Linear Conjugated Chains

Most of the work currently reported is on finite chains, with a possible extrapolation to the limiting case. In a few cases a band structure for the infinite chain is calculated and the response function of the infinite polymer found from the spectrum of band to band transitions. There has been much discussion in recent years of the effect of bond alternation, particularly in combination with variations in donor/acceptor strength, on the response functions. The papers reviewed here mainly represent further development of the above themes. 

Del Zoppo et al.197 have made an ab initio study of a model push-pull polyene and calculated the dependence of the polarizability and first hyperpolarizability on the bond alternation. Vibrational and solvent effects are simulated in the calculation. 

Jacquemin et a/.198,199,200 have continued a series of studies of polymethine-amine. They seek to establish, through studies on small oligomers, that a 6-31G basis set with a suitable form of MP4 is consistent for the investigation of the small chains and plausible for longer ones. They carry out band structure 

The Hubbard model, which has played a significant part in the earlier development of nonlinear optical response theory of molecules, has been revived by Shehadi et al.203 to explain the properties of small bridged metallic polymers. The Hubbard-Peierls hamiltonian has also been used by Shuai et al.,204 in conjunction with a symmetry adapted density matrix renormalization group formulation, to calculate a number of properties, including third harmonic generation in trans-octatetraene. 

Champagne et al.206 have studied solvent effects, through a continuum model, on the a and response functions of polyacetylene chains in the TDHF approximation. They find large increases in the values which they relate to the solvatochromic shifts in the lowest optically allowed transition. Density functional theory has also been assessed207 in connection with the calculation of the same response functions, but has been found to be inadequate due to the inability of the exchange/correlation potentials to satisfactorily represent the effects of the ends of the polymer. Schmidt and Springborg208 have calculated the static hyperpolarizability of polyacetylene and polycarbonitrile in DFT in the presence of external fields. 

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The prototypes of electronically active molecules are linear conjugated chains made from olefinic and aromatic repeat units (Scheme 1). 

The class of compounds that has been most extensively investigated from the point of view of two-photon absorption is that of so-called quadrupolar chromophores. hi essence, these molecifles are linear conjugated chains with electron donating or withdrawing substituents arranged symmetrically with respect to the center of the molecifle (Fig. 8, classes I-IV). With the inversion center being preserved, the lowest order moment supported by these molecules is the quadrupole moment. 

The initial application of quantum mechanics to the electronic states of a perfect linear conjugated chain, as in the Htickel model discussed in Section 4.2.5 and above, led to a model of a one-dimensional semiconductor with well-defined valence and conduction bands. This labelling of the electronic states is widespread in the literature. On the other hand, when electron correlation is included, the electronic states are more localised and an exciton description is more appropriate. The disorder present in all but a few exceptional cases inevitably leads to the conclusion that the electronic states must be localised by chain defects. The extent to which the electronic states of conjugated polymers are localised, i.e. deviate from the band model, has been a matter of debate. There is a growing body of experimental and theoretical evidence, discussed in Sections 9.4.2 and 9.4.3 below, that suggests that the exciton description is closer to the truth. 

Their ability to achieve a high chromophore density (for example, it is possible to introduce three conjugated chains about a single N-atom core in contrast to the two more normally possible with a linear macromolecule) [84]... 

The ESA spectra of this series of A-n-A dyes are shown in Fig. 20. They exhibit broad and intense bands in the visible range (400-600 nm for G37,400-630 nm for G38,450-630 nm for G74, and 450-700 nm for G152) and weak bands in the NIR as revealed in Fig. 20 for G38. We observe that lengthening of the conjugation chain leads to a 30-40 nm red shift of the ESA peaks, which is similar to the behavior of D-rc-D polymethine dyes. This red shift ( 30-40 nm) is much smaller than for the linear absorption bands ( 100 nm). Another experimental feature is connected with the redistribution of the ESA magnitude from the shorter to the... 

By extension one may say that the power laws (5-7) which determine the magnitude of the linear and nonlinear optical coefficients are consequences of this strong electron-lattice coupling. We now make the conjecture that the time response of these coefficients is severely affected by the dynamics of the electron-lattice coupling in conjugated chains when two or more resonant chemical structures can coexist this is the case for many of the organic chains of Figure 2. 

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