Delocalized systems

Much effort was put into studying whether certain carbocations represent rapidly equilibrating or static (bridged, delocalized) systems (more about this in Chapter 9). 

Carbon atoms can also form cyclic compounds. Aromatic hydrocarbons (arenes), of which benzene is the parent, consist of a cyclic arrangement of formally unsaturated carbons, which, however, give a stabilized (in contrast to their hypothetical cyclopolyenes), delocalized system. 

There is little evidence for the operation in reactions of the inducto-meric effect, the time-dependent analogue of the inductive effect. This may be so because the electrons of the [Pg.128]

The most easily obtained information from such calculations is the relative orderings of the eneigy levels and the atomic coefficients. Solutions are readily available for a number of frequently encountered delocalized systems, which we will illustrate by referring to some typical examples. Consider, first, linear polyenes of formula C H 2 such as 1,3-butadiene, 1,3,5-hexatriene, and so forth. The energy levels for such compounds are given by the expression... 

In order for a substitution to occur, a n-complex must be formed. The term a-complex is used to describe an intermediate in which the carbon at the site of substitution is bonded to both the electrophile and the hydrogen that is displaced. As the term implies, a a bond is formed at the site of substitution. The intermediate is a cyclohexadienyl cation. Its fundamental structural characteristics can be described in simple MO terms. The a-complex is a four-7t-electron delocalized system that is electronically equivalent to a pentadienyl cation (Fig. 10.1). There is no longer cyclic conjugation. The LUMO has nodes at C-2 and C-4 of the pentadienyl structure, and these positions correspond to the positions meta to the site of substitution on the aromatic ring. As a result, the positive chargex)f the cation is located at the positions ortho and para to the site of substitution. 

This indicates a change in the formal oxidation state of the iron from -F2.25 to -F2.5, and mixed Fe /Fe species have been postulated. Flowever, it appears likely that these clusters are best regarded as electronically delocalized systems in which all the Fe atoms are equivalent. 

CC bond distances in localized allylic systems have been held at 1. 5A and 1.3A (typical of CC single and double bond lengths, respectively), and at 1.4A for delocalized systems. 

Radicals with adjacent Jt-bonds [e.g. allyl radicals (7), cyclohexadienyl radicals (8), acyl radicals (9) and cyanoalkyl radicals (10)] have a delocalized structure. They may be depicted as a hybrid of several resonance forms. In a chemical reaction they may, in principle, react through any of the sites on which the spin can be located. The preferred site of reaction is dictated by spin density, steric, polar and perhaps other factors. Maximum orbital overlap requires that the atoms contained in the delocalized system are coplanar. 

Values for c in each method are obtained by solving the equation for various values of each c and choosing the solution of lowest energy. In practice, both methods give similar solutions for molecules that contain only localized electrons, and these are in agreement with the Lewis structures long familiar to the organic chemist. Delocalized systems are considered in Chapter 2. 

Kirtman B (1999) Local Space Approximation Methods for Correlated Electronic Structure Calculations in Large Delocalized Systems that are Locally Perturbed. 203 147-166 Kita Y, see Tohma H (2003) 224 209-248 KleiJ AW, see Kreiter R (2001) 217 163-199 Klein Gebbink RJM, see Kreiter R (2001) 217 163-199... 

More recent results53b d have shown that three-coordinate gallium can be incorporated in potentially delocalized systems such as Mes ... 

Dithiolene complexes with the maleonitriledithiolate (mnt) ligand form highly delocalized systems and are widespread in studies of conducting and magnetic materials. The electronic properties have been extensively studied with various computational methods including Hiickel and extended Hiickel approaches to identify the nature of the orbitals involved in intramolecular and intermolecular interactions. These structural properties allow the complexes to interact in the solid state via short stacking S, S and short interstack S---S contacts.10 4-1048... 

All atoms that are a part of the delocalized system must be in a plane or be nearly planar. 

