the Herzberg-Teller mechanism to the surface-enhanced Raman scattering of iron phthalocyanine adsorbed on a silver electrode. Langmuir 14, 4162. 

We first consider a nontotally symmetric mode involved in Herzberg-Teller-type vibronic coupling. In Section IV,A, we showed that coupling through this mode of the resonant state with several excited states ,. .. of the same symmetry leads to contribution to the scattering... 

Chou and Jin have addressed the importance of the vibrational contributions to the polarizability and second hyperpolarizability within the two-level and the two-band models. Their study adopts the sum-over-state (SOS) expressions of the (hyper)polarizabilities expressed in terms of vibronic states and includes two states and a single vibrational normal mode. Moreover, the Herzberg-Teller expansion is applied to these SOS formulas including vibrational energy levels without employing the Plac-zek s approximation. Thus, this method includes not only the vibrational contribution from the lattice relaxation but also the contribution arising... 

Another advantage of the nuclear-ensemble approach is that it is naturally a post-Condon approximation. Because the transition moments are evaluated for geometries displaced from equilibrium position, vibronic contributions to the spectrum are computed without need of Herzberg-Teller type of expansions [5]. Thus, even dark vibronic bands are described by the simulations [15]. 

Equations (11) and (12) are obtained under the hypothesis of negligible vibronic coupling, and they correspond to considering only the Condon factors in the development by Tang and Albrecht [93]. The hypothesis that other terms (Herzberg-Teller terms) are negligible is fully consistent with the choice of a two-state model. The possible existence of other nonnegligible contributions to Raman intensities is irrelevant for the qualitative discussion that follows. 

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. 

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