Pericyclic reactions lowest unoccupied molecular orbital

The Woodward-Hoffmann rules for pericyclic reactions require an analysis of all reactant and product molecular orbitals, but Kenichi Fukui at Kyoto Imperial University in Japan introduced a simplified version. According to Fukui, we need to consider only two molecular orbitals, called the frontier orbitals. These frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In ground-state 1,3,5-hexa-triene, for example, 1//3 is the HOMO and excited-stale 1,3,5-hexatriene, however, 5 is the LUMO. 

LUMO (Sections 14.4, 30.2) An acronym for lowest unoccupied molecular orbital. The symmetries of the LUMO and the HOMO are important in determining the stereochemistry of pericyclic reactions. 

The comparison of the energies of a-, a -, 77- and 77 -orbitals of ethene is shown in Fig. 8.6. The bonding electrons are placed in the two orbitals with lowest energies, ct and 77, in the ground state of ethene. The 77-orbital is the highest occupied molecular orbital (HOMO) and 77 -orbital is the lowest unoccupied molecular orbital (LUMO). Both HOMO and LUMO are referred to as frontier orbitals (see FMO theory ) and are used in analyzing pericyclic reactions. 

In analyzing pericyclic reactions, two molecular orbitals are of particular interest the tt molecular orbital of highest energy that contains one or two electrons (the highest occupied molecular orbital, HOMO) and the molecular orbital of lowest energy that contains no electrons (the lowest unoccupied molecular orbital, LUMO). For electrocyclic reactions, where there is only one TT system, the important orbital is the HOMO. When more than one tt system is involved, as in (ycloaddition, reactions are considered to occur through a transition state in which the HOMO of one component overlaps the LUMO of the other. 

The Woodward-Hoffmann rules can be rationalized by examining the properties of the frontier MOs of the reactants, i.e., the HOMOs (highest occupied molecular orbitals) and LUMOs (lowest unoccupied molecular orbitals) of the reactants. In order to understand pericyclic reactions, then, you need to be able to construct the MOs of a polyene system from the constituent p orbitals. 

Although the chemistry of a compound is determined by all its molecular orbitals, we can learn a great deal about the chemistry of a compound by looking at only the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). These two molecular orbitals are known as the frontier orbitals. We will now see that simply by evaluating one of the frontier molecular orbitals of the reactant(s) in a pericyclic reaction, we can predict the conditions under which the reaction will occur (thermal or photochemical, or both) and the products that will be formed. 

The Diels-Alder reaction and indeed other pericyclic reactions are concerted processes in which there is no intermediate on the reaction pathway. The mechanisms of such processes can be considered in terms of orbital symmetry concepts. A normal Diels-Alder reaction involves an electron-rich diene and an electron-deficient dienophile, and in such cases the main interaction is that between the highest occupied molecular orbital (HOMO) of the diene and the lowest unoccupied molecular orbital (LUMO) of the dienophile (3.4). The smaller the energy difference between these frontier orbitals, the better these orbitals interact and therefore the more readily the reaction occurs. 

Within each class, we will consider the number of electrons in n molecular orbitals in the transition state. Pericyclic reactions may involve either An or 4 + 2 electrons, where is an integer. This distinction is important because the symmetry of the molecular orbitals in thermal or photochemical reactions depends on the number of n electrons in the transition state. The stereochemistry of the products of pericychc reactions depends on the symmetry of these molecular orbitals. We will see that the stereochemistry of a product of a pericychc reaction derived from a 4 7i electron system differs from that of a 4 + 2 7t electron system. Thus, the concepts of orbital symmetry and Hiickle systems that we considered in Chapter 11 and in particular the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) will play a central role in our discussions of pericychc reactions. 

The importance of the HOMO and LUMO in explaining pericyclic reactions is analogous to the way in which we explain the chemistry of the elements. The HOMO of a polyene resembles the outermost-shell electrons of an atom. Similarly, the electrons of the HOMO have the highest energy, and they can participate in chemical reactions with the lowest expenditure of energy. If more electrons are added to the HOMO of a 7t system, they go to the lowest unoccupied molecular orbital, the LUMO. 

Frontier molecular orbital (FMO) theory 62) has provided new insights into chemical reactivity. This, and the simplicity of its application, has led to its widespread use, particularly in the treatment of pericyclic reactions 63). An FMO treatment depends on the energy of the highest occupied (HOMO) and lowest unoccupied molecular... 

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