Molecular Orbital Theory Electron Delocalization

Valence bond theory can explain many aspects of chemical bonding—such as the rigidity of a double bond—but it also has limitations. In valence bond theory, we treat electrons as if they reside in the quantum-mechanical orbitals that we calculated/or atoms. This is a significant oversimplification that we partially compensate for by hybridization. Nevertheless, we can do better. 

In molecular orbital (MO) theory, we do not actually solve the Schriidinger equation for a molecule directly. Instead, we use a trial function, an educated guess as to what the solution might be. In other words, rather than mathematically solving the Schrodinger equation, which would give us a mathematical function describing an orbital, we start with a trial mathematical function for the orbital. We then test the trial function to see how well it works.  

How does this help us The best possible orbital will therefore be the one with the minimum energy. In modem molecular orbital theory, computer programs are designed to try many different variations of a gnessed orbital and compare the energies of each one. The variation with the lowest energy is the best approximation for the actual molecular orbital. 

---

Molecular Orbital Theory Electron Delocalization 458 Key Learning Outcomes 473... 

Molecular Orbital Theory Electron Delocalization We put all of this together in the molecular orbital energy diagram for H2 ... 

In molecular orbital theory, electrons occupy orbitals called molecular orbitals that spread throughout the entire molecule. In other words, whereas in the Lewis and valence-bond models of molecular structure the electrons are localized on atoms or between pairs of atoms, in molecular orbital theory all valence electrons are delocalized over the whole molecule, not confined to individual bonds. 

According to molecular orbital theory, the delocalization of electrons in a polyatomic molecule spreads the bonding effects of electrons over the entire Energy molecule. 

From the heat of combustion of benzenamine we know that it has a 3 kcal mole-1 larger stabilization energy than benzene (Table 21-1). This difference in stabilization energies can be ascribed in either valence-bond or molecular-orbital theory to delocalization of the unshared pair of electrons on nitrogen over the benzene ring. The valence-bond structures are... 

Finally, we return to the opening remarks of the chapter and see how molecular orbital theory explains the colors of vegetation. The presence of highly delocalized electrons in the large molecules found in the petals of flowers and in fruit and... 

The boranes are electron-deficient compounds (Section 3.8) we cannot write valid Lewis structures for them, because too few electrons are available. For instance, there are 8 atoms in diborane, so we need at least 7 bonds however, there are only 12 valence electrons, and so we can form at most 6 electron-pair bonds. In molecular orbital theory, these electron pairs are regarded as delocalized over the entire molecule, and their bonding power is shared by several atoms. In diborane, for instance, a single electron pair is delocalized over a B—H—B unit. It binds all three atoms together with bond order of 4 for each of the B—H bridging bonds. The molecule has two such bridging three-center bonds (9). 

As their names suggest, molecular orbitals can span an entire molecule, while localized bonds cover just two nuclei. Because diatomic molecules contain just two nuclei, the localized view gives the same general result as molecular orbital theoiy. The importance of molecular orbitals and delocalized electrons becomes apparent as we move beyond diatomic molecules in the follow-ing sections of this chapter. Meanwhile, diatomic molecules offer the simplest way to develop the ideas of molecular orbital theory. 

If the molecule contains multiple bonds, construct the n bonding system using molecular orbital theory, as described in this section and in the remaining pages of Chapter 10. Watch for resonance structures, which signal the presence of delocalized electrons. 

From 1933 85>, several theoretical approaches to the problem of the chemical reactivity of planar conjugated molecules began to appear, mainly by the Huckel molecular orbital theory. These were roughly divided into two groups 36>. The one was called the "static approach 35,37-40)j and the other, the "localization approach 41,42). in 1952, another method which was referred to as the "frontier-electron method was proposed 43> and was conventionally grouped 44> together with other related methods 45 48> as the "delocalization approach". 

The following presentation is limited to closed-shell molecular orbital wave-functions. The first section discusses the unique ability of molecular orbital theory to make chemical comparisons. The second section contains a discussion of the underlying basic concepts. The next two sections describe characteristics of canonical and localized orbitals. The fifth section examines illustrative examples from the field of diatomic molecules, and the last section demonstrates how the approach can be valuable even for the delocalized electrons in aromatic ir-systems. All localized orbitals considered here are based on the self-energy criterion, since only for these do the authors possess detailed information of the type illustrated. We plan to give elsewhere a survey of work involving other types of localization criteria. 

The Fermi surface plays an important role in the theory of metals. It is defined by the reciprocal-space wavevectors of the electrons with largest kinetic energy, and is the highest occupied molecular orbital (HOMO) in molecular orbital theory. For a free electron gas, the Fermi surface is spherical, that is, the kinetic energy of the electrons is only dependent on the magnitude, not on the direction of the wavevector. In a free electron gas the electrons are completely delocalized and will not contribute to the intensity of the Bragg reflections. As a result, an accurate scale factor may not be obtainable from a least-squares refinement with neutral atom scattering factors. 

A second quantum mechanical bonding theory is molecular orbital theory. This theory is based on a wave description of electrons. The molecular orbital theory assumes that electrons are not associated with an individual atom but are associated with the entire molecule. Delocalized molecular electrons are not shared by two atoms as in the traditional covalent bond. For the hydrogen molecule, the molecular orbitals are formed by the addition of wave functions for each Is electron in each hydrogen atom. The addition leads to a bonding molecular... 

Molecular Orbital Theory a model that uses wave functions to describe the position of electrons in a molecule, assuming electrons are delocalized within the molecule Molecular Solid a solid that contains molecules at the lattice points Molecule a group of atoms that exist as a unit and are held together by covalent bonds... 

When the unpaired electron is delocalized over a number of atoms, molecular orbital theory must be applied to obtain a molecular description of the resulting magnetic species. In this situation there is less opportunity for substantial contributions from L, and in general the more delocalized the electron the more like a free electron it appears. In some cases, the electron is delocalized over only a few atoms, and in these cases modest contributions from L are expected, especially if one of the atoms is a transition metal. If more extensive delocalization is present, or if all the atoms involved are light, only small contributions (e.g., from 2fi orbitals) may be observed. 

The molecular orbital theory of polyatomic molecules follows the same principles as those outlined for diatomic molecules, but the molecular orbitals spread over all the atoms in the molecule. We say that the electrons that occupy these orbitals are delocalized over the atoms in the molecule. An electron pair in a bonding orbital helps to bind together the whole molecule, not just an individual pair of atoms. The energies of molecular orbitals in polyatomic molecules can be studied experimentally by using ultraviolet and visible spectroscopy (see Major Technique 2). 

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. 

Aromatic systems play a central role in organic chemistry, and a great deal of this has been fruitfully interpreted in terms of molecular orbital theory that is, in terms of electrons moving more-or-less independently of one another in delocalized orbitals. The spin-coupled model provides a clear and simple picture of the motion of correlated electrons in such systems. The spin-coupled and classical VB descriptions of benzene are very similar, except for the small but crucial distortions of the orbitals. The localized character of the orbitals allows the electrons to avoid one another. Nonetheless, the electrons are still able to influence one another directly because of the non-orthogonality of the orbitals. 

---