Molecular orbital theory of polyenes

Molecular Orbital Theory of Polyenes Implicated in the Dehydrochlorination of Poly(vinyl chloride)... 

We introduced the molecular orbital theory of polyenes in Chapter 11. In this chapter, we will restrict our discussion to the symmetry of the molecular orbitals. The symmetric or antisymmetric character of a molecular orbital is described with respect to a vertical mirror plane through the center of the molecule and perpendicular to the plane of the molecule. If the signs of the lobes on the two sides of the mirror plane are the same, the molecular orbital is symmetric. If the signs are not the same, the orbital is antisymmetric. For example, Tii of ethene, the bonding molecular orbital is symmetric 712, the antibonding molecular orbital is antisymmetric (Figure 25.1). 

One of molecular orbital theories early successes came m 1931 when Erich Huckel dis covered an interesting pattern m the tt orbital energy levels of benzene cyclobutadiene and cyclooctatetraene By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar geometries Huckel found that whether a hydrocarbon of this type was aromatic depended on its number of tt electrons He set forth what we now call Huckel s rule... 

Nonbenzenoid cyclic conjugated hydrocarbons are conveniently classified into two categories conjugated hydrocarbons composed of odd-membered rings called, in terminology of molecular orbital theory, nonalternant hydrocarbons, and cyclic polyenes currently known as annulenes. 

This equivalence of the valence bond and molecular orbital descriptions of the bonding in these complexes arises from the alternant1 properties of the metal-butadiene bonding network. A similar equivalence between the two theories occurs for benzene and other polyenes that have alternant 7r-systems (73, 140). 

In this section, we first discuss the bonding in two linear triatomic molecules BeH2 with only a bonds and C02 with both a and n bonds. Then we go on to treat other polyatomic molecules with the hybridization theory. Next we discuss the derivation of a self-consistent set of covalent radii for the atoms. Finally, we study the bonding and reactivity of conjugated polyenes by applying Hiickel molecular orbital theory. 

In this section, we first study the jt bonding in conjugated polyenes by means of the Hiickel molecular orbital theory. Then we will see how the wavefunctions obtained control the course of the reaction for these molecules. 

Previously in Chapter 3 we introduced the Huckel molecular orbital theory and applied it to the n system of a number of conjugated polyene chains. In this section we will apply this approximation to cyclic conjugated polyenes, taking advantage of the symmetry properties of these systems in the process. 

V-UV Application First Excited State of Linear Polyenes. The first electronic absorption band of perfect linear aromatic polyenes (CH)X, or perfect polyacetylene shifts to the red (to lower energies) as the molecule becomes longer, and the bond length alternation (BLA) would be zero. This was discussed as the free-electron molecular orbital theory (FEMO) in Section 3.3. If this particle-in-a-box analysis were correct, then as x > oo, the energy-level difference between ground and first excited state would go to zero. This does not happen, however first, because BLA V 0, next, because these linear polyenes do not remain linear, but are distorted from planarity and linearity for x > 6. 

The band structure of a three-dimensional solid, such as a semiconductor crystal, can be obtained in a similar fashion to that of a polyene. Localized molecular orbitals are constructed based on an appropriate set of valence atomic orbitals, and the effects of delocalization are then incorporated into the molecnlar orbital as the number of repeat units in the crystal lattice is increased to infinity. This process is widely known to the chemical conununity as extended Hiickel theory (see Extended Hiickel Molecular Orbital Theory). It is also called tight binding theory by physicists who apply these methods to calcnlate the band structures of semiconducting and metallic solids. 

The kinetics of the photoisomerization of bilirubin has been studied because of the relevance to phototherapy. The fluorescence of bilirubin increases on binding to human serum albumin. This and other primary photoprocesses have been investigated by picosecond spectroscopy. Karvaly has put forward a new photochemical mechanism for energy conversion in bacteriorhodopsin. An extensive review of the photophysics of light transduction in rhodopsin and bacteriorhodopsin has been made by Birge. The dynamics of cis-trans isomerization in rhodopsin has been analysed by INDO-CISD molecular orbital theory. Similar calculations on polyenes and cyanine dyes have also been reported. A new picosecond resonance Raman technique shows that a distorted... 

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