Molecular mechanics conjugated systems

There is significant bond alternation, however. The bond at the ring fusion is quite long 11.539 A). A molecular mechanics calculation on this molecule that included an SCF-MO treatment of the planar conjugated system found the molecule to be slightly destabilized (4kcal/mol) relative to a polyene reference. " ... 

Molecular structure can have a profound effect on the position in the spectrum where fluorescence occurs, as well as on its intensity. It can be shown by quantum mechanics that the more extended a conjugated system is, the smaller will be the separation in energy between the ground state and the lowest excited singlet state. This is evident in the fact that benzene, naphthalene, and anthracene, having one, two, and three rings, fluoresce maximally at 262 nm, 320 nm, and 379 nm, respectively. 

This separation of the cr framework and the re bond is the essence of Hiickel theory. Because the re bond in ethylene in this treatment is self-contained, we may treat the electrons in it in the same way as we do for the fundamental quantum mechanical picture of an electron in a box. We look at each molecular wave function as one of a series of sine waves, with the limits of the box one bond length out from the atoms at the end of the conjugated system, and then inscribe sine waves so that a node always comes at the edge of the box. With two orbitals to consider for the re bond of ethylene, we only need the 180° sine curve for re and the 360° sine curve for re. These curves can be inscribed over the orbitals as they are on the left of Fig. 1.23, and we can see on the right how the vertical lines above and below the atoms duplicate the pattern of the coefficients, with both c and c2 positive in the re orbital, and c positive and c2 negative in re. ... 

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