Orbitals delocalized

Bands in the solid state can be regarded as grossly delocalized orbitals extending throughout the sample. 

The two sets of coefficients result in two sets of Fock matrices (and their associated density matrices), and ultimately to a solution producing two sets of orbitals. These separate orbitals produce proper dissociation to separate atoms, correct delocalized orbitals for resonant systems, and other attributes characteristic of open shell systems. However, the eigenfunctions are not pure spin states, but contain some amount of spin contamination from higher states (for example, doublets are contaminated to some degree by functions corresponding to quartets and higher states). 

Again it is instructive to compare this with the traditional MO approach, taking the CH4 molecule as an example. The MO single determinant description (RHF, which is identical to UHF near the equilibrium geometry) of the valence orbitals is in terms of four delocalized orbitals, each occupied by two electrons with opposite spins. The C-H bonding is described by four different, orthogonal molecular orbitals, each expanded in... 

Analogy between the [Pg.14]

The vinyl cation (Fig. 40 and III.13) in which the empty p orbital on the positive center is coplanar with the terminal methylene group, is clearly another candidate for hyperconjugative donation. The in-plane orbital readily overlaps with the odd p orbital, with formation of two delocalized orbitals and an energy gain... 

A clue to the nature of the third itt MO can be found in the placement of electrons in the two resonance structures for ozone, which are shown with color highlights in Figure 10-36a. Notice that in one resonance structure, the left outer atom has three lone pairs and a single bond, while the right outer atom has two lone pairs and a double bond. In the other resonance structure, the third lone pair is on the right outer atom, with the double bond to the left outer atom. The double bond appears in different positions in the two stmctures, and one of the lone pairs also appears in different positions. These variations signal delocalized orbitals. 

The double bond shown in different locations in the two resonance stmctures represents a pair of electrons in a delocalized n bonding molecular orbital that spans all three of the oxygen atoms, as shown in Figure I0-37a. One lone pair also appears in different positions in the two resonance stmctures, again signaling a delocalized orbital. This lone pair is spread over both outer atoms but not across the inner atom, as shown in Figure I0-37Z>. This is a nonbonding molecular orbital,. The lone pair shown in different positions in the resonance stmctures occupies the delocalized orbital. 

The six resonance structures of the sulfate ion indicate that delocalized orbitals span the entire anion. 

All these properties of metals are consistent with a bonding description that places the valence electrons in delocalized orbitals. This section describes the band theory of solids, an extension of the delocalized orbital ideas... 

Hg (CN0)2, which explodes when struck. Write a Lewis structure for the CNO anion and describe its bonding, including any delocalized orbitals. 

We expect to find delocalized orbitals in those species for which bonding cannot be... 

Density matrices, natural localized and delocalized orbitals, and the Lewis-structure picture... 

There exists no uniformity as regards the relation between localized orbitals and canonical orbitals. For example, if one considers an atom with two electrons in a (Is) atomic orbital and two electrons in a (2s) atomic orbital, then one finds that the localized atomic orbitals are rather close to the canonical atomic orbitals, which indicates that the canonical orbitals themselves are already highly, though not maximally, localized.18) (In this case, localization essentially diminishes the (Is) character of the (2s) orbital.) The opposite situation is found, on the other hand, if one considers the two inner shells in a homonuclear diatomic molecule. Here, the canonical orbitals are the molecular orbitals (lo ) and (1 ou), i.e. the bonding and the antibonding combinations of the (Is) orbitals from the two atoms, which are completely delocalized. In contrast, the localization procedure yields two localized orbitals which are essentially the inner shell orbital on the first atom and that on the second atom.19 It is thus apparent that the canonical orbitals may be identical with the localized orbitals, that they may be close to the localized orbitals, that they may be identical with the completely delocalized orbitals, or that they may be intermediate in character. 

Dale, Sir Henry 77 Delay 77 Delay, Jean 77 delocalized orbitals 233 Deniker, Pierre 77 Density Functional Theory 55,228,241,271,278 deposition conditions 168 design of the Sawatzky-Kay apparatus 152 Dess-Martin oxidation 11 detailed atomic-level representation 92 determinant 279 diastereoface selectivity 22,... 

Many molecules that have several double bonds are much less reactive than might be expected. The reason for this is that the double bonds in these structures cannot be localized unequivocally. Their n orbitals are not confined to the space between the double-bonded atoms, but form a shared, extended Tu-molecular orbital. Structures with this property are referred to as resonance hybrids, because it is impossible to describe their actual bonding structure using standard formulas. One can either use what are known as resonance structures—i. e., idealized configurations in which n electrons are assigned to specific atoms (cf pp. 32 and 66, for example)—or one can use dashed lines as in Fig. B to suggest the extent of the delocalized orbitals. (Details are discussed in chemistry textbooks.)... 

---