Covalent Excited States of Polyenes

Butadiene and Hexatriene The two covalent VB structures for butadiene are depicted in Fig. 7.9a as Ri and R2. Under the symmetry operations of the point group, the two structures transform as Ag (since both are unchanged by i), and will therefore mix to give rise to two states of the same symmetry. The corresponding wave functions are written in Equations 7.12a and b, with normalization constants that neglect all overlap terms between orbitals on atoms a—d. 

FIGURE 7.9 (a) Covalent resonance structures for butadiene and their overlap integral, (b) A VB mixing diagram of the resonance structures yielding the covalent ground and excited states, (c) The major 1,4-biradical character of the 2 Ag state. 

This chapter focused on a special class of excited states of organic molecules hoping to provide a conceptual qualitative frame that would allow thinking about these excited states and discussing some of their features from the bonding characteristics of the VB wave function. One general rule is already apparent from the treatments of the various molecules In all annulenes, the 

Foresman, M. Head-Gordon, J. A. Pople, M. J. Frisch, J. Phys. Chem. 96, 135 (1992). Toward a Systematic Molecular Orbital Theory for Excited States. 

---