Radical molecular orbital description

Molecular Orbital Description of Arylaminyl Radicals. Aryl-aminyl radicals, as previously discussed, are intermediates in both the photolysis of alkyl N-arylcarbamates (7, 8) and the photolysis of arylamines (18). A simplified mechanism for photolysis of arylamines and alkyl N-arylcarbamates is illustrated in Scheme IV for the general case. An indication of the reactivity of the... 

The Stability of the Allyl Radical 13.3A Molecular Orbital Description of the Allyl Radical... 

Figure 5. Thorn and Hoffmann molecular orbital description of olefin insertion. The organic radical/anion HOMO is stabilized by a Pt d orbital of proper shape.

The actual E of a particular system is often not as informative as is the comparison of the delocalized system with a reference system having localized orbitals. Figure 4.11 shows the reference system for allyl a double bond separated by an imaginary barrier from a p orbital that may have 0 (cation), 1 (radical), or 2 (anion) electrons. The molecular orbital description of that system, then, is simply a sum of the HMOs of the double bond and of the p orbital. Again, it does not matter whether we are talking about the cation, radical, or anion in Figure 4.11. The HMOs of the reference system are simply those of ethene (E = a -H /3, = a — /8) superimposed on the one HMO for an isolated p orbital (E = a). 

We indicate with dashed lines that both carbon-carbon bonds are partial double bonds. This accommodates one of the things that molecular orbital theory tells us that there is a Tt bond encompassing all three atoms. We also place the symbol y beside the Cl and C3 atoms. This presentation denotes a second thing molecular orbital theory tells us that electron density from the unpaired electron is equal in the vicinity of C1 and C3. Finally, implicit in the molecular orbital picture of the allyl radical is this the two ends of the allyl radical are equivalent. This aspect of the molecular orbital description is also implicit in the formula just given. 

According to the molecular orbital description, the conjugated system of the allyl radical involves the formation of three molecular orbitals by overlap of three 2p atomic... 

PROBLEM 12.20 Add electrons to both the resonance and molecular orbital descriptions in Figure 12.47 to form the allyl anion, radical, and cation. 

In Summary Allylic radicals, cations, and anions are unusually stable. In Lewis terms, this stabilization is readily explained by electron delocalization. In a molecular-orbital description, the three interacting p orbitals form three new molecular orbitals One is considerably lower in energy than the p level, another one stays the same, and a third is higher in energy. Because only the first two are populated with electrons, the total it energy of the system is lowered. 

Molecular orbital calculations (ah initio or semiempirical methods) are also often used to provide a description of radical species and their reactions. High levels of theory are required to provide reliable data. However, rapid advances in computer power and computational methods are seeing these methods more widely used and with greater success (for leading references on the application of theory to describe radical addition reactions, see Section 1.2.7). 

This section will cover aspects of monohydride terminal surface reactions that were carried out under free-radical conditions. The description will be circumscribed to the reactions with molecular oxygen and monounsaturated compounds. Mechanistic information for these reactions is scarce mainly due to the complexity of the system, and mechanistic schemes are often proposed in analogy with radical chemistry of organosilane molecules. H—Si(lll) has a band gap of about 1.1 eV while the HOMO LUMO gap in (Me3Si)3SiH is within 8-11 eV and, therefore, has very important consequences for the reactions with nucleophilic and electrophilic species where frontier orbital inter-... 

In the foregoing it has been assumed that the relatively large positive coupling to /3-protons in 7r-radicals such as ethyl occurs as a result of hyperconjugation. This is not necessarily the case, although arguments in favour of the concept are considerable (Symons, 1962). Inevitably, there are several alternative descriptions suitable as a starting point for theoretical calculations. Thus, molecular-orbital theory has been used by some (Bersohn, 1956 Chesnut, 1958), and a... 

What are the geometries of carbon radicals, and how do they differ from those of carbenium ions or carbanions And what types of bonding are found at the carbon atoms of these three species First we will discuss geometry (Section 1.1.1). and then use molecular orbital (MO) theory to provide a description of the bonding (Section 1.1.2). 

It appears from the description of radical ions in Sects. 1 and 3 that redox reactions can significantly change the chemical and physical properties of conjugated 7r-systems. Whether the extended jc-species are treated within molecular orbital theory or within band-structure theory, the inherent assumption in these concepts is that an electron transfer is reversible and does not promote subsequent chemical reactions. While inspection of cyclic voltammetric waves and the spectroscopic characterization of the redox species provide reliable criteria for the reversibility of an electron transfer and the maintenance of an intact (T-frame, it is generally accepted that electron transfer, depending on the nature of the substrate and on the experimental conditions, can also initiate chemical reactions under formation or cleavage of er-bonds [244, 245],... 

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