Highest occupied-lowest unoccupied molecular orbital analysis

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. 

The COMPACT (computer-optimized molecular parametric analysis of chemical toxicity) procedure, developed by Lewis and co-workers [92], uses a form of discriminant analysis based on two descriptors, namely, molecular planarity and electronic activation energy (the difference between the energies of the highest occupied and lowest unoccupied molecular orbitals), which predict the potential of a compound to act as a substrate for one of the cytochromes P450. Lewis et al. [93] found 64% correct predictions for 100 compounds tested by the NTP for mutagenicity. 

Each reaction species must have molecular orbitals available and with the correct symmetry to allow bonding. These will be called frontier orbitals composed of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). In addition to their involvement in bonding between species, these orbitals are of considerable interest in that they are largely responsible for many of the chemical and spectroscopic characteristics of molecules and species and are thus important in analytical procedures and spectroscopic methods of analysis [5-7],... 

In recent years, molecular descriptors such as the energy of the highest occupied molecular orbital (EHomo) ar d the energy of the lowest unoccupied molecular orbital ( IUMO) have gained in popularity for QSAR analysis, as these descriptors are readily calculated from PC-based software such as SPARTAN. Before we discuss EHomo ar d ELumo further, a brief discussion of quantum chemistry is necessary. 

Cycloadditions are controlled by orbital symmetry (Woodward-Hoffman rules) and can take place only if the symmetry of all reactant molecular orbitals is the same as the symmetry of the product molecular orbitals. Thus, an analysis of all reactant and product orbitals is required. A useful simplification is to consider only the frontier molecular orbitals. These orbitals are the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO). The orbital symmetry must be such that bonding overlap of the terminal lobes can occur with suprafacial geometry that is, both new bonds are formed using the same face of the diene. 

With the progress in the chemical calculation of the molecule, analyses with HOMO/LUMO (highest occupied molecular orbital/lowest unoccupied molecular orbital) energy, absolute hardness/absolute electron negativity, and research into these new and old descriptors have been reported recently. Furthermore, new methods with neural network computers, as well as multiregression analysis, cluster analysis, and major component analysis have been applied to investigate the relationship between the property and function of the molecule and of each descriptor. 

Although it is more fruitful to construct a correlation diagram for the detailed analysis of a pericyclic reaction, there is, nevertheless, an altemative method that also enables us to reach similar conclusions. It is an easy and extremely simple approach that is based on the interaction of the frontier orbitals, i.e., the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of the components that are involved in a pericyclic reaction. 

Another aspect of qualitative application of MO theory is the analysis of interactions of the orbitals in reacting molecules. As molecules approach one another and reaction proceeds, there is a mutual perturbation of the orbitals. This process continues until the reaction is complete and the new produet (or intermediate in a multistep reaction) is formed. PMO theory incorporates the eoneept of frontier orbital control. This concept proposes that the most important interactions will be between a particular pair of orbitals. " These orbitals are the highest filled orbital of one reactant (the HOMO, highest occupied molecular orbital) and the lowest unfilled (LUMO, lowest unoccupied molecular orbital) orbital of the other reactant. The basis for concentrating attention on these two orbitals is that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO... 

Equivalent conclusions are drawn by analysis of the frontier orbitals involved in the cycloaddition. For most combinations of reactants, the appropriate orbitals are the highest occupied molecular orbital (HOMO) of the diene of butadiene) and the lowest unoccupied molecular orbital (LUMO) of the olefin of ethylene). Reaction then occurs by interaction of the HOMO and the LUMO, which can be seen from the illustration below to be symmetry allowed, since the orbitals have the appropriate symmetry ... 

In this paragraph, devoted to the analysis of the gap width A, we will use a one-electron picture in which A is the energy difference between the highest occupied orbital (HOMO = highest occupied molecular orbital here the top of the valence band) and the lowest unoccupied orbital (LUMO = lowest unoccupied molecular orbital here the bottom of the conduction band). This amounts to neglecting the excitonic effects which take place in a gap measurement. A discussion of excitons is postponed to Chapter 4. 

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