Orbitals and Symmetry Considerations

A 7i bond is formed from the overlap of two p orbitals that are adjacent and parallel to each other across a ct bond, and a a bond is the result of coaxial approach of two atomic orbitals such as 5 and s, s and p, and p and p. A molecular orbital (MO) is the result of a linear combination of the constituent atomic orbitals and each MO can then be populated by a maximum of two electrons. For a total of n atomic orbitals, there shall be nl2 bonding and an equal number of anti-bonding MOs with n being an even number. With n being an odd number, there shall be (n - l)/2 bonding MOs with an equal number of anti-bonding MOs and one nonbonding orbital. 

Because an orbital is a mathematical representation of a wave function and because multiplying an entire wave function by —1 does not change its energy characteristics, overlap of a minus lobe with another minus lobe is precisely the same as the overlap of a plus lobe with another plus lobe, i.e., x1 + x2 is the same bonding MO as the bonding MO represented by —x1 — x2. In the construction of a t bond from the overlap of two p orbitals, this shall be represented as follows  

The overlap of a hydrogen s orbital with a carbon p orbital to result in crc H and y MOs shall be represented as follows. Here, it must be made very clear that two 

It should be remembered that (a) a mirror plane m is a plane which is perpendicular to the plane of the molecule/orbital and also bisects it and (b) a C2 axis of symmetry is a line that bisects the molecule/orbital through the center and is in plane with it. We will understand these more by considering the symmetry properties of the MOs of an allyl system. 

MOs of ethylene and their symmetry characteristics (A = antisymmetric, S = symmetric) 

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