Overtone resonance Raman scattering beyond the Condon approximation: Transform theory and vibronic properties

Abstract

The time correlator formalism is used to develop the expression for nth order (overtone) resonance Raman scattering (RRS) to include both Raman frequency shifts upon electronic excitation as well as non-Condon vibronic coupling. In particular the compact operator formalism recently introduced by Hizhnyakov and Tehver [J. Raman Spectrosc. 19, 383 (1988)] to obtain several RRS correlators (including overtone scattering with frequency shift, but in the Condon approximation) is used to extend the theory. At the same time a formal advantage is achieved by the limited introduction of the Born–Oppenheimer approximation. Also transform relationships including non-Condon effects are given that link the Raman excitation profile of nth order scattering to the absorption spectrum. Finally, it is emphasized how all three vibronic parameters—potential energy surface displacement, Raman mode frequency changes, and the linear non-Condon coupling parameter—can be quantitatively determined without the need for absolute Raman cross-section measurements. The relative scattering intensity of the fundamental and three (or more) overtones suffices to fix the three. By way of application, the vibronic parameters are determined from published single wavelength overtone RRS in six molecules.

Pronounced Non-Condon Effect as the Origin of the Quantum Beat Observed in the Time-Resolved Absorption Signal from Excited-State cis-Stilbene

“…30 They showed that the overtones appear also through a term that corresponds to the second term of eq 16 under such a condition. 30 This conclusion is readily understood in the framework of eq 16, by considering that the matrix element 〈V f |Q|V i 〉 can have a nonzero value for ∆V > 1 transitions when the potential minima of the i and f electronic states are displaced. With a significant potential displacement, the second term of eq 16 (the Herzberg-Teller coupling) can also give rise to the overtone in the spectra.…”

“…For the overtones in the resonance Raman spectra, it is important to note that the appearance of the overtones only indicates the existence of a significant displacement between the S 1 and S n potentials, but it does not directly imply that the Raman intensity arises from the Franck−Condon mechanism. Actually, Albrecht and co-workers reported a general theory of Raman intensities for a situation where both the potential displacement and the non-Condon effect are significant . They showed that the overtones appear also through a term that corresponds to the second term of eq 16 under such a condition .…”

Femtochemistry of Hydrogen Bonded Complexes after Electronic Excitation in the Liquid Phase: The Case of Coumarin 102

“…Furthermore, time-resolved measurements on hydrogen bonded complexes of C102 with 2,2,2-trifluoroethanol have indicated that the rotation times can be understood as due to long-lived solute−alcohol complexes as a whole . However, it has been mentioned (ref in ref ) that for C102 half of the emission shifts between nonpolar and alcoholic solvents are already present when dealing with 1:1 probe−alcohol complexes. Moreover, as discussed in section 2 of this paper, our results obtained with femtosecond vibrational spectroscopy of hydrogen bonded C102 have unequivocally demonstrated the dynamics of hydrogen bond cleavage within 200 fs after electronic excitation.…”

“…The effects of reorganization of vibrational degrees of freedom may be another possibility that needs to be inspected more carefully, but, in the light of the experimental results presented previously 54 and in this paper, these effects should then lead to a change of electronic state. If one would assume that the electronic state remains the same after optical excitation of C102, one can only explain the ultrafast components in pump−probe and grating scattering experiments by assuming a time-dependent electronic transition moment (in other words, the Condon approximation does not hold). − So far there is no indication for such an effect in resonant excitation of large dye molecules such as C102 in the literature. Additional photon echo experiments in full resonance with the aborption band of C102−(phenol) 1,2 in C 2 Cl 4 could give information on this issue.…”

Resonance Raman Intensities and Charge-Transfer Reorganization Energies

“…An alternative approach to evaluating resonance Raman intensity data is the “transform theory” method, originally developed by Page and co-workers − and since refined and extended by others. − The transform method exploits the close similarity between optical absorption and resonance Raman scattering to show that, under certain approximations, the band shape of the resonance Raman excitation profile can be expressed as a simple function of the Kramers−Kronig transform of the absorption spectrum. Comparison of the band shapes of the experimental and predicted profiles thus can be used to determine the validity of the assumptions made in the analysis, and the overall scaling of the profiles can provide relative, and in some cases absolute, values for the displacements.…”