Orbital MO Theory and Electron Delocalization

Scientists choose the model that best helps them answer a particular question. If the question concerns molecular shape, chemists choose the VSEPR model, followed by hybrid-orbital analysis with VB theory. But VB theory does not adequately explain magnetic and spectral properties, and it understates the importance of electron delocalization. In order to deal with these phenomena, which involve molecular energy levels, chemists choose molecular orbital (MO) theory. 

In VB theory, a molecule is pictured as a group of atoms bound together through localized overlap of valence-shell atomic orbitals. In MO theory, a molecule is pictured as a collection of nuclei with the electron orbitals delocalized over the entire molecule. The MO model is a quantum-mechanical treatment for molecules similar to the one for atoms in Chapter 8. Just as an atom has atomic orbitals (AOs) with a given energy and shape that are occupied by the atom s electrons, a molecule has molecular orbitals (MOs) with a given energy and 

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Molecular Orbital (MO) Theory and Electron Delocalization Central Themes of MO Theory Homonuclear Diatomic Molecules of the Period 2 Elements... 

Bonding in metals involves delocalization of electrons over the whole metal crystal, rather like the n electrons in graphite (Section 3.2) except that the delocalization, and hence also the high electrical conductivity, is three dimensional rather than two dimensional. Metallic bonding is best described in terms of band theory, which is in essence an extension of molecular orbital (MO) theory (widely used to represent bonding in small molecules) to arrays of atoms of quasi-infinite extent. 

Valence bond theory thus gives a good description of the 0-0 cr bonds but a poor description of the tt bonding among p atomic orbitals, whose four electrons are spread out, or delocalized, over the molecule. Yet this is exactly what MO theory does best—describe bonds in which electrons are delocalized over a molecule. Thus, a combination of valence bond theory and MO theory is used. The cr bonds are best described in valence bond terminology as being localized between pairs of atoms, and the tt electrons are best described by MO theory as being delocalized over the entire molecule. 

Anderson and Grantscharova conducted one of the first studies on the CO oxidation on Pt using a molecular orbital theory with a simple molecular model.113 They used an atom superposition and electron delocalization molecular orbital (ASED-MO) method to investigate the electrochemical oxidation of the adsorbed CO on the Pt anodes. They found that the interaction of CO(ads) with the oxidant OH(ads) was effective only at high surface coverage. 

Most organic chemists are familiar with two very different and conflicting descriptions of the 7r-electron system in benzene molecular orbital (MO) theory with delocalized orthogonal orbitals and valence bond (VB) theory with resonance between various canonical structures. An attitude fostered by many text books, especially at the undergraduate level, is that the VB description is much easier to understand and simpler to use, but that MO theory is in some sense more fundamental . 

The qualitative ideas of valence bond (VB) theory provide a basis for understanding the relationships between structure and reactivity. Molecular orbital (MO) theory offers insight into the origin of the stability associated with delocalization and also the importance of symmetry. As a central premise of density functional theory (DFT) is that the electron density distribution determines molecular properties, there has be an effort to apply DFT to numerical evaluation of the qualitative concepts such as electronegativity, polarizability, hardness, and softness. The sections that follow explore the relationship of these concepts to the description of electron density provided by DFT. 

Some of the first quantum-mechanical descriptions of the electrochemical interface were developed by Anderson, utilizing an atom superposition and electron delocalization molecular orbital method (ASED-MO) to generate potential surfaces for the reactant and product states using a cluster model of the electrode surface [27,32,34,49,50]. The activation barrier and equilibrium potential were extracted from the potential surfaces in a manner reminiscent of Marcus theory [51]. Recently, this approach has been... 

There are two approximate starting points in quantum chemistry the molecular orbital (MO) and valence bond (VB) methods. The MO theory derived from the Huckel treatment ignores the interactions between the electrons, whereas the VB theory forms the basis for the electron-paired chemical bond, and for the resonance concept [14]. In MO theory the electrons are delocalized (without any correlation), as contrasted to VB theory, where they are supposed to be localized. 

Ever since the work of Hiickel on the stability of Jt electron systems and the famous 4n + 2 rule for ring systems, energetic criteria have remained a basic measure for the characterization of aromaticity. In molecular orbital (MO) theory, a delocalization energy (DE) can be defined as the difference between the energy Eix of a model system with localized ji electron pair bonds and the energy dei of the real system with a delocalized jt electron distribution. 

The electronic structure of the pyridine system can also be described by means of molecular orbital (MO) theory [77]. All the ring atoms are sp -hybridized. The linear combination of the six 2pz atomic orbitals leads to six delocalized it-MOs, three of which are bonding and three antibonding (see Figure 6.9). 

Confusion often arises between the virtual orbitals 0, of SCF-MO theory and the localized valence antibonds Xb)-Although the spaces spanned by these sets overlap to a considerable extent, expansion of one set in terms of the other (e.g., in LCNBO-MO form) shows that they are far from identical. Indeed, the virtual orbitals are by their nature completely unoccupied, making no physical contribution to the SCF wavefunction or measurable properties. In contrast, the valence antibonds contribute irreducibly to the energy lowering and density shifts associated with electron delocalization, and their non-zero occupancies reflect the important physical effects of delocalization on the wavefunction and molecular properties. 

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