Vibronic coupling benzene

The vibronic coupling model has been applied to a number of molecular systems, and used to evaluate the behavior of wavepackets over coupled surfaces [191]. Recent examples are the radical cation of allene [192,193], and benzene [194] (for further examples see references cited therein). It has also been used to explain the lack of structure in the S2 band of the pyrazine absoiption spectrum [109,173,174,195], and recently to study the photoisomerization of retina] [196],... 

The lowest excited states of benzene are actually of B2u and Bi symmetry, and they can be reached directly by neither one-photon nor two-photon purely electronic transitions (the 0-0 band at energy Eq-o. the origin of the transition, is absent from the spectra). However, excitation into these states can be obtained through vibronic coupling (VC), if a vibrational mode of an appropriate symmetry is coupled to the electronic transition. The IPA or 2PA spectra can then show a series of narrow peaks shifted from the 0-0 band... 

In substituted benzenes, the symmetry is lowered and the transitions into the states that correlate to the B2u and B u states of benzene become allowed by IPA, 2PA, or both. However, when the substituents induce only a weak perturbation on the benzene yr-electron system, the IPA or 2PA spectra of the substituted compounds often closely resemble the spectrum of the unsubstituted parent molecule. Various theoretical models have been developed in an attempt to predict the type of change in the band intensity and characteristics in the 2PA spectra of substituted benzenes and, more generally, of alternant hydrocarbons [34-36]. It was found that the effect of a perturbation is quite different for IP and 2P allowed transitions. In particular, 2P transitions to the state correlated to the benzene B2u state (Lb) are affected more by vibronic coupling than transitions to the state correlated to the benzene Biu state (La, in Platt notation [31,32]). In contrast, inductive perturbations enhance the La band more than the Lb band. The effects of vibronic coupling and inductive substituents are reversed for IP transitions into these states. Experimental... 

In the case of naphthalene, transitions to the two lowest excited states (again, often indicated with Lb and La) are two-photon forbidden, as in benzene. However, due to vibronic coupling, the Lb band is visible in the 2PA spectrum of naphthalene in the 575-650 nm region (see Fig. 5), while La gains intensity in the IPA spectrum and peaks around 275 nm [44-46], but is basically absent from the 2PA spectrum this is again in line with predictions based on the pseudoparity of the states. Polarization ratio data were used to aid the band assignment. A weak 0-0 peak of the Lb band can actually be seen in the 2PA spectrum (at 630.5 nm for naphthalene in cyclohexane [45] and at 631.8 nm in carbon tetrachloride [47]), probably because of local perturbation of the symmetry due to the solvent environment or other effects [44,45]. The 2PA... 

B. Sharf, B. Honig, and J. Jortner, Vibronic Coupling in the Rydberg States of Benzene, to be published. 

Since there are normal modes of B2g and E2g symmetry, both the transitions 1 A g > 1B1 and 1A, —> 1 B2 (which are forbidden by symmetry in a rigid molecule) become allowed through vibronic coupling. These transitions account for the two weaker bands in the benzene spectrum at 2000 and 2600 A. 

Vibrational analysis of the benzene phosphorescence bands indicates that the radiative activity is induced predominantly by e2g vibrations [155, 156]. A weak but observable activity of b2g vibrations has also been found [156, 155, 157]. By introducing spin-orbit- and vibronic coupling through second order perturbation theory Albrecht [158] showed that the vibronic interaction within the triplet manifold is responsible for the larger part of the phosphorescence intensity. This also follows from comparison of the vibrational structure in phosphorescence and fluorescence spectra [159]. The benzene phosphorescence spectrum in rigid glasses [155] reveals a dominant vibronic activity of... 

Table 17 The 7 - So oscillator strengths in benzene calculated with direct vibronic coupling along e2g modes (i- ). Results are displayed for different basis sets and for the 7r-active space.

The nature of vibronic coupling in fused polycyclic benzene-thiophene structures, including benzodithiophene 45, naphthodithiophene 111, and anthradithiophene 112, has been studied using an approach that combines high-resolution gas-phase photoelectron spectroscopy measurements with first-principles quantum-mechanical calculations <2006CEJ2073>. 

In applications of these symmetry selection rules it has to be remembered that the symmetry of a molecule can be lowered by vibrational motions so that symmetry-forbidden transitions may nevertheless be observed—for instance, the two longest-wavelength singlet-singlet transitions in benzene. Vibronic coupling and the shape of the absorption bands will be discussed in the following sections. 

In benzene both the B, and the B states can mix with the E, state through vibronic coupling using an ej, vibration. Since the A, E transition is symmetry allowed, both the A - Bju and the A B, transitions become... 

The vibronic coupling in the PA + is bit more involved than in Ph [21], The De/, equilibrium mmetry of benzene breaks to Civ pon acetyjene substitution. The degenerate X Eig JT state of BZ + splits into X Bi and A Ax electronic states in PA + as revealed by Fig. 3. Contrary to the phenide anion, where removal of a proton splits the JT degeneracy of benzene, in phenylacetylene (PA), perturbation caused by substitution breaks the JT symmetry. 

The complexity in the assignment of molecular spectra is addressed by showing recent results on four representative examples viz., Ph, PA +, N + and AN +. The first two are directly derived from the JT active benzene system. Manifestation of the JT activity in these substituted benzenoid systems is also discussed. The mechanistic details of the observed photostability in the PAH radical cations, N + and AN + are examined. The discussions in this article reveal the need of understanding the complex vibronic coupling mechanisms while dealing with the electronically excited molecules in particular, and the recent advancements in the experimental and theoretical techniques to observe and treat them. 

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. 

Note added in proof. Very recently, A. Furlan, M. J. Riley, and S. Leutwyler [J. Chem. Phys. 96, 7306 (1992)] have reported a resonant two-photon ionization spectrum of the S, vibronic transitions of supersonically cooled triptycene. The excited state exhibits E (8>e Jahn-Teller activity with linear and quadratic vibronic coupling in a single, degenerate, benzene wagging mode. 

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