Highest occupied 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. 

It s important to know how many electrons one has in one s molecule. Fe(II) has a different chemistry from Fe(III), and CR3+ carbocations are different from CRj radicals and CR3 anions. In the case of Re2Cl82, the archetypical quadruple bond, we have formally Re(III), d4, i.e., a total of eight electrons to put into the frontier orbitals of the dimer level scheme, 17. They fill the a, two x, and the 6 level for the explicit quadruple bond. What about the [PtHj2] polymer 12 Each monomer is d8. If there are Avogadro s number of unit cells, there will be Avogadro s number of levels in each bond. And each level has a place for two electrons. So the first four bands are filled, the xy, xz, yz, z2 bands. The Fermi level, the highest occupied molecular orbital (HOMO), is at the very top of the z2 band. (Strictly speaking, there is another thermodynamic definition of the Fermi level, appropriate both to metals and semiconductors,9 but here we will use the simple equivalence of the Fermi level with the HOMO.)... 

Highest occupied molecular orbital free-electron model, 38-39 geometry and stereoselectivity of reactions, 175-177 Hilbert space, definition, 53 Hohenberg-Kohn theorem, 189-190 HOMO, see Highest occupied molecular orbital... 

On the other hand, if a(r) = f(r) the local hardness becomes proportional to the electrostatic potential generated by the molecular Fukui distribution. Since far away from the nuclei the electronic density will be practically equal to the density of the highest occupied molecular orbital pHOMo(r)> and since the Fukui function is closely related to pHOMo(r), one should expect that in this limit both definitions will lead to very similar results. However, at intermediate distances from, and close to, the nuclei they may provide different information on the reactive sites of a chemical species. 

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. 

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]. 

Fig, 4,18 The stereochemistry of many reactions is easily predicted from the symmetry of molecular orbitals, usually the highest occupied n MO (n HOMO). In the ring closure of 1,3-butadiene to cyclobutene the phase (+ or —) of the HOMO (i//2) at the end carbons (the atoms that bond) is such that closure must occur in a conrotatory sense, giving a definite stereochemical outcome. In the example above there is only one product. The reverse process is actually thermodynamically favored, and the cis dimethyl cyclobutene opens to the cis, trans diene. No attempt is made here to show quantitatively the positions of the energy levels or to size the AOs according to their contributions to the MOs... 

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... 

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

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