Molecular orbitals delocalized

Molecular orbitals which have been formed by linear combination of AOs from three different atoms are referred to as three-center or 3c orbitals. Note that in both these molecular orbitals the coefficients in front of two the ligand AOs are equal in magnitude (but not necessarily in sign). 

Each of the two bonding MOs contains two electrons, hence four electfons occupy bonding orbitals, just as in the description in terms of 2c, 2e bonding in the preceding section. What is new is that each of the four electrons is distributed over the entire molecule. 

One may imagine the combination of AOs to form three-center bonding and antibonding MOs to take place in two steps First the ligand AOs combine as they would in an X2 molecule with an internuclear distance equal to the distance between the halogen atoms in MX2  

These orbitals may be described as ligand symmetry orbitals. Since the halogen atoms are far apart, the symmetry orbitals will have nearly the same energy. In the second step the ligand symmetry orbitals are combined with the metal AOs to form two bonding and two antibonding 3c MOs. This process is presented pictorially in Fig. 10.6. 

If the coefficients c and a in (10.6a) and (10.6b) are equal, that is if the metal s and Pz orbitals contribute equally to the 3c MOs, it can be shown that the description in terms of two 3c bonding MOs is identical to the description obtained by sp hybridization followed by formation of two 2c MOs. This condition is generally not fulfilled. In such cases hybridization introduces an arbitrary restraint on the molecular orbitals, and if employed in calculations, it would reduce the accuracy of the results. 

So far we have discussed chemical bonding only in terms of electron pairs. However, the properties of a molecule cannot always be explained accurately by a single structure. A case in point is the O3 molecule, discussed in Section 9.8. There we overcame the dilanma by introducing the concept of resonance. In this section we will tackle the problem in another way— by applying the molecular orbital approach. As in Section 9.8, we will use the benzene molecule and the carbonate ion as examples. Note that in discussing the bonding of polyatomic molecules or ions, it is convenient to determine first the hybridization state of the atoms present (a valence bond approach), followed by the formation of appropriate molecular orbitals. 

Benzene (CeHg) is a planar hexagonal molecule with carbon atoms situated at the six comers. All carbon-carbon bonds are equal in length and strength, as are all carbon-hydrogen bonds, and the CCC and HCC angles are all 120°. Therefore, each carbon 

Unlike the pi bonding molecular orbitals in ethylene, those in benzene form delocalized molecular orbitals, which are not confined between two adjacent bonding atoms, but actually extend over three or more atoms. Therefore, electrons residing in any of these orbitals are free to move around the benzene ring. For this reason, the structure of benzene is sometimes represented as 

We can now state that each carbon-to-carbon linkage in benzene contains a sigma bond and a partial pi bond. The bond order between any two adjacent carbon atoms is therefore between 1 and 2. Thus, molecular orbital theory offers an alternative to the resonance approach, which is based on valence bond theory. (The resonance structures of benzene are shown on p. 387.) 

Bectrostatic potential map of benzene shows the electron density (red color) above aiKl below the plane of the molecule. For simplicity, only the framework of the molecule is shown. 

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In Chapter 9, we considered a simple picture of metallic bonding, the electron-sea model The molecular orbital approach leads to a refinement of this model known as band theory. Here, a crystal of a metal is considered to be one huge molecule. Valence electrons of the metal are fed into delocalized molecular orbitals, formed in the usual way from atomic... 

Another example which illustrates beautifully the mixing of a group orbitals to form delocalized molecular orbitals is benzene. First of all the six crcc bond orbitals interact to give six linear combinations which are delocalized over the entire carbon skeleton. The amplitudes of the various bond orbitals in each [Pg.23]

Certain groups attached to an aromatic ring can donate electrons into its delocalized molecular orbitals. Examples of these electron-donating substituents include —NH2 and —OH. Electrophilic substitution of benzene is much faster when an electron-donating substituent is present. For example, the nitration of phenol, C6H5OH, proceeds so quickly that it requires no catalyst. Moreover, when the products are analyzed, the only products are found to be 2-nitrophenol (ortho-nitrophenol, 37) and 4-nitrophenol (pnra-mtrophcnol, 38 . 

All the atoms of butadiene lie in a plane defined by the s p hybrid orbitals. Each carbon atom has one remaining p orbital that points perpendicular to the plane, in perfect position for side-by-side overlap. Figure 10-42 shows that all four p orbitals interact to form four delocalized molecular orbitals two are bonding MOs and two are antibonding. The four remaining valence electrons fill the orbitals, leaving the two p orbitals empty. 

We first note that a localized NBO description is an equally valid way to view a delocalized molecular-orbital wavefunction. In the case of N2, for example, 0mo is expressed in terms of doubly occupied MOs 0, i = 1-7,... 

Given the ubiquitous character of molecular orbital concepts in contemporary discourse on electronic structure, ionization energies and electron affinities provide valuable parameters for one-electron models of chemical bonding and spectra. Electron binding energies may be assigned to delocalized molecular orbitals and thereby provide measures of chemical reactivity. Notions of hardness and softness, electronegativity,... 

A theoretical value for the magnitude of dJ/dEz was obtained using the delocalized molecular orbital approach of Gil and Teixeira-Dias 17> who calculated substituent effects on. The Pople expression for the contact contribution to the coupling constant 1 c-h1 °f a methyl group can be written... 

XAS studies of, table, 34 276 Oxide electrocatalysts, 38 122-135 atom superposition and electron delocalization molecular orbital approach, 38 133-135... 

ASED (Atom Superposition and Electron Delocalization) molecular orbital calculations on the formation of monomeric 1-triazolylborane by the process BH3-I-triazole H2-f H2B(Tz) indicate... 

Delocalization of electrons can be pictured by utilizing either the resonance (valence bond, VB) or assumed delocalization (molecular orbital, MO) concepts. This is illustrated in Figure 6.2 fora two-unit (biphenylene) repeating segment of polyphenylene. 

The perfectly octahedral species conform to the expectations based on the simple MO derivation given above. The nonoctahedral fluoride species do not, but this difficulty is a result of the oversimplifications in the method. There is no inherent necessity for delocalized MOs to be restricted to octahedral symmetry. Furthermore, it is possible to transform delocalized molecular orbitals into localized molecular orbitals. Although the VSEPR theory is often couched in valence bond terms, it depends basically on the repulsion of electrons of like spins, and if these are in localized orbitals the results should be comparable. 

Butadiene contains two double bonds, i.e. four carbon atoms which contribute one p orbital each there are then four delocalized molecular orbitals which are shown in Figure 3.17 as having no node (t/>i), one node two nodes (t/>3) and finally three nodes (t/>4). The bonding or antibonding character of an orbital is obtained by counting the number of bonds and... 

Formulate the bonding in NH2 in terms of delocalized molecular orbitals. The molecule is trigonal-pyramidal (C3V point group). Compare the general molecular-orbital description with a localized tetrahedral model for NH3. Discuss the values of the following bond angles H—N—H, 107° H— P—H (in PH2), 94° and F—N —F (in NF3 ), 103 °. 

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