The origin of cyclopropenone chemistry goes back to the successful preparation of stable derivatives of the cyclopropenium cation <5 3), the first member of a series of Huckel-aromatic monocyclic carbo-cations possessing a delocalized system of (4n + 2)-7r-electrons. This experimental confirmation of LCAO-MO theory stimulated efforts to prepare other species formally related to cyclopropenium cation by a simple resonance description of electron distribution, namely cyclopropenone 7 and methylene cyclopropene (triafulvene) 8 ... 

On substitution of allyllithium with methyl groups, the structures are distorted tt complexes becoming more jj -like. The previously described allyllithiums are contact ion pairs (CIP) whose dissociation is too low to permit study of the free carbanion. However, this is not the case for a more delocalized system such as 1,3-diphenylallyl whose lithium salts can exist as solvent separated ion pairs (SSIP) in ethereal solutions for which the organic moiety could be treated essentially as a free carbanion55 Boche and coworkers studied the effect of substitution at C(2) in their 1,3-diphenylallyl lithiums on the rotational barriers... 

All models of this type have become known colloquially by the misnomer free-particle model. Diverse objects with formal resemblance to chemical systems are included here, such as an electron in an impenetrable sphere to model activated atoms particle on a line segment to model delocalized systems particle interacting with finite barriers to simulate tunnel effects particle interacting with periodic potentials to simulate electrons in solids, and combinations of these. 

The density reaches maxima at x/L = and i.e. roughly between C atoms 1 and 2, 3 and 4, and 5 and 6, a result which suggests three essentially localized double bonds. However, there is considerable density in the region of the formal single bonds, suggesting a fairly delocalized system of so-called 7r-electrons. 

For delocalized systems that require eclipsing across a double bond the torsion angle free of strain may be defined as o — 0, now representing an attraction rather than a repulsion between second-neighbour bonds. 

As suggested by the original resonance theory of Pauling and Wheland,51 such delocalization effects appear to represent some type of average of multiple resonance structures. A general goal of resonance theory is to represent each property (P)true of the true delocalized system in resonance-averaged form... 

Although there is a huge body of research on the kinetics of outer-sphere electron-transfer reactions of mononuclear transition-metal complexes, there are only a small number of papers on dinuclear systems. When the valences of the two metal centers are localized, current evidence indicates that the metal centers typically react essentially independently. On the other hand, for delocalized systems this can hardly be the case. Experimental study of electron transfer with such... 

It has long been known that unsaturated compounds containing a delocalized system of 71 electrons can rearrange into cyclic compounds or other n systems. Such reactions were only incidentally studied until 1930. 0. Diels and K. Alder published their first paper on diene synthesis (which was later given the name Diels-Alder reaction) in 1928. Subsequent work of K. Alder and G. Stein (1933 and 1937) proved the generality of the reaction and its high regio and stereo selectivity. This led to the interest on thermal transformations in unsaturated compounds. 

Heteroindacenes have been prepared and studied by Hafner and co-workers.198 199 The syntheses of 1,3,5,7-tetra-te/t-butyl-4-azaindacene, its AA-oxide, and l,3,5,7-tetra-tot-butyl-4-phospha-s-indacenes have been recently reported (Scheme 66).200 The 12-jt-electron delocalized systems have been studied by dynamic NMR and X-ray and were subjected to molecular orbital calculations, and there is strong evidence of electron delocalization. However, X-ray crystallographic data for 4-phospha-s-indacene 164 and the 4-7V-oxide 164 show that there is a dual orientation in the crystal this disorder with two different orientations of the molecule does not allow for conclusions regarding bond lengths or delocalization, and the mediated structures show a D2h symmetry rather than C2h with localized double bonds. 

There exist systems in which, in principle, J can be directly measured. An example is the J-oxo silicon pthalocyanine dimer studied by Hush and Cheung (29). It is found directly from the valence ultraviolet photoelectron spectrum of the dimer that the energy gap, 2J, in the radical dimer monocation is 0.32 eV, and that, in the gas phase, this is a delocalized system (x/2J <1). Measurements of this kind are only easily made on initially uncharged systems. 

Incorporation of tricoordinate phosphorus to three delocalized systems resulted in 30, a planar compound (B3LYP/6-31 H-G(d,p)) exhibiting equalized... 

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