Frontier orbital concept

When both the 1,3-dipoIe and the dipolarophile are unsymmetrical, there are two possible orientations for addition. Both steric and electronic factors play a role in determining the regioselectivity of the addition. The most generally satisfactory interpretation of the regiochemistry of dipolar cycloadditions is based on frontier orbital concepts. As with the Diels-Alder reaction, the most favorable orientation is that which involves complementary interaction between the frontier orbitals of the 1,3-dipole and the dipolarophile. Although most dipolar cycloadditions are of the type in which the LUMO of the dipolarophile interacts with the HOMO of the 1,3-dipole, there are a significant number of systems in which the relationship is reversed. There are also some in which the two possible HOMO-LUMO interactions are of comparable magnitude. 

H2, N2, or CO dissociates on a surface, we need to take two orbitals of the molecule into account, the highest occupied and the lowest unoccupied molecular orbital (the HOMO and LUMO of the so-called frontier orbital concept). Let us take a simple case to start with the molecule A2 with occupied bonding level a and unoccupied anti-bonding level a. We use jellium as the substrate metal and discuss the chemisorption of A2 in the resonant level model. What happens is that the two levels broaden because of the rather weak interaction with the free electron cloud of the metal. 

The description of the bonding of unsaturated hydrocarbons to metals was originally developed by Dewar, Chatt and Duncanson and is now known as the well-established DCD model based on a frontier-orbital concept [82]. In this model, the interaction is viewed in terms of a donation of charge from the highest occupied -orbital into the metal and a subsequent backdonation from filled metal-states into the lowest unoccupied -orbital, see Figure 2.33. Contrary to the case of the standard Blyholder model for CO and N2 the DCD frontier-orbital model is supported by experimental XES measurements [83]. In the present section, we will show how we can experimentally identify and quantify the contributions of the different -orbitals involved in the interaction with the surface. The DCD model will be shown to very well describe the chemical bonding of ethylene on Cu and Ni surfaces. Furthermore, the differences in bonding of benzene to Cu and Ni will be discussed. 

Parr and collaborators [8-12] showed how Fukui s frontier-orbital concept could be grounded in a rigorous many-electron theory, density-functional theory (DFT) [8,16-18], They used the ensemble formulation of DFT to introduce the expectation value Jf of the total electron number as a continuous variable. They then defined the Fukui functions... 

The Ambiguity of the Frontier-Orbital Concept and the Complexity of Chemical Responses... 

We have now seen that the effort of Parr and collaborators [8-12] to put Fukui s frontier-orbital concept of chemical reactivity on sound footing in density-functional theory through the definition of the Fukui function and the local and global softness works only for extended systems. This restriction to extended systems raises a sixth issue. In both the local softness and the Fukui function, Eqs. (54) and (53a), the orbitals at the chemical potential represent both the LUMO and the HOMO in the Fukui sense. However, there is a continuum of unoccupied KS states above the chemical potential accessible even to weak chemical perturbations any linear combination of which could in principle be selected as the LUMO, and similarly for states below fi and the HOMO. This ambiguity in the frontier-orbital concept obviously applies as well to localized systems when there is more than one KS state significantly affected by a chemical perturbation. 

Using a frontier orbital conception the educt should also show some product-developing properties. Indeed, not only do the connecting atoms in all our examples (Fig. 1) possess the same sign in the HOMO as is required for a disrotatory process, but also the magnitude of their coefficients are in a proper correlation with the calculated LtiS values. 

Eleven years later, Houk and Yamaguchi (1984, p. 442) stated that, with respect to FMO analysis of regioselectivity and reactivity for diazonium betaines, it had not yet been necessary to change this description in any substantial way . We agree, if this statement refers to basic principles (application of frontier orbital concepts), but... 

In this review we will discuss the current state of knowledge in relation to the classical frontier orbital concept in terms of interactions between highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) [1,2, 3]. 

Ap = 139.3 for protonation at 0 and Ap = 125.8 kcal/mol for protonation at F follow from an ab initio MO calculation [2] using the Moller-Plesset method [1] to include correlation energy. A Hartree-Fock calculation yields 137.2 and 124.7 kcal/mol [2]. Thus, protonation at O is energetically favored over that at F, which is also indicated by previous ab initio calculations [3, 4] and by combining the frontier orbital concept (see [5]) with data from the UV photoelectron spectrum [6]. 

The mixed derivative (a2E/5v(r)5N), represaiting the first derivative of the elecfton density function p(r) with respect to N has been proved to be a generalization of Fukui s frontier orbital concept and, in honour of K. Fukui [12], termed Fukui... 

We attempt to extend the Hard-Soft Acid-Base (HSAB) principle for the reactions in solutions to interactions in solids. First we point out the important link between the absolute hardness of acid-and-base and the average energy gap. Then we discuss the electronic band structures of various solids, e.g., metals, semimetals, semiconductors and insulators. On the basis of energy gaps, we elaborate various consequences of the acid-base interactions in solids. The applications of HSAB principle and the frontier orbital concept to the solid adhesion and surface interactions between metals and polymers will be verified by experimental results reported in the literature. The new findings reported in this paper should be beneficial to those who are carrying out research in or processing thin-film microelectronic devices or thick-film multilayer structures. 

According to the frontier orbitals concept, in the absence of nucleophile (F ), cation Na+ is located symmetrically relative to acetylene. When both ions are... 

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