Frontier-orbital

Fig. 3. The four essential porphin ir-molecular orbitals ( frontier orbitals a2u and aju are filled, eg are unoccupied figure taken from Ref. (49), with permission)...

Frontier orbital theory can sometimes be remarkably efficient in explaining organo-metallic chemistry (pp. 207, 228 see also ref. 6). However, it is sometimes necessary to take the subjacent orbitals into account alongside the five d orbitals. Frontier orbital theory is difficult to operate in these cases because of frequent inversions of orbital... 

The last years have seen a great development of the hetero Diels-Alder reactions of thiocarbonyl compounds, due to their rather high reactivity, as reported by many groups, including those of Kirby, Bonini, Capozzi, DeglTnnocenti, Vallde, Okazaki, Koizumi, Saito and Huisgen. A simple orbital frontier treatment allows comparison of the reactivity of C=S vs C=0 [119]. 

Highest Occupied Molecular Orbital (Frontier MO) Internal (Stability/Instability)... 

HO and LU refer to the orbital frontier nomenclature of Highest Occupied and Lowest Unoccupied ... 

Frontier orbital Frontier electron theory is based on the idea that a reaction should occur at the position of largest electron density in the frontier orbitals. In the case of an electrophilic reaction, the frontier orbital is the HOMO, and the LUMO in the case of a nucleophilic reaction. 

Scheme 3 Orbital frontier interactions foj- thermal and catalyzed reaction...

The electron density of the highest filled orbital (frontier-electron density) is greatest at C 1 and C-4 therefore, these are predicted to be the positions most readily attacked by electrophilic reagents. 

For attack by nucleophilic reagents, one can consider that the attacking reagent will tend to place a pair of electrons in the lowest unoccupied molecular orbital (frontier orbital). 

Whereas the same freedom in the choice of MO representations evidently affects the individual MOs, the contour surfaces of individual MOs, such as highest occupied and lowest unoccupied (HOMO and LUMO) orbitals, frontier orbitals, and various localized and delocalized orbitals,have been often used in the interpretation of various molecular properties and processes. The level sets F a) and contour surfaces G(a) of individual MO s /(r) are defined in the usual way ... 

For these local functions a conservation of the HOMO or LUMO orbital type involved in the calculation of a given ionization case is noted, with the specification that in the situation (b) the difference rather than the summation of probabilities for the orbital frontier functions is involved. 

Simple Approaches to Quantifying Chemical Reactivity 3.4.2.1 Frontier Molecular Orbital Theory... 

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

The new bonds will be made between those two ends of the reactants where the orbital coefiicients of the frontier orbitals match best, where both have the largest coefficients. 

The importance of FMO theory hes in the fact that good results may be obtained even if the frontier molecular orbitals are calculated by rather simple, approximate quantum mechanical methods such as perturbation theory. Even simple additivity schemes have been developed for estimating the energies and the orbital coefficients of frontier molecular orbitals [6]. 

I. Fleming, Frontier Orbitals and Organic Chemical Reactions, Wiley, New York, 1976. 

Emphasis was put on providing a sound physicochemical basis for the modeling of the effects determining a reaction mechanism. Thus, methods were developed for the estimation of pXj-vahies, bond dissociation energies, heats of formation, frontier molecular orbital energies and coefficients, and stcric hindrance. 

HOMO and LLMO, also known as Frontier orbitals, are important in in tcrprcLitig results of a calculation (see Frontier Molecular Orbitals on page 141). You can use these m olecular orbiLals to comptiLe the lowest excited electronic singlet state of molecules and the ground states of radicals. 

When you request an orbital, yon can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LL MO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

The way the substituents affect the rate of the reaction can be rationalised with the aid of the Frontier Molecular Orbital (FMO) theory. This theory was developed during a study of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffinann and, independently, by Fukui Later, Houk contributed significantly to the understanding of the reactivity and selectivity of these processes. ... 

Figure 1.3. Frontier orbital energies (eV) and confidents for acrolein and protonated acrolein. In the latter case the upper numbers refer to the situation where bond lengths and angles correspond to those of acrolein. The lower numbers are more suitable for a hydroxyallyl cation. The actual situation is assumed to be intermediate. The data are taken from ref. 104.

Note that the stereochemistry comes out right. H s a and b are cis because they were cis in the starting quinone and the Diels-Alder reaction is stereospecific in this respect. H is also cis to and H " because the Diels-Alder reaction is stereoselectively endo. These points are described in more detail in Norman p.284-6 and explained in Ian Fleming Frontier Orbitals and Organic Chemical Reactions, Wiley 1976, p. 106-109. How would you make diene A ... 

HOMO and LUMO energies FMO reactivity indices Refractivity Total energy Ionization potential Electron affinity Energy of protonation Orbital populations Frontier orbital densities Superdelocalizabilities... 

Nevertheless, the puzzling fact to be explained is that the harder ring nitrogen prefers the softer electrophilic center and that this preference is more pronounced than the one observed for the amino nitrogen. Much remains to be done to explain ambident heterocyclic reactivity it was shown recently by comparison between Photoelectrons Spectroscopy and kinetic data that not only the frontier densities but also the relative symmetries of nucleophilic occupied orbitals and electrophilic unoccupied orbitals must be taken into consideration (308). 

Use frontier orbital analysis to decide whether the dimeriza... 

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

Frontier orbitals (Section 10 14) Orbitals involved in a chem ical reaction usually the highest occupied molecular orbital of one reactant and the lowest unoccupied molecular orbital of the other... 

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