Frontier second highest occupied molecular orbital

The second explanation is based on the frontier orbitals—the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied orbital (LUMO) of the other. Thus if we compare a [2 + 2] cycloaddition 6.172 with a [4 + 2] cycloaddition 6.173 and 6.174, we see that the former has frontier orbitals that do not match in sign at both ends, whereas the latter do, whichever way round, 6.173 or 6.174, we take the frontier orbitals. 

The basic idea of this theory can be suimnarized in the form of a sinq>le rule expressing the condition for an easy course of reaction by the requirement of the maximal positive overlap between the highest occupied molecular orbital HOMO and the lowest unoccupied molecular orbital LUMO. The practical use of this simple rule can be again best demonstrated by concrete exaitq)les. The sinqrlest situation is in the case of cycloadditions where the role of frontier orbitals is played by the HOMO of the first and the LUMO of the second component. In order to demonstrate the practical use of the above simple criterion let us analyze first the well known case of the Diels-Alder reaction. The situation is in this case depicted by the following Scheme. As can be seen from this scheme, the nodal structure of frontier orbitals is in this case favorable for the positive overlap in the regions of newly created bonds so that the reaction is allowed. 

HOMO stands for the highest occupied molecular orbital. In 1981, Hoffmann was awarded the 1981 Nobel Prize in Chemistry for this work (shared with Kenichi Fukui who developed a related model using frontier molecular orbital theory). Because Woodward had died in 1979, he was not eligible to win what would have been his second Nobel Prize for Chemistry. 

The first term is the screened electrostatic interaction between the donor and acceptor charges Qi and Q2 - assumed to be point charges - at the equilibrium distance Rn in the adduct. The second term accounts for covalent effects. The factor of 2 indicates that two electrons are shared. The c coefficients are the molecular wave-function weights on atoms 1 and 2. The energies Em and E are equal, to a first approximation, to the frontier orbital energies the base HOMO (HOMO = highest occupied molecular orbital) and the acid LUMO (LUMO = lowest unoccupied molecular orbital), i.e. to the base first ionization potential and to the acid electron aflSnity. A typical frontier orbital diagram is shown in Fig. 6.1. 

The first paper of the frontier-electron theory pointed out that the electrophilic aromatic substitution in aromatic hydrocarbons should take place at the position of the greatest density of electrons in the highest occupied (HO) molecular orbital (MO). The second paper disclosed that the nucleophilic replacement should occur at the carbon atom where the lowest unoccupied (LU) MO exhibited the maximum density of extension. These particular MO s were called "frontier MO s . In homolytic replacements, both HO and LU.were shown to serve as the frontier MO s. In these papers the "partial" density of 2 pn electron, in the HO (or LU) MO, at a certain carbon atom was simply interpreted by the square of the atomic orbital (AO) coefficient in these particular MO s which were represented by a linear combination (LC) of 2 pn AO s in the frame of the Huckel approximation. These partial densities were named frontier-electron densities . 

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