MOLECULAR ORBITALS OF CONJUGATED π- (PI) SYSTEM

According to molecular orbital theory the p and orbitals on the sp²- Hybridised carbon of a conjugated polyene interact to form a set of π molecular orbitals that energies depend on the number of nodes and they having between the nuclei. The molecular orbitals with has been fewer nodes are in the lower energy than isolated p atomic orbitals are normally bonding MOs. Molecular orbitals with more nodes are higher energy levels than isolated p orbitals and are anti-bonding MOs; π molecular orbitals of 1,3 - butadiene and and ethylene below the figure.

1,3-Butadiene 

Ethylene 

A similarly sort of the molecular orbitals description can be derived for any conjugated pi electron system. For example 1,3,5 - Hexatriene has double bond and six pi molecular orbitals. In the ground state only have three bonding orbitals ψ1, ψ2 and ψ3 are fully filled orbitals. On irradiation with uv light, however an electron is promoted from the highest energy level filled orbitals ψ3 to the lowest - energy unfilled orbital (ψ4*) to giving the excited states in which ψ3 and ψ4* are each half - filled. 

Molecular orbitals their nodes having to do with the pericyclic reaction. Everything is according to  pericyclic reaction can takes place only if the symmetries of the reactant MO are the same and must be of the correct algebraic signs for bonding to occurs in the transition state is leading to as a product. 

 orbitals match up, or correlate the reaction is to be symmetry allowed. If the reaction is symmetry disallowed. The symmetry allowed reaction often reaction occurs under relativity mild conditions, by symmetry disallowed reaction can not occur by concerted paths. However they take place by nonconcerted, higher energy pathways, or they don't take place at all. 

The Hoffman - Woodward rules for pericyclic reactions to required analysis of reactants and product molecular orbitals. According to Scientist, Fukui, we need to consider only two molecular orbitals it's called the frontier orbitals. This frontier orbitals are the highest level occupied molecular orbitals HOMO and lowest unoccupied molecular orbitals LUMO. In the ground state of 1,3,5-hexatriene, for example, ψ3 is the HOMO and ψ4* is the LUMO above the figure. In excited state 1,3,5- hexatriene, however ψ4* is the HOMO and ψ5* is the LUMO.