Delocalized bond

We have seen so far that MOs resulting from the LCAO approximation are delocalized among the various nuclei in the polyatomic molecule even for the so-called saturated a bonds. The effect of delocalization is even more important when looking to the n electron systems of conjugated and aromatic hydrocarbons, the systems for which the theory was originally developed by Huckel (1930, 1931, 1932). In the following, we shall consider four typical systems with N n electrons, two linear hydrocarbon chains, the allyl radical (N = 3) and the butadiene molecule (N = 4), and two closed hydrocarbon chains (rings), cyclobutadiene (N = 4) and the benzene molecule (N = 6). The case of the ethylene molecule, considered as a two n electron system, will however be considered first since it is the reference basis for the n bond in the theory. 

The elements of the Hiickel matrix are given in terms of just two negative unspecified parameters, the diagonal a and the off-diagonal /S for the nearest neighbours, introduced in a topological way as  

Therefore, Hiickel theory of n electron systems distinguishes only between linear chains and rings. It is useful to introduce the notation  

The typical Hiickel secular equations for N n electrons are then written in terms of determinants of order N, such as  

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The other C=N systems included in Scheme 8.2 are more stable to aqueous hydrolysis than are the imines. For many of these compounds, the equilibrium constants for formation are high, even in aqueous solution. The additional stability can be attributed to the participation of the atom adjacent to the nitrogen in delocalized bonding. This resonance interaction tends to increase electron density at the sp carbon and reduces its reactivity toward nucleophiles. 

Localized chemical bonding may be defined as bonding in which the electrons are shared by two and only two nuclei. In Chapter 2 we shall consider delocalized bonding, in which electrons are shared by more than two nuclei. 

The two chief general methods of approximately solving the wave equation, discussed in Chapter 1, are also used for compounds containing delocalized bonds. In the VB method, several possible Lewis structures (called canonical forms) are drawn and the molecule is taken to be a weighted average of them. Each in Eq. (1.3),... 

Bond Energies and Distances in Compounds Containing Delocalized Bonds... 

The classic work on delocalized bonding is Wheland, G.W. Resonance in Organic Chemistry, Wiley NY, 1955. 

Localized bonds are easy to apply, even to very complex molecules, and they do an excellent job of explaining much chemical behavior. In many instances, however, localized bonds are insufficient to explain molecular properties and chemical reactivity. In the second half of this chapter, we show how to construct delocalized bonds, which spread over several atoms. Delocalization requires a more complicated analysis, but it explains chemical properties that localized bonds cannot. 

We begin our exploration of delocalized bonds with ozone, O3. As described in Chapter 7, ozone in the upper stratosphere protects plants and animals from hazardous ultraviolet radiation. Ozone has 18 valence electrons and a Lewis stmcture that appears in Figure 10-36a. Experimental measurements show that ozone is a bent molecule with a bond angle of 118°. 

The molecules (or atoms, for noble gases) of a molecular solid are held In place by the types of forces already discussed In this chapter dispersion forces, dipolar interactions, and/or hydrogen bonds. The atoms of a metallic solid are held in place by the delocalized bonding described in Section 10-. A network solid contains an array of covalent bonds linking every atom to its neighbors. An ionic solid contains cations and anions, attracted to one another by electrical forces as described in Section 8-. 

Metals do not dissolve in water, because they contain extensive delocalized bonding networks that must be disrupted before the metal can dissolve. A few metals react with water, and several reacf with aqueous acids, but no metal will simply dissolve in water. Likewise, metals do not dissolve in nonpolar liquid solvents. 

The Lewis structures ofiBF3 andlH3 BO3 indicate that these species contain delocalized bonds. The [BF4] 1 and [B (OH)4 ], in... 

Polar intermetallics are loosely referred to as electron-poorer relatives of Zintl phases in which the active metals do not contribute all of their valence electrons, rather they bond with the more electronegative components to some degree. The structures cannot be simply accounted for by octet rules because of substantial delocalized bonding among the atoms. 

Since a is the energy of a 7r electron in a 2p a.o. and since (3 refers to an electron in a bond, both of these quantities are negative, and the energies above therefore occur in increasing order. The energy associated with the delocalized bond in the molecular ground state is... 

The energy associated with the 4 electrons in their atomic orbitals is 4a and so the dissociation energy of the delocalized bond in butadiene is 4.4/3. Each orbital contributes an amount of energy ej = a + m.j/3 and it is said to be bonding, anti-bonding or non-bonding for positive, negative or zero values of mr... 

It is often of interest to compare the 7r-electron densities in bonds rather than on atoms. Although cross terms above were assumed to vanish because of the HMO zero-overlap assumption, they are actually not zero, especially not between a.o. s on nearest neighbours. The coefficients of the cross terms can hence be interpreted as a measure of overlap in the bonds. On this basis bond order is defined as pim = Yljnjcijcmj- For the 1-2 bond in butadiene pl2 = 2chc2i + 2c2iC22 = 0.88 = P34. p23 = 0.40. These values showthat the delocalized bond contributes more strongly to bind the end pairs than the central pair and gives a simple explanation of the experimental fact that the end bonds are shorter than the central bond. 

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