Lowest unoccupied molecular orbital definition

In the donor-acceptor interaction, the acceptor provides its lowest unoccupied molecular orbital (LUMO) and the donor participates at the expense of its highest occupied molecular orbital (HOMO). These orbitals are frontier orbitals. In the corresponding ion radicals, the distribution of an unpaired electron proceeds, naturally, under frontier-orbital control. This definitely is reflected in ion radical reactivity. 

By definition, the Fukui function represents the change in electron density due to addition or removal of electrons from the system. Recalling results from the frontier molecular orbital theory, where the magnitude of the highest-occupied and lowest-unoccupied molecular orbitals are used to discern the propensity of a molecular site to attack by electron acceptors and electron donors, respectively, we deduce that the... 

The term species may mean a discrete molecule, a simple or complex ion or even a solid exhibiting non-molecularity in one or more dimensions (graphite as an example). Free atoms seldom act as Lewis acids and bases. They usually have one or more unpaired electrons and flieir reactions are more accurately classified as free radical. The donor orbital is usually die highest occupied molecular orbital HOMO, and the acceptor orbital is usually the lowest unoccupied molecular orbital or LUMO. The molecular orbital definitions have a number of important consequences ... 

Another definition of aromaticity that does not depend explicitly on either experimental results or on comparison with reference compounds is derived from the concept of absolute hardness, 17, which is defined as one-half of the energy difference between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of a system (equation 4.70). According to Koopmans theorem, Ehomo is related to the ionization potential of the species, while Elumo is related to its electron affinity. A large gap between these two orbitals implies resistance to both oxidation and reduction, and low chemical reactivity is one of the defining characteristics of aromaticity. 

A Figure 9.47 Definitions of the highest occupied and lowest unoccupied molecular orbitals. The energy difference between these is the HOMO-LUMO gap. 

By definition, Lewis acid catalysts involve a metal center as an electron pair acceptor that accepts the electron pair from a nucleophile. This property makes them effective in many organic reactions and indispensable for the production of a large category of chemicals from simple alkylated compounds to complicated polymers or pharmaceuticals [6]. Also, the differences between the energy levels of the highest occupied molecular orbital (HOMO) of the reactant (nucleophile) and the lowest unoccupied molecular orbital (LUMO) of the Lewis acid (electrophile) make Lewis acid catalysis more complicated than the corresponding Br0nsted catalysis [7]. 

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