Overview of Polyene Singlet States

In the case of a planar linear polyene the molecular orbitals may be classified according to their symmetry under reflection through the molecular plane, a orbitals are symmetric under reflection, n orbitals are antisymmetric. In discussing the low energy excited singlet states of linear polyenes it is appropriate to limit attention to many electron states built from orbitals with n symmetry (the 7C-electron approximation). In the simplest treatments these 7C-electron orbitds may be written as linear combinations of 2p-7c atomic orbitals, one per sp2 hybridized carbon atom. In the case of an all-trans planar polyene which has 2/m symmetry, these 7C-electron orbitals will transform as Ay or Bg. Since the number of electrons is even, the many electron states will have either Ag or Bu symmetry. 

The discussions of linear polyene electronic structure that follow are made clearer by reference to a simple quantum mechanical model. In this section we briefly sketch the model that we use. A fuller description will be published elsewhere [3]. 

Since Schulten and Karplus showed that the experimentally observed ordering of polyene excited states reflected the importance of electron correlation in these molecules [2], the idea that explicit consideration of electron-electron coulomb interaction is essential for a correct description of polyene electronic structure has been reinforced by a number of theoretical studies [4-8]. Unfortunately, as theory more closely agrees with experiment, it also becomes more complex and computationally intensive. This is the reason that we have 

The appeal of this model is its simplicity, the fact that, as will be seen later, a single set of the four parameters P,S, A, and B accurately reproduce all the polyene 2 Ag and l Bu excitation energies that have been measured in low temperature hydrocarbon solution, and the ease with which it can be extended to substituted linear polyenes. 

The convergence of the linear polyene Sq to S2 excitation energy to a finite limit as the length of the conjugated chain increases is strong evidence that there is bond length alternation in the long chains. This is supported by the limited number of direct structure determinations that have been published. 

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