Effective Conjugation Coordinate

A most recently developed description of the problem interprets the amplitude mode model in terms of a molecular concept of chains with cyclic boundary conditions (Zerbi et al., 1989). An effective conjugation coordinate Qja with a corresponding force constant fja is defined. The vibrational frequencies are calculated as a function of , which plays the same role as A in the amplitude mode model. Accordingly, the Raman intensity is obtained from the respective ja components of individual modes. This new concept, like the amplitude mode model, properly describes the relative intensities of different modes, but the correct line shapes and line intensities for excitation with different laser lines can not be obtained, since transition matrix elements are not evaluated explicitly. 

Because of the strong coloration, depending on their state of oxidation, intrinsically conducting polymers have frequently been studied with SRRS [507, 508]. Molecular vibrations could be assigned based on various approaches. Most frequently band positions of the monomers and of already known oligomers were compared with those of the polymers. Alternatively, band positions were calculated based on an effective conjugation coordinate [509-516]. In a typical example shown in Fig. 5.84, SRR spectra of poly aniline are displayed as a function of electrode potential. 

Raman spectrum of neutral poly( -phenyIene) is well explained by the effective-conjugation-coordinate model [95],... 

A set of resonantly enhanced Raman spectra of PPy in an aqueous solution of 1-M HCIO4 is shown in Figure 67. Raman spectra measured both ex situ as well as in situ have been reported frequently [694-703]. Pertinent results and conclusions are incorporated in Table XXIV. The effective conjugation coordinate suggested by Tian and Zerbi [342] also was applied to the interpretation of Raman spectra, and their results are incorporated in the table. Low frequency Raman modes of PPy caused by fractal vibrational modes were reported and discussed by Jin et al. [704]. With laser excitation at Aq = 514.5 nm, bands at 65,77, and 116 cm were observed they were explained in terms of a fractal description of localized vibrations. 

In a study of PITN with in situ and ex situ resonance Raman spectroscopy combined with a vibrational analysis, Wallnofer et al. [1055] obtained further details of PITN in its various doped and undoped states. A theoretical foundation for the interpretation of vibrational spectra of PITN was provided by Faulques et al. [1056]. Their results were taken into consideration in e previous discussion of Raman and infrared spectra. Zerbi et al. [1057] reinvestigated PITN prepared chemically with Raman spectroscopy er situ because they believed that previous results were inconclusive. Their results, based on the effective conjugation coordinate, imply that PITN in its electronic ground state is present in the quinoid form. 

Gelan and coworkers [32] also examined the Raman spectra of the model compounds, both quinonoid and aromatic, which include 6, 7, and 9, and compared these to the spectrum of polyisothianaphthene (1). Here, the vibrational bands of 1 were shown to match more closely with those of the quinonoid structures 6 and 7 than those of the aromatic structures such as 9 that were studied. In another recent paper [38], the Raman spectra of the model compounds and that of the pristine polyi.sothia-naphthene (1) are again compared. Using the effective conjugation coordinate theory to interpret the spectra, it is again concluded that the structure is quinonoid. 

The hypothesis that only one coordinate in the vibrational space is important in the description of electron-phonon coupling forms the basis of the model of the effective conjugation coordinate fl [43], which has been the starting point in the treatment of the vibrational dynamics of conjugated systems. 

Following the classical approach of vibrational dynamics (as in the case of o--bonded polymers) [67], the experimental data from the oligomers could in principle be used to obtain the phonon dispersion curves of the ideally infinite polymer. In the case of 7r-bonded systems, complications arise because the skeletal modes are strongly CL-dependent and cannot be treated in the standard way. The rationalization of the behavior of the totally symmetric Raman-active normal modes leads to the definition of a CL-dependent intramolecular potential on which the effective conjugation coordinate (ECO theory is based (see Section IV). 

Equations (15) and (16) define the so-called effective conjugation coordinate of ECC theory. The important conclusion that can be derived from Eqs. (11) and (17) is that only normal modes that contain an oscillation of the dimerization amplitude ( R vibration) can have relevant Raman cross sections. Then the two relevant lines of the Raman spectrum of polyenes are necessarily assigned to normal modes that involve a large contribution by the fl oscillation (FI modes in the ECC theory). More precisely, the treatment of the dynamical problem of polyenes in terms of ECC theory assigns the two strong Raman lines to two different combinations (in-phase and out-of-phase) of the R oscillation with C—H wagging vibration. 

In conclusion, a critical reading of the data reported in Table 28.1 and 28.2 and Figs. 28.6, 28.8, and 28.18 shows that the physics of the polyene systems can be interpreted in a unified way by the introduction of the concept of effective conjugation coordinate" strongly coupled with tt electrons. Moreover, with the help of ECC theory, it is possible to extract relevant information on the electronic structure and molecular geometry from... 

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