MOs and their symmetry properties

Since pericyclic reactions proceed with a cyclic reorganization of bonding electron pairs, it is necessary to evaluate changes in the associated MOs that take place in going from reactants to products. These orbitals may be classified by two independent symmetry operations a mirror plane (m) perpendicular to the functional plane and bisecting the molecule, and a twofold axis of rotation (C2). 

Let us first define the symmetry properties of Is- and 2p-orbitals (Fig. 8.1) and MOs formed by the overlap of two or more atomic orbitals with respect to a plane of symmetry (m) or an axis of symmetry (C2) (Figs. 8.2-8.4). 

Schematic, qualitatively correct tt-MOs can be easily generated from a linear array of n p-atomic orbitals by following a few simple rules  

The lowest energy MO always has all p-orbitals in phase, making it symmetric (S) with respect to end-for-end reflection. This MO has no vertical nodes. 

The next MO, which has one nodal plane (a single vertical node), is antisymmetric (A) with respect to end-for-end reflection. An example is the tt -MO of ethylene. 

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We are now well equipped to consider the various MOs and the symmetry characteristics present in. v-c/.v-hutadiene. The two it bonds are comprised of four atomic p orbitals, their allowed combinations give rise to a set of four MOs, two bonding and two anti-bonding. These MOs and their symmetry properties with respect to two symmetry elements, namely m and C2, are given below. 

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